v108 3 s 2017 s in insi i nins 95 issn 1991-1696 africa … · 2017-06-05 · v108 3 s 2017 s in...

Vol.108 (3) September 2017 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 95

September 2017Volume 108 No. 3www.saiee.org.za

Africa Research JournalISSN 1991-1696

Research Journal of the South African Institute of Electrical EngineersIncorporating the SAIEE Transactions

Vol.108 (3) September 2017SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS96

(SAIEE FOUNDED JUNE 1909 INCORPORATED DECEMBER 1909)AN OFFICIAL JOURNAL OF THE INSTITUTE

ISSN 1991-1696

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SPECIALIST EDITORSCommunications and Signal Processing:Prof. L.P. Linde, Dept. of Electrical, Electronic & Computer Engineering, University of Pretoria, SA Prof. S. Maharaj, Dept. of Electrical, Electronic & Computer Engineering, University of Pretoria, SADr O. Holland, Centre for Telecommunications Research, London, UKProf. F. Takawira, School of Electrical and Information Engineering, University of the Witwatersrand, Johannesburg, SAProf. A.J. Han Vinck, University of Duisburg-Essen, GermanyDr E. Golovins, DCLF Laboratory, National Metrology Institute of South Africa (NMISA), Pretoria, SAComputer, Information Systems and Software Engineering:Dr M. Weststrate, Newco Holdings, Pretoria, SAProf. A. van der Merwe, Department of Infomatics, University of Pretoria, SA Dr C. van der Walt, Modelling and Digital Science, Council for Scientific and Industrial Research, Pretoria, SAProf. B. Dwolatzky, Joburg Centre for Software Engineering, University of the Witwatersrand, Johannesburg, SAControl and Automation:Prof K. Uren, School of Electrical, Electronic and Computer Engineering, North-West University, S.ADr J.T. Valliarampath, freelancer, S.ADr B. Yuksel, Advanced Technology R&D Centre, Mitsubishi Electric Corporation, JapanProf. T. van Niekerk, Dept. of Mechatronics,Nelson Mandela Metropolitan University, Port Elizabeth, SAElectromagnetics and Antennas:Prof. J.H. Cloete, Dept. of Electrical and Electronic Engineering, Stellenbosch University, SA Prof. T.J.O. Afullo, School of Electrical, Electronic and Computer Engineering, University of KwaZulu-Natal, Durban, SA Prof. R. Geschke, Dept. of Electrical and Electronic Engineering, University of Cape Town, SADr B. Jokanović, Institute of Physics, Belgrade, SerbiaElectron Devices and Circuits:Dr M. Božanić, Azoteq (Pty) Ltd, Pretoria, SAProf. M. du Plessis, Dept. of Electrical, Electronic & Computer Engineering, University of Pretoria, SADr D. Foty, Gilgamesh Associates, LLC, Vermont, USAEnergy and Power Systems:Prof. M. Delimar, Faculty of Electrical Engineering and Computing, University of Zagreb, Croatia Engineering and Technology Management:Prof. J-H. Pretorius, Faculty of Engineering and the Built Environment, University of Johannesburg, SA

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VOL 108 No 3September 2017

SAIEE Africa Research Journal

Analysis of Bursty Impulsive Noise in Low-VoltageIndoor Power Line Communication Channels: Local Scaling Behaviour ........................ .................................... 98M.O. Asiyo and T.J.O. Afullo

On the Analysis of Reed-Solomon Codes for OFDM Systems over Rician Fading Channels .... .............................................. . 108O.O. Ogundile, E. O. Ijiga and D.J.J. Versfeld

Convergence of the Fast State Estimation for Power Systems ........ ........................................................... 117M. A. Rahman and G.K. Venayagamoorthy

Development of a SEM-Quantitative Approach for Risk Based Inspection and Maintenance of Thermal Power Plant Components .......... ................................ 128S.N. Singh and J-H.C. Pretorius

SAIEE AFRICA RESEARCH JOURNAL EDITORIAL STAFF ...................... IFC


ANALYSIS OF BURSTY IMPULSIVE NOISE IN LOW-VOLTAGEINDOOR POWER LINE COMMUNICATION CHANNELS: LOCALSCALING BEHAVIOUR

Mike O. Asiyo∗ and Thomas J.O. Afullo†

∗ Discipline of Electrical, Electronic & Computer Engineering, School of Engineering, University ofKwaZulu Natal, Durban, 4041, South Africa E-mail: [email protected]† Discipline of Electrical, Electronic & Computer Engineering, School of Engineering, University ofKwaZulu Natal, Durban, 4041, South Africa E-mail: [email protected]

Abstract: Power line communication (PLC) channels are prone to multipath propagation due toimpedance mismatch, and impulsive noise whose characteristics are still not well established in theliterature. Moreover, measurements show that this impulsive noise appear in bursts, non-Gaussianand cyclostationary and as such cannot be modeled as the convenient additive white Gaussian noise(AWGN). Transceivers optimized for AWGN may not necessarily perform well for the PLC noise.Therefore, investigating the characteristics of PLC noise is very important for accurate modeling of thesame. This study presents multifractal analysis of bursty impulsive noise measured from power linenetworks from three different environments. We employ multifractal detrended fluctuation analysis,which is a well-developed multifractal analysis technique for non-stationary time series data and easyto implement to analyze measured noise data. Results show that power line noise exhibits bothlong-range dependence (LRD) and multifractal scaling behavior with different strengths depending onthe environments where they were captured. The multiscaling behavior is due to long-range correlationinherent in the power line noise. The source of this local multiscaling behavior is determined by analysisa shuffled series of the original data captured from the power network. Multifractal analysis is able toshow clearly both the strengths and frequency of occurrence of bursts occurring in PLC noise whichcan then be applied in accurate modeling of the noise. The significance of these results is that newpower line noise models should be developed that captures both LRD and multifractal scaling for moreaccurate performance evaluation of power line communication systems. The existing noise modelsthough able to replicate temporal dependence of PLC noise, are not able to capture this local scalingbehavior which results show is inherent in PLC noise.

Key words: Power Line Channels, Bursty Impulsive Noise, Long range temporal correlations,Multifractal Analysis.

1. INTRODUCTION & MOTIVATION

Power line communication (PLC) is becoming popular forbroadband applications, multimedia sharing and is partof smart grid systems due to its ubiquitous nature and itis economically viable since no extra wiring is requiredfor communication purposes. However, like any othercommunication channel, PLC has challenges of multipath(due to impedance mismatch), path loss and impulsivenoise [1, 2]. As such high speed data transmission isstill a daunting task. The most difficult challenge ischaracterizing and modelling the PLC noise.

Noise in power line communication networks isnon-Gaussian and as such can not be modelled asthe convenient additive white Gaussian noise. The noise isknown to be impulsive and in most cases, occur in bursts.Therefore, it can be referred as bursty impulsive noise [3].Due to unique nature of this noise in power line channels,modulation and decoding schemes optimized for Gaussianchannels may not necessarily work well in PLC systems.This has contributed to the increased growth in the interestof PLC noise modelling and analysis. PLC noise isgenerated from within and without the network and can beclassified into: coloured background noise, narrowband

interference, periodic impulsive noise synchronous tomains, periodic impulsive noise asynchronous to mains,and asynchronous impulsive noise [4]. For conveniencein modelling, these five groups are normally classifiedinto two major groups; background noise and impulsivenoise [4–6].

A recent survey on impulsive noise modelling groupsthe models into models with memory and those withoutmemory [7]. The popular memoryless models areBernoulli-Gaussian, Middleton Class A and symmetricAlpha-Stable distribution models [6, 7]. Even though thememoryless models are able to capture the non-Gaussianand impulsive nature of PLC noise, they fail to capturethe temporal correlation that is inherent in PLC noise.To model this temporal correlation, Markov chain basedmodels have been developed. A partitioned Markovchain model was developed in [4] which is able tocapture the bursty nature of PLC noise by consideringimpulsive states and impulsive free states. This modelis a generalization of Gilbert-Eliott model [8]. The mainchallenge with this model is that it has binary output and isonly suitable for binary communication channels. In [5],a Markov-Gaussian model is developed from the sameprinciple as the Bernoulli-Gaussian model, but with an


additional parameter which quantifies the channel memory.Even though Markov-Gaussian model is a continuousnoise model, its main drawback is that it is restricted toonly two states: impulsive free and impulsive sequencestates. In each of the states, noise samples follow Gaussiandistribution with impulsive states having noise variancewhich is very high compared to the variance of theimpulsive free state.

The authors in [3] extended Middleton Class A modelby incorporating an additional parameter that allows forcontrolling noise impulse memory. The model knownas Markov-Middleton introduces noise memory throughhidden Markov chain and it is a continuous noise modelwith finite states and the same PDF as the Middleton ClassA model. In each of the finite states, the noise variance isa function of the physical parameters of the noise (numberof simultaneous impulsive emissions, impulsive index andstrength of the impulsive noise). The noise can be assumedto be a superposition of impulsive source emissionsthat are Poisson distributed both in space and time andhave temporal correlation. In all the memory models,the additional parameter capturing the noise memory isdetermined from noise measurements and details can befound in [4], [5] and [3].

There are also other studies on the characteristics of PLCnoise which have concentrated on amplitude distributions,impulse width and impulse rate (see [4, 9–12]) withoutconsidering much the frequency and strength of burstswhich are prevalent in PLC noise and impacts heavilyon communication system development and performanceanalysis. Even though our interest is on indoor low-voltagePLC applications, it should be noted that impulsive noiseis a challenge even in other applications (e.g., see [13]).A shift of focus has recently turned into models andanalysis considering the cyclostationary nature of PLCnoise [14–19]. This resurgence of interest in PLC noisemodelling shows the importance as well as complexity ofnoise experienced in power line channels.

Fractal structure of PLC noise and its impacts on PLCsystems is not yet well published in the literature. Theauthors in [20] have done studies on self-similarity andfractal analysis of PLC noise and they observe that PLCnoise exhibits long-range dependence (LRD). Long-rangedependence can be determined by estimating the Hurstparameter H, which is a measure of intensity of LRD.LRD measures high variability in flow or arrival in timeseries data/signal. There is a relationship between channelmemory and H parameter. The questions that this studiesis trying to answer is whether the Hurst parameter (derivedfrom second order moment) alone is good enough tocharacterize the correlation structure of PLC noise. Inother words, in this study, we perform multifractal analysisto PLC noise measured from three different locations(University Electronic Laboratory, Postgraduate Office,and stand-alone Apartment). Multifractal analysis issuperior to LRD analysis. It is a statistical tool that is ableto measure the frequency with which bursts of differentstrengths occur in a signal [21].

Multifractal theory is a well developed technique and hasbeen used in various fields in analysis and modelling ofscaling behaviour of measures/functions in time seriesprocesses. Some of the signal and processing analysisbased on multifractal include bit error rate process analysisof 11 Mbps wireless MAC-to-MAC channels [22], internettraffic and network traffic measurement estimations [21,23], image feature extraction [24], stock market analysis[25, 26], biomedical analysis [27, 28] and so on. We stressthat in this study, noise model is not being developed,but the study is concerned with investigating multifractalnature of PLC noise and the origins of these multifractalsin PLC noise. Noise model that captures the multifractalnature of PLC noise and its impact on the performanceanalysis of PLC systems is still work in progress and willbe published later. To the best of knowledge of the authors,this is the first paper addressing the issue of multifractalanalysis of PLC noise and sets a very good backgroundinto multiplicative cascades modelling of PLC noise.

The rest of paper is organized as follows: Section 2. detailsthe methodology employed in this study; Section 3., theprocedure for obtaining noise measurements used in thestudy is outlined and noise measurement samples are alsoprovided to show the different data being analysed. Resultsand discussion are in Section 4., where we specificallyshow that PLC noise is long-range correlated and exhibitsmultifractal scaling behaviour. The models discussed fromthe previous section even though have been extensivelyutilized in error performance analysis in PLC networks,they do not capture this new finding. In Section 5.,conclusion of the paper is presented with a proposal forfurther study emanating from the results in this paper.

2. MULTIFRACTAL ANALYSIS

Multifractal spectrum provides a good measure ofcharacterizing non-stationary time series signals. Methodsfor estimating multifractal spectrum are well developedand continue to excite much research. Selection ofmethods to be used for analysis depend on the requiredprecision, type of data and computational speed [24].Moreover, the methods are not equivalent and quite oftenproduce different results. The interest is normally toextract fractal/multifractal properties of a given signalrather than seeking for exact fractal dimension. Amongthe well developed and most accurate is the wavelettransform modulus maxima (WTMM) [29–32]. However,its computational cost is the major hindrance to itsapplication.

This paper is an extension of [33] in which preliminaryresults of multifractal analysis were reported. Here weapply two methods: multifractal detrended fluctuationanalysis (MDFA) [34] and multifractal detrending movingaverage analysis (MDMA) [26]. Their choice is due to easeof implementation and fast computational applicability.Again, their accuracy have been seen to be comparableto WTMM [34, 35]. Both have been developed fornon-stationary time series signals and there are MATLABcodes available on-line that can be modified by the


intended users for their implementation [26, 36].

2.1 Autocorrelation Function

Autocorrelation function (ACF) can be a good startingpoint for correlation analysis of time series data. Itprovides correlation of ith measurement with that of(i + l)th one for different time lags l. It can be usedas a preliminary indicator of existence of long-rangedependence in a time series data. Considering a time seriesdata {xi}N

i=1 with i = 1, · · · ,N, N representing the length ofthe series, the auto-covariance function is given by

R‘(l) = 〈xixi+l〉=1

N − l

N−l

∑i=1

xixi+l (1)

where xi = xi − 〈x〉 and 〈x〉 is the mean of the series.The ACF Rxx(l) is then given by R‘(l) normalized by thevariance of the series 〈x2

i 〉. The time series is short rangedependent when its ACF declines exponentially (Rxx(l) ∝exp(−l/lo)) for l → ∞. When ACF declines as power-law(Rxx(l) ∝ l−γ) for l → ∞ and 0 < γ < 1, then the series issaid to have long-range dependence.

Due to unknown trends and noise in time series data, directcalculations of Rxx(l) is usually not advisable. Moreover,autocorrelation analysis and power spectrum analysis failto capture the correlation behaviour in most non stationarytime series due to unknown trends that might be in thetime series. However, there are methods available fordetermining the local scaling behaviour of time seriesdata. These methods differ in the way fluctuations aredetermined and the type of polynomial trend eliminated ineach window size [37].

2.2 Multifractal Detrended Fluctuation Analysis

Multifractal Detrended Fluctuation Analysis is a gener-alization of DFA to cater for non-stationary time seriesdata and the procedure consists of five steps [34]. Let usconsider a series xi of length n and is of compact support,the procedure for MDFA involves the following: The firststep involves the construction of time series ‘profile’ (thisstep converts the noise time series to random walk-likeseries) from the original data as

y(k)≡k

∑i=1

(xi − x) k = 1, · · · ,n (2)

where x is the mean of the time series.

