CC BY
11Journal of Siberian Federal University. Engineering & Technologies 6 (2013 6) 617-624
УДК 621.316.1
An Improved Multi-Objective Bpso-Based Method for Radial Distribution Networks Reconfiguration
Ebrahim Ghandehari, Shahrokh Shojaeian* and Javad Pourabadeh
Islamic Azad University, Khomeinishahr branch P.O. Box 84175-119, Isfahan, Iran
Received 15.01.2013, received in revised form 28.04.2013, accepted 09.09.2013
The present paper will introduce an improved BPSO algorithm for radial distribution networks reconfiguration. In this regard PSO algorithm has extensively been used in many of the previous literatures; however, here a new method will be introduced in order to update swarm position which is not only simple andfast but also has high accuracy. The objective function hasfour weighted components representing load balancing, total losses of network, voltage deviation and system reliability. The test network is a standard distribution system with 3 feeder and 16 switches. Accuracy and speed of proposed method are compared with three other well-known algorithms to ensure its efficiency.
Keywords: BPSO algorithm, Reconfiguration, Restructuring, Distribution network.
Introduction
Transmission of electrical energy is the most important task of distribution systems and due to the yearly growing of consumers' loads; these networks will become larger and more complex. Most of distribution networks all over the world are radial and every consumer is fed just from one side. Since these distribution networks are complex and also many plants have been made, it can cause different states for the consumers' feeding. But there are a lot of switches in distribution networks which can change the structure of the network. These switches can be divided into two categories including sectionalizing (normally close) switches and tie (normally open) switches. Change in the structure of network by altering status of its switches which called reconfiguration or restructuring, not only determine the type of consumers feeding but also has more applications. Some of these applications include load balancing, minimizing total losses of system and improving voltage deviation and reliability of network. Utterly reconfiguration is useful when some faults occur in the network. This activity minimizes de-energized loads after faults. So the existing switches are used for both management and maintenance, but the existing paper focuses only on system management. Some other applications of network reconfiguration include increasing capacity of network, reconfiguration with fewest switches, system development, finding optimum place for distributed generation (DG), etc. that are not the subject of the study here. Since there are a lot of switches in the network, reconfiguration issue is a complex optimization problem which has a lot of limitations. Some of these limitations are
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* Corresponding author E-mail address: [email protected]
radial structure of network and consumers voltage deviation. Finding optimal structure of network on the one hand and its applicability on the other hand is very important, in a way that if practical limitations aren't negle cted , the optimal answer won't be acceptable [1-9].
Recently, reconfiguration has been carried out by practical experience of operators, but today operation of distribution networks is an engineering challenge, because optimal solution is always considered and due to mass and complexity of these problems, the only possible way is to use specialized software. The main goal of optimization is minimization of costs and improving services. There are a lot of methods for reconfiguration which has advantages and disadvantages. Already many literatures rtudied arconfiguration problem aad a lot ofmethods has been applied on it. The results of vhese studies provide acceptable solutions . Reconfiguration problem was firat considered tn [1] in order ta minimize totrl losees by a heurittic aed hybrid optimisation algorithms. In [2] recanfiguraaion was done by branches changing. This laeuristic meahod closes one switch avd opens the ohher swirch, rhen calculades the network loases. Changing the status or the awitches can be done by a lot og algorithms, Out since gower sytlem prag.ems are comginrtorial optimization, they are difficult to rolve by traditional linear or nonlinear methods [3]. Authors ot recent literatures use optimization methohs such at genetic algorithm (GA) [4, 5], fuzzy systems [6[ 7], bee colony (BC) [8, 9], uimulated annesling (SA) [10,11], Tabu searches [12,13], heuoistic algorithms (that are not in the scope of this paper) [14, t5]etc. Recently,' PSO aigorithm is considered in [16, 17], because it has some advantager ,namely, simple structure, good speed and high accuraay. This prper uses this algorithm, too.
One moee important issue in the reconfiguration problem is objective function. The most important ob.ective in the; receni literatures is loss minimization. But there are more objectives which can be considered, too, such as reliability [ 17g voltage devivtion [188], .ood ttaloncing [19], transtent behaviors of rhe network [20] and smart grid interactions [21] and sir on. Urually ode ar two objectives art; optimize d si multaneously lout seme time si more, ehan two obtecives are conaidered ns optimization [222]. This papen optimizes four objectives including load Italancing, total losaes nf network, voltage deviation and system reliability.
