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E L S E V I E R Electric Power Systems Research 34 (1995) 85 90 .......

Distribution feeder loss analysis by using an artificial neural network

C.T. Hsu a, Y.M. Tzeng a, C.S. Chen a, M.Y. Cho b

a Department of Electrical Engineering, National San Yat-Sen University, Kaohsiung, Taiwan b Department of Electrical Engineering, National Kaohsiung Institute of Technology, Kaohsiung, Taiwan

Received 7 February 1995

Abstract

This paper proposes an artificial neural network (ANN) based feeder loss analysis for distribution system analysis. The functional-link network model is examined to form the artificial neural network architecture to derive various loss calculation models for distribution feeders with different configurations. The ANN is a feedforward network that uses a standard back-propagation algorithm to adjust the weights on the connection path between any two processing elements. The typical daily load curve of the study feeder for each season is derived to field test data. A three-phase load flow program is then executed to create the ANN training sets to solve the exact feeder loss. A sensitivity analysis is performed to determine the key factors of feeder loss, which are feeder loading and power factor, primary and secondary conductor length, and transformer capacity. The above key factors form the variables of the ANN input layer. By applying the artificial neural network with pattern recognition capability, this study has developed the seasonal loss calculation models for both an overhead and an underground distribution feeder. Two practical feeders in the Taiwan Power Company (Taipower) distribution system have been selected for computer simulation to demonstrate the effectiveness and accuracy of the proposed ANN loss models. By comparing the loss models derived by the conventional regression technique, it is found that the proposed loss models can estimate feeder loss in a very effective manner and provide a better tool for distribution engineers to enhance system operation efficiency.

Keywords: Distribution systems; Feeder loss; Neural networks

I. Introduction

Utility companies usually assess operating efficiency by the amount of real power loss over a whole power system. It is noted that distribution system loss has become a topic of increasing concern because of rapid load growth and the wide geographical area it covers. Conventional loss analysis using detailed system model- ing is difficult and impractical to perform because of the tremendous amount of data required. However, it is found that pr imary conductors, secondary conductors, and distribution transformers normally contribute most of the real power loss in a distribution system and variations in feeder load imbalance and phase voltage imbalance will also introduce the change in load de- mand and system loss.

Up to now, various methodologies for system loss calculation have been applied by utilities to solve distri- bution system analysis. For instance, the percent load- ing method, simplified feeder model, load duration curve derivation, and load window [1-6] have been introduced in previous papers. The exact and simplified feeder loss models [7], developed by the present authors, are used for distribution feeder loss analysis

0378-7796/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved

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by Taipower. The exact feeder loss model is mainly designed to evaluate feeder loss in a very detailed manner and a lot of effort is required to prepare the input data for computer simulation. It provides quite precise loss information such as primary and secondary conductor loss, transformer copper and core loss, as well as the total amount of feeder loss. On the other hand, the simplified feeder loss model is designed to estimate the real power loss of a distribution system from several key factors such as feeder length and conductor size, loading level and power factor. Al- though less effort is required, feeder loss solved by the simplified loss model is often not accurate enough.

In the Taipower distribution system, a feeder may serve a mixture of load to various types of customers. To perform the computer simulation, the feeder load curve for each season has to be obtained by integrating the typical load pattern of each type of customer [8]. By applying the simplified feeder loss model derived by a conventional regression technique, the real power loss obtained will be varied according to the load profile of other feeders with the same configuration. Therefore, the accuracy of feeder loss obtained by the simplified

86 C.T. Hsu et al./Electric Power Systems Research 34 (1995) 85 90

feeder model is often degraded [7] due to a narrow effective data range and inefficient data manipulation.

In this paper, the artificial neural network (ANN) technique is used for fast pattern recognition and re- gression of the feeder loss model so that distribution system loss can be solved more accurately with less effort for feeder loss calculation. The topology of the proposed ANN, the selection of the input and output variables, the training set structure, and training method are discussed in this paper. A functional-link back-propagation network with sine layers is selected for our ANN model because it is very effective in the area of regression applications. Several ANN seasonal feeder loss models are proposed to support distribution system analysis.