In the second step, the profile y(k) is then divided intonon-overlapping segments of equal length s, that is, ns=int(n/s). If the length n of the series is not a multipleof s, then a small portion of it may remain. To utilize thisportion also, the procedure is repeated from the oppositeend, making 2ns segments altogether.

In the third step, local trend for each of the 2ns segmentsis determined by least-square fit of the series. Then the

variance is determined as

F2(s, l) =1s

s

∑k=1

{y[(l −1)s+1]− yl(k)}2 (3)

for each segments, l = 1, · · · ,ns and,

F2(s, l) =1s

s

∑k=1

{y[n− (l −ns)s+1]− yl(k)}2 (4)

for each segments l = ns + 1, · · · ,ns, where yl(k) is thepolynomial fit in segment l.

The qth order fluctuation function can then be obtained byaveraging of all the segments in the fourth step as

Fq(s) = { 12ns

2ns

∑v=1

[F2(s,v)]q/2}1/q (5)

where q is a variable that can take any value apart fromzero. Steps (2) to (4) are repeated for several different timescales s.

The last step is to determine the scaling behaviour of thefluctuation functions by plotting on log-log scale Fq(s)versus scale s for each value of q. If the time series exhibitslong-range correlation, then Fq(s) increases with increasein scale s as a power-law

Fq(s)∼ sh(q). (6)

The multifractal scaling exponent h(q) in (6) is knownas generalized H exponent and is the well-known Hparameter for q = 2 for stationary time series. Formonofractal series, the exponent h(q) is independent of qand it is dependent on q for multifractal time series data.Multifractal scaling exponent h(q) is related to standardmultifractal formalism scaling exponent τ(q) as

τ(q) = qh(q)−D f (7)

where D f is the fractal dimension of the geometricalsupport of the multifractal measure and for time seriesdata, D f = 1 [34] [26]. For multifractal time series,τ(q) is a non linear function of q. An alternative wayof characterizing multifractal series is by the singularitystrength function α(q) and the multifractal spectrumfunction f (α) [26, 34] via Legendre transform

α(q) =dτ(q)

dqand f (α) = qα− τ(q) (8)

2.3 Multifractal Detrending Moving Average Algorithm

Multifractal detrending moving average (MDMA) al-gorithm [26] is a generalization of the detrendingmoving average (DMA) algorithm [38] initially designedfor fractal analysis for non-stationary time series data.MDMA was developed to analyse both multifractal timeseries and multifractal surfaces. Its algorithm can be


summarized as follows [26].

The first step is to construct a sequence of cumulative sumsy(t) assuming a time series x(t)N

1 , where N is the length ofthe time series, i.e.,

y(t) =t

∑i=1

x(i) t = 1,2, · · · ,N (9)

The second step is to determine the residual sequenceby detrending the signal series by subtracting themoving average function from the cumulative sums seriescomputed in step one.

r(i) = y(i)− y(i) (10)

where n−�(n−1)θ� ≤ i ≤ �N − (n−1)θ� and y(t) is themoving average function in a moving window,

y(t) =1n

�(n−1)(1−θ)�

∑k=−�(n−1)θ�

y(t − k) (11)

where n is the window size and θ is a parameterdetermining the position of the window. θ takes valuesin the range [0,1]. Mostly, three special cases are normallyconsidered, namely, θ = 0 (backward moving average), inwhich the moving average function is calculated over thepast n− 1 data points of the signal. The second case isfor θ = 0.5 (centred moving average) for which movingaverage function is calculated over half past and half futuredata points of the signal. The last case is when θ = 1(forward moving average) on which the moving averagefunction is calculated on n− 1 data points of the signal inthe future.

In the third step, the residual sequence r(i) is dividedinto N non overlapping segments of the same size n,where N = �N/n− 1�. Denoting each segment by rv, theroot-mean-square function Fv(n) can be calculated by

F2v (n) =

1n

n

∑i=1

r2v(i) (12)

The forth step involves determining the qth order overallfluctuation function Fq(n) as

Fq(n) = { 1Nn

Nn

∑v=1

Fqv (n)}

1q (13)

Finally, in the last step, the values of segment size n canbe varied to determine the power-law relation between thefunction Fq(n) and scale n as

Fq(n)∼ nh(q). (14)

When h(q) has been estimated, then scaling exponentdependent on q can be determined from (7). Similarly,singularity strength and multifractal spectrum can be

estimated from (8).

3. MEASUREMENT SET-UP AND ACQUISITIONPROCEDURE

Characterization and modelling of noise present inpower line communication system requires rigorous noisemeasurement campaign. For this study, PLC noisemeasurements were recorded using the set up shown inFigure 1. The set up comprises a coupling unit used forprotecting Digital Storage Oscilloscope (DSO) from highpower network currents. The coupling unit also acts likea high pass filter, allowing only signals of interest to passthrough. The DSO employed here as a receiver is capableof recording 14 million data point samples and was setto sample noise at a rate of 50 Mega-samples per second.This implies that we are able to capture noise from lowercut-off frequency of the coupling unit (100 KHz) to 25MHz frequency range.

Three scenarios are used in this study. First, noisemeasurements was done in one of the postgraduate studyoffices with electrical loads being fluorescent lights,desktop computers and air conditioners. Sample is shownin Figure 2(a). It should be noted that these electricloads are the PLC noise generators and the adjacentoffices connected to the same bus-bars have similar loads.Secondly, noise from Electronic Laboratory (Figure 2(b))was measured when students were undertaking theirpracticals. In addition to fluorescent lights and airconditioners, electronic loads with components like SCRsand measurement equipment were connected to the powernetwork. Lastly, PLC noise was measured in a stand-alonefive bedroomed apartment (Figure 2(c)). The electricalloads here include lights, television set, washing machine,two fridges and a vacuum cleaner. The first two scenariosare situated within University of KwaZulu Natal and thethird one is located away from the University. Thesescenarios are just representatives of actual PLC channelsand there is nothing so special about their location apartfrom the different loads in these locations which also actas noise generation sources.

Noise measurements were done when all of these loadswere running/switched on, and from Figure 2, it canbe seen that each of the different environments generateunique noise samples due to different noise sources.Moreover, the switching times (ON and OFF) of theseloads are also random and the noise is expected to showthis randomness without correlation. However, previousstudies have established that PLC noise though generatedfrom different sources randomly, is correlated as reportedin the previous section. It is also known that some extranoise from without the power grid are coupled to the indoornetwork via conduction or radiation [4].


CouplingCircuitry

DigitalStorage

Oscilloscope PC

Powerline Network

Figure 1: Power line noise measurement set up

4. RESULTS & DISCUSSION

4.1 Unfiltered PLC Noise Analysis

Multifractal spectrum and their corresponding q−orderdependent scaling exponent estimated from two methods(MDFA and MDMA) for PLC noise data measured fromvarious environments are shown in Figures 3 and 4respectively. From these figures, it is evidenced that thePLC noise has a scaling behaviour that is sensitive to smallfluctuations within its segments. This is characterized bythe left truncated multifractal spectrum shown in each ofthe locations by both the methods. The q−order dependentscaling exponent graphs give an indication that PLC noiseis multifractal as the scaling exponent of the original timeseries data is dependent on q−order of the fluctuations, thatis, the scaling exponent is non linear. When the time seriesdata is shuffled, the scaling exponent is more or less linear,which implies monofractal behaviour.

Table 1 and Table 2 respectively provide values ofsingularity spectrum parameters for Figures 3 and 4. Themost important parameter is the spectrum span (∆α =αmax − αmin) which is a measure of irregularity of thesignal/time series. From Table 1, the values of spanfor noise from various locations show that PLC noisefrom office has a spectrum distribution which is more nonuniform than both noise from laboratory and apartmentwhich seem very close. When the data is shuffled, thespan is negligible except for the one of office data. In theoffice data, the span of original data is 0.93 and that of theshuffled data is 0.41. The implication for these values isthat the shuffled data shows weaker multifractal behaviourthan the original data. Similar results are seen for noisecaptured in an apartment, however, for laboratory data, theshuffled series show no evidence of multifracticity.

Results from second method (MDMA) gives an indicationthat it is the laboratory data that show this weakmultifractal behaviour in the shuffled series (Table 2).Since the multifractal behaviour of PLC noise is not yetknown, we can not conclude from the results which of themethods gives a better analysis than the other. However, itis evident from the two methods used in the analysis thatPLC noise exhibits multifractal behaviour but the nature

(a) Office

(b) Laboratory

(c) Apartment

Figure 2: Noise measurement samples


and source of this behaviour requires further investigation.

Another important parameter of measure is α0. Viewingthe singularity spectrum as frequency distribution ofsingularity strength, α0 provides the value of thesingularity strength which is most frequent in thedistribution. The value of α0 provides the measure ofcorrelation characteristics of the signal/time series. Boththe methods show that PLC noise exhibits long-rangecorrelation since the most frequent singularity strengthranges between 0.5 and 1.

Table 1: Singularity Spectrum Parameters in Figure 3

Location Data Measure Indicesα0 αmin αmax ∆α

Office Original 0.77 0.45 1.38 0.93Shuffled 0.88 0.73 1.14 0.41

Laboratory Original 0.46 0.37 1.10 0.73Shuffled 0.50 0.48 0.56 0.08

Apartment Original 0.79 0.64 1.35 0.71Shuffled 0.76 0.64 0.90 0.26

Table 2: Singularity Spectrum Parameters in Figure 4

Location Data Measure Indicesα0 αmin αmax ∆α

Office Original 0.64 0.38 1.06 0.68Shuffled 0.50 0.48 0.55 0.07

Laboratory Original 0.63 0.52 1.28 0.76Shuffled 0.77 0.69 0.84 0.15

Apartment Original 0.79 0.63 1.26 0.63Shuffled 0.49 0.45 0.51 0.06

4.2 Filtered PLC Noise Analysis

PLC Noise that was captured in the frequency band of0.1 MHz to 25 MHz was decomposed into low frequency(0.1 − 10 MHz) and high frequency (10 − 25 MHz)components. The decomposed components were thenanalysed by the MDFA technique with a view to investigatemultifractal characteristics of these noise components.Interesting results can be seen in Figure 5 where it isseen that the multifractal characteristics of PLC noise ingeneral is mainly being contributed by the low frequencycomponents. In [10], it was reported that noise spectrumhas relatively high values at low frequency than at highfrequencies. This was attributed to many sources of lowfrequency noise in the power network and short-waveradios in the low frequency band. We can also concludefrom the findings in this study that these low frequencysources are the main contributors of the scaling behaviourinherent in PLC noise. Again, it is known that man-madeimpulsive noise is mainly in the low frequencies [11] andat these low frequencies, the noise PSD is high [39].

Since the multifractal behaviour of PLC noise is dueto bursty impulsive noise, the results showing that lowfrequency components of PLC noise is more multifractalthan the high frequency component (which is monofractalor very weak multifractal for the cases of office andapartment scenarios) is valid. Low frequency componentsof PLC in from office and laboratory data retain thesame shape (left truncated concave shape) of multifractalspectrum as the unfiltered time series data. However, thelow frequency component of apartment data has a fullconcave multifractal spectrum. These results continueto confirm that different locations have sources whichcontribute to the noise characteristics uniquely. We intendto isolate the individual noise sources and characterisetheir behaviour according to the frequency and strengthsof impulsive noise they generate. Investigating thecharacteristic of individual noise sources is a commonpractice in PLC communications and will be an interestingfuture work.

5. CONCLUSION

Multifractal analysis of PLC noise measured from anoffice environment, University electronic laboratory anda stand-alone apartment reveal that PLC noise exhibitsmultifractal behaviour, meaning that it can not beaccurately characterized by a single power-law scalingexponent. This multifractal characteristics is mainlyencountered in the low frequency band (< 10 MHz) wherethere are many sources of bursty impulsive noise. Resultsfrom the findings also show that PLC noise has long-rangedependence behaviour. However, neither of the methodsused in the analysis was able to reveal the source ofmultifractal behaviour seen in PLC noise and hence furtheranalysis will be performed to investigate the source ofmultifractal behaviour. It will also be interesting to capturenoise from individual noise generators and investigate theirscaling behaviour. Furthermore, the findings of this studypoint to the fact that there is need for new models to bedeveloped for PLC noise that will be able to capture moreaccurately its LRD and multifracticity nature. The impactof these noise characteristics on performance analysisof power line communication systems also needs to beinvestigated and forms our future research.

ACKNOWLEDGEMENT

This work was partially supported by the School ofEngineering, University of KwaZulu Natal.

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ON THE ANALYSIS OF REED-SOLOMON CODES FOR OFDMSYSTEMS OVER RICIAN FADING CHANNELS

O.O. Ogundile∗† , E. O. Ijiga† and D.J.J. Versfeld†

∗ Department of Physics and Telecommunication, Tai Solarin University of Education, Nigeria.E-mail: [email protected]† School of Electrical and Information Engineering,University of the Witwatersrand, Johannesburg,South Africa. E-mail:[email protected] and [email protected].

Abstract: The relative strength between the direct and the scattered paths of the received signal inwireless communication as described by the Rician factor K specifies the quality of the transmissionlink. Fading in Rician channel models influence the performance of Orthogonal Frequency DivisionMultiplexing (OFDM) systems. Accordingly, channel estimation together with different Forward ErrorCorrection (FEC) schemes are used to provide significant performance gain for OFDM systems overfading channels. In most literature, the performance of FEC schemes such as Turbo and LDPCcodes have been analysed for OFDM systems over frequency-selective Rician fading channels. Thispaper evaluates the performance of Reed-Solomon (RS ) codes over frequency-selective Rician fadingchannels. The performance of RS codes is firstly studied for different Rician K factors and Dopplerfrequencies. Secondly, the performance of RS codes is reviewed assuming different code rates

(kn

)for both hard-decision and soft-decision decoding algorithms. The Euclidean algorithm (EA) is usedas the RS hard-decision decoding algorithm while the Parity-check Transformation Algorithm (PTA)is deployed as the RS soft-decision decoding algorithm. The results for the various channel andcoding conditions are documented through computer simulations. The simulation results validatethe importance of a high Rician K factor. Interestingly, the simulation results verify that adopting alow-rate code do not necessarily improve the error rate irrespective of the Rician K factor. This analysisis relevant in order to establish the performance of combined RS codes with OFDM systems overfrequency-selective Rician fading channels.

Key words: Code rates, Doppler frequency, OFDM system, RS codes, Rician channel, Rician K factor.

1. INTRODUCTION

Orthogonal Frequency Division Multiplexing (OFDM)is a transmission technique based on multi-orthogonalcarriers which are simultaneously transmitted. OFDM isused for contemporary wireless communication systemsand applications because it offers high data transmissionrate, and efficient use of the limited spectrum resource.In addition, it is an effective technique to combatfrequency-selective fading channels, as it is robustto Inter-symbol Interference (ISI) and Inter-carrierInterference (ICI) [1–3]. The motivation behind the useof OFDM is to cleave modulated signal (carriers) such asM-ary Quadrature Amplitude Modulation (M-QAM) intosizeable number of sub-carriers using the Inverse DiscreteFourier Transform (IDFT) [1, 4]. In such a way, moreinformation can be transmitted per bandwidth.

