Distribution Feeder Load Balancing Using Support Vector Machines J.A. Jordaan, M.W. Siti, and A.A. Jimoh Tshwane University of Technology Staatsartillerie Road, Pretoria, 0001, South Africa
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Abstract. The electrical network should ensure that an adequate supply is available to meet the estimated load of the consumers in both the near and more distant future. This must of course, be done at minimum possible cost consistent with satisfactory reliability and quality of the supply. In order to avoid excessive voltage drop and minimise loss, it may be economical to install apparatus to balance or partially balance the loads. It is believed that the technology to achieve an automatic load balancing lends itself readily for the implementation of different types of algorithms for automatically rearranging the connection of consumers on the low voltage side of a feeder for optimal performance. In this paper the authors present a Support Vector Machines (SVM) implementation. The loads are first normalised and then sorted before applying the SVM to do the balancing.
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Introduction
The distribution system technology has changed drastically, both quantitatively and qualitatively. This may be ascribed to the fact that with increase in technological development, the dependence on electric power supply has increased considerably. Consequently, while demand has increased, the need for a steady power supply with minimum power interruptions and fast fault restoration has also increased. To meet these demands, automation of the power distribution system needs to be widely adopted. All switches and circuit-breakers involved in the controlled networks are equipped with facilities for remote operation. The control interface equipment must withstand extreme climatic conditions. Also, control equipment at each location must have a dependable power source. To cope with the complexity of the distribution, the latest computer, communication, and power electronics equipment in distribution technologies are needed to be employed. The distribution automation can be defined as an integrated system concept. It includes control, monitoring and some times, decision to alter any kind of loads. The automatic distribution system provides directions for automatic reclosing of the switches and remote monitoring of the loads contributing towards phase balancing. The distribution system will typically have a great deal of single–phase loads connected to them. Therefore distribution systems are inherently unbalanced. C. Fyfe et al. (Eds.): IDEAL 2008, LNCS 5326, pp. 65–71, 2008. c Springer-Verlag Berlin Heidelberg 2008
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The load is also very dynamic and varies with time; these factors contribute to increase difficulties in controlling the distribution voltage within certain limits. In addition to this most of the time the phases are unequally loaded and they produce undesired negative and zero sequence currents. The phase voltage and current unbalances are major factors leading to extra losses, communication interference, equipment overloading and malfunctioning of the protective relay which consequently results into service quality and operation efficiency being reduced [1]. Phase unbalance is also manifested in increased complex power unbalance, increased power loss, enhanced voltage drop, and increased neutral current. Traditionally, to reduce the unbalance current in a feeder the connection phases of some feeders are changed manually after some field measurement and software analysis. Although in some cases this process can improve the phase current unbalance, this strategy is more time-consuming and erroneous. In this paper the use of support vector machine (SVM) based load balancing is proposed as a novel procedure to perform the feeder phase balancing. In most of the cases, the phase voltage and current unbalances can be greatly improved by suitably arranging the connection phases between the distribution transformers and a primary feeder. It is also possible to advance the phase current unbalances in every feeder segment by means of changing the connection phases [2]. The phase voltage unbalances along a feeder can also be improved in common cases by system reconfiguration, which involves the rearrangement of loads or transfer of load from heavily loaded areas to the less loaded. In the modern power distribution system, the sectionalizing switches and the tie switches for feeder reconfiguration are extensively used [1]. The authors in [3] presented the way to control the tie switches using heuristic combinatorial optimization-based method. The only disadvantage with the tie-switch control is that, in most of the cases, it makes the current and the voltage unbalances worse. The reference [4] presented the use of the neural networks to find the optimum switching option of the loads among the different phases. The layout of the paper is as follows: in section 2 we discuss the current methods of load balancing and introduce the new proposed method of treating the load balancing problem, section 3 shows the numerical results obtained, and the paper ends with a conclusion.