Recently, PSO algorithm hns previously been used at many literatures for reconfiguration peoblem and has a known structure. This algorithm is based on the social behavior of birds (particles) flocking looking for food. Answers of considered problem can be represented as a particle. At first the particles initialize randomly. Then every particle will change its position based on the best searching experience of individual (Pbest) and the best tearching experience of population (Gbest). WhenPbest and Gbest are obtained, every paetiele updates its position by:
Bpso algorithm
vidW = wvm + ci x rand() x (Pbest — xld) + c2 x dand() x (Gbest — xld)
,new _
(1)
.new _
*id + vid
new
(2)
Where vid is the original velocity of the ith particle, vidnew is the new velocity of the ith particle, w is the inertia weight, ci and c2 are the acceleration constants, xid is the previous position of the ith particle,
xldnew is the new position of the ith particle and rand() is a random number ranging between 0 and 1. Fig. 1 explains how particle positions is updated.
Reconfiguration in the above mentioned form is a binary problem. For this reason, binary version of PSO (BPS O) should be used. In BPSO algorithm a sigmoid function (3) is used for position updating.
StoT) = T~, -„new (3)
1 + e vid
Position update ai PSO is done in two stoges. At first particle velocity is updaied by (1). Then with (2) sigmoid function is calculoted and finally new position is obtained by (4).
IF (randQ < S(vpdew)) THEN x?aew = 1 ELSE xf/w = 0 (4)
New calculated particles pos)tion) nlay be mappropriate. For example, due to loss of radial steuctute of the network, some loads will be die eneegized. So feasibilityof ganerated codes iliould be verified. Already some mefhdds weie inlaoduced fo check these codea everyone whereof has advantages and disadvantages. This paper proposed a new simple and effective way to update particles positions.
The first step to solve reconfiguration problem is representation of network structure with a comprehensive code for computer. To show the status of N switches in a distribution feeder a string of N bit can be used. For each switch, '1' shows considered switch status is closed and '0' shows it is open. For example, for the feeder shown in Fig. 2 the above mentioned code is (1 1 1 0 1 1 1 1) [23].
Then the problem is to find optimum code for the network which results in minimum value of the objective function, for a distribution network with N switches there are 2N possible codes which all of them are not necessarily appropriate. Eliminating inappropriate codes solution space will be reduced significantly.
The main idea of this paper is a new method for particles position updating. At the first step, an appropriate code is considered and updated normally. Then the feasibility code is checked. For the appropriate codes the algorithm will be continued. Inappropriate codes will be updated again by (4).
Feeder 1 S1
S2 S3 S4 S5
S6
S7
Ueede r 2 S8
Fig. 2. S imple strutture ofa netwotle
hmhr I
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Fuilki I
Li ©
IS
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IS ^
KD (g) Q
20 2*
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26
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Fig. 3. The3-feeder distribution network used for simulations
This procedure should be continued until dhe updated code become one of the possible codes. This method hasnot only a good speed, but also perfect accuracy. It is clear that generated codes certainly are one erf the appropriate structures of network. The distinction of possible structures is an easy method too. There are three methods oU making distinct codes that will be explained at following paragraphs. All methods are implemented by logical instructions.
- The Fwst method: Generate a random binary code and restructure Ihe network by it. If all buses awe fed juei from tune; side, thit code is appropriate; otlferwiset it csn't. The speed oa this method ir kew.
- The Srrond method: Fig. 3d explains this method. Here the network has ihree feeders dad it is obvious thes there muet not be any closed loopbetween them, and all buses must be fed too. So all connection ways between feeders should be found and every relative code must have just one 0, else that code is inappropriate. The other important limitation is that switches of loads or feeders should be 1. Tor explain this method, see Fig. 3. Connecdion ways between feeders include down branch (codes s3, 14, 26, 25 and 23), left branch (codes 12, 15, 19 and 18) and right branch (codes 17, 21 and 24). In every above three codes there should be just one 0 to meet network structure feasibility. All appropriate states of network are equal to multiplication of the number of all collected codes. For example in Fig. 2 the number of appropriate codes is 60, this number is gotten from the multiplication of five down codes (13, 14, 26, 25 and 23) by four left codes (12, 15, 19 and 18) by three right codes (17, 21 and 24). This method is harder but very faster and reliable.
- The Third method: Desired codes can be generated manually or by Microsoft Office Excel and saved in a database. This way is not automatic but is very fast.
Most important advantage of this method is its simple structure, because other similar methods are very difficult and presumably low speed (due to complicated calculations) [23, 24].
Reconfiguration process
Reconfiguration process needs a fast and accurate load flow method to evaluate objective function. In this paper the well-known forward/backward load flow methods is used [2]. Then this method has been rewritten in MATL AB® and become the principal oe the wort Then forward/backward load flow is done to find all bus voltages and pnwer llowing through all sections. Then the value of objective function is calculated and sent to BPSO algorithm. BPSO algorithm is repeated to meet the desired convergence.