Nonetheless, in the studies of OFDM systems, potentchannel estimation is essential due to the demodulationtechnique employed in OFDM systems, and the varyingnature of the fading channels. Coherent demodulationfor OFDM systems require reliable channel estimationtechniques, most especially at high Doppler frequenciesand for time-varying fading channels [1, 5]. In order toachieve coherent demodulation in Line of Sight (LOS)wireless communication channels usually modelled witha Rician distribution, the channel properties are firstlyestimated. Different channel estimation techniques have

been proposed in literature for OFDM systems over Ricianfading channels. For instances, see [1, 6–9]. The majoremphasis have been to improve the quality of the receivedsignal, most especially when the power in the scatteredpaths is more than the power in the direct paths (RicianK factor < 1). The ratio of the power in the direct pathsand other scattered paths (referred to as the Rician Kfactor) serves as the scaling factor in Rician distributedchannels. It is desired that K is as high as possible inorder to achieve coherent demodulation. However, due tothe variation in the channel’s properties, the value of K ispresumptive. Thus, it is paramount to estimate the fadingeffect in Rician channels so as to improve the probabilityof detecting the message that was transmitted correctly.

Despite these reliable channel estimation techniquesproposed in literature, Forward Error Correction (FEC)schemes such Turbo codes and Low Density ParityCheck (LDPC) codes are combined with these channelestimation techniques to improve the performance ofOFDM systems over frequency-selective Rician fadingchannels. In [10–14] the performance of Turbo codes andLow Density Parity Check (LDPC) codes were validatedfor Rician fading channels. In this paper, the performanceof Reed-Solomon (RS ) codes over frequency-selectiveRician fading channels is analysed assuming OFDMsystems. Firstly, we studied the performance of RS codesfor different Rician K factors and Doppler frequencies


RS encode16-QAM

modulationInsertpilot

S/P P/S DAC

ADC

IDFT Cylic prefixinsertion

Cylic prefixremoval

S/PP/S DFTRemovepilot

Channelestimate +compensate

Removepilot

Removepilot

RS decode

Inputmessage

Outputmessage

Rician fading+

AWGN

Figure 1: OFDM-RS system model set-up

FD. Afterwards, the performance of RS codes isreviewed assuming different code rates

(Cr =

kn

)for both

hard-decision and soft-decision decoding algorithms,where n is the codeword length and k is the informationsymbol length.

RS codes form a prime class of linear block codesefficient in correcting random symbol errors and bursterrors [15–17]. RS codes are very popular linearblock codes because they meet the singleton bounds;as such, they are referred to as Maximum SeparableDistance (MSD) codes [18]. Accordingly, a (n, k) RScode is capable of correcting up to �(n− k)/2� errorswhen hard-decision decoding algorithm is deployed.Reliable hard-decision decoding algorithms for RS codesin literature include [19–22]. On the other hand, RSsoft-decision decoding algorithms such as [18, 23–27] cancorrect beyond the MSD error bound. However, this paperadopts the Euclidean algorithm (EA) [17, 21] as the RShard-decision decoding algorithm while the Parity-checkTransformation Algorithm (PTA) [18] is deployed as theRS soft-decision decoding algorithm.

Besides, in the OFDM-RS experimental set-up, weadopted M-QAM (M=16) as the underlying modulationscheme. To ally the 16-QAM modulation symbols withthe RS symbols, the size of the RS symbols is selected tobe 4 bits. Therefore, the RS codes of heed have a n=15.In pursuance of varying the code rate Cr, k is adjustedbetween k = 5 − 11. The channel estimation techniqueused in this paper is based on the Pilot Symbol AssistedModulation (PSAM) Least Square (LS) method [1, 3].Moreover, we assume the comb-type pilot arrangementfor the channel estimation [1,3]. The pilot symbol spacingof the LS estimator and the channel’s Doppler frequencyFD are varied in order to give concrete remarks. Theresults for the various channel and coding conditions aredocumented through computer simulations as shown inFig 4-Fig 10.

The importance and contribution of this paper is as follows.The Rician channel used in this paper supports both urbanand commercial wireless communications. With RS codesbeing an important class of FEC schemes, it is thereforeparamount to validate the performance of RS codes insuch a channel as in the case with other FEC schemes. Inaddition, the performance of RS codes is evaluated withOFDM systems over this channel. OFDM-RS systemsare used in different wireless communication applicationssuch as Digital Video Broadcasting (DVB), Digital AudioBroadcasting (DAB), WiMAX, Digital Subscriber Line(DSL), Long Term Evolution (LTE), and long distancesatellite communications [28]. Consequently, this paper isrelevant in asserting the performance of OFDM-RS overfrequency-selective Rician fading channels when thesewireless applications are deployed.

The rest of this paper is arranged as follows. Section 2describes the OFDM-RS system model. Specifically,this section explains the RS coding process, theOFDM transmission technique, the channel model,and the channel estimation technique adopted in thispaper. The performance of the OFDM-RS system infrequency-selective Rician fading channel is presentedwith analysis in Section 3. In particular, this sectionanalyses the performance for different Rician K factor,Doppler frequencies FD, and code rate Cr. Section 4summarises the findings of this paper with discernibleremarks.

2. OFDM-RS SYSTEM MODEL

Consider the OFDM-RS system experimental set-up ofFig. 1. The input to the system is encoded using a(n, k) RS code. The encoded data of length n ismapped to 16-QAM complex symbols. Pilot symbolsare inserted in the mapped data periodically assumingcomb-type pilot based arrangement as shown in Fig. 2[3]. Afterwards, we apply the default OFDM transmissionprocedure which includes the Serial-to-Parallel (S/P)conversion, IDFT, Parallel-to-Serial (P/S ) conversion,cyclic prefix insertion, and Digital-to-Analogue conversion


(DAC). The reverse of these steps are performed after thechannel. Subsequently, the pilot symbols are removedin order to estimate/compensate for the channel fadingeffect. The compensated received signal is hereby fedinto the RS decoder which outputs the decoded message.The OFDM-RS system model is therefore expatiated asfollows.

Frequen

cy

Time

Data symbol Pilot symbol

Figure 2: Comb-type pilot arrangement

2.1 Reed-Solomon Encoding

The input message can be encoded to form a systematiccodeword or non-systematic codeword. For the purposeof this paper and easy adaptation of the RS PTA softdecoder [18], we will simply use systematic RS encoder.In the systematic form, the message polynomial M(x) isembedded in the codeword C(x) as depicted in Fig. 3.Thus, we encoded the input message k as follows. Let the

C(x)

Message

k n − k

Parity

Figure 3: Systematic RS codeword

k input message be represented by a message polynomialM(x) of degree k−1 as:

M(x) =M0+M1x+M2x2+ . . .+M(k−1)x(k−1), (1)

where the coefficients M0, M1, M2, M(k−1) are m (m = 4)bits message symbol which indicates an element of theGF(qm). The message polynomial is hereby scaled by afactor x(n−k) such that:

M(x) =M(x)x(n−k). (2)

The resulting message M(x) is divided by the fieldgenerator polynomialG(x) which gives a quotientQ(x) andremainder R(x) defined as:

Z(x) =M(x)G(x)

= Q(x)+R(x)G(x). (3)

In this case, we define the G(x) with symbols from GF(q)and with roots α, α2, . . ., αn−k as [17]:

G(x) = (x−α)(x−α2), . . . , (x−α(n−k))

= g0+g1x+, . . . ,+gn−k−1x(n−k−1)+ x(n−k),(4)

where α is the primitive element in GF(q). In its extendedform, the k×n generator matrixG of the RS code is definedas:

G =

1 0 . . . 0 p1,1 p1,2 . . . p1,(n−k)0 1 . . . 0 p2,1 p2,2 . . . p2,(n−k)....... . .

......

......

...0 0 . . . 1 pk,1 pk,2 . . . pk,(n−k)

=[

Ik×k Pk×(n−k)].

(5)

In order to perform the RS EA and PTA decoding, theparity check matrix H needs to be predefined. Thus, forthe (n,k) RS code theH is defined as:

H =

p1,1 p1,2 . . . p1,k 1 0 . . . 0p2,1 p2,2 . . . p2,k 0 1 . . . 0...

......

.......... . .

...p(n−k),1 p(n−k),2 . . . p(n−k),k 0 0 . . . 1

=[

P(n−k)×k I(n−k)×(n−k)].

(6)

The systematic RS codeword is therefore formed by fusingthe message polynomialM(x), the scaling factor x(n−k) andthe remainder R(x) as given by:

C(x) =M(x)xn−k +R(x). (7)

From Eqn. 7, the generated codeword contains themessage symbols and the parity symbols as shown inFig. 3.

With the RS encoder in place, the RS decoder can be set upto achieve either hard-decision or soft-decision decoding.The EA [17, 21] is adopted for the RS hard-decisiondecoding, and the PTA proposed in [18] is assumed for thesoft-decision decoding. The EA [17, 21] has been provento perform at par with the conventional RS hard-decisiondecoding algorithm proposed in [19, 20]; thus, theEA [17, 21] is capable of correcting up to �(n− k)/2�errors. The EA performs RS decoding by iterativelyfinding the error location polynomial and error locationevaluator from the computed syndrome. Consequently, thealgorithm evaluates the error location numbers and valuesin order to correct the errors.

On the other hand, the PTA [18] is a soft-decision RSdecoding algorithm that corrects beyond the �(n− k)/2�error bound depending on the derived reliabilityinformation from the channel output. As with mostsoft-decision FEC schemes, the performance of the PTAdepends strongly on the derived reliability information.


The PTA is a symbol level RS soft decoder that transformsthe parity-check matrix H iteratively so as to performa syndrome check [18]. With every iteration, the PTAfine-tunes the derived reliability information according tosome rules. Note that the derived reliability information isof dimension M×n, where M and n are defined as above.For an efficient and less computational intensive wayof deriving the reliability information from the channeloutput, refer to [29, 30]. The decoding performanceof the PTA depends on the correction factor δ chosenin the algorithm. The smaller the value of δ, the moreefficient is the decoder. However, reducing the valueof δ will increase the decoding time complexity ofthe PTA. A correction factor δ = 10−3 is assumed inthis paper in order to achieve a good Symbol Error Rate(SER) performance at moderate decoding time complexity.

2.2 OFDM Transceiver

The (n,k) RS codeword is mapped to a 16-QAM complexdata. Thus, the OFDM modulator is designed as follows.The number of sub-carriers (O) is set to O = 2L. Thesub-carriers are numbered as i = 1,2, . . . ,O − 1, and theOFDM symbols are assigned u = 1,2, . . . ,U − 1. Pilotsymbols p are inserted periodically in the OFDM symbolassuming comb-type pilot arrangement. We assume allpilot symbol takes on the same value and equal spacing inorder to lessen the channel estimation error [31]. Note thatL is the ratio of the total number of data sub-carriers (J)to the number of pilot sub-carriers (Op). Subsequently, theOFDM frame structure is first fed into the S/P conversionblock. The OFDM frequency domain signal is transformedinto time domain in the IDFT block as [2, 3]:

s(E) =

ρ−1∑T=0

s(T )e j(2πET/ρ)

√ρ

, (8)

where ρ is the DFT length and s(T ) is the OFDMfrequency domain signal. In most cases, the carrier ispadded with zeros so that it matches the length of thefilter size during the transformation process. The resultingtime domain signal is fed into the P/S conversion block.Cylic prefix is added to the time domain OFDM signal inorder to limit the effect of ISI. The time domain signal isup-converted in the DAC block before transmitted overthe frequency-selective Rician fading channel.

At the receiver end, the time domain OFDM signal is firstdown-converted in the ADC block, The cyclic prefix isremoved before passing the signal into the S/P conversionblock. Thus, the time domain OFDM signal is transformedback to the frequency domain as [2, 3]:

y(T ) =

ρ−1∑E=0

y(E)e− j(2πET/ρ)

√ρ

, (9)

where y(E) is the received time domain OFDM signal.

Given that the ISI is eliminated by the cyclic prefix, thereceived signal at the P/S conversion block is defined as:

R(l) = ZX(l)H(l)+N(l), (10)

where X(l) is the transmitted data and pilot frame, N(l)is the complex Additive White Gaussian Noise (AWGN)with variance σ2 = No/2, and H(l) is the combinedfrequency response. The matrix of the DFT is the definedas [2, 3]:

Z =

N00ρ . . . N0(ρ−1)

ρ...

. . ....

N(ρ−1)0ρ . . . N(ρ−1)(ρ−1)

ρ

, (11)

with a weight of [2, 3]:

NETρ =

e− j(2πET/ρ)√ρ

. (12)

The Channel State Information (CSI) is known only atthe pilot positions in reality. Accordingly, the CSI atthe data symbol position is estimated using the knownproperties of the pilot symbols. Different approaches canbe used to estimate the CSI at the data positions. For alow computational complexity, we estimate the CSI at thedata symbol positions using the comb-type pilot based LSchannel estimation method [1, 3].

2.3 LS Channel estimator

In its simplest form, the pilot symbols are insertedperiodically in the modulated data signal X(i) in comb-typepilot based arrangement as defined by [3]:

X(i) = X(aL+b) ={

Xp(a), b = 0,inf. data, b = 1, . . . ,L−∞,

(13)where Xp(a) is the ath pilot carrier value. Therefore, thefrequency response at the pilot sub-carrier using the LSchannel estimation method is defined as [3]:

H(p) = (X(p))−1R(p), (14)

where X(p) and R(p) are the transmitted and receivedpilot sub-carriers respectively. Having derived thefrequency response at the pilot sub-carrier, we apply linearinterpolation [3, 32] to estimate the frequency response atthe data sub-carrier. Accordingly, the frequency responseat the data sub-carrier i, aL < i < (a+ 1)L, is estimatedas [3, 32]:

H(i)=H(aL+b)= bH(p)(a+1)L−1+H(p)(a)−bH(p)(a)L−1,

for 0 ≤ b <L. (15)

2.4 Channel Model

The zero mean complex Gaussian Rician fading channelmodel assumed in this paper is developed by including aLOS path to a Rayleigh distributed channel. The complexGaussian process is simulated as described by the Sum of


Sinusoids (SOS) model in [33] which statistical propertiesmatch the Clarke isotropic scattering model [34]. Wemodeled the LOS path as a zero mean stochastic sinusoidsas proposed in [35]. Therefore, the simulated Ricianfading channel model assumed in this paper is expressedas [33, 36]:

W =Wre+ jWim, (16)

where Wre and Wim are the real and imaginary partsrespectively, and are they are expressed as:

Wre =

N∑

v=1

cos(2πFDt cosϕv + θv)+√

K cos(2πFDt cosϕ0 + θ0)

×(√

K +1)−1 (√N

)−1. (17)

Wim =

N∑

v=1

sin(2πFDt sinϕv +ϑv)+√

K sin(2πFDt sinϕ0 + θ0)

×(√

K +1)−1 (√N

)−1. (18)

The number of propagation paths is denoted as N , and ϕvis the angle of arrival of the vth propagation path definedas [36, 37]:

ϕv = (2πv−π+Θ) (4N)−1 , v = 1, . . . ,N . (19)

Note that when ϕv = 0, FD is the maximum Dopplerfrequency, and t is the time of arrival of the vth propagationpath. The angles Θ, ϑv, and θv are distributed invariablyover [−π,π], and are statistically independent [36].Moreover, θ0 is the preparatory random phase distributedinvariably over [−π,π], and ϕ0 is the preparatory angle ofarrival. From Eqns. (17) and (18), if the Rician K factortends toward zero (K = 0), it implies that there are noLOS components; as such, Eqn. (16) can be regarded asa Rayleigh fading channel model.

