1562 ieee transactions on smart grid, vol. 3, no. 3, september 2012...

1562 IEEE TRANSACTIONS ON SMART GRID, VOL. 3, NO. 3, SEPTEMBER 2012

An Intelligent Control Strategy for PowerFactor Compensation on Distorted Low Voltage

Power SystemsShunfu Lin, Member, IEEE, Diogo Salles, Student Member, IEEE, Walmir Freitas, Member, IEEE, and

Wilsun Xu, Fellow, IEEE

Abstract—Due to the proliferation of harmonic producing-loads,harmonic resonance has become a major hurdle for performingpower factor compensation in commercial power systems, suchas office towers and shopping complexes. This paper presents anintelligent power factor compensation controller that can performpower factor correction without exciting harmonic resonanceunder varying demand conditions. Practical and robust controlalgorithms are proposed for the purpose of easy implementationin a micro-controller. In addition, the controller relies on commonlow cost sensing devices and does not require additional measure-ments. As a result, the proposed controller can be constructed asa retrofitting device to replace existing power factor correctioncontrollers with little effort. Analysis of representative case studiesis conducted to illustrate how the proposed controller performs.

Index Terms—Capacitor switching, commercial buildings, har-monic resonance, power factor control.

I. INTRODUCTION

E LECTRICAL energy efficiency is of prime importance tocommercial facilities, such as office towers and shopping

complexes. The application of power factor (PF) compensationhas long been accepted as a necessary step to improve the effi-ciency of these low voltage electrical installations [1]–[3]. Thisis usually achieved by installing capacitors downstream to thesupply transformer at the entrance point of the facility. Such ca-pacitor units are switched in and out of circuits as the demandfor VAR compensation of the building load fluctuates. If ap-plied properly and controlled, capacitors can improve the per-formance of distribution circuits since, by providing the reactivecurrent locally, less power needs to be provided by the distribu-tion network resulting in lower losses, improved line voltage,

Manuscript received January 28, 2012; revised April 24, 2012; accepted May13, 2012. Date of publication July 13, 2012; date of current version August 20,2012. This work was supported by the Natural Resources Canada through theTechnology, Innovation Program as part of the Climate Action Plan for Canadaand by FAPESP, Brazil. Paper no. TSG-00041-2012.S. Lin is with the Department of Electric Power and Automation Engi-

neering, Shanghai University of Electric Power, Shanghai, 200090 China,(e-mail: [email protected]).D. Salles and W. Freitas are with the Department of Electrical Energy

Systems, University of Campinas, 13083-852, Campinas, Brazil (e-mail:[email protected], [email protected]).W. Xu is with the Department of Electrical and Computer Engineering, Uni-

versity of Alberta, Edmonton, AB T6G 2V4, Canada (e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TSG.2012.2201756

and, ultimately, reduced facility billing charges (utility penal-ties) [1]–[5].However, facility operators have reported frequent failures

or trips of these PF correction capacitor banks. One impor-tant reason is the proliferation of harmonic-producing loads;solid-state power conversion devices are prime examples. Theproblem is that capacitors might aggravate the existing har-monic distortion since, although these devices do not generateharmonics, they provide a network path for possible localor general parallel resonance conditions, which contributesto a significant amplification of harmonic currents producedby the facility loads. In cases of resonance, this current maybe very large and may damage the capacitors. Therefore, theconsideration of PF compensation capacitor installation shouldalso include harmonic resonance analysis at the design stage[1]–[3], [5], [6].According to [5], possible solutions to avoid harmonic

problems include the following: 1) ungrounding grounded-wyecapacitors; 2) changing capacitor bank sizes and locations; 3)adding a reactor to an existing bank; 4) adding a filter capacitor;and 5) controlling the capacitor switching scheme to avoidresonance. The objective of this paper covers the fifth approachand consists of developing a practical and robust control algo-rithm for the capacitor bank switching scheme that is capableof achieving both power factor correction and resonance avoid-ance requirements. Previous works proposed optimizationalgorithms for this purpose; however, they are time-consumingand it is not guaranteed they converge to the optimal solutionunder time-varying load and system impedance conditions[7], [8]. More recent works have focused on the installationof passive and active harmonic filters [9]–[11]. This approachcan be complex (e.g., stresses in the filters need to be con-sidered, the harmonic spectrum of the nonlinear loads needto be determined, etc.) and be costly (e.g., installation andmaintenance costs) to the facility’s owner. Another commonsolution is to add reactors in series with existing capacitorbanks [12]. However, the system parameters vary dynamicallywith the power system configurations and loads. Therefore,the harmonic resonance might occur even if a combination ofcapacitors connected in series with reactors has been installed.Reference [13] proposed replacing the reactors with powerelectronics inverters.The concept of the controller proposed in this paper is

simpler; whenever resonance conditions exist, the capacitorbank should be changed in size to shift the resonant point to