2. Feeder loss and sensitivity analysis

2. I. Derivation of the feeder load curve

In order to support an ANN for loss model develop- ment to manipulate feeder loss in a more practical way, the typical daily load curves of feeders M J66 and LI32, which are located in Taipower's Kaohsiung district, have been derived by field tests and statistical analysis. The power consumption recorders are installed at sub- stations to collect the energy consumption of the study feeders at 5-minute time intervals over one year.

Power factor

Feeder ~ - - - - - ~ loading

Primary conductor length Secondary conductor length T r a n s f o r m e ( ~ Capacity ~ /

Simplified

feeder

loss

model Feeder loss

Fig. 1. The relationship between feeder loss and the key factors.

transformer core loss will decrease slightly due to the larger voltage drop. It is proposed that the system loss is linearly proportional to the primary conductor length.

(iv) Effect of transformer capacity. Transformer core loss in a distribution system is determined by the bus voltage and the total transformer capacity [1]. If the total transformer capacity is increased, the transformer core loss will become larger and the transformer copper loss will become smaller because a larger transformer kvinding is used.

The feeder loss is affected significantly by the above key factors, as shown in Fig. 1. The simplified feeder loss model is treated by the ANN as a black box that represents the complex relationship between the input layer of key factors and the output layer of feeder loss.

2.2. Feeder loss sensitivity analysis

In order to derive the ANN feeder loss models, a sensitivity analysis of the feeder loss with respect to the feeder loading, conductor size and length, and total transformer capacity is performed for the study feeders. Computer simulations by exact three-phase load flow analysis are executed by varying the above key factors for each study case. The relationships between feeder loss and the key factors which will affect the system loss are investigated.

(i) Effect of feeder loading. An increase in the feeder loading will introduce a larger current flow so that the line loss and transformer copper loss are increased too. It is proposed that the system loss varies with the square of the feeder loading.

(ii) Effect of power factor. An improvement in the power factor of feeder loading results in a decrease in the reactive component of current flow so that the conductor loss and transformer copper loss will be reduced. In general, the feeder loss decreases with the square of the power factor.

(iii) Effect of conductor length. The longer the pri- mary and secondary conductors, the larger the resis- tance, so the line loss will increase if the same magnitude of feeder loading is served by the feeder. The

3. ANN approach for feeder loss calculation

Up to now, the applicatiens of ANNs to power system analysis can be categorized into three main areas: regression, classification, and combinatorial opti- mization [9-15]. The neural networks 'generate their own problem solving knowledge by learning from train- ing sets. By this approach, the supervisory learning method, which simultaneously provides input and out- put signals as training sets, is applied for building ANN models. The training process is executed by adjusting the connection weights between the processing elements (PEs) according to appropriate learning rules. The training process is completed when the mismatch be- tween the actual output and the desired output is within the specific allowable tolerance.

In this paper, the ANN approach is proposed, using the typical feeder load curve to determine the power loss for an underground and an overhead feeder. A functional-link network with sine layers and a standard back-propagation training algorithm is applied in this study. The general description of the back-propagation algorithm, the layer perceptron model, learning scheme, ANN architecture, and PEs can be found in many previous papers and textbooks [9-15].

C.T. Hsu et al./Electric Power Systems Research 34 (1995) 85-90

Table 1 Test results of feeder M J66 for the eight ANN models

87

Network model bkpl bkp2 bkp3 bkp4 bkp5 bkp6 bkp7 bkp8

No. of layers 3 3 3 3 3 3 3 3 No. of PEs of input layer 6 6 6 6 6 6 6 6 No. of PEs of hidden layer 11 11 10 10 10 8 8 11 No. of PEs of output layer 1 1 1 1 1 1 1 1 Transfer function sigmoid sigmoid sigmoici sigmoid sigmoid sigmoid sigmoid sigmoid Learning no. 10000 10000 10000 10000 10000 10000 10000 10000 Error (%) 5.6 12.3 6.8 3.1 2.19 14.1 4.1 5.1

3. I. Selection of the A N N architecture

The selection of the proposed functional-link net- work model was determined by examining eight differ- ent A NN models [16] as shown below:

(1) the cumulative back-propagation network (bkpl),

(2) the predictive cumulative back-propagation net- work (bkp2),

(3) the fast back-propagation network (bkp3), (4) the functional-link back-propagation network

tensor model (bkp4), (5) the functional-link back-propagation network

sine model (bkp5), (6) the Prune back-propagation network (bkp6), (7) the standard back-propagation network (bkp7), (8) the predictive back-propagation network (bkp8). The above ANN models have the same standard

back-propagation algorithm with minor modifications of the convergence strategy. Table 1 represents the test results of these ANN models for feeder M J66. After experimentation, all ANN models converged to their final states. It is noted that different ANN models are designed for different network structures so that better convergence can be achieved. The error introduced by bkp5 is 1.19%, which is the smallest error among these ANN models. The term 'error' is defined as the mis- match between the actual output and the desired out- put. Therefore, it is suggested that the functional-link network sine model (bkp5) should be selected in this study to derive the ANN feeder loss models. It is also noted that the proposed ANN model differs from the standard back-propagation network by introducing ad- ditional PEs in the input layer to improve the conver- gence speed during the learning process. The additional PEs include interaction layer PEs and sine layers. The number of PEs in both the interaction layer and the sine layers is equal to the number of PEs in the input layer and the number of sine layers is equal to the number of PEs in the hidden layer. It is noted that the bias PE in the input layer has not yet been taken into

account. For example, if the number of input layer nodes is 5 and the number in the hidden layer is 10, then the additional input layer nodes to be generated is C~ = 10. These layers, with another 10 orthogonal basis layers and the output layer will form the ANN struc- ture. The variable signals of the input and output layer and the structure of each layer are expressed as follows.

Input layer. Based on the discussion in Section 2, five key factors that strongly affect the feeder loss are adopted as the variable signals for the input layer. Therefore, six PEs are defined as feeder loading, power factor, primary conductor length, secondary conductor length, transformer capacity and a bias term to form the input layer of the proposed ANN model.

Hidden layer. The structure of the hidden layer not only reflects the complexity of the mapping relationship between the input layer and the output layer, but also affects the network convergence characteristics. There is no unique rule to determine the structure of the hidden layer for different problems. After the experiments per- formed in this paper, it was decided that one hidden layer with eight nodes will generate the best results.

Output layer. Only one PE node is included in this layer. Its output is the feeder loss within the range [0, 1].

basis layer ersion )

additional layer bias

Fig. 2. Proposed ANN architecture.

88

record l 0.4161 record2 0.4451

0.4735 0.4748

0.4762 0.4782

0.4987

0.5459

0.5904 record n 0.5968

C.T. Hsu et al./Electric Power Systems Research 34 (1995) 85-90

feeder power primary secondary transformer actu~ loading factor condu~or condu~or capacity loss

length length 0.887 0.8200 0.9310 0.18102 0.10282 0.887 0.8200 0.9285 0.18102 0.11078

0.887 0.8200 0.9270 0.18102 0.11819 0.887 0.8200 0.9326 0.18102 0.11912 0.887 0.8200 0.9308 0.18102 0.11921

0.887 0.8200 0.9238 0.18102 0.11948

0.887 0.8200 0.9176 0.18102 0.12370

0.887 0.8200 0.9079 0.18102 0.13655

0.887 0.8200 0.9000 0.18102 0.15107 0.887 0.8200 0.8982 0.18102 0.15347

Fig. 3. Sample training set of feeder M J66.

Fig. 2 shows the architecture of the proposed A N N feeder loss model. The bias represents the threshold feedforward term which is used to connect the nodes of the hidden layer, interaction layer, sine layer, and the output layer.

3.2. Training the ANN models

In the ANN learning process, the delta learning rule which tunes the connection weights to reduce the differ- ence between the desired output and the actual output is used to train the neural network. Different combina- tions of training schemes such as learning numbers, sequences of training data, and transfer functions are chosen and tested to ensure that the ANN models are continuously refined. Fig. 3 represents the training set sample for feeder M J66, which is obtained by executing the exact feeder loss model and the feeder statistical data. The variable signals of the above key factors are fed to the input layer PEs. All the variable signals in the input layer PEs are normalized by their own base value within the range [0, 1] to guarantee that convergence can be easily achieved. In this manner, the ANN mod- els are trained and good convergence characteristics are obtained.