3. PERFORMANCE ANALYSIS

This section presents the computer simulations run inMATLAB. The feasibility of the system is analysedby comparing the SER performance over a specifiedrange of Signal to Noise Ratio (SNR). The SER versusSNR performance is compared for different code ratesCr, Rician K factors, Doppler frequencies FD and pilotspacings based on the parameters in Table 1. In theOFDM-RS system configuration, perfect synchronisationis assumed in order to limit the effect of ICI and ISI.The cyclic prefix is selected such that it is more than themaximum average path gain. Additionally, it is ensuredin the simulation set-up that the first of the four tapsused always have a zero path delay which approximatelycorresponds to an ideal synchronisation.

The key goal of this paper is to analyse the performance ofRS codes for OFDM systems in frequency-selective Ricianfading channels. Therefore, this section is structured asfollows. The performance of RS codes is first studied fordifferent Rician K factors, Doppler frequencies FD, and

Table 1: Simulation parameters

Parameters Specifications

DFT size, ρ 64Code rates, Cr 5/15, 7/15, 9/15, 11/15Sampling rate 10kHzDoppler frequencies, FD 100Hz, 150Hz, 200HzSignal constellation 16-QAMPilot arrangement Comp-typePilot spacings 4, 6Rician K factor 1, 5, 10Channel model Rician fadingNumber of taps/Multipath 4RS decoders EA, PTA

pilot spacings in Section 3.1 while assuming a fixed coderate Cr. Thereafter, the OFDM-RS system is compared fora range of code rates Cr in Section 3.2 in order to verifythe effect of Cr on the system performance.

3.1 SER Analysis for Different K, FD, and Pilot Spacing

Rician K Factors: The performance of RS codes isinvestigated for different Rician K factors as shown inFig. 4 and Fig. 5. A perfect channel condition is assumedin the simulation set-up for a fixed Doppler frequency(FD = 100Hz), while we vary the Rician K factor. Acode rate, Cr =

515 and Cr =

715 are used in the simulation

results of Fig. 4 and Fig. 5 respectively. As depictedin both figures (Fig. 4 and Fig. 5), the performance ofthe OFDM-RS system degrades as the Rician K factorreduce irrespective of the code rate. This establishesthe importance of the Rician K factor in a Rician fadingchannel: the lower the Rician K factor, the harsher is theRician channel fading effect irrespective of the OFDM-RSsystem configuration. Moreover, as expected, thePTA outperforms the hard-decision Euclidean algorithmirrespective of the value of K.

Doppler Frequencies FD: In this case, the performance ofthe RS codes is verified for different Doppler frequenciesFD. As shown in Fig. 4 and Fig. 5, a higher RicianK factor improves the performance of the OFDM-RSsystem. Thus, we select K=10 in the simulation runs,and a fixed code rate, Cr =

515 . Moreover, a pilot

spacing of 4 is assumed in the LS channel estimation.Fig. 6 verifies the performance of the OFDM-RS systemon frequency-selective Rician fading channel. Fig. 6compares the performance of the OFDM-RS systemfor perfect channel condition (no pilot symbols), andwith known pilot symbols. As shown in Fig. 6, theperformance of the OFDM-RS system plummets as theDoppler frequency increases in comparison to the perfectchannel condition. With fading channels, the higher theDoppler frequency the faster the channel fading effect.Therefore, it is difficult to track or estimate the channelfading effect in a fast fading channel. This is the reason


SNR[dB]5 10 15 20 25 30

Cod

ewor

d Er

ror R

ate

10-5

10-4

10-3

10-2

10-1

100

K=1, EuclideanK=1, PTAK=5, EuclideanK=5, PTAK=10, EuclideanK=10, PTA

Figure 4: Comparison of soft-decision and hard-decisionRS decoding for different Rician K factors, Cr =

515

SNR[dB]5 10 15 20 25 30

Cod

ewor

d Er

ror R

ate

10-5

10-4

10-3

10-2

10-1

100

K=1, EuclideanK=1, PTAK=5, EuclideanK=5, PTAK=10, EuclideanK=10, PTA

Figure 5: Comparison of soft-decision and hard-decisionRS decoding for different Rician K factors, Cr =

715

why the performance of the OFDM-RS system drops asthe Doppler frequency increases. In addition, irrespectiveof the value of Doppler frequency, the PTA outperformsthe hard-decision Euclidean algorithm as shown in Fig. 6.

Pilot Spacings: The performance of the OFDM-RS systemis also verified for different pilot spacings. In thesimulation runs, we assumed two different pilot spacings(4 and 6), a fixed code rate, Cr =

515 , and a Doppler

frequency, FD = 100Hz. Similarly, a Rician factor, K =10 is selected in the simulation set-up. Fig. 7 showsthe SER versus SNR performance of the OFDM-RSsystem for the varied pilot spacing. The figure comparesthe SER performance of the two pilot spacings with aperfect channel condition. As represented in the figure,the performance of the OFDM-RS system degrades asthe pilot spacing increases from 4 to 6. Thus, thechannel estimation process can be improved by using

SNR[dB]5 10 15 20 25 30

Cod

ewor

d Er

ror R

ate

10-5

10-4

10-3

10-2

10-1

100

Perfect, EuclideanPerfect, PTAFD=100, EuclideanFD=100, PTAFD=150, EuclideanFD=150, PTAFD=200, EuclideanFD=200, PTA

Figure 6: Comparison of soft-decision and hard-decisionRS decoding for different FD with a pilot spacing of 4, andK=10.

a smaller pilot spacing. This however increases thebandwidth and energy consumption, and reduces the datatransmission rate. Most channel estimation techniques aremore efficient with smaller pilot spacings because withlarge pilot spacing, the channel fading effect becomescomplex and difficult to estimate. This results in theperformance degradation in the OFDM-RS system as thepilot spacing increases. Likewise, as shown in Fig. 7, thesoft-decision PTA offers better performance in comparisonto the hard-decision Euclidean algorithm for any givenpilot spacing.

SNR[dB]5 10 15 20 25 30

Cod

ewor

d Er

ror R

ate

10-5

10-4

10-3

10-2

10-1

100

Perfect, EuclideanPerfect, PTAPilot spacing = 4, EuclideanPilot spacing = 4, PTAPilot spacing = 6, EuclideanPilot spacing = 6, PTA

Figure 7: Comparison of soft-decision and hard-decisionRS decoding for different pilot spacing with FD = 100Hz,and K=10.

3.2 Optimal Code Rate

The effect of the Rician K factor on the RS code rate, Cr isverified in this section. In the simulation runs, we selected


four different codes rates, Cr =515 ,

715 ,

915 , 11

15 , and a fixedDoppler frequency, FD = 100Hz. Besides, a pilot spacingof 4 is assumed in LS channel estimation. Fig. 8, Fig. 9,and Fig. 10 verify the code rate performance comparisonfor the OFDM-RS system with Rician factors K=1, K=5and K=10 respectively. The figures compare the coderate performance for a perfect channel condition, and withknown pilot symbols. Fig. 8a, Fig. 9a, and Fig. 10aestablish the performance of the OFDM-RS system forhard-decision decoding while Fig. 8b, Fig. 9b, and Fig. 10bdepict the performance of the system for soft-decisiondecoding. With emphasis to Section 3.1, and as shownin Fig. 8, Fig. 9, and Fig. 10, the value of the RicianK factor has significant effect on the rate performance ofthe system. However, from the figures, it can seen thatdecreasing the code rate do not necessarily improve theperformance of the OFDM-RS system over the channeleven at high Rician K factor. In fact, Cr =

915 gives the best

performance both for the hard-decision and soft-decisionRS decoding algorithms, and for K=1-10.

SNR[dB]6 8 10 12 14 16 18 20 22

Cod

ewor

d Er

ror R

ate

10-2

10-1

100

Perfect, Euclidean, Cr=5/15Perfect, Euclidean, Cr=7/15Perfect, Euclidean, Cr=9/15Perfect, Euclidean, Cr=11/15FD=100, Euclidean, Cr=5/15FD=100, Euclidean, Cr=7/15FD=100, Euclidean, Cr=9/15FD=100, Euclidean, Cr=11/15

(a) RS hard-decision

SNR[dB]6 8 10 12 14 16 18 20 22

Cod

ewor

d Er

ror R

ate

10-2

10-1

100

Perfect, PTA, Cr=5/15Perfect, PTA, Cr=7/15Perfect, PTA, Cr=9/15Perfect, PTA, Cr=11/15FD=100, PTA, Cr=5/15FD=100, PTA, Cr=7/15FD=100, PTA, Cr=9/15FD=100, PTA, Cr=11/15

(b) RS soft-decision

Figure 8: Comparison of code rates for K=1 FD = 100Hz

From the studies of FEC, it is well known that low-rate

codes are proficient in correcting more errors as comparedto high-rate codes. Although, this comes with the price ofreduced energy per codeword symbol. The reduced energyper codeword symbol means there are more errors to becorrected and this reduce the error correction performance.Therefore, there is a point at which decreasing the coderate will not offer any more performance improvementsin error rate [38]. This is why the Cr =

915 system gives

the best performance as shown in Fig. 8, Fig. 9, andFig. 10. Consequently, when comparing the performanceof different code rate, it is paramount to maintain the totalenergy transmitted per symbol message constant. This willensure a fair comparison between the different code ratesystems as presented in this section.

SNR[dB]6 8 10 12 14 16 18 20 22

Cod

ewor

d Er

ror R

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10-3

10-2

10-1

100



SNR[dB]6 8 10 12 14 16 18 20 22

Cod

ewor

d Er

ror R

ate

10-3

10-2

10-1

100




4. CONCLUSION

This paper has studied the performance of OFDM-RSsystems on frequency-selective Rician fading channels.From the simulation runs generated, the followingconclusion can be deduced. Firstly, RS codes is a suitableFEC scheme and can be used with OFDM systems on


SNR[dB]6 8 10 12 14 16 18 20 22

Cod

ewor

d Er

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10-4

10-3

10-2

10-1

100



SNR[dB]6 8 10 12 14 16 18 20 22

Cod

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d Er

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10-5

10-4

10-3

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100




frequency-selective Rician fading channels. Secondly, aswith any other FEC scheme, the performance of RS codescan be improved on Rician fading channels by increasingthe Rician K factor as presented in Section 3.1. Finally,as presented in Section 3.2, adopting a low-rate code inthe OFDM-RS system do not necessarily improve the errorrate as compared to high-rate code even at high Rician Kfactor. Note that a codeword length n=15 is adopted in thispaper. However, the result in this paper can be extendedto longer codeword length, where a higher QAM signalconstellation (M) can be used.

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CONVERGENCE OF THE FAST STATE ESTIMATION FOR POWERSYSTEMS

Md. Ashfaqur Rahman1,2 and Ganesh Kumar Venayagamoorthy1,3

1 Real-Time Power and Intelligent Systems Laboratory, Holcombe Department of Electrical andComputer Engineering, Clemson University, Clemson, SC 29634, United States2 Department of Electrical and Computer Engineering, North South University, Dhaka, BangladeshEmail: [email protected] School of Engineering, University of Kwazulu-Natal, Durban 4041, South Africa Email:[email protected]

Abstract: Power system state estimation is a fundamental computational process that requires bothspeed and reliability. To meet the needs, some variants of the constant Jacobian methods have beenused in the industry over the last several decades. The variants work very well under normal operatingconditions with nominal values of the states. However, the convergence of the methods are notanalysed mathematically and it may contain pitfalls. In this study, the convergence of the constantJacobian methods are analysed and it is shown that the methods fail under high variations of the states.To increase the reliability of the processes, a multi-Jacobian method is proposed. Through simulation,a special case is shown for IEEE 68, and IEEE 118-bus systems where the Jacobian calculated withthe nominal value fails, and the proposed multi-Jacobian method succeeds.

Key words: Convergence, dishonest Gauss Newton method, fast decoupled state estimator, parallelprogramming, weighted least squares estimator.

1. INTRODUCTION

Proper operation of the power system largely dependson proper monitoring. State estimation is a core partof the monitoring system. The purpose of estimationis to remove errors from an overdetermined set ofmeasurements. It yields a noise-free consistent set of statevariables that is used for contingency analysis, optimalpower flow, load forecasting etc [1, 2]. As a large numberof applications depend on the output of the estimator, it isvery important to ensure it’s reliability.Due to the high accuracy, Weighted Least Squares (WLS)estimator became the universally accepted solution forstate estimation [3, 4]. It was originally developed byCarl Friedrich Gauss in 1795 [5] and was proposedfor power systems by Fred Schweppe in 1970 [6, 7].The most time-consuming part of the WLS estimatoris the computation of the Jacobian matrix. To avoidmatrix inversion, Cholesky decomposition is used and itis followed by a back substitution. Though it makesthe process quite fast, it is not suitable for parallelimplementation [8].One of the major variants of the WLS estimator that is verypopular in the industry is the fast decoupled (FD) estimator[9]. It takes the advantage of the constant Jacobian as wellas the decoupling of the real and reactive powers [10].Keeping the Jacobian constant is generally known as thedishonest Gauss Newton method [11]. If the Jacobian iskept constant for all the samples of measurements, it iscalled Very DisHonest Newton (VDHN) method [12]. TheFD estimator exploits the advantages of decoupling withthe advantages of VDHN.

In VDHN, the Jacobian is calculated at a nominal value[13]. The calculated Jacobian is used until there is anychange in the topology. Though the method is verypopular, the convergence is not analysed in the literature.It may be due to the difficult nature of the multi-statenonlinear estimators.In this study, the nature of convergence of VDHN isanalysed and it is found that the constant Jacobiancalculated at the nominal values may fail under specificcircumstances. It is also shown that the range ofconvergence can easily be extended with some simplemodifications. Though extended convergence takes alonger time, it can be very useful at times. The speedand the reliability can be achieved at the same time with amulti-Jacobian solution.The analysis of convergence is shown with a single state.The issue of constant Jacobian for multi-state estimation isshown through simulation of IEEE 68, and IEEE 118-bustest systems. A single case of failure can pose a potentialthreat for the power system. As the advantage of thedishonest method comes with the parallel implementation,the estimations are executed on a GPU platform [14].The main contribution of the paper is as follows,

• The nature of convergence of the dishonest GaussNewton method is analysed geometrically for a singlestate. It is shown that the constant Jacobian taken ata higher slope can increase the range of convergencesignificantly.

• Through simulation, it is shown that the constantJacobian taken at the flat start can work well for


normal operations on the linear range. But, it failsto converge for high diversity of the states.

