Phasor measurements estimation on distributionnetworks using machine learning

Silviu Nistor, Aftab Khan and Mahesh SooriyabandaraTelecommunications Research Laboratory, Toshiba Research Europe Limited

32 Queen Square, Bristol, BS1 4SL, United KingdomEmail: {silviu.nistor,aftab.khan,mahesh}@toshiba-trel.com

Abstract—The uptake of distribution generation on electricitydistribution networks imposes the operators to install new mea-surement devices such as phasor measurement units to achievenetwork observability. In this paper, we propose a framework forestimating synchronized phasor measurements for a virtual nodeusing the measurements from the other nodes in the network.This system uses a machine learning method, in particularsupervised regression models, to provide estimates. We show theperformance of the proposed framework comparing two widelyused regression methods i.e., Generalized Linear Models andArtificial Neural Networks. We extensively evaluate the proposedapproach utilizing a real-world dataset collected from a mediumvoltage ring feeder. Our results indicate very low error rates; theaverage error for voltage magnitude was approx. 0.2V while forphase angle was 0.7mrad. Such low errors indicate the potentialfor reducing the scale of the measuring infrastructure requiredon distribution networks and increasing their reliability.

I. INTRODUCTION

Conventionally, distribution networks transported electricityfrom the transmission substations to the end consumers. Theone way flow of electricity and radial topology meant thatconservative dimensioning of the network was sufficient toensure the correct operation, without too many real-timemeasuring points. However, over the last decade, more con-sumers, communities and businesses have installed distributedgenerators. The integration of the electricity system with thetransport (e.g. electric vehicles) and heating (e.g. fuel cell co-generation units) infrastructures is also taking place at themedium and low voltage levels of the electricity grid. Withthese technologies come a series of challenges which requirethe network operators to have complete network observability,similar to the transmission system operators. However thedistribution network requires significantly more measuringdevices than the transmission network to achieve this.

In this paper, we investigate the performance of a machinelearning (ML) driven engine to replace physical measure-ment devices on the electricity networks. A dataset of realmeasurements from the same network are utilized to trainmodels for estimating measurements. These trained modelsare capable of providing pseudo measurements based only onthe real measurements from the other nodes. The applicationsfor the ML engine include the reduction of the numberof physical measurement devices installed or, in case of atemporary failure of the measurement device, fill in for the

lack of measurements. To evaluate this, we use syncro-phasormeasurements from 7 nodes within a real distribution network(measurements collected during an innovation project). Wecompare the performance of the proposed approach against thecurrent standards for Phasor Measurement Units (PMUs). Weemploy two supervised ML approaches namely, GeneralizedLinear Models and Artificial Neural Networks.

Wide Area Monitoring Systems with PMUs are used to pro-vide phasor measurements (current or voltage) syncronised tothe same time reference. They can offer an accurate snapshotof the state of the power network they are connected to. Phasormeasurements have been used on the transmission networkfor observability and for stability applications. Recently, suchmeasurement devices have also been installed on the distri-bution networks. An extensive list of potential applications isgiven in [1] including unintentional islanding detection and astate estimation (SE) algorithm.

SE algorithm is a mathematical method to output a descrip-tion of the power system by computing the best estimate ofthe state variables (V , θ) based on measurements from PMUsand SCADA system, pseudo-measurements from smart metersand network topology. The rest of the secondary variables (realand reactive power flows through the lines and nodal powerinjections) can be calculated from the state variables. Becausethe PMUs bring direct measurements of state variables and asthey are synchronized they are regarded as accurate and areexpected be assigned higher weights in the SE algorithm.

Different machine learning algorithms applied in powersystem sector have been described in the literature to extractinformation from measurements either to estimate pseudo-measurements or network topology. These approaches can beseparated into two categories: network information driven andnetwork information independent. In the former category, theformulation of the problem to be solved with ML includes atleast one equation from AC or DC circuit analysis. An exampleof this type of algorithm is described in [2] where the topologyof a distribution network is detected using the correlationsbetween voltage measurements and a sparse Markov randomfield. In [3] the state variables (V, θ) of a section of a dis-tribution network are found using a Bayesian linear estimatorbased on a linear approximation of the power flow equationsconsidering smart meter and PMU type of measurements.

