Fuzzy based reconfiguration algorithm for voltage stability enhancement of distribution systems

Expert Systems with Applications 37 (2010) 6974–6978

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Fuzzy based reconfiguration algorithm for voltage stability enhancement of distribution systems M. Arun, P. Aravindhababu * Department of Electrical Engineering, Annamalai University, Annamalainagar 608 002, Tamil Nadu, India

a r t i c l e

i n f o

Keywords: Fuzzy logic Voltage stability Radial distribution systems Network reconfiguration

a b s t r a c t Voltage stability has recently become a challenging issue in many power systems. The distribution systems are reconfigured with a view to reduce the system losses and offer a better voltage profile for the utilities. This paper presents a new fuzzy based reconfiguration algorithm that enhances voltage stability and improves the voltage profile besides minimising losses, without incurring any additional cost for installation of capacitors, tap-changing transformers and related switching equipments in the distribution system. Test results on a 69-node distribution system reveal the superiority of this algorithm. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Progressive increase in energy demands and rapid depletion of the existing generation and transmission resources due to various economic, environmental and regulatory changes have evolved a new type of problem, referred to as voltage instability or voltage collapse in power systems. Voltage collapse is generally triggered by large disturbances such as loss of generation, transmission lines or transformers and characterized by a slow variation in system operating point due to the inability of the network to meet the increasing demand for reactive power in such a way that the voltage magnitude gradually decreases until a sharp accelerated change occurs. Many utilities around the world have experienced major blackouts caused by voltage instabilities (Arya, Choube, & Shrivastava, 2008; Kundur, 1993; Salama, Saied, & Abdel-Maksoud, 1999; Taylor, 1994). In recent years, the distribution systems experience a sharp increase in load demand on account of the extensive growth of the utilities. Besides, with the advent of deregulation in the power industry, there is a greater focus on managing the network assets efficiently rather than reinforcing the network’s capacity. The operating conditions are thus more and more closer to the voltage stability boundaries. In addition, distribution networks are subjected to distinct load changes everyday. In certain industrial areas, it is observed that under certain critical loading conditions, the distribution system suffers from voltage collapse (Prada & Souza, 1998). Hence there is an urgent need to explore ways to enhance voltage stability (VS) in distribution systems.

* Corresponding author. Tel.: +91 4144 237360. E-mail addresses: [email protected] (M. Arun), aravindhababu_18@ rediffmail.com (P. Aravindhababu). 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.03.022

Network reconfiguration is a process of altering the topological structure of the distribution feeders by changing the open/close status of the sectionalising and tie-switches. During normal operating conditions, networks are reconfigured for loss reduction to reduce system real power losses, and achieve load balancing in order to relieve the network overloads. The voltage stability of the distribution systems can be enhanced, if the loads are rescheduled more efficiently by reconfiguring the network, that allows to smoothen out peak demands, improve the voltage profile and increase the network reliability. Although there are many research papers discussing the reconfiguration algorithms for loss minimisation of distribution systems (Carpaneto & Chicco, 2008; Carreno, Romero, & Padilha, 2008; Chang, 2008; Enacheanu et al., 2008; Sivanagaraju, Viswanatha Rao, & Sangameswara Raju, 2008; Zhu et al., 2009), hardly any work related to improvement of voltage stability through reconfiguration is reported (Kashem, Ganapathy, & Jasmon, 2000; Sahoo & Prasad, 2006; Sivanagaraju, Visali, Sankar, & Ramana, 2004). In the last three decades, fuzzy logic has found its role in many interesting power system applications, such as, load forecasting, power system stabilizer design and reactive power control (Momoh & Tomsovic, 1995) because of its usefulness in reducing the need for complex mathematical models. Fuzzy logic employs linguistic terms which deal with casual relationships between the input and output variables. It becomes easier to manipulate and rig out solutions, particularly where the mathematical model is not explicitly known or is difficult to solve. A new fuzzy based algorithm that uses the voltage stability index suggested in Chakravorty and Das (2001), for enhancing the voltage stability of a radial distribution system through network reconfiguration is proposed in this paper. This method attempts to improve the voltage profile and reduce the system losses in