The objective function
The objective; function used in this paper has four weighted components including: load balancing, total losses of network, voltage deviation and syste m reliab ility. It is shown as following:
Objective Function
= a.Loss+ p. Voltage Deviation (5)
+ y. Reliability
+9. Load Balancing
where a, (, y and0 are weighting coefficients wluch show relative importance of the components. These coefficients are obtained with Mstorical experiences and strategies of each distribution system company. In chus paper thry are chosen 1, 2, 0.0015 and 31respectively. Total losses and cumulative voltage deviation will be obtained by equatlons (6) and (7).
Loss = li^n t— pb (6)
vi
Vsltage deviatisn = EiiLliV - l)2 pis (7)
where VS mis the voOtage magnitudd of the ia bus and Pi, Qit and ri ¡are; the aciive and reactive power and resistance of rhe ith section respectively.
In this paper reliability of distribution networks are taken into account by system indices. For each load center an avceage failure sate (X in #/year), an average repair time (r in hours), and an average outage time (U in hours/year) can be calcinated [2 5], whe re:
U n x.s (8)
The system reliability indices used in this paper are System Average Interruption Frequency Index (SAIFI) and System Average .nterruption Duoation Index (SAIDI). They can be obtained by the followmg equationo:
nTinf (9)
SAIFI n EEJ (10)
Where Ni is the number of customer; at ith load point. Reliability is evaluated by equation (11). Also, considering different we ighting factor (yi and y2 instead of y) for SAIFI and SAIDI is possible.
Reliability = SAIFI + SAIDI (11)
Reliability parameters for considered system are listed in the paper appendix. Load baloncing component will be obtained by the following equation. Ii is total curtent magnitude oh the ith feeder.
Load Balancing = S?LiS}=i lh _ Ij| (12)
Simulation and results
For a well-known distribution network shown in Fig. 3 which litis been used in many previous researches, the proposed method wai applied. Network parameters can be found in [18]. This network includes 3 main feeders, 13 tie iwitches and 3 sectionalizing switches. Its nominal power (Sb) is №OMVA. Fig. 3 shows original condition of tthe network, at these 15, 2 1 ant126 state swiiches are open and other switches arr close. To show the speed and effecthene ss of the proponed method, a comparison is made between this method and three other weli-known algorithms. Table 1 shows reconfiguration CPU times to mittimize load balancing, totai lossesi volthge deviation and reliability of the network by foui methods. All algoriihms converge io the same solution. It is clear that running time for the proposed method is much lower and if the network bussesincrease, the (CPU time difference will be obviously more.
(Conclusion
This paper proposed an improved BPSO algorithm for radial distribution networks reconfiguration which applies a new method to update swarmposition. It is not only simple and fast but also has high
Table 1. Simulation results for proposed method and three other algorithms
Algorithm Solution (open switches) CPU time Population
BPSO 17, 19 aM 26 1.01 4
ACSA [18] 17, 19 and 26 1.81 5
SA [18] 17, 19 and 26 2.07 500
GA [18] 17, 19 and 26 2.32 5
S
O $
UJ
10"
10
1 J J J J
■ j i j
10 20
Iteration
Fig. 4. Convergence curve of the proposed method
accuracy. The objective function has a four weighted component including: load balancing, total losses of network, voltage deviation and system reliability. Test network was a standard network by 3 feeders and 16 switches. Comparison of the proposed method with three well-known algorithms shows its better efficiency.
Appendix
Table 2. System indexes of the test network
r 1 Section r 1 Section r 1 Section r 1 Section
4 0.18 15-16 4 0.16 9-12 3 0.16 2-8 2 0.15 1-4
3 0.18 5-11 2 0.15 3-13 4 0.16 8-9 2 0.15 4-5
2 0.14 10-14 3 0.15 13-14 4 0.16 8-10 2 0.15 4-6
4 0.14 7-16 2 0.15 13-15 4 0.16 9-11 3 0.14 6-7
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Усовершенствование многоцелевого метода BPSO для радиальной конфигурации распределительных сетей
И. Гандехари, Ш. Шожэйан, Д. Пурабадех
Исламский университет Азад-Хомейни Шахр филиал
А/Я 84175-119 Исфахан, Иран
В статье изложен улучшенный алгоритм метода BPSO для радиальных распределительных сетей. Предложенный метод введен с целью его упрощения, увеличения скорости расчетов и имеет высокую точность. Целевая функция имеет четыре взвешенные компоненты, представляющие баланс нагрузки, общие потери в сети, отклонения напряжения и надежность системы. Тестовой сетью принята стандартная система распределения с тремя фидерами и 16 переключателями. Точность и скорость предложенного метода по сравнению с тремя другими известными алгоритмами подтверждают его эффективность.
Ключевые слова: метод BPSO, перенастройка, распределительная сеть.
