Load profile assignment of low voltage for power retail market applications

customers

R.F. Chang and C.N. Lu

Abstract: To facilitate retail choice in a competitive power market, the knowledge of hourly load shape by customer class is necessary. Requiring a meter as a prerequisite for lower voltage customers to choose a power supplier is not considered practical at the present time. A technique which uses load research and customers' monthly energy usage data for a preliminary screening of customer load profiles is presented. Two data mining techniques, namely, the fuzzy c-means (FCM) method and an artificial neural network (ANN) based pattern recognition technique, are utilised in this work. The proposed method can be used by the Energy Service Provider (ESP) to assign customers to specific load profiles with certainty factors. Customers with less certainty in the assignment will need meter installation or further investigation in order to determine which classes they belong to. Test data are from actual measurement and the customer information system (CIS) of Taiwan Power Company (TPC). Promising results on assigning existing under 220V customers to their proper load profiles are illustrated.

1 Introduction

In some parts of the world, the demand threshold for a competitive electricity supply has been phased out ~

customers are able to choose their electricity suppliers. Requiring a meter for each customer to participate in retail choice may impose unnecessary costs that could place barriers to allowing all customers access to retail choice. If a customer does not opt to have an hourly interval meter, load profiling will enable their participation in retail choice.

Average hourly load profiles, usually organised by customer rate class, are used as a proxy for individually metered customer data. Current load profiling methods can be classified into three general categories: static load profiling: dynamic modelling and dynamic metering [ I , 21. Static load profiling is based on load research data from a historical time period and may account for weather effects. There are different ways of choosing the historic estimates. These include selecting a proxy day based on similar weather conditions, similar hourly control area load and day-types, etc. Dynamic modelling is also based on historical load research data hut incorporates a weather response function into the profiling method. Hourly regression equations, by season, month and/or day type, can be developed to estimate the customers' load profile as a function of weather. Dynamic metered load profiling samples load data throughout the service territory using interval meters on a small fraction of customers. This requires that load research sample meters be read, data validated and load profiles produced daily.

While in principle it is possible to create dozens of profiles to represent types of users, many electricity customers have relatively similar patterns of demand. For instance, in the

IFF 21N1

context of the 1998 UK market agreements, the pool members have agreed that eight generic profiles (two for domestic, and six for nondomestic customers) are to represent large under-100 kW customers [3 , 41.

Considering using load profiles for billing and settlement activities in the retail and wholesale markets, a customer needs to he assigned to a particular load profile class [I, 31. For different types of customers, various factors may have different effects on the daily load profiles. Load profiles of residential customers, which vary in the brands (influenced by housing type and size, household income, profession) and types of appliances they own, and their daily/monthly activity pattern. These influence factors can be exploited for low voltage customers load profile assignment, but experiences have shown that they are difficult to obtain and there is a doubt about the validity of these data obtained by survey or other methods [5].

To facilitate the retail choice in the power market, a novel technique which uses existing under -220 V customers' monthly energy usage information for load profile class assignment is proposed in t h s paper.

2 Load profiling

In building typical load profiles, the Neymum stratification sampling method was applied to select the customers for power measurement. Intelligent meters were programmed to record the customer real and reactive power demand every 15min. Since different customers have different maximum demands, a conversion of the demands in per unit was conducted to have homogeneous curves [6].

A fuzzy clustering technique is used to produce dominant load profiles. Clustering of numerical data forms the basis of many classification and system modelling algorithms. The purpose of clustering is to identify natural groupings of

an objective function that represents the distance from any given data point to a cluster centre weighted by that data point's membership grade.

The objective function is as follows [I:

where

n = number of load profiles c = number of clusters m = 'fuzzification' parameter, in general, m = 2 xk= averaged bad profile of kth customer, which is an R" vector oj= ith cluster centre, which is an RZ4 vector pjk = membership function value of kth customer load profile in ith cluster

In each iteration, the cluster centre is updated by the following equation [7, 81:

and the membership grade is modified by (3):

fori = 1;2: 3: . . . , c

where 2

(d,(,")' = llxk - or ' l l for 1 5 i 5 c, 1 5 k 5 n (4)

1Ixk - is the norm on R" derived from the inner product.

Given the measured customer load profiles (xks), the procedure used to determine the typical load profiles (u;s) is as follows:

Step 1. Choose the values of c and m, let 2 5 c < n , I sm < CO, and initialise p(O). Step 2. Calculate c-means vectors U?) and (d$))'.

