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УДК 621.311.1.004.12
CHANGING THE TOPOLOGY OF THE
DISTRIBUTION NETWORK USING C U C K O O S E A R C H A L G O R I T H M F O R P O W E R L O S S M I N I M I Z AT I O N A N D V O L T A G E P R O F I L E I M P R O V E M E N T
*Tran Van Thang, postgraduatestudent *Ha Duc Nguyen, postgraduatestudent **Nguyen ThanhThuan, postgraduatestudent ***Valeev I.M., Doctor of technical, Professor
*Kazan National Research Technological University (KNRTU), Russia **Dong An polytechnic, Viet Nam ***Kazan state power engineering university (KSPEU), Russia e-mail: nguyenlong1252@gmail.com
This paper proposes a reconfiguration methodology based on a cuckoo search algorithm (CSA) for minimizing active power loss and the maximizing voltage magnitude. The CSA method is a new algorithm inspired from the obligate brood parasitism of some cuckoo sp e-cies, which lay their eggs in the nests of other host birds of other species for solving optimization problems. Compared to other methods, CSA method has fewer control parameters and is more effective in optimization problems. The effectiveness of the proposed CSA has been tested on distribution network systems (69-node) and the obtained test results have been compared to those from other methods in the literature. The simulation results show that the proposed CSA can be an efficient and promising method for distribution network reconfiguration problems.
Keywords: distribution network reconfiguration, Cuckoo search algorithm, particle swarm optimization, continuous genetic algorithm, power loss reduction.
Introduction
The distribution network transfers the electrical energy directly from the intermediate transformer substations to consumers. While the transmission networks are often operated with loops or radial struc-
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tures, the distribution networks are always operated radially. By operating radial configuration, it significantly reduces the short-circuit current. The restoration of the network from faults is implemented through the closing/cutting manipulations of electrical switch pairs located on the loops, consequently. Therefore, there are many switches on the distribution network. Distribution network reconfiguration (DNR) is the process of varying the topological arrangement of distribution feeders by changing the open/closed status of sectionalizing and tie switches while respecting system constraints upon satisfying the operator's objectives.
Many researches have been carried out to solve distribution network reconfiguration problems using different methods for the last two decades. Merlin and Back [1] were the first to report a method for distribution network reconfiguration to minimize feeder loss. They formulated the problem as a mixed integer nonlinear optimization problem and solved it through a discrete branch-and-bound technique. Civanlar et al. [2] proposed a switch exchange method from which a simple formula for the estimation of the loss reduction by a particular switching option is developed. In [3], a binary group search optimization (BGSO) has been presented to handle the reconfiguration problem with power losses indices as an objective function. Duan et al. [4] have solved the reconfiguration problem for both the indices of power loss reduction and reliability improvement by using an enhanced genetic algorithm (EGA). In this work, GA has been improved on crossover and mutation operations to determine the switch operation schemes. In [8], a particle swarm optimization (PSO) was applied successfully to handle the reconfiguration problem with multi-objective functions. Algorithms proposed for network reconfiguration problem, generally, can be classified into two following main classes: (1) heuristic algorithms [1; 2], such as discrete branch-and-bound technique and switch exchange algorithm and (2) intelligent algorithms [3-8], such as EGA, HSA and PSO.
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Nomenclature
APioss • loss total power loss of the system after reconfiguration
APi0SS • loss total power loss of the system before reconfiguration
Nbr: total number of branches
Nbus: total number of buses
Ns : the number of substations
Pi: real power load at bust
Qi: reactive power load at bus i
Vi : voltage magnitude at busi
Vmin : minimum acceptable bus voltage
Vmax : maximum acceptable bus voltage
I i: current at branch i
Imax : upper limit of line current as defined by the manufacturer The cuckoo search algorithm developed by Yang and Deb is a new algorithm for solving optimization problems inspired from the obligate brood parasitism of some cuckoo species, which lay their eggs in the nests of other host birds of other species. This is a more efficient algorithm compared with GA and PSO [9]. Yang and Deb [19] have analysed the CSA and found out why CSA is efficient. Recently studies have demonstrated that CSA is an efficient method for solving optimal problems.
Cuckoo search algorithm for distribution system reconfiguration
Cuckoo search algorithm
The cuckoo search algorithm (CSA) is a recently developed optimization algorithm by Yang and Deb [10]. In comparison with other search algorithms, the CSA is an efficient population- based heuristic evolutionary algorithm for solving optimization problems with the advantages of simple implementation procedure and few control parameters. This algorithm is based on the obligate brood parasitic behaviour of some cuckoo species combined with the Levy flight behaviour of
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some birds and fruit flies. As stated by authors [10], there are mainly three principal rules during the search process as follows:
1. Each cuckoo lays one egg (a design solution) at a time and dumps its egg in a randomly chosen nest among the fixed number of available host nests.