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Nomenclature EA-1 and EA-2 existing algorithm-1 and 2, respectively FLS fuzzy logic system PA proposed algorithm VS voltage stability VM voltage magnitude VSI voltage stability index minimum value of VM in the system VMmin minimum value of VSI in the system VSImin L; M and H linguistic variables representing low, medium and high, respectively l distribution line nt number of tie-loops r km þ jxkm resistance and reactance of line-l sum of real power loads of all the nodes beyond node-m Pkm plus the real power load of node-m itself plus the sum of the real power losses of all the branches beyond node-m.

addition to enhancing voltage stability. The method is tested on a 69-node radial system and the results are compared with that of the methods suggested in Sahoo and Prasad (2006), Sivanagaraju et al. (2004). 2. Proposed reconfiguration algorithm Modern distribution systems are large in nature and liable to face unexpected events. Though in some cases, these uncertainties are represented by probability, more often it is clear that the uncertain functions are intrinsically fuzzy in nature and difficult to handle effectively by probability. Fuzzy set theories offer a compromise in the sense better solutions can be found that cannot be easily determined by other methods and are readily applicable to power system problems (Momoh & Tomsovic, 1995). The aim of the present work is to obtain an optimal switching combination that enhances the voltage stability of radial distribution systems based on the VSI suggested in Chakravorty and Das (2001). The algorithm uses fuzzy logic to search for the most suitable tie-switch to be closed in order to improve the VS of the system. The VSI, which varies between unity at no load and zero at voltage collapse point, for line-l or for node-m of Fig. 1 can be determined using

VSIðmÞ ¼ V 4k  4fPkm xkm  Q km r km g2  4fPkm rkm  Q km xkm gV 2k

ð1Þ

sum of reactive power loads of all the nodes beyond node-m plus the reactive power load of node-m itself plus the sum of the reactive power losses of all the branches beyond node-m Pm þ jQ m real and reactive power load at node-m POm and Q Om nth-node real and reactive power load at 1.0 per unit of voltage, respectively suitability index of tie-line-t SIt voltage magnitude at node-k Vk a load factor DVSIt normalized VSI difference across tie-line-t DVMt normalised voltage magnitude difference across tieline-t t tie-line/tie-switch s Sectionalised switch Q km

variables for FLS are DVSIt , the normalized VSI difference across tie-line-t and DVMt , the normalised voltage magnitude difference across tie-line-t and the output linguistic variable is SIt , the suitability index of tie-line-t for reconfiguration. The fuzzy terms describing the identified variables are low (L), medium (M) and high (H). The sets defining the DVSIt ; DVMt and SIt , for each tie-line-t are as follows:

DVSIt ¼ fL; M; Hg DVM t ¼ fL; M; Hg SIt ¼ fL; M; Hg A one-dimensional triangular and trapezoidal membership functions with the range of values as shown in Fig. 2 are chosen for input and output linguistic variables. The choice of membership degrees in the interval [0,1], does not matter, as it is the order of magnitude that is important. Especially relevant to this application of reconfiguration,

L

M

H

0.0 0.5 1.0 Normalised VSI difference (ΔVSI)

2.1. Fuzzy logic system L

M

H

The proposed fuzzy logic system (FLS) determines the suitability of each tie-line one by one and the one having the highest suitability value is chosen as the most appropriate tie-line-t for reconfiguration. The intuitive and heuristically chosen input 0.0 0.5 1.0 Normalised VM difference (ΔVM) L

M

H

0.0

0.5 Suitability Index (SI)

1.0

m

k l

Pkm + jQkm

rkm + jx km

Pm + j Qm Fig. 1. Sample distribution line.