Step 3. Update p$+') , for all i, k . Note that 5 p!;") = I

and pi"+" E [0, I ] .

Step 4. Stop if b,?" - J,?] < E ; othenvise r = r + I , go to step 2.

i= I

It starts with an initial guess for the cluster centres which are intended to mark the mean location of each cluster. Additionally, it assigns every data point a membership grade for each cluster. By iteratively updating the cluster centres and the membership grades for each data point, it iteratively moves the cluster centres to the 'nght' location within a data set. The final cluster centres are considered the typical load profiles of the samples, and p* indicates the membership grade of sample k in the ith cluster.

3 Neural networks based load profile assignment

While household size, lifestyle and property type could be used as hasic inputs for low voltage customer load profile class assignment, these data would require a great deal of

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effort to collect, and there is a doubt about the validity of these data. It is thought more appropriate if customers' actual electricity usage data in CIS are utilised for existing customers' toad profile assignment. Many combinations of customer monthly energy usage data, such as moving averages and seasonal changes, could be derived and used as inputs for load profile assignment. In one of the input sets tested, the following data were used:

kWh E!. 'J = k m j ' i # j , i = January-December, ;

= January ( 5 )

kWh; - kWj+l E?. = , i = January-December, ; 'I kWbj

= January (6) where i and; are mouth indices. km, and kWh, are the kWh values in months i and;, respectively. The E& and E$ represent the normalised monthly energy usages and changes.

ANN is proposed for customer load profile assignment. Customer energy usage data such as the E b and E$ are used as inputs to the ANN model. The outputs are the certainty factors corresponding to each class hjg) that indicate the certainty with which the assignment is believed. Certainty factors are between 0.0 and 1 .O. An output node with 1.0 indicates a perfect confidence on the assignment to that particular load profile. The ANN structure used in this study is shown in Fig. I .

bias input data

t + + output data

+ Fig. 1 Arr!@cuil nmrrol network srnslure

The transfer function of the hidden layer is a log-sigmoid function. The network parameters are adjusted, based on a comparison of the output and the target, until the network output matches the target. An adaptive learning procedure is adopted in this study. First, the initial network output and error are calculated. At each epoch (learning iteration) new weights and biases are calculated using the current learning rate. New outputs and errors are then calculated. If the new error exceeds the old error by more than a predefined ratio (typically l.04), the new weights and biases are discarded. In addition, the learning rate is decreased, typically by multiplying by a-dec = 0.7. If the new error is less than the old error, the learning rate is increased, typically by multiplying by m-inc = 1.05. Each variable is adjusted according to gradient descent with momentum [9],

&E dX = y'dx-, +a'?' - dx

where dX,l,e, is the previous change to the weight or bias, SE is the squared error (over the entire training set), y is the momentum coefficient and a is the learning rate.

( 7 )

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To make it more efficient in the ANN training, it is useful to reduce the input dimension by performing correlation analysis. An effective procedure for performing this operation is the principal component analysis. This technique has three effects: it orthogonalises the compo- nents of the input vectors (so that they are uncorrelated with each other); it orders the resulting orthogonal components (principal components) so that those with the largest variation come first; and it eliminates those components which contribute the least to the variation in the data set [IO]. In this paper, singular value decomposition is used to compute the principal components. The original input vectors are multiplied by a matrix whose rows consist of the eigenvectors of the input covariance matrix. This produces transformed input vectors whose components are uncorrelated

The proposed procedure for the low voltage customers load profile assignment is shown in Fig. 2. Customers

load s u w q data

0.9

0.8

0.7

0.5

2 0.4

0.3

0.2

0.1

small number generic prafiies and jtls

inputs include monthly energy usage and changes; outputs are the certainly lactors corresponding to

diflerent load profile classes

ANN training

- .

.

.

-

- -

-

customers that needs load

max (certainly factor)

> 0.75 customer

Customer's load profile assiqnmenl

identification

assignment application

i: the number of generic load profiles

Fig. 2 Procedure/or loudprofle assignment

without dominant class certainty factor outputs would need more information in order to assign them to their proper load profile classes.

4 Test results and discussions

Actual measurement data of 300 low voltage customers are used in this study. Based on the FCM method, Figs. S 5 show the load profiling results with 4, 5 and 6 classes, respectively. Except for the off-peak hours, classes Cz and C3 in Fig. 4, and classes C, and C, in Fig. 5 are similar. The number of generic profiles should be determined based on the market requirement.