• A multi-Jacobian method is proposed for secureoperation. It is able to withstand disturbances in thepower system.

The rest of the paper is organized as follows. Thebackgrounds of the concerned estimation methods, i.e.WLS, and the dishonest method, are described in Section2. The convergence of the dishonest method for a singlestate is analysed in Section 3. The required time forthe constant Jacobian methods for different slopes areshown and a simple multi-Jacobian estimator is proposedin Section 4. A special case of failure for the nominalJacobian is shown in Section 5. The paper is concludedwith plan for future works in Section 6.

2. BACKGROUND

Measurements are collected from different parts of thesystem in the forms of power flows, power injections,voltage magnitudes, and current magnitudes [15]. Thecollected measurements contain errors of different levelsthat needs to be removed to get a clearer view of thesystem. Let, z denotes an ms × 1 measurement vectorwith errors. So, the relation between z, the nonlinearfunction of the measurements h(.), the state vector x, andthe measurement error e is written as,

z = h(x) + e (1)

In power system state estimation, voltage magnitudesand angles are considered as the state variables as theyform the set with minimum cardinality that can describethe whole system [3]. The angle of the reference bus istaken as the reference angle and all other bus angles aredetermined with respect to that. If there are N buses, thestate vector x is represented as,

x = [θ2 θ3..θN V1 V2..VN]T (2)

Here, θ and V , with proper subscripts, represent voltageangles and magnitudes respectively. A system with Nbuses will have 2N − 1 state variables. In the processof estimation, the number of measurements exceeds thenumber of states to form an overdetermined system [16].The accuracy is measured by the L2-norm of the residuesthat are calculated as the difference between the originalmeasurements and the estimated measurements [17].Minimizing the norm is the objective of the optimizationproblem,

minx

||z− h(x)|| (3)

where, x is the estimated state vector.

2.1 Weighted Least Squares Estimation

Like other nonlinear problems, WLS estimator linearisesthe system over a small range. Then it applies linearoperations to get an updated value. The system islinearised again based on this updated value and uses thelinear estimation. This process is repeated unless theestimated value converges. In this method, x is startedwith a close value to the solution. In the beginning, whenthere is no previous value, all voltage magnitudes start as 1and all voltage angles as 0 which is known as flat start [18],

x = [0 0...0 1 1...1]T

After collecting the measurements and constructing theJacobian matrix H(x) at flat start, the following steps arerepeated until the state vector converges to a solution,

• step 1: ∆x = [HT(x)WH(x)]−1HT(x)W(z −h(x))

• step 2: x = x+∆x

• step 3: update h(x) with new x

• step 4: update H(x) with new x

Here, the matrix, W denotes the relative weights of themeasurements that are usually taken as the inverse of thecorresponding error variances [19]. The WLS method isalso known as the honest Gauss Newton method.

2.2 Dishonest Gauss Newton Method

In the dishonest Gauss Newton method, step 4 of the WLSmethod is not executed [11]. H is calculated for flatstart at the beginning and updated after a certain period.As mentioned earlier, if H is kept constant until thereis any change in the topology, the method is called verydishonest.The constant H reduces the computation of step 1. As Hremains constant, (HTWH)−1HTW does not change.Therefore, a constant matrix can be multiplied with thevector z − h(x) to complete step 1. The matrix-vectormultiplication is very suitable for parallel implementationon a GPU. The steps can be reorganized as,

• Before estimation: Calculate M =(HTWH)−1HTW for flat start

• During estimation:

– Take previous estimation, x and new measure-ment set, z

– Repeat the following steps till convergence,

∗ step i: Calculate residuals, r = z− h(x)

∗ step ii: Calculate ∆x = Mr

∗ step iii: Calculate x = x+∆x


Though the method described in [11] proposes the flatstart values for calculating H before estimation, it will beshown that it is not mandatory for convergence. In fact,instead of using one Jacobian, different Jacobians can beused for handling different situations of the system such aslarge changes in real and reactive power flows.

3. CONVERGENCE ANALYSIS OF DISHONESTMETHOD

Before analysing the nature of convergence of thedishonest method, it is important to illustrate thedifference between the honest and the dishonest method.To make it simpler, a single variable function, y =f (x ) is analysed. The applicability of this analysison multi-variable functions will be made clear throughsimulations.Let, the iterations start at x = x0 with an objective ofy = yf (Fig. 1(a)). The slope at x0 is denoted with m0. Inthe honest method, m0 is used with the difference betweenf(x0) and yf to find the new position, x1. For x1, the slopeis calculated as m1 and the process is repeated to find thesolution.On the other hand, the dishonest method starts with afixed slope, m. The difference is always multiplied withthis constant to find the new position of x as shownin Fig. 1(b). The use of a constant slope, m doesnot only eliminate the calculation of m, but it alsochanges the division operation to multiplication (m−1).The contribution is not significant for a single variablesystem, but it becomes an important improvement formulti-dimensional large-scale systems.However, the dishonest method does not ensure conver-gence for any slope, m. The choice of m depends on thefunctions, the region of operations, the target values, andon the starting values. Calculating the Jacobian for theextreme target and extreme starting values can make theprocess slow. So, for each function, the Jacobian can bedeveloped for a normal, and some extreme conditions.In power system state estimation, there exist a few specifictypes of functions between the state variables and themeasurements. It is sufficient to find a suitable m for thesefunctions. From the standard power flow equations, themajor functions can be written as,

• Pij , Qij = a1Vj + b1 = f1 (Vj )

• Pij , Qij = a2V2i + b2Vi = f2 (Vi)

• Pij , Qij = a3sin(θij) + b3cos(θij) + c3 = f3 (θij )

• θij = θij (PMU based phase difference)

• Vi = Vi (PMU based values)

Here, the flows are measured from bus i to bus j.The measurement of current is excluded in this study. Asthe last two equations do not include any function, theyare skipped in this analysis as well. The power injections

m0

m1

m2

x0 x1x2x3

xf

xf

x0 x1 x2

m

m

(a)

(b)

y=f(x)

y=f(x)

yf=f(xf)

yf=f(xf)

Figure 1: The working principle of Gauss Newton method,(a) honest, and (b) dishonest.

are the combinations of power flows; so their analysisresemble that of the flows. Before jumping to the specificfunctions, the nature of convergence is discussed first.

3.1 Nature of Convergence

The state can converge under two major scenarios. Theyare referred as the underdamped and the overdamped case.In the first case, there is an overshoot and it follows azigzag path to reach the final value. In the overdampedcase, there is no overshoot, and x changes monotonicallyto reach the final value as shown in Fig. 2. In somesituations, a mixture of the two cases appears in the sameproblem.

3.2 Linear Functions

The analysis of the linear function is simple. Theoverdamped and the underdamped cases are shown inFig. 3. There is no event where both cases can appearsimultaneously.


1 2 3 4 5 6 7 8 9 102

2.5

3

3.5

4

4.5

5

Iterations

Posi

tion,

x

Underdamped caseOverdamped case

Figure 2: Two ways of convergence of dishonest GaussNewton method, underdamped and overdamped case.

To analyse the condition for convergence, the value of mis started with the maximum. For m → ∞, the processreduces to an incremental search method. By reducing theslope, the convergence can be made faster. It stays underoverdamped case for a1 < m < ∞, where a1 is the slopeof the line. With further reduction, the process convergesup to a certain limit under underdamped case. After that,it fails to converge.

Lower Limit of m: In Fig. 3(b), if the process startswith x0 to find yf = f (xf ), it changes according to thefollowing equations,

at k = 0, x0 = x0

at k = 1, x1 =yf − f (x0 )

m+ x0

at k = 2, x2 =yf − f (x1 )

m+ x1

(4)

If x2 is closer to xf than x0, it will be able to converge.In case of xf > x0, the condition of convergence can bewritten as,

x2 > x0

⇒ m >yf − f (x0 )

f −1 (2yf − f (x0 ))− x0

(5)

The expression of (5) is common for any system withmonotonically increasing slope. For linear functions, itcan be written as,

m >a1(yf − f (x0 ))

−b1 − a1x0 + 2yf − f (x0 )(6)

x0 x1

xf

x0 x1x2

x2 x3

x3x4

(a)

(b)

y=a1x+b1

y=a1x+b1

yf=f(xf)

yf=f(xf)

Figure 3: Two cases of convergence for a linear functionwhen the objective value is higher than the starting value,(a) overdamped, (b) underdamped.

as, f −1 (x ) =x − b1a1

By replacing y = f (x ) = a1 x + b1 in (6), the finalexpression can be derived as,

m >a12

(7)

For linear functions, (7) shows that the minimum slopedoes not depend on the starting or the final value. Itonly depends on the slope of the line. If the quadraticand sinusoidal functions can be linearised over a smallportion, it is also applicable for that. This is the proofwhy a constant Jacobian always works for a change overthe linear region of the system.However, it is noticeable that the best value for m is notthe value given by (5) or (7). Using a marginal value canlead to a very large number of iterations. Those are theminimum values for which convergence can be secured.The best value for a linear function is the constant slope, i.e., m = a1.

3.3 Quadratic Functions

The underdamped and the overdamped cases for thepositive side of a quadratic function are shown in Fig. 4.By taking a large value for m, convergence can always be


ensured. But, having a big m makes the steps small andthe number of iterations increases. The slope should betaken in such a way that it ensures convergence within alimited number of iterations.

x0' x0 x1x2

x0 x1 x2 x3

y=a2x +b2x2

y=a2x +b2x2

yf=f(xf)

yf=f(xf)

(a)

(b)

Figure 4: Convergence of a quadratic function in twodifferent ways when the objective is higher than thestarting value, (a) overdamped, (b) underdamped.

If the slope is reduced, a mixture of the overdamped andthe underdamped response is found first. With furtherreduction, a complete underdamped case is found asshown in Fig. 4(b).

Lower Limit of m: The analysis is the same as the linearfunctions. For quadratic functions of Pij , and Qij , f −1 (.)can be written as,

f −1 (x ) =−b2 ±

√b22 + 4a2 x

2a2(8)

where, f (x ) = a2 x2 + b2 x (9)

As the voltage magnitude can only be positive, the

expression of (5) can be written as,

m >2a2(yf − f (x0 ))

−b2 − 2a2x0 +√b22 + 4a2(2yf − f (x0 ))

(10)

Any value of m above this value will make the systemconverging. The minimum value depends on yf , x0, a2,and b2. The value increases with the increase of yf . Therelation between m, and x0 is complicated. To avoid thecomplication, the slope at maximum possible xf is takenas the value of m that works for every x0. If x0 is closeto xf , it is the most efficient slope as analysed in Section3.2. If not, the process operates in the overdamped casethat is inefficient, but it is still better than calculating anew Jacobian for practical power systems as shown inSection 4.1. For the 118-bus system, one iteration of theWLS estimator takes around 42 times more time than thedishonest one, while around six iterations of dishonestmethod gains the same accuracy of the WLS method.It is not expected that the starting point will always belower than the target value; it may also be at a higherposition. In case of xf < x0, the searching occurs in thedownward slope. The two cases are shown in Fig. 5. Theanalysis is very much similar to the upward case, and asimilar expression can be derived.

x0x1

xf

x0

x1

x2

xf

(a)

(b)

Figure 5: Convergence of a quadratic function for twodifferent ways of convergence when the objective valueis lower than the starting value, (a) overdamped, (b)underdamped.

However, there has to be a single m irrespective of theposition of xf . The problem is resolved by taking the


solution for the upward search. It is evident from the factthat for any xfu, xfd, and x0, if xfd < x0 < xfu, then,mu > md. It can also be inferred that there will be onlythe overdamped case for the downward search with thisvalue of m.

3.4 Sinusoidal Functions

Though the two typical cases can appear in sinusoidaloperations, it is a bit complicated, as the slope ofthe function does not increase monotonically. Theoverdamped case is simple as shown in Fig. 6(a). In theunderdamped case, if the slope at x1 is less than m, theconvergence cannot be ensured. So, (5) is applicable in arange of x where the slope is greater than m.

x0

x1

xf

x0

x1

xf

(a)

(b)

Figure 6: Two cases of convergence for sinusoidal function,(a) overdamped, (b) underdamped. As the slope at x1 cutsthe function at another point, the convergence cannot beensured.

For power system, the phase angle of a bus with respectto the reference bus can vary a lot. Two connectedbuses usually keep a constant phase difference to maintainan expected real power flow between them. In case oftypical faults, disturbances, or sudden load changes, thephase difference of the connected buses can change, butit usually does not exceed ±20◦. In this short region,the sinusoidal function can be considered linear and theanalysis for linear function can be applied. An easierchoice is the maximum slope of this region that can ensureconvergence. The maximum slope for a sine functionoccurs at θ = 0 and that for a cosine function occursat θ = π

2 . Due to the comparative values of a3, andb3, a value close to zero is preferred. However, takingthe maximums slope can make it a slower process, anda better value can be obtained by choosing the closestpossible value. For any transmission line ij, the angle

corresponding to the maximum slope, θm can be foundwith Algorithm 1.

Algorithm 1 Selection of θij

1: θmin = min(possible values of θij)2: θmax = max(possible values of θij)3: if θmin > 0 then4: θm = θmin // closest to zero5: else if θmax < 0 then6: θm = θmax // closest to zero7: else8: θm = 09: end if

4. MULTI-JACOBIAN METHOD

In the previous section, it is shown that the constantJacobian calculated at the nominal values can fail withdiverse states. On the other hand, a Jacobian with higherslopes can converge slower than the Jacobian with thenominal slope. A combined effort yields the propersolution.

4.1 Timing Profile of Constant Jacobians

To develop a comprehensive approach, it is importantto have a practical view on the required time of theestimations using constant Jacobians. As mentionedearlier, the main advantages of the constant Jacobianmethods come from the parallel implementation. So, theprofiling is executed with parallel implementation on aGPU.

Setup of the Experiment: To test the dishonest methodbased state estimation, it is implemented on IEEE 118-bustest system with 186 transmission lines. Measurementerrors are added artificially that vary in between 0.25-4%of the original values. The original values are collectedunder typical conditions of the states, i.e. |Vi| → 1.0, andθi → 0, for i = 2..N . For parallel estimation, an NVIDIATesla K20c GPU card with compute capability 3.5 is used.Based on the three steps, three different kernels are writtenthat use different numbers of blocks and threads [20]. Oneof the major advantages of GPU is that it does not requireany extra time to launch and finish a kernel. Therefore,the kernels can be executed sequentially without any delay[21]. The details of the GPU implementation can be foundin [22].For simulation, three sets of magnitudes are chosen tobuild the Jacobian matrix, |Vi| = 0.9 pu, 1.0 pu, and 1.2pu. For all cases, the angle is set according to Section 3.4.The required time is the product of the required numberof iterations and the execution time of each iteration.The communication time is added with it. The trend ofconvergence of the WLS and the dishonest methods areshown in Fig. 7.