Fig. 2. Membership function chosen for linguistic variables.

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each switching process as to whether the resulting configuration is radial. The flow of this algorithm is outlined below.

Table 1 Fuzzy decision matrix. AND

DVM

DVSI

L M H

L

M

H

L L M

L M H

M H H

the interest lies in the ranking of tie-lines, which are suitable for reconfiguration and the tuning of membership function is less significant. In fuzzy logic based approaches, the decisions are made by forming a series of rules that relate the input variables to the output variables using if–then statements. A set of multiple-antecedent fuzzy rules are established for determining the suitability of tie-line-t for reconfiguration. The inputs to the rules are DVSIt ; DVMt and the output consequent is SIt . The rules are summarised in the fuzzy decision matrix in Table 1. Having related the input variables to the output variable, the fuzzy results must be defuzzified through what is called a defuzzification process, to achieve a crisp numerical value. The most commonly used centroid or centre of gravity defuzzification strategy (Cox, 1999; Terano, Asai, & Sugeno, 1991) is adopted.

2.2. Selection of sectionalized switch Once the tie-line-t is chosen by the FLS, a sectionalised switch-s, whose VSI is lower than the other, among the two neighbouring switches of the tie-line-t is selected. The tie-line-t is closed and the switch-s opened. The resulting configuration is accepted only if the network is radial and serves to enhance the voltage stability, else the changes are undone and the search is continued by omitting this tie-loop. A sample distribution system, shown in Fig. 3, which has three tie-loops with tie-lines marked by dotted line, is considered with the assumption that every branch has a sectionalised switch. The SI, computed by FLS, for tie-line-17 is considered to be maximum and the VSI of line-14 assumed to be lower than that of line-6. The process is continued by closing line-17 and opening line-14. The change in configuration is considered to be relevant only if the VSI values that are computed after power flow (Aravindhababu & Ashokkumar, 2008) reveal an improvement in voltage stability by comparing the lowest value of VSI before and after the change in configuration; else a flag is set for this tie-loop. This process is allowed to proceed till there is no further improvement in VSI values or flag is set for all the tie-loops. In the sequence of switching process, any attempt to open line-5, when line-3 is already opened, will disconnect certain nodes from the system and may result in the configuration not being radial. A check is therefore made for

12

16

2

8

3

4

5

6

14 15 10 Fig. 3. Sample distribution system.

The proposed algorithm is tested on a 69-node distribution system (Sivanagaraju et al., 2004). The loads are represented by their active P O and Q O components at 1.0 per unit of node voltage. The effect of loads variation at node-m is represented as follows:

Pm ¼ a  POm  V nm

ð2Þ

Q m ¼ a  Q Om  V nm

ð3Þ

7

13 9

3. Simulation

where n = 0 for constant power load = 1 for constant current load =2 for constant impedance load

11 1

1. Read the system data. 2. Set flagðiÞ ¼ 0; i ¼ 1; 2; . . . ; nt. 3. Perform distribution power flow (Aravindhababu & Ashokkumar, 2008). 4. Compute VSI at all the nodes and set VSImin ð0Þ ¼ MinðVSIÞ. 5. Choose tie-loop i = 1, whose tie-line-t is in between nodes k and m. 6. If flagðiÞ ¼ 1, Set SIt ¼ 0 and go to step (7). Else, Compute DVMt ¼ VMk  VMm and DVSIt ¼ VSIk  VSIm Call FLS with DVMt and DVSIt as inputs and obtain the suitability index SIt and go to step (7). 7. If i < nt, then set i ¼ i þ 1 and go to step (6), Else go to next step. 8. Choose the tie-loop-i with largest SIt value for reconfiguration. 9. If VSIk < VSIm , open sectionalised switch-s connected to node-k; Else, open sectionalised switch-s connected to node-m; 10. Close the tie-switch-t in tie-loop-i. 11. Check whether all the nodes are radially connected. If yes, go to step (13). Else, undo the switching operation performed in steps (9) and (10), set flagðiÞ ¼ 1 and go to step (12). 12. Check whether flag ¼ 1 for all tie-loops. If yes, Improved configuration is obtained, Print the results and STOP. Else, go to next step. 13. Carryout distribution power flow and compute VSI at all the nodes. 14. Check whether VSImin ð0Þ < MinðVSIÞ. If yes, set VSImin ð0Þ ¼ MinðVSIÞ and go to step (5). Else, undo the switching operation performed in steps (9) and (10), set flagðiÞ ¼ 1 and go to step (3).