Using the Fuzzy e-means technique, each customer in the load survey samples are assigned to a specific class

IEE Prm-Gemr. Trumm Drnrih.. Vol 150, No. 3, May 2W3

0.9

0.8

0.7

0.5

a 0.4

0.3

0.2

0.1

0

Fig. 3

hours

4-clus load profiles

25 0 , % ,

0 5 10 15 20

Fig. 4

0.9

0.8

0.7

0.5

2 0.4

0.3

0.2

0.1

hours

5-class load profiles

0 0 5 10 15 20 25

hours

Fig. 5 6-class load profiles

according to the pz@ obtained. If Six generic profiles are used, Fig. 6 shows those customer load profiles that are assigned to class C I in Fig. 5. Figs. 7 and 8 show typical monthly energy usage (E;) and change patterns (E$> of customers in different classes, respectively. They seem 10 have different characteristics that can be exploited for load profile assignment.

Ten sets of randomly sampled training data, each having 250 customers drawn proportionally from each class, are used to train the ANN, and the remaining 50 customers' data in each case are used to test the performance of the

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1 .o

0.9

0.8

0.7

0.5

2 0.4

0.3

0.2

0.1

0

Fig. 6

Y I , Y , , P ,

5 10 15 20 25 hours

Claw I mtomers load profiles

Table 1: Load profile assignments test results

Test case No. of Training Test no. epochs accuracy accuracy

1

2

3

4

5

6

7

8

9

10

Average

339

425

354

544

334

455

343

246

436

42 8

390.4

2501250

249/250

2501250

2501250

2501250

2491250

250/250

2501250

2491250

2491250

99.84%

50150

48150 47150

47150

48/50

46150

48/50

48/50 47150

49/50 95.6%

No. of input layer nodes= 22; no. of hidden layer nodes= 28; no. of output layer nodes = 6

and the hidden layer has 28 nodes. The average number of epochs in the ANN training is 390.4. As shown in Table 1, on average, only one customer in the training sets and three customers in the testing sets are misclassified or uncertain if the final ANN models are used for customer load profiling.

Table2 shows the results of similar tests but with different numbers of output (generic profile) and hidden

Table2 Effects of ANN structures

No. of No. of Average Average Average Average load hidden no. of training training test profiles layer epochs time, s accuracy accuracy classes nodes

I

Feb Apr Jun Aug Oct Dec

Normalised customer monthly energy usage excursious Fig. 7 (Equation (5 ) )

4 11

4 22

4 44

5 11

5 22

5 44

6 11

6 22

6 44

414.8

477.0

567.5

727.6

388.2

295.2

571.8

378.5

458.8

11.08

17.85

31.92

19.12

14.28

17.44

.15.36

14.47

28.75

100%

100%

100%

99.99%

100%

100%

99.8%

99.92%

99.88%

95.6%

97.0%

96.2%

97 2% 95.4%

95.8%

96.6%

95.4%

96.2%

Jan Mar May Jul Sep Nov

Normaliwd monthly energy usage clmges (Equation (6)) Fig. 8

ANN. Initially, the ANN leaming rate is set at 0.01 and momentum at 0.9. It is trained for a maximum of 5000 epochs or until the network sum-squared error falls beneath 0.001, Table 1 shows the 10 case results. In these tests, there are 6 output nodes corresponding to 6 different load profiles. Twenty-two customer usage data are used as inputs

266

No. of input layer nodes=22

layer nodes. Similarly to those shown in Table 1, each case in Table2 shows the average results of 10 randomly sampled cases. The average numbers of epochs are between 295 and 728. The average accuracies of the classification using the training and testing data sets are from 99.8% to 100% and from 95.4% to 97.2%, respectively. As for the optimal number of hidden nodes, current ANN technology suggests that the number should be between the average and the sum of the input and output node numbers.

The principal component analysis is used to reduce the dimension of the input vectors. Table 3 shows the transfer matrix, which transfers original input data sets to new input data sets that have 13 entries, i.e.