1949-3053/$31.00 © 2012 IEEE

LIN et al.: AN INTELLIGENT CONTROL STRATEGY FOR POWER FACTOR COMPENSATION 1563

Fig. 1. Typical power factor compensation arrangement for commercial powersystems.

another frequency [6]. However, one important issue must besolved; how to determine if the resonance condition existsunder varying demand conditions? It is not safe and intel-ligent to decide the suitable number of switched capacitorsunits assuming constant system impedance since it varies fordifferent operating conditions. In order to solve this issue, theproposed controller uses pre- and postdisturbance (due to thecapacitor switching) steady-state waveforms of the voltagesand currents at the interface point to estimate the harmonicsystem impedance [14]–[16]. It must be highlighted that theproposed controller relies on common low cost sensing devicesand does not require additional measurements. As a result, thecontroller can be constructed as a retrofitting device to replaceexisting power factor correction controllers with little effort.This paper is organized as follows. Section II discusses the

conventional control approach for power factor compensation.Section III describes the characteristics associated to the har-monic resonance problem. Section IV presents the developmentof the proposed capacitor controller. Section V presents casestudies to evaluate the proposed approach. Section VI summa-rizes the main findings of this paper

II. COMMON REACTIVE POWER COMPENSATION SCHEME

As mentioned before, the traditional approach for powerfactor compensation in commercial facilities consists of placingcapacitor banks in parallel with the load at the entrance pointof the facility, offsetting the inductive loading (lagging powerfactor) of the equipments. Fig. 1 shows a common power factorcompensation arrangement used in commercial power systems.As one can observe, the scheme typically consists of one ormore breaker switched capacitor units along with an intelligentcontrol unit, current (CT) and voltage (VT) transformers, whichare connected at the low side of the supply transformer.These banks often include three to nine capacitor units con-

nected in three-phase grounded-wye, ungrounded-wye, or deltaconfigurations [5]. In practice, commercial installations employswitched capacitor banks, instead of fixed banks, in which thecapacitors units are switched on and off automatically to com-pensate for changing load conditions (minimum condition upto peak load) [17], [18]. Fig. 2 illustrates a typical kilovar de-mand over a 24 h period [5]. This curve can be determinedby a recording kilovar meter or calculated using kilowatt andpower factor measurements. The fixed banks satisfy the baseload requirements, and the switched banks compensate for theinductive kilovar peak during the heavier load periods [5], [17].

Fig. 2. Application of switched and fixed capacitors for a time varying kvardemand condition.

Fig. 3. Conventional strategy for power factor correction through switched ca-pacitor banks.

In order calculate the capacitive kilovars necessary to correctto a new, higher power factor, one must subtract the inductivekvar of the corrected power factor from the existing

power factor. The difference is the amount of capaci-tive kvar to be added to the system. The following formula is aconvenient way of doing this [5]:

(1)

where:

kW is the system kilowatt load;

kvar is the amount of capacitive kilovar to be added.

The capacitor switching control scheme illustrated in Fig. 1is based on a local automatic controller. The control sensesvoltage and current, and uses either these parameters directlyor a derived parameter like power factor to compare against athreshold. Fig. 3 shows a flowchart that illustrates the conven-tional strategy of the automatic controller based on themeasuredpower factor.According to the flowchart above, the following steps are per-

formed for PF correction [4], [19]:


Fig. 4. Parallel resonance at a point of common coupling (PCC).

1) The power factor control is performed by controlling theopening and closing of the capacitor switches based on themeasured power factor.

2) The control unit measures voltage (VT) and current (CT)on the feeder side (as shown in Fig. 1) and the results of thecomputed power factor is compared to the predeterminedtarget power factor setting.