17

The power demands at all the nodes are increased in uniform steps through a multiplication factor a till the load flow diverges. The results for the three different types of load and for different load factors are obtained and compared with that of the existing algorithms EA-1 and EA-2, suggested in Sahoo and Prasad (2006) and Sivanagaraju et al. (2004), respectively. The detailed results, containing status of tie-switches, losses, lowest values of voltage stability index (VSI-min) and voltage magnitude (VM-min), when n = 0 and a = l.0, before and after reconfiguration are given in

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Tie-switches Losses (kW) VSImin VMmin (pu)

After reconfiguration

69,70,71,72,73 317.7 0.587 0.875

EA-1

EA-2

PA

69,20,12,58,64 158.8 0.705 0.916

10,70,14,58,63 143.4 0.749 0.929

69,70,14,58,61 134.6 0.754 0.931

Table 3 Variation of losses, VSI-min and VM-min for constant power load. Load multiplication factor

Before reconfiguration Losses (kW)

1.0 1.1 1.2 1.3 1.4 1.5 1.55

317.7 395.5 484.6 587.6 704.9 839.0 913.3

VSImin

0.587 0.549 0.512 0.475 0.438 0.402 0.384

After reconfiguration VM min

0.875 0.861 0.846 0.830 0.814 0.796 0.787

Losses (kW)

VSImin

VM min

EA-1

EA-2

PA

EA-1

EA-2

PA

EA-1

EA-2

PA

158.8 195.3 236.5 282.6 333.9 390.7 421.3

143.4 175.8 212.1 253.4 296.9 345.9 372.2

134.6 164.9 198.8 236.4 278.0 323.6 348.0

0.705 0.677 0.650 0.622 0.595 0.568 0.555

0.749 0.725 0.701 0.678 0.654 0.631 0.620

0.754 0.731 0.707 0.684 0.661 0.638 0.627

0.916 0.907 0.898 0.888 0.878 0.868 0.863

0.930 0.923 0.915 0.907 0.899 0.891 0.887

0.931 0.925 0.917 0.910 0.902 0.894 0.890

Table 4 Variation of losses, VSI-min and VM-min for constant current load. Load Multiplication factor

Before reconfiguration Losses (kW)

1.0 1.3 1.6 1.9 2.2 2.5 2.8 3.1 3.11

253.7 428.7 649.4 915.8 1227.7 1585.4 1988.6 2437.5 2453.2

VSImin

0.626 0.538 0.458 0.389 0.327 0.273 0.226 0.185 0.184

After reconfiguration VMmin

0.890 0.856 0.823 0.790 0.756 0.723 0.690 0.656 0.655

Losses (kW)

VSImin

VMmin

EA-1

EA-2

PA

EA-1

EA-2

PA

EA-1

EA-2

PA

137.4 232.2 351.7 495.9 664.9 858.5 1077.0 1320.1 1328.6

127.4 215.3 326.1 459.8 616.5 796.0 998.6 1224.0 1231.9

120.2 203.1 307.7 433.9 581.8 751.3 942.4 1155.1 1162.6

0.725 0.654 0.589 0.529 0.474 0.423 0.376 0.333 0.332

0.764 0.701 0.643 0.589 0.538 0.490 0.445 0.404 0.403

0.768 0.707 0.649 0.596 0.545 0.498 0.454 0.412 0.411

0.923 0.899 0.876 0.853 0.830 0.806 0.783 0.760 0.759

0.935 0.915 0.896 0.876 0.856 0.837 0.817 0.797 0.797

0.936 0.917 0.898 0.879 0.859 0.840 0.821 0.802 0.801

Table 5 Variation of losses, VSI-min and VM-min for constant impedance load. Load multiplication factor