The network information independent methods employ ablack box approach, where the variables that need to be978-1-5090-4000-1/17/$31.00 c©2017 IEEE

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Pre-Processing(Data Filtering, Time Intersection)

Feature Representation

Supervised Regression Model(Generalized Linear Model, Artificial Neural Network)

Phasor Measurements

Processed DataFeature Vectors

𝑓𝑟1𝑘1 , 𝑓𝑟2

𝑘2 , … , 𝑓𝑅𝐾

𝑇

Phasor Estimates

Ground Truth

𝑦𝑡

𝑦

Training

Test

Fig. 1. Block diagram for estimating phasor measurements using supervised regression models. Training and test phases are separately highlighted.

estimated by the algorithm are not connected to the measure-ment available through physical equations. These estimatedvariables are then used in SE or power flow analysis. In [4] anML approach was used for load forecasting. Repeating patternshidden inside the load time series are used to define rulesgoverning the load variation. These were found using a paralleldistributed processing model. In [5] support vector machine(SVM) and Kohonen network (SOM) have been used to detectpre-emergency operating points of the network starting fromthe voltage measurements, which can help in preventing net-work voltage collapses. Fault detection considering substationmeasurements and weather data using Neural Networks (NN)and Naıve Bayes (NB) was tested in [6].

The ML method introduced in this study with applicationsin power systems can be categorized as a network informationindependent approach. Our study contributes to the state of theart with an extensive investigation for estimating directly thestate variables (V , θ), rather than pseudo-measurements. Weargue that, given enough data points for training, the physicalmeasurement equipment can be replaced by the virtual mea-surements based on our approach. Virtual measurements areobtained by an ML engine using regression models.

The proposed method can be used as a solution to themulti-stage optimal PMU placement problem [7] in which agradual deployment of PMUs across the distribution networkis required because of the high number of nodes. Our ML

engine can create virtual nodes capable of providing estimatesuntil the physical equipment is installed. Further, when theyare installed and network observability is achieved, the MLalgorithm can offer redundancy and reliability of the solutionin the case of failures in measurement devices.

II. METHODOLOGY

A mathematical representation for the instant voltage is:

v(t) =√2 · V · cos(2πft+ θ) (1)

Where V is the RMS value of the voltage amplitude, f isthe instantaneous frequency and θ is the angular starting pointfor the waveform. A PMU reports all the three measurementsneeded to reconstruct the instant voltage for a certain time.

The current standard for PMUs, IEEE C37.118 [8], specifiesthat the Total Vector Error (TVE) should be kept below1%. TVE aggregates the errors from the three sources oferror (V, θ, f). If taken separately, the error for the voltagemagnitude limit would be 1%, while the error for the voltageangle is 10mrad [9].

There are several phasor measurement devices on themarket, suitable for the use in transmission networks, butsuitable devices for the distribution part of the network arestill at development stage. Because of the particularities ofthe distribution network (the short length between nodesand the small reactance of the lines) the accuracy of the

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2

1

3

4

5

76

Fig. 2. SUNSEED Map: Electricity distribution network with PMU locations.

measurement nodes must be higher than of those installed onthe transmission network. The PMU in the SUNSEED1 projectoffers an accuracy for the voltage magnitude of 0.1%, whilefor the voltage angle 0.34mrad. Another issue which needs tobe highlighted is the requirement of a high number of PMUsto achieve network observability. According to [10], between1/3 and 1/5 of nodes must be fitted with PMUs in order toachieve complete observability. This could mean a significantinvestment for distribution network operators (DNOs). Ourapproach is to reduce this number by using machine learning tosubstitute physical equipment with virtual measurement points.

As can be seen in Figure 1 phasor measurements are initiallypre-processed. In this step, pre-processing techniques suchas data interpolation for missing data or filters for noisymeasurements can be used. For evaluation purposes, we extractan intersection of timestamps where data from all the nodes isavailable. This can be utilized at the training phase only wheresynchronised data is required to train such a framework. Thisstep results in a processed data of nodes within a networkwith measurements from the same timestamps. This data isthen used for establishing features to train for estimating targetvariables.

In our feature representation stage (cf Figure 1), syn-chronised raw measurements are directly used with minimaladdition of extra features. Due to this, the feature extractionstage is significantly faster than traditional approaches whereseveral statistical or geometric features are extracted over atime window of measurements. They also have a significantlimitation for this application as the output target in suchscenarios is an aggregated estimate whereas the proposedsystem has the capability of producing estimates for a giventime stamp based on the real direct measurements. Also note,

1https://sunseed-fp7.eu/

TABLE ISUMMARY OF VARIOUS ATTRIBUTES RELATED TO THE COLLECTED

DATASET.

Dataset Overview

Total Nodes (N ) 7Total Samples 174213Sampling Rate 1HzMeasurements (M ) 9 ((V1, ..., V3), (θ1, ..., θ3), h, pspv , pspθ)Total Features 7 nodes × 9 measurements = 63Train/Test Split 75/25

that there is no explicit segmentation stage as each set ofmeasurements from all nodes at a given timestamp are directlyused (i.e., the total number of segments are the same as thetotal number of data points).