3) Using measured and target power factors and the capacitorinformation, the control unit determines if one or more ca-pacitor banks need to be switched on or off to bring the ac-tual power factor as close as possible to the targeted powerfactor setting.

Based on the above considerations, automatic capacitorcontrollers have been developed and marketed for commercialpower system designers and operators. While such controllerswork well for traditional passive loads such as motors, moreand more facility operators have reported frequent capacitorfailures or trips. As a result, reactive power compensationcannot be achieved.This problem is caused by the parallel resonance between

the capacitor and the upstream impedance. This resonance isexcited by the harmonic currents produced by modern facilityloads such as office electronics and variable frequency drives.Industry, therefore, has a strong need for capacitor controllersthat can perform power factor correction on one hand and canavoid harmonic resonance on the other. In addition, the con-troller shall not require additional sensors or inputs and canretrofit current controllers with zero alteration to the existingfacility. In the next section, the resonance problem is explainedin detail.

III. HARMONIC RESONANCE PROBLEM

With any application of capacitor banks, there is alwaysthe risk of resonance. This is due to the interaction of thebank’s capacitance with the inductive reactance characteris-tics of the supply system. Harmonic currents at or near theresonant frequency can create high harmonic voltages acrossthe high parallel impedance and the capacitor may not be ableto withstand the resonance voltage, leading to fuse blowingor capacitor damage [5], [18]. In order to facilitate the de-scription of the resonance problem, Fig. 4 is used to representa harmonic-producing commercial facility with a shunt PFcorrection capacitor connected at the PCC with the distributionsystem. In this figure, the impedance and current sourcerepresent the linear and nonlinear loads of the facilities,

respectively [20]. Assume that the supply system can be rep-resented by a Thévenin impedance of , where h

Fig. 5. Frequency response of the combined system and capacitor impedances.

is the harmonic order (or per-unit frequency normalized to thefundamental frequency).The total impedance seen by the harmonic current

source can be determined as

(2)

The inductive reactance of the supply systemimpedance increases and the capacitive reactancedecreases as the frequency increases, or as the harmonic orderincreases. At a given harmonic frequency in any system wherea capacitor exists, there will be a crossover point where theinductive and capacitive reactances are equal .Consequently, the total impedance approaches infinityand a very high voltage harmonic may result if the commercialfacility harmonic current has a frequency close to

(3)

where is the system short-circuit level and is thecapacitor size. The above frequency is called the resonance fre-quency of the system. In this case, the resonant componentsand are in parallel. The resulting resonance is called par-allel resonance. The parallel resonance phenomenon can alsobe visualized from a frequency scan plot, as shown in Fig. 5.This figure illustrates how both system and capacitor reactanceschange with the frequency. At the resonance frequency both re-actances are equal and total impedance seen from the capacitorlocation will tend to a very large value. It is extremelyunlikely that these two impedances are exactly identical, butnear resonance can be very damaging as well. For example,consider a system fault level of 250 MVA and a capacitor bankrating of 10.8 Mvar. Substituting these numbers on (3) yieldsthe following:

The parallel resonance order of 4.83 is too close to the 5th har-monic order and if any magnitude of 5th harmonic current flowsfrom the harmonic-producing loads into the power system at thecapacitor bus, the capacitor may not be able to withstand the res-onance voltage, leading to fuse blowing or capacitor damage.


TABLE ICAPACITOR LOADING LIMITS ESTABLISHED BY

THE IEEE STANDARD 1036-1992

A practical (rule of thumb) way to find out whether parallelresonance should be a concern is to use (4), which shows howfurther away the resonance frequency should be from anydominant harmonic frequency .

(4)

However, the condition given by (4) is not sufficient becauseresonance frequency shift can occur due to capacitance devia-tion [21], for example. Therefore, the final condition to decideif a certain combination of capacitors should be switched is toverify if the stress levels on the capacitors bank meet the limitsdefined in Table I.When large levels of voltage and current harmonics are

present, the ratings are quite often exceeded, resulting infailures. Therefore, the consideration of power capacitor in-stallation should include harmonic resonance analysis at thedesign stage. Several solutions can be employed for harmonicresonance damping as follows [5]:1) ungrounding grounded-wye capacitors;2) changing capacitor bank sizes and/or locations;3) adding a reactor to an existing capacitor bank;4) adding a filter capacitor;5) controlling the capacitor switching scheme to avoidresonance.