0 1 2 3 4 5 6 7 8 90

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Iteration number

Nor

m o

f the

resi

dues

(pu)

0 0.5 1 1.5 2 2.50

0.05

0.1

0.15

0.2

0.25

0.3

Time (ms)

Nor

m o

f the

resi

dues

(pu)

WLSDishonest with |V|=0.9 puDishonest with |V|=1.0 puDishonest with |V|=1.2 pu

(b)

(a)

Figure 7: The trend of norms of the estimations with (a)iterations, (b) time. The required time is taken from theserial implementation. It is very low for dishonest methodin parallel programming with CUDA.

Analysis of the Results: It can be seen that the WLSmethod converges very close to the final value within onlyone iteration. On the other hand, the dishonest methodwith |Vi| = 1.0 converges faster than other values of|Vi|. None of the dishonest methods take more than fouriterations to achieve the same accuracy of one iteration ofthe WLS method.However, due to the non-parallelisable part of the WLSestimator, one iteration of the WLS method takes around2.7 ms while one iteration of the dishonest method takesaround 64µs. The communication time is around 26µsthat is added to each measurement sample with multiplenumber of iterations. As a result, around 42 iterationsof the dishonest method can run at the same time of oneiteration of the WLS estimator. In serial implementation,around six iterations can run and the required time lookslike Fig. 7(b).

4.2 Proposed Method

The proposed method is a simple addition to the existingmethod. From Fig. 7, it is clear that there exists a trade-offbetween the range and the speed of convergence for thedishonest method. The higher the slope, the bigger therange, and the slower the speed. As the power systemrarely runs into any non-converging situation with nominalJacobian, the main process runs with the existing method.At the same time, a few optional Jacobians are added in the

process. The optional Jacobians are calculated with largerslopes (|Vi| = 1.2, 1.4 etc.) and saved before starting theprocess. In case the nominal Jacobian fails, the optionscan be tried one by one as shown in Fig. 8. The number ofoptions can be set with practical experiences.

5. ILLUSTRATIVE EXAMPLES OF FAILURE

It is already shown that a higher slope ensures convergenceof the dishonest method. Though it is easy to derivethe expression for the range of convergence for a singlestate, it is difficult for the multi-state case. However, theimportance of the proposed method for the multi-state casecan be realized through simulation.

Estimation with Jacobian at |V|=1.0

Converged?

Estimation with Jacobian at |V|

Take new sample

yes

yes

no

no

Start

Define, incr=0.2

System online?

|V| |V|+incr

Stop

Converged?

yes

no

Figure 8: A simplified flowchart of the proposedmulti-Jacobian method.

To show the case of failure, two Jacobians (at |Vi| = 1.0and at |Vi| = 1.2) are applied on IEEE 68, and IEEE118-bus test systems operating under disturbances. The68-bus system has 16 machines with 83 transmission lines.The details of the systems can be found in [23] (68-bus),and [24] (118-bus). The states for the failed cases are


shown in Table II, and III of the Appendix. As the anglesstay very close to zero, the nominal Jacobian is taken atthe highest slopes at θ = 0. The voltage magnitudes varya lot under the specified case.The norms of the residues over the iterations of estimationare shown in Figs. 9, and 10. For both cases, it can beseen that the norms decrease in the beginning for bothJacobians. Then the nominal Jacobian (|Vi| = 1.0) startsa gradual increase after around ten iterations. It continuesincreasing and the process explodes eventually. On theother hand, the Jacobian with |Vi| = 1.2 converges withthe iterations. These two examples clarify the importanceof the proposed method.

5 10 15 20 25 300

100

200

300

400

500

600

Number of Iterations

Nor

m o

f the

resi

dues

(pu)

Jacobian with |V|=1.0Jacobian with |V|=1.2

Figure 9: The trends of convergence for a specialcase of 68-bus system where the nominal Jacobianfails to converge and the Jacobian at |V|=1.2 convergessuccessfully.

An important point to be noted that the norm can increaseafter a low value for |Vi| = 1.0. This means that ashort distance with the starting value of the states, x0

does not ensure convergence. The convergence dependson the closeness of the point of Jacobian and the point ofoperation.As analysed in Section 3., the Jacobian should requirehigher |Vi| for higher variations of the voltage magnitudesof the buses. The minimum required |Vi|s are shown fordifferent standard deviations of the magnitudes in Fig. 11.

5 10 15 20 25 300

50

100

150

200

250

300

350

400

450

Number of Iterations

Nor

m o

f the

resi

dues

(pu)

Jacobian with |V|=1.0Jacobian with |V|=1.2

Figure 10: The trends of convergence for a specialcase of 118-bus system where the nominal Jacobianfails to converge and the Jacobian at |V|=1.2 convergessuccessfully.

It can be seen that the nominal Jacobian fails for a standarddeviation more than 0.1222. It is also observable that theminimum |Vi| keeps a linear relation with the standarddeviation of the states.It is important to remember that, the existing method withthe Jacobian calculated at |Vi| = 1.0 that worked upto avariance of 0.1222 is still a very strong tool. Because,under normal operating conditions, the variance usuallydoes not exceed 0.05. Even with 10-20% load change ofthe 68-bus system, the magnitudes does not change muchand they can be easily estimated. However, with very lowprobability, the states may reach some values that maynot be possible to estimate using |Vi| = 1.0. Two suchcases are shown in the Appendix. In one study, one outof 20000 samples failed to converge with |Vi| = 1.0.Though the probability of such cases is low, it can becrucial as the states may undergo very high change duringthat time. Under these failed cases, the safer choice willbe to calculate the Jacobian with a higher value of |Vi|, notwith a lower one.The single and the multi-Jacobian methods are comparedin Table I. The range of convergence refers to themaximum variation of the states with which the method

Table I: Comparison of the Single and the Multi-Jacobian Methods

Qualities Single Jacobian method Multi-Jacobian methodRange of Convergence Limited High and not limitedSpeed of Convergence Fast Equal/slower than the single-Jacobian method

Application All cases, except very high variations All casesof voltages

Computation requirement Low HighStorage requirement Low High


0.14 0.16 0.18 0.2 0.22 0.24 0.261

1.05

1.1

1.15

1.2

1.25

1.3

1.35

Standard deviation of voltage magnitude (pu)

Min

imum

|V| f

or c

onve

rgab

le Ja

cobi

an (p

u)

Figure 11: The minimum voltage magnitude to calculatethe Jacobian that is required for convergence of 68-bussystem. The Jacobian needs to be calculated with higherslope with increasing standard deviation of the states.

can converge. The speed of convergence is the inverseof the time required to converge. The computationalrequirement is shown for the case where both methodsconverge. The storage requirement denotes the memoryneeded for saving the M-matrices for different |Vi|.

6. CONCLUSIONS

A special issue of convergence for the traditional constantJacobian based estimator for power systems has beenaddressed in this study. It is shown that the Jacobiancalculated with the nominal values of the states may failunder special circumstances. The problem can easily besolved using an alternative Jacobian taken at a higherslope. To keep both the speed and the reliability of theestimator, a multi-Jacobian method is also proposed.The issue of convergence for large variations of the statesneeds to be investigated for all computational processes ofpower systems where the Jacobian is kept constant like thestability analysis or the optimal power flow. The analysisrequires further research to explore the possibility of acomplete expression of convergence for the multi-statecase. It will help us to find more loopholes in the processesof the constant Jacobian.

7. ACKNOWLEDGEMENT

This work is supported in part by the US National ScienceFoundation (NSF) under grant #1312260, #1408141 andthe Duke Energy Distinguished Professor EndowmentFund. Any opinions, findings and conclusions orrecommendations expressed in this material are those ofthe author(s) and do not necessarily reflect the views ofNSF or Duke Energy Foundation.

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APPENDIX

Table II: Values of the state variables, |V |, and θ for thefailed case of 68-bus system as shown in Fig. 9

Bus |V| θ Bus |V| θ1 1.000000 0.000000 35 0.903346 0.2948542 1.123044 -0.290585 36 0.660723 0.4126013 1.077397 -0.297812 37 1.011343 0.5504044 1.004883 -0.318400 38 1.042428 0.0309625 0.958901 -0.312663 39 1.008511 0.5549836 0.965078 -0.327882 40 1.225189 -0.0582757 0.912044 -0.262654 41 1.240158 -0.3931238 0.895098 -0.239621 42 1.339963 -0.1439909 0.758673 0.152988 43 1.009167 0.54978510 1.019755 -0.397631 44 1.009798 0.54951811 0.998357 -0.374395 45 1.071776 0.34742112 0.943231 -0.378499 46 1.123650 0.08443213 1.017465 -0.386901 47 1.103357 0.02347014 1.021613 -0.363019 48 1.161692 0.01245415 1.052775 -0.386312 49 1.208029 0.09186616 1.098565 -0.424251 50 1.363774 0.15273417 1.097677 -0.367931 51 1.190591 0.30406618 1.085835 -0.333407 52 1.504477 -0.04991419 1.190758 -0.553913 53 1.125044 -0.28958520 1.074964 -0.548420 54 0.967078 -0.32688221 1.099046 -0.493611 55 1.021755 -0.39663122 1.147669 -0.600822 56 1.192758 -0.55291323 1.136976 -0.596297 57 1.076964 -0.54742024 1.109760 -0.433404 58 1.149669 -0.59982225 1.181595 -0.332462 59 1.138976 -0.59529726 1.167035 -0.355902 60 1.183595 -0.33146227 1.120066 -0.331762 61 1.204773 -0.48876728 1.190985 -0.434027 62 1.043612 0.00747729 1.202773 -0.489767 63 0.911234 -0.15381930 0.916075 0.031617 64 0.662723 0.41360131 1.041612 0.006477 65 1.013343 0.55140432 0.909234 -0.154819 66 1.242158 -0.39212333 0.863357 0.014014 67 1.341963 -0.14299034 0.822119 0.271059 68 1.506477 -0.048914


Table III: Values of the state variables |V |, and θ for thefailed case of 118-bus system as shown in Fig. 10

Bus |V| θ Bus |V| θ1 1.000000 0.000000 60 1.308048 0.2178172 1.254920 0.009599 61 1.337683 0.2333513 1.164455 0.015533 62 1.269382 0.2227044 1.001670 0.080460 63 1.370614 0.2108365 1.179872 0.088314 64 1.233405 0.2417286 1.295964 0.040666 65 1.320579 0.2963577 1.415903 0.032987 66 1.356102 0.2933908 1.227277 0.176278 67 1.313056 0.2473139 1.459855 0.302815 68 1.410197 0.294612

10 1.494270 0.435285 69 1.468543 0.33737211 1.164272 0.035779 70 1.094830 0.20786912 1.118547 0.026704 71 0.980916 0.20036413 0.958780 0.011868 72 1.329444 0.17994314 1.352468 0.014486 73 1.279064 0.19669915 1.122560 0.009774 74 0.989765 0.19146316 1.309046 0.021642 75 1.153070 0.21362817 1.218902 0.053582 76 1.357104 0.19373218 1.156968 0.015010 77 1.022439 0.28012519 1.041672 0.006632 78 1.280089 0.27488920 0.970780 0.021991 79 1.053564 0.28012521 0.943039 0.049742 80 1.302247 0.31922122 1.339004 0.094422 81 1.254347 0.30421123 1.115642 0.180293 82 1.156091 0.28920124 1.275740 0.178373 83 1.260887 0.30979625 1.051693 0.301244 84 1.149754 0.35395326 1.256510 0.332311 85 1.357216 0.38118027 0.971014 0.081681 86 1.287170 0.35726928 1.032003 0.051487 87 1.177100 0.36180729 1.115463 0.034208 88 1.243606 0.43580930 1.271346 0.141721 89 1.272952 0.50649531 1.347401 0.036303 90 1.375289 0.39479332 1.317138 0.072082 91 1.422980 0.39514333 1.034026 -0.000698 92 1.303967 0.40369534 1.105628 0.010996 93 1.186419 0.35116035 1.407531 0.003491 94 0.962161 0.31363636 1.076834 0.003491 95 0.981334 0.29670637 1.015842 0.019199 96 1.368939 0.29391338 1.279548 0.108909 97 1.416611 0.30037139 1.057154 -0.039444 98 1.308081 0.29199440 1.080127 -0.057945 99 1.188759 0.28571041 0.913231 -0.065450 100 1.445616 0.30298942 1.213370 -0.037350 101 0.979749 0.33056543 1.146151 0.010647 102 1.130653 0.37751544 1.012095 0.054978 103 0.956386 0.24033245 1.285239 0.087266 104 1.212708 0.19233546 1.224372 0.136485 105 1.194589 0.17278847 1.092231 0.175580 106 0.913465 0.16842448 1.165665 0.161617 107 1.191761 0.11973049 1.095608 0.179245 108 1.092674 0.15201850 1.239512 0.143641 109 0.925283 0.14416451 0.938937 0.097913 110 1.408138 0.12950352 1.203241 0.081158 111 0.992275 0.15830153 0.910561 0.064228 112 1.196231 0.07539854 1.331205 0.080111 113 1.371510 0.05358255 1.068414 0.075049 114 1.246506 0.06614856 0.955070 0.078365 115 0.922720 0.06614857 1.213467 0.099309 116 1.172455 0.28710758 1.219227 0.084474 117 1.139809 0.00000059 1.322104 0.151844 118 1.276773 0.196350


DEVELOPMENT OF A SEM-QUANTITATIVE APPROACH FOR RISK BASED INSPECTION AND MAINTENANCE OF THERMAL POWER PLANT COMPONENTS S Narain Singh1,2, and J.H.C Pretorius2 1 Eskom, Group Technology, Production Engineering Integration Coal Department Eskom Enterprises Park, Building No 1,2nd floor, Simba road, Sunninghill, Johannesburg, 2000 P.O. Box 1091, Johannesburg, 2000 South Africa 2 Faculty of Engineering and the Built Environment, University of Johannesburg, P O Box 524, Auckland Park, 2006, South Africa Abstract: This paper deals with the development of a semi-quantitative Risk Based Inspection programmes for the Eskom fossil fired generating fleet. This study comes as a result of internal and external factors that affect Eskom from producing electricity in a safe, sustainable manner to ensure security of electricity supply. Eskom has embarked on a risk based maintenance approach to meet the statutory and safety requirements as stipulated by the Depart of Labour as well as to potentially reduce outage costs. The European CWA15740 approach was used to develop the Risk Based Management System. Key words: Risk Based Inspection, Probability of Failure, Consequence of Failure, Component damage mechanism, Pressure Equipment Regulation, Multi Level Risk Assessment, Pressure Equipment Regulation (PER), Risk Based Inspection and Maintenance Application Procedures (RIMAP), Energy Availability Factor (EAF), Unplanned Unit Capability Loss Factor (UCLF), Planned Unit Capability Loss Factor (PCLF)

1. INTRODUCTION Eskom currently faces the challenge of balancing ever tightening production, safety, economic and statutory pressures in an environment where Specialist skills and resources are critically scarce on a global scale. The current Eskom fleet is often operated to the maximum design limit and sometimes beyond to meet the current electricity demand[1]. Over the last few years Eskom’s performance has declined from and EAF perspective[2]. Eskom’s philosophy of 90:7:3 (90 % energy availability, 7 % planned maintenance and 3% unplanned maintenance) cannot be achieved[3]. Eskom’s third Multi Year Price Determination process started in 2012 after the end the MYPD2 determination with Eskom asking NERSA for a tariff increase of 16% of a period of 5 years[4]. The application proved unsuccessful as Eskom was only granted an 8% increase. and Eskom now finds itself with a funding gap of R255 billion[5]. Plant performance has steadily decreased with up to 9000 MW (20% of the installed EAF) of unplanned maintenance (UCLF) being done [2, 6]and at some stages as much as 25% of EAF has been unavailable[7]. The use of gas turbines to get more power onto the grid has substantially affect costs[2, 8]. This unavailability of electricity has led to regular load shedding with the cost of load shedding being six times more than the cost to run the gas turbines[9]. The introduction of the new Pressure Equipment Regulation which regulates the pressure equipment

operations have further added complexity to the Eskom operating environment. This new regulation states that all equipment operating at a pressure ≥50kPa are regarded as pressure equipment and as such must be hydrostatically pressure tested at a test pressure 1.25 times the design pressure at a frequency of 36 months. Eskom currently pressure tests at a 72 month interval, however the new regulation does not permit the 72 month interval. Reverting to a 36 month philosophy would lead to further complexity as the operating philosophy of 80:10:10 [3] cannot be achieved as PCLF would double. As an alternative to the requirement for periodic 36 month pressure tests, the PER offers an option of implementing a certified Risk Based Inspection (RBI) programme as part of a plant life cycle management strategy. This paper outlines the development of a multi level risk assessment process that allows Eskom to comply with the statutory requirement of the PER while maintaining security of supply and achieving future savings to make up some cost savings to supplement the 8% tariff increase. The European RIMAP (Risk Based Inspection and Maintenance Application Process) CWA15740 process. Initial literate surveys indicate that the Risk Based approach on fossil fired power stations is the first of its kind both nationally and internationally. The European methodology of CWA154740 has not been rolled out in its entirety at any utility; most risk approaches have followed the API580 methodology.