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Table 3 A transfer matrix -0.15 -0.17 -0.25 -0.29 -0.30 -0.30 -0.31 -0.32 -0.31 -0.29 -0.25 0.02 0.15 0.11 0.20 0.11 0.03 -0.08 -0.15 -0.08 -0.19 -0.13 -0.33-0.41-0.30 0.07 0.17 0.17 0.06 0.05-0.02-0.17-0.17 0.21 0.25 0.11-0.37-0.36 0.13 0.15 0.06 0.21 0.19 0.04 -0.45-0.24 0.06 0.07-0.01-0.09 0.01 0.05 0.13 0.16 0.21 0.54-0.26-0.15 0.04 0.22 0.17-0.30-0.13-0.23-0.09 0.10 -0.19-0.03 0.17-0.02-0.08 0.10 0.06-0.07-0.14-0.15-0.20 0.20-0.10-0.50 0.19 0.04-0.51 0.17 0.36 0.25-0.03 0.07 -0.06 0.29 0.09 0.07 0.03-0.08-0.14-0.14-0.15-0.15-0.27-0.16-0.30-0.29-0.12-0.21 0.49-0.15 0.02 0.08 0.04 0.45 -0.05 0.10 0.14 0.14 0.15 0.06 -0.20 -0.09 -0.11 -0.04 0.04 0.13 -0.24 -0.08 -0.10 0.01 0.11 0.67 -0.42 0.01 -0.22 -0.28 -0.18 -0.03 -0.20 0.22 -0.01 0.08 0.04 0.02-0.09 0.02 0.02 -0.23 -0.22 0.38 -0.19 0.31 -0.23 0.04 0.04 0.19 -0.47 0.41 -0.02 0.17-0.05-0.16-0.11 -0.05 0.03 0.16 0.03 0.01 0.00 0.17 -0.28 0.20 0.14-0.08-0.07-0.21 -0.36 0.70 0.19-0.14 0.06-0.13 0.03 0.06-0.09-0.02-0.05 0.13 0.12-0.02-0.18-0.10 0.29-0.23-0.07 0.41-0.14 0.11-0.52 0.00 0.37 0.39 0.06-0.19 0.12 0.25 0.08-0.03 0.05 0.04-0.07-0.03 0.07-0.16 0.31 -0.30-0.04 0.32 0.35-0.21 0.06 0.43-0.29-0.31 0.06-0.18 0.05-0.12 0.05-0.02-0.03 0.04 0.00 0.26 0.22-0.01 0.28-0.11 0.39-0.46 0.00 0.09-0.21 0.13-0.38 0.38-

-0.28-0.08-0.18-0.04 0.00-0.03-0.11 0.00-0.08-0.04 0.41 -0.50 -0.16-0.35-0.22-0.21 -0.28-0.19-0.20-0.08 0.09-0.18 0.20 0.07 0.24-0.38 0.29-0.22-0.22-0.18-0.14 0.14 0.13 0.25 0.15 0.00-0.56 0.06-0.20-0.14 0.03 0.12-0.07 0.11

Table 4 Effects of principal component analysis

No. of load No. of hidden Average no. of Average training Average training Average test profiles classes layer nodes epochs time. s accuracy accuracy

1 1 22 44 11 22 44 11 22 44

398.4 452.2 463.0 361.5 239.5 225.2 653.4 578.8 358.78

9.6 15.13 26.58 9.15 8.64 12.19 18.16 10.8 22.73

99.92% 99.84% 99.88% 100% 99.96% 100% 99.92% 99.88% 99.91%

96.0% 96.4% 96.6% 97.0% 95.4% 95.6% 93.2% 93.2% 92.2%

No. of input layer nodes= 13

where [TM,,,] , , 22 is the transfer matrix and E,,,,,. is an R" vector. Table 4 shows that the average numbers of epochs are lower (between 225 and 653). The average accuracy of training and testing results is from 99.84% to 100% and from 92.2% to 97.0%> respectively. Compared to those shown in Table 2, Table 4 shows that, when using principal component analysis, the training and execution times can be reduced without sacrificing much in the performance of the A N N .

5 Conclusion

Billing, forecasting and settlement activities in retail and wholesale markets require the knowledge of the hourly load shape by customer class or some other criteria. This paper proposes a method that uses load research and customer energy usage data as bases for load profiling and class assignment. The method can be used by ESP to assign customers to pre-defined load profile classes with certainty factors. Test rcsults indicate that ANNs with biases, a sigmoid layer and a linear output layer are capable of assigning customer load profile or, at least, performing preliminary screenings. Based on the test results, it shows that different combinations of customer's monthly energy

data could be used to provide fairly accurate results in the load profile assignments.

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