The installation of filters can bring unacceptable additionaloperational and capital costs to the PF correction scheme and,furthermore, a detailed harmonic study must be conducted toensure that the application of the filters will not cause other sideeffects on both the facility and the distribution power system,such as parallel resonance at harmonic frequencies other thanthe one targeted by the filter. We think that focusing on a moreintelligent algorithm to control the capacitor switching schemeto achieve both power factor correction and resonance avoid-ance requirements is more of interest for consumers and utilities.Employ an adaptive control to monitor the harmonic dis-

tortion and switch the capacitors to avoid resonance might beappropriate for commercial loads where there are numerousswitched capacitors coming on and off line randomly [18]. Ba-sically, the idea is to develop a controller that relies on commonlow cost sensing devices and does not require additional mea-surements. As a result, the controller can be constructed as aretrofitting device to replace existing power factor correctioncontrollers with little effort. Therefore, a new strategy for thePF correction capacitors bank controller is proposed in thispaper and it is discussed in detail in the next section. It isimportant that the controller is able to achieve both powerfactor and resonance avoidance requirements under varyingdemand conditions.

IV. PROPOSED CONTROL ALGORITHM

Based on the previous discussion, the problem to be solvedis to determine the number of capacitor units to be switchedthat can yield the highest power factor for the facility withoutcausing excessive harmonic stress on the capacitors. Since thereare limited numbers of capacitor combinations, the simplest al-gorithm is to scan through these combinations and pick the bestcandidate. This approach is doable but is not efficient. Anotherextreme is to formulate the problem as an optimization problem.Such an approach complicates the problem, it is not guaranteedto converge and it might be time-consuming. More importantly,they cannot be easily implemented into amicrocontroller. In thispaper, a practical, efficient, and robust algorithm is proposed.Easy implementation is one of the main considerations of thealgorithm.It is important to note that the switching control algorithm

is only one of the components of the controller. The algorithmneeds the system impedance information as input. There isalso a need to detect if a capacitor is being overstressed due tochanging harmonic conditions. Therefore, the proposed con-troller actually has at least the following three major functions:A. measurement of the system impedance;B. detection of resonance condition;C. determination of capacitor units.The following subsections provide description of each one of

the above functions.

A. Measurement of the System Impedance

In the previous section, it was discussed that in order to detecta resonance condition, it is necessary to determine the systemimpedance. One important issue is that the system impedance isnot constant, but varies due to loading and topological changeson the system. Therefore, the following issue must be solved,how the harmonic resonance condition can be determined for atime varying load demand and topology?A number of impedance measurement methods have been

developed, which can be classified into two types: the tran-sients-based methods and the steady-state-based methods. Thetransients-based methods inject transient disturbances intothe system. The frequency-dependent network impedancesare extracted from voltage and current transients [14]. Themain problems associated with these methods are the needfor a high-speed data acquisition system and for the sourceof disturbances. The steady-state-based methods use pre- andpostdisturbance steady-state waveforms [14]–[16]. Typicaldisturbances are harmonic current injections produced by anexternal source or switching of a network component. Sincethere are no transients involved, the methods can only de-termine network impedances at harmonic frequencies. Sincethere is no need for a high-speed data acquisition system, thesteady-state method can be implemented with many common,low-cost power quality monitors and it relies on the commonvoltage and current transformer sensors illustrated on Fig. 1.The simplest form of the steady-state measurement methodinvolves the switching of a network component at the locationwhere the network impedance is to be measured. Assumingthat there is a shunt capacitor available for switching, the basicidea of this method can be summarized as follows [14], [15]:


Fig. 6. Relationship of the resonance frequency and the number ofswitched shunt capacitor units.

1) Record the steady-state waveforms of the capacitor volt-ages and currents. If the capacitor is not connected, its cur-rents are treated as zero.

2) Changes are then made to the status of the capacitor. Forexample, a capacitor unit can be switched on or off to meetthe power factor requirement.

3) The postdisturbance steady-state voltage and currentwaveforms are recorded.