2 2.1
Problem Description Representation of the Feeder
In South Africa a distribution feeder is usually a three-phase, four-wire system. It can be a radial or open loop structure. The size of the conductor for the entire line of the feeder is the same. These feeders consist of a mixture of loads, e.g. commercial, industrial, residential, etc. Single-phase loads are fed by singlephase two-wire service, while three-phase loads are fed by three-phase four-wire service. In Fig. 1 each load can be connected through the switch selector only to one of the three phases.
Distribution Feeder Load Balancing Using Support Vector Machines
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Fig. 1. Three-phase System
The daily load pattern is a function of time and of the type of customers. The resulting power system voltages at the distribution end and the points of utilization can be unbalanced due to several reasons. The reasons include the following: fundamental phase angle deviation; unequal voltages magnitude at the fundamental system frequency (under voltage and over voltages); asymmetrical transformer winding impedances [5], etc. A major cause of this unbalance is uneven distribution of single-phase loads that are continually changing across a three-phase power system. Normally the consumption of consumers connected to a feeder fluctuates, thus leading to the fluctuation of the total load connected to each phase of the feeder. This in turn implies that the degree of unbalance keeps varying. The worse the degree of unbalance the higher the voltage drop and the less reliable the feeder is. Minimum power loss reconfiguration is aimed at by means of controllable switch-breakers installed at each of the connections on the network feeders, since both the loads and the switch-breaker status are physically distributed. In the general formulation of the phase balancing problem, the load values are the independent variables, whereas the switch-breaker statuses are the optimization variables. The objective can be fulfilled performing a control strategy in which the status of each switch-breaker depends on the total load from each feeder. In this way, the network can be optimally operated and it is not necessary to know the load in advance. For the real implementation of a control system, the following elements are necessary: – A measurement system for real loads. – Data system for the load data connecting to each point.
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– Transmission system for sending the input signals to the switch breaker. – The control cannot start if the above described components and system are not properly installed and in correct condition. 2.2
Current Phase Balancing Technique
Most of the township houses in South Africa on average use about three kilowatt power. The major electricity usage is for lighting and domestic works in the domestic environment. However, sudden power increase, like the use of heaters, etc., often times introduces an unknown power in the distribution system, which could damage the transformers and burn the cables, causing unbalance in the network. To balance the network, the engineers and the technicians must change the phases manually after some field measurements. The changes made to upgrade transformation in different areas affect the size of the conductor, but in most of the cases, the size of the phase conductor for the entire line of the feeder is the same. However, a number of phase conductors may be different in different sections for economic reasons. The power losses depend on the real and the reactive power flows, which are related to the real and reactive loads. 2.3
Proposed Solution
The proposed solution to the load balancing problem is based on a SVM implementation. The loads are first normalised by dividing by the maximum value and then sorted in ascending order before applying the SVM to do the balancing. In Fig. 2 an example of three sets of loads is shown. The unsorted load patterns differ greatly, while the sorted load patterns (the loads in each data set is sorted) show a similar curve. This sorting of the loads should enhance the performance of the SVM. It should be noted that the sorted load curves for each set of normalised loads do not look the same. However, since all curves start at a low value and increase to a maximum value of one, the use of SVMs is preferred above other non-linear regression methods. For this application we will only work with 15 loads. This means we may have many sets of loads, where each set has 15 loads. The inputs to the support vector machine are the different sets of 15 load currents at each of the consumers and the outputs indicate to which phase each load should be connected. The output of the network is in the range {1, 2, 3} for each load, i.e., which switch (to the specific phase) should be closed for that specific load. In this case the SVM will have 15 inputs and 15 outputs.