The recall process is very efficient and will be very effective if the ANN models are properly trained. Fig. 4 shows the flowchart of the overall solution procedure.

Derivationoffeederdailyloadpattem I

total transformers capacity, feeder length, load level and power factor

Execute t l~-ph~ load flow amdysis to I t

create ANN trainlng sets for test~g f~xlers t + Perform sensitivity analysis to determine vKiables

for input layer of artif~ial neural netwvtk

Train the functional link back~ropagation network to derive the ANN feed~ loss models

Fig. 4. The flowchart of the overall A N N solution process.

Table 2 Taipower distribution feeders for computer simulation

Feeder MJ66 Feeder L132

Load type residential/commercial residential/industrial Primary 3C-500 XLPE 2300m 3 × 477AL 14809m conductor type 3 C - # 1 X L P E 5470m 3 x # 2 A L 13333m and length 2 C - # 1 X L P E 610m 2 x # 2 A L 8262m

I C - # 1 X L P E 220m l x # 2 A L 5651m Secondary 100CU 6650m 100CU 2600 m conductor type 60CU 1150 m 60CU 8400 m and length 22CU 400m 22CU 38700 m Transformers 1-~b 27 units 1-~ 130 units

3-~ 7 units 3-cb 18 units open-wye open-delta open-wye open-delta 57 units 133 units

Voltage level 22.8 kV 11.4 kV Configuration underground overhead

The daily load curves of the study feeder are first obtained by field measurements and statistical analysis. Three modules coded in F O R T R A N are used to solve the feeder loss calculation and sensitivity analysis to form the training sets of the ANN. The fourth module applies the artificial neural network builder to derive the ANN feeder loss model.

4. Numerical examples

In the Taipower distribution system, the distribution voltage levels are 22.8 kV and 11.4 kV for underground and overhead feeders, respectively. In this paper, the underground feeder M J66 and the overhead feeder LI32 were selected for the case study to demonstrate the effectiveness and efficiency of the proposed ANN models. Table 2 shows the statistical data of the test feeders. The primary and secondary conductor lengths, as well as the total distribution transformer capacity were first obtained. The ANN based loss models for both feeders at various seasons and yearly were then solved for feeder loss analysis. The conventional regres- sion method was also applied to derive the polynomial feeder loss model for purposes of comparison.

Tables 3 and 4 represent the simulation errors of the feeder loss calculation over a 24-hour period of the study of the feeders when executing both the proposed ANN loss model and the regression loss model. It is found that the error with the proposed model is within the range 0.1%-4.0% and the mean error for feeder M J66 in Table 3 is 1.24%. However, the simulation e r ro r with the regression loss model is 4.84%. Similar results are obtained for feeder LI32 in Table 4. It is concluded that the feeder loss models solved by the proposed ANN method for distribution feeder loss analysis can provide a better tool for distribution engi- neers to estimate feeder operation efficiency in a very effective manner.

C.T. Hsu et al./Electric Power Systems Research 34 (1995) 85 90 89

Table 3 Simulation error of feeder loss analysis (M J66)

Table 4 Simulation error of feeder loss analysis (LI32)

Hour Feeder Error (%) loading (MW) Conventional ANN model

regression

Hour Feeder Error (%) loading (MW) Conventional ANN model

regression

1 4.502 3.33 0.12 2 4.232 3.53 0.10 3 3.900 4.03 1.50 4 3.397 5.07 4.00 5 3.102 5.56 2.10 6 2.647 7.31 1.70 7 2.311 8.56 2.00 8 2.421 8.56 0.60 9 3.075 12.00 3.40

10 3.647 12.50 3.80 11 4.161 5.80 0.20 12 4.451 5.48 0.18 13 4.735 4.47 0.20 14 4.748 4.86 2.00 15 4.762 4.99 1.80 16 4.751 4.86 0.90 17 4.782 4.30 0.50 18 4.987 2.49 1.50 19 4.459 0.31 1.20 20 5.904 0.66 0.37 21 5.968 0.63 0.35 22 5.642 0.55 0.26 23 5.080 3.11 0.53 24 4.810 3.16 0.50