4) Discrete Fourier transform (DFT) is applied to the pre- andpostdisturbance waveforms. For each harmonic, the fol-lowing system equations can be developed:

(5)

(6)

where and are the predisturbance hth har-monic current and voltage, and and are thepost-disturbance hth harmonic current and voltage. andare the internal system voltage and system impedance,

respectively.5) The system harmonic impedances can be determined fromthe above two equations as follows:

(7)

The impedance does not include the switched capacitorimpedance. Practical implementation and field experiencesregarding this method to calculate can be found on [16].

B. Detection of Resonance Condition

As mentioned before, from the system impedance and the ex-isting capacitor impedance, the resonance frequency can be cal-culated through (3). For a certain system impedance (or systemfault level, ), the number of capacitor units thatlead to a harmonic resonance frequency equal or closeto the dominant harmonic frequencies. Fig. 6 illustrates, for aparticular system impedance, how the harmonic resonance fre-quency changes as more and more capacitor units are switchedon. For the figure below, the system is represented by a trans-former of 1600 kVA with reactance of 6.0% and each capacitor

unit has a capacity of 50 kvar. From this figure, it is clear that theresonance frequency can be shifted from a harmonic frequencyby changing the number of switched capacitor units.A practical way to verify if is too close to any harmonic

frequency is to apply (4). In the example of Fig. 6, if 11capacitors are switched ON, the resonance frequency is tooclose to the 7th harmonic order (point A in the figure), there-fore, the bank should be increased or decreased. If two morecapacitor are switched (13 in total), is around 6.4 (point Bin the figure), which is further away from 5th and 7th harmonicorders. However, it is also necessary to evaluate for the currentcombination of capacitor units if its loading conditions meet thelimits specified by Table I.One can also observe from Fig. 6 that more than one combi-

nation of capacitor units can be considered to avoid resonance.In the following subsections, it will be shown the criteria to se-lect the most appropriate combination. In this paper, each com-bination refers to a particular number of capacitor units to beswitched on to the circuit.

C. Determination of Capacitor Units

The final step is to determine the number of capacitor unitsthat can be switched without violating power factor and reso-nance constraints. From the previous subsection, it is possibleto estimate, from the current system impedance, the combina-tions of capacitor units that can be switched so that the reso-nance frequency is further away from the harmonic fre-quencies. This can be done through the following steps:1) The system impedance calculated from the lastcapacitor switching is used as input.

2) Substituting (3) in (4) yields (8), from which it is possibleto determine the combinations of capacitors thatcan be switched. Normally, the dominant harmonic fre-quencies are the odd harmonic orders from 3 to 29

(8)

3) Among the combinations found in step 2), it is possibleto determine which combinations (kvar) lead to a powerfactor between utility lower and upper

limits. This verification can be done as follows:

(9)

4) From the combinations found in step 3), select the combi-nation that lead to minimum switching relative to the cur-rent capacitor bank configuration.

5) Calculate the anticipated loading for this combination thisusing the indices presented in Table I.

6) If loading indices meet the standard limits, switch the com-bination, otherwise discard this option from the combina-tions obtained in step 3) and go back to step 4) to select asuboptimal solution.

The next subsection combines the previously discussed func-tionalities into a single flowchart.


Fig. 7. Flowchart of the proposed capacitor bank controller.

D. Proposed Controller Flowchart

Fig. 7 presents the flowchart of the proposed capacitor bankcontroller combining the previously discussed functionalitiesto achieve acceptable utility power factor level as well as har-monic resonance avoidance. The flowchart is composed of thefollowing steps:1) Read voltage and current from VT and CT sensors as illus-trated in Fig. 1 and switch on a capacitor unit.

2) Read postswitching voltage and current and calculate har-monic system impedance from (7).

3) Determine the combinations of capacitor units that meetthe resonance constraint given by (8).

4) Read voltage/current and calculate power factor (PF).5) If PF is within utility lower and upperlimits go to step 6), otherwise go to step 7). Normally,

is around 0.92 (depending on each utility com-pany) and is equal to 1.

6) If the capacitor bank loading indices (defined in Table I)are below standard limits go back to step 4), otherwise goto step 7).

7) Using (9), determine the combinations of capacitor unitsfrom those determined in Step 3) that leads to PF between

and .8) Select the combination that leads to minimum switchingrelative to the current capacitor bank configuration.