In total we use 9 measurements for every nodein the network, as seen in Table I, which include{(V1, V2, V3), (θ1, θ2, θ3), hour, pspv, pspθ} where(V1, V2, V3) are the voltage magnitudes for each of thethree phases, (θ1, θ2, θ3) are the voltage phase angles, houris the hour of the day feature (computed using the associatedtime stamps). pspv and pspθ are the positive sequence voltagemagnitude and phase respectively.

Feature data from the previous step is then used to trainindividual models for separate target variables.Note, in ourfeature representation, no measurements from the test nodeare used reflecting a real-world scenario in which a real nodewhen replaced with a virtual node will have no measurementsfrom the virtual node.

In this work, we utilize a supervised machine learningframework in which labeled data is provided in the form oftrue measurements at the training stage. In particular, we useregression models that are appropriate for estimating numericmeasurements (as opposed to using classification models inwhich the target is categorical in nature):

a) Generalized Linear Model (GLM): : Input featuresf are used to fit GLMs [11] for estimating the target dataindividually. The GLM model assigns coefficients to each ofthe input feature in the form of a linear equation capable ofestimating the target variable. This linear model is of the form:

yqp ∼ 1 + [fk1r1 + fk2r1 + ...+ fKR ] (2)

where, M = {k1, k2, ...,K}, N = {n1, n2, ..., L}, q ∈ M ,p ∈ N , r = {{r1, r2, ..., R} : r ∈ N and r /∈ p}.

b) Neural Network (NN): : We also use the same setof input features to train multiple Neural Networks [12] forall of the target variables. In particular, we use Bayesianregularization [13] for training the models with 100 nodes.

III. SUNSEED USE CASE

The algorithm described in the previous section was evalu-ated using real data collected in the SUNSEED project [14].This project investigate converging communication infrastruc-tures of DNO and telecommunication companies for futuresmart grids applications. The field trial, conducted in Slovenia,

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(a) (b)

Fig. 3. Voltage and Phase estimation results are shown using both GLM and NN regression models. Comparisons are made against respective baselines.Average error rates are also indicated.

involved deploying smart meters, power measurement devicesand PMUs in several locations. Figure 2 shows the GIS mapwith nodes labeled by number.

Syncronised voltage phasor measurements are collectedusing PMUs installed on two 20kV urban feeders from theKromberk area. Apart from the loads, the feeder connectphotovoltaic (PV) panels and a co-generation unit thereforereverse power flow is common. The feeders are part of anew strong network with underground cabling. The PMUstake 3 phase measurements from the secondary side of the20/0.4kV transformers. The measurements are sent securelyto a Mongodb database and form part of the input of adistribution state estimation application developed during theSUNSEED project.

As shown in Figure 1, we evaluate the proposed frameworkusing the nodes within the same network which are filteredout and an intersection of timestamps is established. Features,as described in Section II are then used to train the twotypes of supervised regression models. We then compare thetwo methodologies against the baseline represented by thehardware accuracy specified in IEEE C37.118.

A. Experiments and Results

In order to evaluate the performance of the proposed frame-work using the two regression models, we perform several setsof experiments. For evaluation purposes, a consistent metricof Mean Absolute Error is utilised calculated as below:

e =1

st

st∑i=1

|yi − yi| (3)

where st represent the total number of test samples, yi isthe true value of a target variable (for example Voltage ona certain node) and yi represents the estimated value for atarget variable.

Figure 3a shows the voltage estimation results using bothGLM and NN. Baseline of 2.30V is used [9]. It can beseen that in all cases, the estimation results have low errorscompared against the baseline. In general GLM estimationperforms better compared against the NN estimation. Similarlyin Figure 3b, phase estimation results are shown using bothGLM and NN. A baseline of 10mrad is used [9]. In this case,GLM outperforms both the baseline and the NN estimationresults. NN estimation on average has a higher error ratecompared against the baseline.

Based on these results, it can be inferred that a certainlinear relationship exists between phasor measurements fromdifferent nodes and therefore can be more accurately modeledusing a linear model. However, with more training data andhigher complexity neural networks (such as deep learningmethods), these results can further be improved.

In Figures 4a and 4b), voltage and phase estimation resultsare respectively shown using GLM with respect to the numberof samples in the training data. Models are trained usingthe total number of samples (x-axis; incremented within the75% of training data) and errors are reported on the test set(remaining 25% of data as defined in the previous experiment).In the case of voltage, estimation results outperform thebaseline at around 1000 samples (representing 1000s of data)whilst for phase, this is achieved at 44600 samples. Thismeans that for phase estimation, a substantial amount of data,compared with the voltage, is required in order to make preciseestimations.