1 1.688 3.91 0.14 2 1.612 3.22 0.09 3 1.536 2.09 1.39 4 1.492 1.38 4.04 5 1.489 0.96 2.15 6 1.407 0.28 1.,66 7 1.480 0.87 2.02 8 2.368 4.69 0.59 9 3.158 4.56 3.19

10 3.305 3.66 3.77 11 3.340 1.66 0.23 12 2.909 1.69 0.13 13 2.739 2.02 0.24 14 3.218 1.20 1.98 15 3.242 1.11 1.70 16 3.106 0.55 0.84 17 2.698 1.24 0.37 18 2.555 0.07 1.39 19 2.420 2.15 1.06 20 2.270 2.91 0.31 21 2.235 3.12 0.20 22 2.139 4.22 0.12 23 1.989 4.20 0.59 24 1.856 4.67 0.55

Figs. 5 and 6 represent the daily load patterns and feeder loss solved by the exact loss model and the ANN loss model for feeders M J66 and LI32, respectively. It is noted that the load characteristics of these two feeders are quite different because feeder M J66 serves the mixed load of residential and commercial customers while feeder LI32 serves both residential and small industrial customers. From the loss analysis, it is found that the feeder loss varies with the hourly loading because of transformer copper loss and the conductor resistive loss become larger when the load current is increased. Also, the feeder loss can be solved by the A N N loss model quite precisely with less computing time and less effort in preparing the input data than with the exact feeder loss model. It is also noted that more learning numbers as well as a longer training time are required to complete the training procedure if more training sets are presented. Results solved by the recall process show that feeder loss error introduced is about 0.34%.

5. Conclusions

In this paper, an artificial neural network based loss model has been developed for distribution feeder loss analysis. The functional-link network model is selected

--o--exact loss model ' ANNs loss model feeder loading * regression loss model

115 ~ iiiiiii iiiii iiiiiiii ~ "~4

95 3

q 7 , 2 55~ , , r - , o ' ' '1

1 6- 12 18 24

Time

Fig. 5. Daily loss pattern of feeder M J66 in summer.

200 180 16o

140 120 1oo 8O 60

--o--exact loss model loss " ANNs loss model feeder loading * regression loss model

3.5

2.5 2 1.5 at

0.5 0

6 12 18 24 Time

Fig. 6. Daily loss pattern of feeder L132 in summer.

90 C.T. Hsu et a l . / Electric Power Systems Research 34 (1995) 85-90

to build various feeder loss models with different configurations and load characteristics. The artificial neural network is a feedforward network that uses a s tandard back-propagat ion algori thm to adjust weights on the connect ion path between any two processing elements. The feeder daily load patterns and the power loss informat ion solved by three-phase load flow analy- sis are used to derive the A N N feeder loss models. Sensitivity analysis o f feeder loss with respect to several key factors is performed to determine the training set o f the A N N input layer.

With the pat tern recognition capabili ty o f the arti- ficial neural network, this study has developed seasonal A N N loss models for bo th overhead and underground distribution feeders. F r o m the compute r simulation, it is found that more accurate feeder loss can be obtained by the proposed A N N method than with the conven- tional regression method.

The fact that the connectivity between customers and distribution t ransformers in Taipower ' s distribu- t ion system has not been identified yet increases the difficulty o f feeder loss analysis by exact computer simulation methods. However, the A N N approach can solve the feeder loss quite accurately without requiring the connectivity informat ion between distribution trans- formers and the customers served. After the A N N model has been trained, the recall process becomes so fast that time required for loss calculation can be saved. The A N N loss models proposed in this paper can be cont inuously improved by retaining the same artificial neural ne twork architecture with new input data as the feeder is reconfigured. Therefore, for a distribution system with hundreds o f feeders, the proposed A N N loss models can solve the whole system loss wi thout the effort o f preparing large amounts o f data for computer simulation. It is recommended that the proposed A N N feeder loss models be used by distribution engineers as an effective tool to estimate distribution system opera- tion efficiency.

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