TABLE IIPARAMETERS OF A TYPICAL DISTRIBUTION POWER TRANSFORMER

TABLE IIIACTIVE AND REACTIVE POWER DEMAND OF THE CASE STUDY FACILITY

9) If the bank loading indices (defined in Table I) are belowthe standard limits switch the selected combination, other-wise go to step 11).

10) After the switching, if the capacitor bank loading indicesare below standard limits go back to step 2), otherwise goto step 11).

11) Remove the combination selected in step 8) from thosedetermined in step 7). Go back to step 8).

One can observe from the flowchart of Fig. 7 that the pro-posed controller is simple and practical and has other advantageas follows:• It does not require additional measurements relying oncommon voltage and current transformer sensors.

• The controller does not require the installation of reactorsand filters.

• Furthermore, the controller not only checks if the harmonicresonance frequency is further away from any har-monic frequency, but the capacitor stress levels are alsoverified to ensure the selection of the most appropriatecombination of capacitor units.

• The controller takes into account the time-varying systemconditions to determine both the power factor and the res-onance condition.

• The proposed controller also preserves the objective ofconventional controllers, which is to achieve the highestfacility power factor.

In the following section, some case studies are conducted toevaluate how the proposed controller performs.

V. CASE STUDIES

A case study is analyzed in this section to illustrate theproposed control method. Suppose the parameters of a typicalpower transformer feeding a commercial building as shown inTable II.


TABLE IVHARMONIC CURRENT LIMITS OF THE INVESTIGATED SYSTEM

ACCORDING TO IEEE 519-1992 [20]

Fig. 8. Equivalent circuit of the transformer and switched on shunt capacitors.

From the parameters of the power transformer, the secondary-side short-circuit current at the PCC is

The facility is equipped with a PF correction scheme com-posed of units of shunt capacitor of 20 kVAR each one. The de-mand of active and reactive power from the facility is providedin Table III. In this table, the maximum demand load current(fundamental frequency) is

Therefore, the ratio of to is approximately equal to 24.According to the standard IEEE519-1992 [20], the harmoniccurrent limits corresponding to each harmonic order could becalculated, shown in Table IV.It is known that the system impedance mostly depends on the

impedance of the power transformer for LV distribution system.According to the parameter of the power transformer and shuntcapacitors, the equivalent circuit of the transformer and shuntcapacitor could be drawn in Fig. 8, in which, the values are inp.u. units and base value is 1000 kVA. and are the re-sistance and inductance of the power transformer, is the har-monic order, is the number of the switched on capacitorsand are the resistance and capacitance of the combinationof switched on capacitors.From Fig. 8, the resonance frequency corresponding to dif-

ferent combinations of switched on capacitors can be deter-mined, as shown in Fig. 9.Fig. 9 shows that when the number of switched on capacitors

is 6, 8, 12, 19, or 20, the resonance frequency does not meetthe constraint defined by (8), which means that the resonancefrequency is so close to the characteristic harmonics that the

Fig. 9. Harmonic resonance frequencies obtained for different combina-tions of switched on capacitors (n).

TABLE VCOMBINATIONS OF SWITCHED ON CAPACITORS LEADING TO HARMONICRESONANCE FREQUENCY CLOSE TO TYPICAL HARMONIC ORDERS

Fig. 10. Total impedance obtained for different harmonic ordersand combinations of switched on capacitors .

capacitors could be damaged. Table V shows the values of theresonance frequency for these combinations.Taking the base impedance as 0.23 ohms, the total

impedance from Fig. 8 can be calculated for differentand , as shown in Fig. 10.Table IV gives the current limits corresponding to each har-

monic order in LV distribution system. If multiplying the currentlimits and the total impedance , the voltage limit in eachharmonic order can be determined. Therefore, the total RMSworking voltage of the capacitors can be expressed as

(10)

where is the fundamental voltage, is the harmonic voltageand is the maximum harmonic order. The maximum workingvoltage of the capacitors for different combinations of switchedon capacitors considering the case study is shown in Fig. 11.


Fig. 11. Total working voltage of capacitor bank for different combina-tions of switched on capacitors (n).

Fig. 12. Number of the switched on capacitors and corresponding power factorbefore and after compensation using conventional control strategy.

It is observed that the working voltage of the capacitors ex-ceed the 110% when the number of the switch-on capacitors isequal to 6, 8, 12, or 20.