Before reconfiguration Losses (kW)

1.0 2.0 3.0 4.0 5.0 6.0 6.1 6.2 6.3

212.3 722.1 1400.1 2169.6 2985.2 3817.7 3901.5 3985.1 4085.1

VSImin

0.655 0.443 0.308 0.219 0.159 0.118 0.114 0.111 0.107

After reconfiguration VMmin

0.900 0.816 0.745 0.684 0.632 0.586 0.582 0.577 0.572

Losses (kW)

VSImin

VMmin

EA-1

EA-2

PA

EA-1

EA-2

PA

EA-1

EA-2

PA

121.4 433.1 875.1 1406.7 1999.3 2632.3 2697.3 2762.5 2827.6

126.5 415.8 851.6 1384.6 1986.3 2636.5 2703.2 2770.5 2838.1

108.8 396.2 815.4 1332.0 1919.8 2560.0 2662.3 2692.9 2773.0

0.741 0.558 0.426 0.330 0.258 0.204 0.199 0.195 0.190

0.771 0.609 0.483 0.387 0.313 0.255 0.249 0.245 0.240

0.776 0.615 0.490 0.394 0.319 0.261 0.256 0.251 0.245

0.928 0.864 0.808 0.758 0.716 0.672 0.668 0.664 0.661

0.938 0.883 0.834 0.789 0.748 0.711 0.707 0.704 0.700

0.940 0.886 0.837 0.792 0.752 0.715 0.712 0.708 0.704

Table 2. It is fairly evident that the losses are reduced when compared with that in the available approaches. Besides the PA serves to offer a much better voltage profile and contributes to enhancing voltage stability. The variation of losses, VSI-min and VM-min with respect to load factor-a for constant power, constant current and constant impedance loads are provided in Tables 3–5. These tables highlight the fact that the PA provides a better configuration for

different types of loads at various load levels. The proposed algorithm is thus suitable for practical implementation. 4. Conclusion A new fuzzy based reconfiguration scheme has been developed for radial distribution system with a view to enhance its voltage

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stability. This approach coined using a simple VSI has been found to improve the voltage profile and reduce the system losses. The elegant nature of the algorithm besides serving to eliminate additional infrastructural cost, will go a long way in enabling it to be suitable for on-line applications for systems of any size. Acknowledgements The authors gratefully acknowledge the authorities of Annamalai University for the facilities offered to carry out this work. References Aravindhababu, P., & Ashokkumar, R. (2008). A fast decoupled power flow for distribution systems. Electric Power Components and Systems, 36(9), 932–940. Arya, L. D., Choube, S. C., & Shrivastava, M. (2008). Technique for voltage stability assessment using newly developed line voltage stability index. Energy Conversion and Management, 49(2), 267–275. Carpaneto, E., & Chicco, G. (2008). Distribution system minimum loss reconfiguration in the hyper-cube ant colony optimisation framework. Electric Power Systems Research, 78(12), 2037–2045. Carreno, E. M., Romero, R., & Padilha, A. (2008). An efficient codification to solve distribution network reconfiguration for loss reduction problem. IEEE Transactions on Power Systems, 23(4), 1542–1551. Chakravorty, M., & Das, D. (2001). Voltage stability analysis of radial distribution networks. International Journal of Electrical Power and Energy Systems, 23(2), 129–135. Chang, C-F. (2008). Reconfiguration and capacitor placement for loss reduction of distribution systems by ant colony search algorithm. IEEE Transactions on Power Systems, 23(4), 1747–1755.

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