Figure 5 shows an example node and its associated true andpredicted voltage estimation results. Several points in the timeline are zoomed in. It can be seen that error rates are very lowin majority of the cases (i.e., predicted results very closelymatch the true measurements on this node).

Figure 6 shows the effect of added number of nodes to

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(a) Voltage Estimation (b) Phase Estimation

Fig. 4. Voltage and Phase estimation results are shown with respect to the number of samples. All of these results are obtained using GLM with a fixed testset.

Fig. 5. True and predicted voltage estimation results for Node 2 of the SUNSEED network. Several parts of the results are zoomed in to illustrate low errorrates even when the true signal has high variance.

both voltage and phase estimation results. In each case, asingle node is tested and training is performed using all thecombinations of the remaining nodes. For example, for 3number of training nodes, separate models are trained using allcombinations of 3 nodes out of 6 nodes and using the 7th nodefor test. This is repeated for all nodes to be tested separately.Average results are then shown in Figure 6. It can be seenthat as more nodes are added, estimation results improve witherrors reducing. For Voltage, 3 nodes onwards, the results arestable and in all cases the error is lower than the baseline of2.30V [9]. For Phase, all 6 nodes are needed for the errors tobe below the baseline of 10mrad [9].

In summary, these results indicate a very high level ofaccuracy and shows that data-driven virtual nodes (trainedusing machine learning) are capable of replacing physicalmeasurement equipment used for power system applications.

B. Discussions

Because both voltage magnitude and phase angle have smallvariations on the MV and LV networks in comparison to thetransmission system, the estimations of any state variablesmust be accurate as they can introduce large errors in theSE or load flow softwares. The high precision measurementstaken with the PMUs installed in the SUNSEED project areessential for achieving the performance reported in SectionIII-A. The results show that the GLM method described hereperforms very well in estimating the voltage magnitude at acertain network node based on the measurements from othernodes of the network. Both the error estimated for individualnodes and the average error are below the precision requiredin the C37.118 standard as can also be seen in Figure 3a.Although they are still below the limit of the standard, the

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Fig. 6. Estimation results with respect to the total number of nodes.

estimates of node 1 are less accurate than the rest of the nodes.For justification we need to observe the network configurationin Figure 2. Node 1, apart from being connected to the ringfeeder, is also connected to another feeder (left of the map).This means that the voltage at node 1 is also influencedby the demand and generation of another feeder where nomeasurements were taken, making it harder to estimate.

For phase angle estimation, Figure 3b, the GLM methodoutputs an average error below the value specified in thestandard. Node 1 has a higher value due to the networktopology, as described in the previous paragraph.

The minimum number of samples required for GLM toobtain below 1% error for magnitude was approximately 1000while for phase angle 44600 samples are required. Therefore,for an accurate estimation system, higher of the two numbersmust be used, which corresponds to 5.5 hours of data. Thisanalysis is important as it enables setting the minimum time forthe measuring campaign when installing an ML based solutionfor network observability. In Figure 5 we have showed thatthe performance of the GLM method does not deteriorate andstays reliable even with significant network voltage variations.

The results displayed in Figure 6 show that the error inthe target node is heavily dependent on the number of nodesused for training. For voltage magnitude the largest reductionin estimation is realized from the first node to the second.Further on, from 2 to 3 and so on, the gain diminishessignificantly. For phase angle, estimation accuracy increasesalmost linearly as more nodes are used in the training data.Different applications tolerate different error rates, thereforeestablishing the number of nodes required to achieve thataccuracy level can be performed with such an analysis. Thiscan lead to significant cost savings in implementing suchsolutions.

IV. CONCLUSION

In this paper, we proposed a method that uses machinelearning to estimate synchronized phasor measurements. We

validated our approach using voltage phasor measurementsfrom a field trial on an electricity distribution ring feeder.The results showed that the estimation framework is highlyreliable and capable of replacing the hardware measurementequipment. The average error for voltage magnitude andphase angle was 0.2V and and 0.7mrad, respectively. Inparticular, GLMs performed better than the NN model andthe baseline. The estimation error decreased with the increasein the total number of nodes considered for training, howeverwe found that the rate of decrease is dependent on the type ofmeasurement.

For future work we aim to quantify the benefits of usingsuch an ML-driven approach when applied to a state estimationalgorithm.

ACKNOWLEDGMENTThis work is partially funded by the European Commission,

under Grant agreement no. 619437 “SUNSEED”. The SUN-SEED project is a joint undertaking of 9 partner institutionsand their contributions are fully acknowledged.

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