A. PF Correction With Traditional Control Strategy

Assume the required threshold PF range for the facility is. According to the flowchart of the traditional

capacitor controller shown in Fig. 3, the required bank size nec-essary to meet this PF range can be calculated from (1). Fig. 12shows the existing and corrected power factor with the tradi-tional strategy and the number of switched on capacitor unitsconsidering the demand profile provided in Table III.It is obvious that, the number of the switched on capacitors

is equal to 6 for sample points 1 and 2 and 8 for sample points3, 4, and 5. From Fig. 11, one can observe that these combina-tions cause the bank working voltage to exceed the 110% limitdefined in [5].

Fig. 13. Number of the switched on capacitors and corresponding power fac-tors before and after compensation using proposed control strategy.

B. PF Correction With the Proposed Control Strategy

Supposing the system harmonic impedance could be pre-cisely measured by using the capacitor switching, for simplicity,the system harmonic impedance is assumed to be

For the first sample point given in Table III, the number ofswitched on capacitors can be firstly determined as 6 to meet

. From the system impedance , theresonance frequency is calculated as , which doesnot respect the requirement defined by (8) and means thatcannot be selected as 6. Instead, if , the new PF can beestimated as , which is acceptable. Similarlyfor other cases, the corrected PF can be calculated for all thesample points given in Table III, as shown in Fig. 13.One can observe from both Figs. 13 and 11 that the new con-

trol strategy avoids the harmonic resonance problem, which, inturn, it can prevent damage to the capacitor bank of the facility.

VI. CONCLUSION

This paper presents a new control strategy for power factorcompensation on distorted low voltage power systems. The pro-posed strategy can perform power factor correction without ex-citing harmonic resonance under varying demand conditions.Practical and robust control algorithms are proposed for the pur-pose of easy implementation in a microcontroller. In addition,the controller relies on common low cost sensing devices anddoes not require additional hardware circuits. As a result, theproposed controller can be constructed as a retrofitting deviceto replace existing power factor correction controllers with littleeffort and low cost. Analysis of representative case studies val-idates the proposed strategy and illustrates how the proposedcontroller performs.

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[20] “Task force on harmonics modeling and simulation, modeling and sim-ulation of the propagation of harmonics in electric power networks, partI: Concepts, models, and simulation techniques,” IEEE Trans. PowerDel., vol. 11, no. 1, pp. 452–465, Jan. 1996.

[21] IEEE Standard for Shunt Power Capacitors, IEEE Std. 18–2002, 2002.[22] IEEE Recommended Practices and Requirements for Harmonic Con-

trol in Electrical Power Systems, IEEE Std 519–1992, 1993.

Shunfu Lin (M’12) received the B.S. degree in applied physics and the Ph.D.degree in nuclear technology and application from the University of Scienceand Technology of China in 2002 and 2007, respectively.He worked for the Corporate Technology of Siemens Limited China as a Re-

search Scientist in power monitoring and control of low-voltage distributionsystem from July 2007 to September 2009. He was a Postdoctoral Fellow at theDepartment of Electrical and Computer Engineering of University of Alberta,Canada from October 2009 to October 2010. He is currently a DistinguishedProfessor at the Shanghai University of Electric Power, China. His research in-terests include power quality and power measurement.

Diogo Salles (S’04) received the B.Sc. and M.Sc. degrees in electrical engi-neering from the University of Campinas, Campinas, Brazil in 2006 and 2008,respectively, where currently he is working toward the Ph.D. degree.From 2010 to 2011, he was a visiting Ph.D. student at the University of Al-

berta, Edmonton, Canada. His research interests are power quality and analysisof distribution systems.

Walmir Freitas (M’02) received the Ph.D. degree in electrical engineering fromthe University of Campinas, Campinas, Brazil in 2001.He is currently an Associate Professor, University of Campinas. His areas of

research interest are analysis of distribution systems and distributed generation.

Wilsun Xu (M’90–SM’95–F’05) received the Ph.D. degree from the Universityof British Columbia, Vancouver, Canada, in 1989.Currently, he is a Professor and aNSERC/iCORE Industrial Research Chair at

the University of Alberta, Edmonton, Canada. His research interests are powerquality and distributed generation.

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