2. RISK BASED APPLICATION IN THE POWER

INDUSTRY

Risk Based approaches have gained favour over the traditional maintenance approaches mainly due to the risk process’s ability to accurate assess the condition of functionally important components and to then optimise operating and maintenance planning [10]. In the nuclear industry maintenance professionals are becoming involved in carrying out risk based evaluations[11]. Historically knowledge of risk based activities have existed in the field of Probabilistic Safely Assessments (PSA), a field in which maintenance professionals do not play a major role. The nuclear industry as well as Regulators are now using risk approaches to rationalise regulations as well as to optimise resource utilisation[11]. Application of RBI within the coal fired power generation is limited with few coal fired power stations applying this philosophy. National thermal Power Corporation in India is the world’s third largest power utility. The utility has successfully applied RBI to all of its 105 power units ensuring that the units run safely and reliably[12]. Progress Power in the United States applied RBI to 19 of its power generating units. The risk based approach enabled the utility to replace 140 of its major tube components for $70 million less that the convention approach which treats all hazards equally[12]. In power distribution systems the crucial areas of Asset Management are maintenance and re-investment decisions. Risk Based Inspection is a technology that assists in prioritising maintenance activities[13]. Experience in power distribution systems has shown that the majority of system failures are contributed from a small number of high risk components. Risk Based inspection can be used to identify and prioritise maintenance activities of these high risk components effectively prolonging the useful life of the component while achieving the same level of risk[13]. Swedish law requires Distribution System Operators (DSO) to compensate customers if they experience outages for period’s greater than 12 hours. A major portion of the DSO’s costs have gone to customer compensations [14]which can be up to 50% of the customers annual tariff depending on the duration of the outage. DSO’s are now moving to a risk based approach to minimise customer outages[15].

3. THE RIMAP APPROACH The RIMAP process started out as a European project to with the aim to develop a unified risk based decision making process within the inspection and maintenance arena. This process would be applicable to the power, chemical, petrochemical and steel industries respectively[16]. The research into the development of RIMAP was partly funded by the European Commission. Risk-based planning and execution of inspection and maintenance (RBIM) is a comprehensive philosophy for

managing asset integrity. RIMAP provides guidance for RBIM, quality assurance and follow-up of activities and work processes within an organisation that is used for risk based asset management. It is important to maintain the link between the engineering planning and the actual execution of RBIM (RIMAP workbook). The Process to assess risk is based on a combination of the probability and consequence of failure. This combination of probability and consequence is assessed using a bow tie model[16]. The outcomes of the assessment is then used to prioritise maintenance interventions. 3.1. The RIMAP Process General Requirements: The RIMAP process relies on the application of sound engineering practices as it is based mainly on expert input. It is necessary to ensure that the risk acceptance criteria and the objectives of the assessment are clearly defined. The assessment team must comprise of a multi-disciplinary team with competencies in inspection, maintenance, materials, corrosion, electrical, fixed and rotating equipment, safety, health plant knowledge and risk and reliability assessment Initial Planning: In this step the objectives of the study are defined and the boundaries for the assessment are identified. The assessment team is setup and the data sources are identified. The necessary software required are defined. Data Collection and Validation: Once the data sources have been identified the data is gathered. This data is generally collected from multiple sources. The possibility that the data could be of poor quality is high therefore it is necessary for the data to be validated by the assessment team and the data is then stored in a well-structured database. Multi Level Risk Analysis: In this step the PoF, CoF and overall risks are calculated. The multilevel risk analysis ranges from an initial screening step to a very detailed quantitate assessment. The screening analysis is meant to be relatively fast, simple and cost effective. The components are analysed using criteria such as high, medium and low risk. A components that fall into the high and medium risk criteria should be considered for further analysis whereas low risk components would follow a minimum surveillance maintenance approach, this is done to ensure that the assumptions made during the assessment are valid. The detailed risk assessment follows the same principles as the screening analysis although in greater detail.


Damage mechanisms are identified per component and degradation rates are determined. Additional criteria are used in refining the PoF, CoF and overall risk determination. Decision Making and Action Plan: Based on the outcomes of the risk assessment the team develops the optimal inspection strategy. The strategy should ensure resource and cost optimisation. Execution and Reporting: The maintenance plan developed by the risk assessment is executed and the findings of the maintenance interventions are recorded noting the condition of the component. These findings are then fed into the risk assessment for further risk refinement. Performance Review: The purpose of the evaluation of the risk-based decision-making process is to assess its effectiveness and impact in establishing the inspection and maintenance programs thus allowing for continuous improvement. The evaluation process involves both internal and external assessment conducted by the operating organization and by independent experts, respectively. Internal assessment can be triggered by a deviation from the process, or a change in knowledge or the plant that requires a risk re-assessment. The RIMAP methodology is a guide; it is not prescriptive making it industry independent. The process is based on best practices and it gives guidance on what a comprehensive RBI process should entail. These factors make it an ideal process for Eskom to adopt. There are however limitation this methodology in that it is heavily dependent on good quality data, it applies to equipment on in the in service phase and is it applicable o to the secondary plant in a nuclear power stations. Further the documentation supporting the RIMAP process is of a large quantity and it may prove difficult for and individual to go through all this documentation[17].

4. DATA GATHERING The data gathering aspect of the RBI process is vital for an effective RBI assessment[18, 19]. The data used for the risk assessment must be of a high quality [20] as poor and ambiguous data could lead to the results of the risk assessment being conservative in nature in that may of the risks associated with the components being assessed may be overstated. All data collected must be verified and validated to ensure that the data is accurate and applicable to the risk study. Data required for a RBI assessment is divided into two categories namely design data and operating data. Design data provides information on the construction and design criteria of a component. Operating data gives

information on the conditions (operating temperature, operating pressure, etc.) under which the component is in service. In doing a RBI assessment a minimum or base data set is required for the assessment. For the Eskom project the following data was collected: 4.1. Design and Construction Data The design and construction data is required to assess aspects of structural integrity. This data is generally used as a benchmark against which test and inspection activities can be compared to. The quality of the material used in construction of the component can also be determined of records of fabrication inspections are available. These inspections would typically indicate issues such as poor materials, weld defects, weld repairs and construction concessions. This information is useful in determining areas of possible deterioration. NDT reports during component construction can give an indication of the quality of workmanship that was involved during construction. 4.2. Test and Inspection Reports Inspection reports can be used to trend deterioration rates of a period of time. These trends can then be used by the RBI assessment team to determine the safe operating regime of a component. It is necessary to ensure that all inspection reports are analysed on not just the latest report. It is also important to assess the NDT techniques listed in the inspection reports to determine the effectiveness of the chosen technique. 4.3. Modifications and Repairs Any repairs or modification carried out on equipment under assessment must be reviewed to ensure that it was repaired according to the necessary codes of construction. It is also necessary to determine the reason behind the repair or modification to assess if this would have an impact of the probability of failure determination. 4.4. Maintenance Records Maintenance records are required to assess the effectiveness of the maintenance interventions. The records also give an indication of “as found” conditions. These “as found” conditions need to be assessed by the RBI team to determine if there are active damage mechanisms present as well as to assess if the maintenance interventions are effective enough to arrest any active damage mechanisms. 4.5. Protective Devices The type and condition of protective devices should be reviewed to establish their suitability under a RBI regime. Protective devices can present particular problems as they usually operate infrequently, or may never operate at all;


they may be susceptible to the external environmental conditions or be affected by the contents of the system. Data storage within Eskom is spread across fourteen power stations over four provinces (Mpumalanga, Limpopo, Free State and the Western Cape) and the head office, Megawatt Park in Johannesburg. This spread of information makes the gathering of data somewhat complex. To ensure that the relevant and accurate data was collected multiple teams were used with resources from both the head office and relevant power stations being used. Data storage was done using Microsoft Excel and collaboration with the data gathering teams and the power stations was done using Microsoft SharePoint. This ensured quicker updates of data sets and at the same time created a record and paper trail of all changes to the data. All final data sets were then stored for use by the RBI assessment team in the Eskom Document Management System, Hyperwave. Data validation is performed to ensure that the data collected is accurate and relevant. There are various levels of validation to ensure data accuracy. Initial validation is carried out by the data collectors as the data is collected, this is an informal approach and the Excel spreadsheet filter function is used in this validation and a 100% check is performed on all the data captured. The second check is performed by the head office lead engineer in conjunction with the power station system engineer. A 100% check is once again performed on the data. The third validation is performed by the relevant plant Specialist. This is a sample check and depending on the amount of errors found the sample size increases. Once all checks are completed the data is signed off by the Power Station Engineering Manager and the relevant plant Specialist. The data is then loaded onto the document management system for use by the risk assessment team. The data gathering aspect is an important step in the Risk Based Inspection process as errors and inaccuracies in data will affect the outcomes of the assessment. The validation steps are necessary to improve data accuracy thus ensuring an effective risk assessment.

5. THE SEMI QUANTITATIVE RISK BASED MODEL

The risk model is based on the RIMAP CWA15740 methodology. In conjunction with the ISO31000 standard rules were developed to ensure a robust process was developed that conforms to international norms. The model consists of three levels of assessment:

A level one risk assessment that is qualitative in nature

A level two risk assessment that is semi-quantitative in nature, and,

A level three assessment that is quantitative in nature

5.1. Level One Risk Assessment The level one assessment is a fully qualitative assessment in which screening is performed to screen out the very low risk components. The level one assessment assesses probability and consequence of failure of the component under study and the risk for the component is calculated based on the result of the PoF and CoF assessment. Determining level one probability of failure: The first level of assessment is a screening assessment that is used to screen components that pose a low risk to the organisation. A simple evaluation of PoF is carried out by determining which of a number of specific criteria will influence the probability of a failure occurring. For example, if a component is operating at conditions above the design parameters it will be more likely to fail than if it were operating at conditions below the design parameters. Hence for this case a response of “high” would be the input for the criterion “operating conditions” whereas if it is known that the component operates below design the input would be “low”. The terms “high” and “low” equate to high and low score respectively. In performing the level one screening assessment only the most likely active damage mechanisms must be considered and the worst case scenario in terms of failure must be considered together with the probability that this failure would occur. The following rules are applied for the level one screening assessment:

The risk assessment must always be conservative.

If there is any uncertainty associated with any factor or if no information is available then the default position is always “high”.

A total of ten criteria are assessed to determine the probability of failure Figure 1 lists the criteria used to determine the probability of failure along with the weighting applied to each criteria.

Criteria Weighting

Component age 0.0724

Material 0.0543

Year of last inspection 0.1448

Presence of degradation 0.1448

Rate of degradation 0.1448

Operating conditions 0.1629

Potential for mal-operation 0.0724

Design concerns 0.0543


Industry experience 0.1267

Prior repairs or damage 0.0543

Table 1: Probability of failure criteria and the associated weighting. Table two lists the elements used to determine whether a criteria ranks either high or low when determining probability.

Criteria High (weighting =10)

Low (weighting =1)

Component age If the component is old (over 150,000 service hours) or new (< 50,000hours service or replaced with <50,000 service hours).

If the component is between 50,000 and 150,000 service hours.

Material If known material problems or defects exist.

If no known material problems or defects exist.

Year of last inspection

If not recent i.e. >3years (25,000 operating hours)

If recent i.e.3 years or less (25,000 operating hours).

Presence of degradation

If there is a history or knowledge or indications of an active degradation mechanism.

Degradation mechanisms identified, inspections carried out and no indications found.

Rate of degradation

If conservative estimate of degradation indicates problem within 70,000 operating hours (9 years).

If conservative estimate of degradation indicates no problem within 70,000 operating hours (9 years).

Operating conditions

If operating is known or suspected to be at greater than design operating conditions.

If operating is known to be generally less than design operating conditions.

Potential for mal-operation

If mal-operation is known to occur or possible to occur e.g. large temperature excursions, passing valve, significant chemical excursions, large

If mal-operation is unlikely or cannot/does not occur.

thermal transients, fast ramp rates, etc.

Design concerns

If component is considered to have potential design issues e.g. is seam welded HT components, or large change in section at weld, etc.

If component is considered to have no design issues.

Industry experience

If there is knowledge within the industry of the component failing.

If there is no knowledge of the component failing.

Prior repairs or damage

If it is known or suspected that repairs have been made or serious levels of damage found in the past.

If no repairs or serious damage have occurred or been found in the past.

Table 2: Assessment criteria to determine if component ranks high or low.

Each criterion is weighted according to the level of influence it has on the probability of causing failure. For each component assessed, each criterion is scored relative to a qualitative measure of how likely it is to affect the component. As indicated above for the level 1 assessment this is a simple “high” or “low” which in the assessment equates to a numerical score. Probability of failure scoring: Each criterion is given a score relative to High = 10 or Low = 1. This score is then multiplied by the weighting of the criterion. Each criterion is similarly evaluated then all criteria scores are summed together, Equation (1).