3
Numerical Results
For this experiment we tested many linear and non-linear SVM regression methods. For the results we show only the non-linear Radial Basis function (RBF) kernel SVM. For the implementation we used MATLAB [6] and the Least Squares Support Vector Machines toolbox from [7]. The RBF kernel is given by
Distribution Feeder Load Balancing Using Support Vector Machines
Fig. 2. Sorted Loads vs Unsorted Loads
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J.A. Jordaan, M.W. Siti, and A.A. Jimoh Table 1. Results of the Two SVMs Parameter Percentage of the loads where this method gave best balancing U1−2 U1−3 U2−3 UT
Unsorted Sorted 28.8% 71.2% 33699 A 25292 A 38945 A 24551 A 30636 A 16923 A 103280 A 66766 A
Table 2. Results of the SVM and the Heuristic Method Parameter Percentage of the loads where this method gave best balancing U1−2 U1−3 U2−3 UT
K (xi , xj ) = e−
Heuristic Sorted 27.6% 72.4% 35695 A 25292 A 37869 A 24551 A 36887 A 16923 A 110451 A 66766 A
xi −xj 2 σ2
,
(1)
where σ 2 is the variance of the Gaussian kernel. We investigate the performance of two different SVMs, one using the unsorted loads as training data and one using the sorted loads. To evaluate the performance of the different SVMs, the current unbalance between the different phases (between phases one and two (U1−2 ), one and three (U1−3 ), and two and three (U2−3 )) and the total unbalance (sum of the unbalance between the different phases (UT )) will give an indication which method performs the best. In total there were 1663 sets of loads used as training data and 500 sets of loads were used to test the load balancing. The results of the test data for each of the methods are shown in Table 1. Note that the current unbalance values shown, are the total over all 500 sets of loads in the test data set. From the table we can clearly see that the SVM that was trained with the sorted load data outperformed the SVM that was trained with the unsorted data. For 71.2% (356 loads out of 500) of the loads the sorted SVM gave the best load balancing, while the unsorted SVM gave the best balancing only for 28.8% (144 loads) of the loads. Looking at the unbalance factor, one can also see that for the sorted SVM the total unbalance over the 500 loads is 64.6% of the unbalance of the unsorted SVM. Thus, by sorting the loads, we could reduce the total unbalance by a significant percentage. We also compared the method with a heuristic method (which does not require prior training) for load balancing [8], where the results are shown in Table 2. We see that the SVM method with sorting outperforms both the SVM with unsorted loads and the heuristic method.
Distribution Feeder Load Balancing Using Support Vector Machines
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Conclusion
Phase and load balancing are important components to network and feeder reconfiguration. In distribution automation these problems have to be continuously solved simultaneously to guarantee optimal performance of a distribution network. In this paper the phase balancing problem at the distribution transformers has been formulated as a current balancing optimization problem using SVM models. Before the load data is applied to the SVM, it is normalised and sorted in ascending order. It is shown that the SVM that was trained with the sorted load data has a much better load balancing than the SVM that was trained with the unsorted load data.
References 1. Chen, T., Cherng, J.: Optimal phase arrangement of distribution transformers connected to a primary feeder for system unbalance improvement and loss reduction using generic algorithm. IEEE Trans. Power Systems 17 (2000) 2. Civanlar, S., Grainger, J.: Distribution feeder reconfiguration for loss reduction. IEEE Trans. PWRD-3, 1227–1223 (1998) 3. Baran, M., Wu, F.: Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans. Power Delivery 7 (1989) 4. Ukil, A., Siti, W., Jordaan, J.: Feeder load balancing using neural network. In: Wang, J., Yi, Z., Żurada, J.M., Lu, B.-L., Yin, H. (eds.) ISNN 2006. LNCS, vol. 3972, pp. 1311–1316. Springer, Heidelberg (2006) 5. von Jouanne, A.: Assessment of voltage unbalance. IEEE Trans. On Power Systems 15(3) (2000) 6. Mathworks: MATLAB Documentation - Neural Network Toolbox. Version 6.5.0.180913a Release 13 edn. Mathworks Inc., Natick, MA (2002) 7. Pelckmans, K., Suykens, J., Van Gestel, T., De Brabanter, J., Lukas, L., Hamers, B., De Moor, B., Vandewalle, J.: LS-SVMlab Toolbox User’s Guide, Version 1.5. Catholic University Leuven, Belgium (2003), http://www.esat.kuleuven.ac.be/sista/lssvmlab/ 8. Ukil, A., Siti, M., Jordaan, J.: Feeder Load Balancing Using Combinatorial Optimization-based Heuristic Method. In: 13th IEEE International Conference on Harmonics and Quality of Power (ICHQP), Wollongong, New South Wales, Australia (2008)