Criteria Score [(c1*w1) + (c2*w2) + (c3*w3) + (c4*w4) + …..(c10*w10)] (1)

Where c1 = criterion 1, 2, 3…10 w1 = weighting 1, 2, 3…10 This gives the component Probability score. However in order to produce an indicative probability of failure (PoF) the score needs to be modified by a Generic Failure Frequency (GFF). The Generic Failure Frequency (GFF) is a methodology that is used based on experience to identify failure frequencies of various components. It is typically developed using expert judgement and history of failures of components. The


GFF for the Eskom study for the level 1 assessment are based on the DNV system[21]. For each component being assessed the RBI assessment Team will determine the appropriate GFF for the component. The cumulated criteria score is then multiplied by the assigned GFF as follows:

PoF = [(c1*w1) + (c2*w2) + (c3*w3) + (c4*w4) +…..(c10*w10)] *GFF (2)

Using the GFF together with the score provides an indication of the Probability of Failure in any given year. Since the majority of damage mechanisms are time dependant, the probability of component failure would increase with time. To take account of this a factor is used with the GFF such that the longer the period required between inspections, the higher the risk. This multiplier is exponentially based such that in

Year 1 the factor is 1, Year 6 the factor is 10 and Year 12 the factor is 100

This allows the risk of a component to be evaluated and compared over time e.g. if the risk of a component in year 1 is 1x10-4, it will be 1x10-3 after 6 years of further service and 1 x 10-2 after 12 years of further service. This aids decision making around the acceptable service interval between inspections. Level one consequence of failure calculation For the Eskom RBI process three major categories are taken into account:

Safety and health Business Environmental

The Safety and health category takes precedence over the business and Environmental category The above criteria are used together with the Hazard Category (SANS 347 Pressure Classification), and the nature of failure (leak or Burst). As in the case of the PoF determination a “High”, “Low” classification is used for each Criterion except for the Hazard category which has 3 main Classes (IV highest to Class II). Lower classifications (Category I and Sound Engineering Practice (SEP) do not require a RBI process to be used to manage their integrity. The criteria used are shown in Table 3. A logarithmic numeric is used for the high criteria (10) and low criteria (0.1) is used for scoring. For each component to be assessed the RBI Team will assign a score which will be factored by the weighting. The Hazard category is based on the dimensions/volume of the component and the contents. This produces a component CoF.

Criteria Weighting

Hazard Categorisation 0.667

Failure type 0.667

Safety 5.999

Health 0.067

Environment 0.067

Business (lost MW/H 0.267

Business (repair costs) 0.0.067

Table 3: CoF Criterion with weightings Calculating level one overall risk: The risk of a component failing is the product of the PoF and the CoF i.e.

Risk = PoF x CoF The Level one risk plat is plotted on the matrix below (figure 1). Should the level 1 risk fall into the green area of the matrix then the risk is regarded as very low and the normal routine maintenance interventions are followed.

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Eskom level 1 RBI Matrix

Prob

abilit

y Cat

egor

y

Consequence Category Figure 1: Level one risk matrix If the calculated risk lies within the Green area the risk is at an acceptably low level and no other assessment is required. Here the current routine maintenance strategy is to be reviewed for applicability and updated where necessary. If the calculated risk lies in the Yellow (medium risk) or Red (high risk) regions then the component must go forward to be evaluated under level two. 5.2. Level two risk assessment During the level one risk assessments all low risk components were screened out and all high risk components are elevated to a level two semi quantitative assessment. Unlike the level one PoF assessment which was high level in nature, the level two PoF assessment is of a greater detail. In this assessment the number of


criteria to which the component under study is assessed against is greater than the level one assessment. Level two probability of failure assessment: A total of nineteen criteria are used in the level two PoF assessment. These criteria are:

Component Age (since installed) Total Starts per year Typical start-up rate /Loading rate Potential Material Problems Repairs / damage Time since Last inspection Adequacy of scope (for the damage mechanism

considered) Adequacy of Techniques (for the damage

mechanism considered) Calculated Rate of Degradation Quality of Water/Steam Chemistry Potential for Mechanical Fatigue stressing Potential for Thermal Fatigue Stresses Potential for Local mechanical over-stressing Presence of Local Hot spots Nominal operating temperature Corrosion susceptibility Frequency of temperature excursions Severity of Temperature excursions Design Concerns

The aim of the level two PoF assessment is to determine in greater detail the factors that may affect or influence the identified damage mechanisms for the component under study. Not all criteria listed above may affect the potential damage mechanism however they will be assessed to ensure all possible criteria have been taken into consideration. For the component under study all feasible damage mechanisms as well as failure types are considered. All inactive damage types are noted and recorded. Level two scoring The scoring system for each criterion is expanded into 5 classes:

Very low (weighting 0.01) Low (weighting 0.1) Medium (weighting 1) High (weighting 10) Very high (weighting 100)

The criteria above are related to a score that is logarithmic in nature. The score for each criterion is multiplied by a weighting and is then summed up to provide the score for the component under study. The total of all the criteria scores is normalised by dividing each cumulative score by the sum of the criterion weights, Equation (3). This is carried out to ensure that selection of mid-point values results in a mid-range PoF

value irrespective of the weighting assignment on each criterion. [(c1*w1) + (c2*w2) + (c3*w3) + ...(c19*w19)] / (w1+ w2 + w3 +…w19) …. (3) The Generic Failure Frequency (GFF) is once again used but for the level two actual failure frequencies from industry experience are used where available. In instances where there is no industrial GFF data then the team will revert to the DNV GFF values that are used in the Level one PoF determination. Level two consequence of failure assessment: The Level two CoF calculation follows the same methodology as the level one calculation. However additional criterion and new weighting are assessed as illustrated in table 4, however the logarithmic weighting used in the PoF assessment remains unchanged.

Criteria Weighting

Hazard Categorisation 0.01

Failure type 0.25

Estimated area affected by failure

0.5

Number of people in area 0.75

Typical time in area (per day)

0.75

Injury type 1.5

Environment 1

Lost megawatt hours 10

Repair cost 1

Table 4: Level two CoF criteria with weightings Calculation of the Safety CoF is carried out as follows: CoF = {[(C1 x W1) + (C2 x W2)] x [(C3 x W3) + (C4 x W4) + (C5 x W5) + (C6 x W6)1.5]}……………….….(4)

Calculation of the Business CoF is carried out as follows:

CoF = {[(C1 x W1) + (C2 x W2)] x [(C8 x W8) + (C9x W9)]}……………………………………...…..……….(5)

Calculation of the Environmental CoF is carried out as follows:

CoF = {[(C1 x W1) x (C2 x W2)] x [(C7 x W7)]}…....(6)


Calculation of the level two risk: The Level two risk calculation is performed in the same manner as the Level one risk calculation (Risk = PoF x CoF). When dealing with multiple damage mechanisms the RIMAP bowtie approach is used in which the overall risk associated with the component is calculated used by multiplying the highest CoF value of all the active damage mechanisms with the sum of the PoF values of all the active damage mechanisms. Once the overall risk for the component under study is calculated the risk is plotted onto the level two Risk Matrix (figure 2).

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Eskom RBI Matrix

Prob

abilit

y Cat

egor

y

Consequence Category Figure 2: Level 2 risk matrix This risk matrix is broadly split into categories of equivalent risk, but extended to capture High Impact Low Probability events (HILPS). Each colour represents a risk category with an associated action as follows:

High Level three Assessment required

Medium Detailed Inspection Programme to be developed

Low Routine Inspection Programme to be developed

Very Low Routine maintenance to be reviewed and revised as appropriate

As indicated above, if the calculated risk is within the White area the risk is at an acceptably low level and no other assessment is required and the current routine maintenance strategy applies. If the risk resides in the Green region the risk level is considered to be low but a routine inspection programme is to be developed. If the component risk is in the yellow region then the risk level is relatively high and more information of the condition of the component is required, hence detailed inspection and/or further more detailed assessments should be carried out. The red zone indicates that the risk level is unacceptable and the component must go forward to be evaluated using a level three quantitative assessment;

Each type of risk (safety & health, environmental and business) is plotted separately and again the business related risk acceptance level may be higher than that for safety or environmental provided the risk levels of the latter are low. 5.3. Level three risk assessment The level three assessment is a fully quantitative process and is based on based on detailed calculations of remaining life until failure occurs. The specifics of the calculation approaches to be used are varied and will dependant on the component design, material condition and the operating conditions. The level three calculation process would ideally start with a simple calculation to determine remaining life. If the simple calculation indicates that there is an acceptable time interval before failure occurs then no further calculations would be necessary. Alternatively if the simple calculation reveals an unacceptable time interval to failure then a more detailed calculation would be carried out to refine acceptability. Level three probability of failure calculation: The level three analysis is essentially calculations to determine remaining life of the component under study. These assessments will be carried out by the Specialist Metallurgists and relevant Plant Specialists. Level three probability of failure scoring: The scoring for level three considers only the calculated time for failure. This is illustrated in table 5.

Risk Level

Time to calculated failure

Action

Very High < 2 years Repair/replace/mitigate

High 2-4 years Re-inspect within 6-12 months/replace/repair within 18 months

Medium 4-6 years Re-inspect within 2 years/repair/replace within 3 years

Low 6-8 years Re-inspect within 3 years/repair/replace within 5 years

Very Low >8 years Re-inspect within 4 years

Table 5: Level three Probability of Failure calculation Level three consequent of failure assessment The level two consequence of failure criteria are once again used in the assessment of the level three consequence of failure assessment.


Level three risk assessment: The PoF and CoF of the level three assessment are plotted on the Level two matrix once again. The risk rankings of the level two criteria are also followed. Development of mitigation strategy for level 3 high risk components: If a component is found to have a very high risk ranking once the level three assessment is completed then a mitigation strategy document is developed by the Level three RBI assessment team. This strategy document summarises the results of the level three analysis and includes recommendations. If the recommendations indicate that the risk level is very high and that immediate action is required, the report is then presented to the Technical Governance Committee for review, approval and implementation by the affected power station. Where mitigation is possible, the RBI risk level is updated to reflect the refined risk level. Monitoring is developed to ensure compliance is undertaken by an appropriate means, such as a Temporary Operating Instruction or a Safety Instruction. 5.4. Development of test and inspection plans For the high or very high risk components a detailed inspection is required. A RBI Inspection, Maintenance and Test (IMT) plan development team shall be convened to develop the appropriate RBI IMT Plan. The Plan is reviewed by the Subject Matter Experts for the component under study to assure that the plan is adequate, relevant and will mitigate the risks identified. All Outage Tasks are scheduled for the next Outage by the Plant System Engineer. Quality Control Plans are to be developed by Maintenance/Plant System Engineer and these QCP’s have been approved upfront by the AIA. Finally all plans are implemented during the planned unit outage. 5.5. Post outage risk assessment The RBI Team will evaluate the inspection reports after the Outage and re-assess the degradation rates etc. ready for the revised risk assessment. The RBI Team is then re-convened to the repeat Level 2 Risk Assessment using the new inspection information to determine the current Risk Level. The level of risk after 6 years will be determined. Any components in the high risk category may require re-inspection earlier than 6 years. The findings shall be compiled in a formal RBI Report and presented to the Site RBI Steering Committee for Approval.

6. CONCLUSION This RBI model that has been developed using the European CWA 15740 standard. This developed risk model consists of 4 distinct phases namely:

Data gathering and validation phase in which the relevant component data pertaining to design, operation and test and repair information is collected as the input for the risk assessment to be performed. This data is verified and validated to ensure that,

A level one screening assessment in which qualitative criterion are employed to determine component risk. Based on the qualitative criterion if a component is perceived to be of a high risk then a further level of assessment is required

A level two assessment in which a mix of qualitative and quantitate criterion (semi-quantitative) are used to determine component risk

Finally a level three assessment which is fully quantitative is employed to deal with unacceptably high risks based on the outcomes of the level two assessments.

This model was developed with the aim of ease of application and availability of resources (people, information and technology) in mind.

7. REFERENCES [1] Bezuidenhout, M., et al., Risk Management of

Plants with Finite Design in Eskom. 2012. [2] Nani, C., Kendal Power Station Five Year

Improvement Plan. 2015, Eskom Johannesburg. p. 125.

[3] Govender, T., Integrated Sustainability Strategy for Eskom Generation. 2013, Eskom: Johannesburg. p. 136.

[4] Eskom, Unpacking MYPD3 Eskom's Third Revenue and Tariff Application in Eskom Eskom, Editor. 2012, Eskom Johannesburg. p. 57.

[5] Gopal, D., Introducing Generation Specific Value Packages. 2014.

[6] Lacock, R., Tutuka Power Station Five Year Improvement Plan. 2015, Eskom Johannesburg. p. 41.

[7] Ntsokolo, M., Group Executives Dashboard. 2015, Eskom: Eskom

[8] Conradie, T., Lethabo Power Station Five Year Improvement Plan. 2015, Eskom Johannesburg. p. 52.

[9] Eskom, Media Assessment 2015 Eskom Johannesburg. p. 18.

[10] Coble, J.B., et al., Incorporating Equipment Condition Assessment in Risk Monitors for Advanced Small Modular Reactors. 2013, Pacific Northwest National Laboratory (PNNL), Richland, WA (US).


[11] IAEA, Implementation Strategies and Tools for Condition Based Maintenance at Nuclear Power Plants, in Nuclear Power Engineering. 2007: Austria.

[12] American Society for Mechanical Engineers. Inspectors Harness the Power of Probability. 2011 [cited 2011 May 2015]; Available from: https://www.asme.org/engineering-topics/articles/safety-and-risk-assessment/inspectors-harness-the-power-of-probability

[13] Jalili, L., et al., Designing A Financially Efficient Risk-Oriented Model for Maintenance Planning of Power Systems: A Practical Perspective.

[14] Wallnerstrom, C.J. and L. Bertling. Risk management applied to electrical distribution systems. in Electricity Distribution-Part 1, 2009. CIRED 2009. 20th International Conference and Exhibition on. 2009. IET.

[15] Wallnerström, C.J., et al. Review of the Risk Management at a Distribution System Operator. in Probabilistic Methods Applied to Power Systems, 2008. PMAPS'08. Proceedings of the 10th International Conference on. 2008. IEEE.

[16] Kauer, R., et al. Plant Asset Management: RIMAP (Risk-Based Inspection and Maintenance for European Industries)-The European Approach. in ASME/JSME 2004 Pressure Vessels and Piping Conference. 2004. American Society of Mechanical Engineers.

[17] Shepherd, B., Safety implications of european risk based inspection and maintenance methodology. HSE Research Reports. UK: Prepared by Mitsui Babcock Technology for the Health and Safety Executive, UK, 2005.

[18] Ablitt, C. and J. Speck. Experiences in implementing risk-based inspection. in 3rd MENDT-Middle East Nondesctructive Testing Conference,(November 2005), Bahrain. 2005.

[19] Wintle, J.B., et al., Best practice for risk based inspection as a part of plant integrity management. 2001: Great Britain, Health and Safety Executive.

[20] RIMAP Consortium, Risk Based Inspection and Maintenance for the European Industries (RIMAP). 2008, European Committee for Standardisation: Brussels. p. 60.

[21] Mathieson, P., F. Saint-Victor, and A. Hussain, RBI Upstream Working Procedures and Guidance S. Angelsen, Editor. 2000, Det Norske Veritas: Europe. p. 42.


NOTES


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