2. The best nests with high quality of egg (better solution) will be carried over to the next generation.
3. The number of available host nests is fixed, and a host bird can discover an alien egg with a probability Pa E [0,1]. In this case, it can either throw the egg away or abandon the nest so as to build a completely new nest in a new location.
Implementation of CSA for DNR.
Based on the three rules in Section 'Cuckoo search algorithm', the CSA method is implemented for DNR as follows.
Initialization.
To maintain the radial topology of the network in DNR process, the number of open branches should always be equal to the number of tie-switches (Nts) and could be obtained through Eq. (1)
Nts = Nbr- (Nbus-Nss) (1)
Therefore, the number of switches which must be open after reconfiguration is specific and must be used as a variable in algorithm.
These switches are called tie-switches (SW). Therefore, every member of the initial population is a radial structure of the network. In DNR process using CSA, each radial structure of thenetwork is considered as a host nest. A population of N host nests is represented by Xi = [X[,...,Xld-1,X^jwith i = 1,2,...,N. In which each Xi represents a solution vector of variables given by:
Xi = [SW{,SW2,...,Xld]withd = 1,2,..., Nts (2)
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Where SW^(d = 1,2,... ,Nts), are the tie-switches of corresponding to nest d to maintain the radial topology of the network.
In the CSA, each egg can be regarded as a solution which is randomly generated in the initialization. Therefore, each nest i of the population is randomly initialized as follows:
Xt = round[SW^in ,d + rand x (SW,^ax d
swu,d) (3)
Based on the initialized population of the nests, the radial topology checking algorithm is run to check the nests and the load flow is run and the fitness of each nest is calculated by the objective function.
The initialized population of the host nests is set to the best value of each nest Xbesti (i = 1,...,N) and the nest corresponding to the best fitness function is set to the best nest Gbest among all nests in the population.
Generation of new solution via Levy flights.
All the nests except for the best one are replaced based on the quality of new cuckoo eggs, which are produced by Levy flights from their position as follows:
Xnew = round [Xbesti + a x rand x AXnew ] (4)
wherea> 0 is the step size parameter; rand is a normally distributed random number in [0,1] and the increased value AX™ew is determined by:
Axpew = fi^F x Id x (Xbesti - Gbesti) (5)
whererandx and randy are two normally distributed stochastic variables with standard deviation^(fi) and ay (^)given by:
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=
у (1+Р )xsin!^)
У( Цт)xpx2(fl 2Х)
(6)
= 1 (7)
whereP is the distribution factor (0.3< p <1.99) and y is the gamma distribution function. The radial topology checking algorithm is run to check the nests and the fitness value is calculated using Eq. (1) and the nest corresponding to the best fitness function is set to the best nest Gbest.
Alien eggs discovery.
The action of discovery of an alien egg in a nest of a host bird with the probability of Pa also creates a new solution for the problem similar to the Levy flights. Existing eggs will be replaced with a good quality of new generated ones from their current positions through random walks with step size as follow:
Xnew = round [Xbesti + Kx AXnew ], (8)
where K is the updated coefficient determined based on the probability of a host bird to discover an alien egg in its nest:
K _ |1 ifrand < Pa v 0 ntherwise
And the increased value AXf™ is determined by:
AXnew = rand x [randpx (Xbesti) - randp2 (Xbesti)] (10)
wherer and is the distributed random numbers in [0,1] andrandp! (Xbesti), randp2(Xbesti) are the random perturbation for positions of the nests in Xbesti. For the newly obtained solution, the
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radial topology checking algorithm is run to check the nests and the value of the fitness function is calculated using Eq. (11) and the nest corresponding to the best fitness function is set to the best nest Gbest.
Objective functions
The reconfiguration is defined as the process of changing the topology of system for a certain objective. The DNR is accomplished by changing open/close state of switches. In this study, the objective is to minimize total system active power loss and voltage deviation. The objective function can be described as follows [5]:
Minimize: F = A PRoss + VD (11)
The net power loss reduced (A PRss)is taken as the ratio of total power loss before and after the reconfiguration of the system:
a Pioss = (12)
loss
The total power loss of the system is determined by the summation of losses in all line sections:
Ploss = ZfiT^X (13)
The voltage deviation index (A VD) can be defined as follows:
AVd = max p^) Vi = 1,2.....Nbus (14)
The reconfigured process will try to minimize the (A VD) closer to zero and thereby improves voltage stability and network performance.
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Constraints.
During network reconfiguration, the power flow analysis should be derived. For each proposed configuration, the power flow analysis should be carried out to compute the nodal voltage, power loss of system and current of each branch. The constraints of objective function are as follows:
(1) For the proposed configuration, the computed voltages and
(2) The radial nature of distribution network must be maintained and all loads must be served.
The generating new cuckoos and discovering alien eggs steps are alternatively performed until the number of iterations (Iter) reaches the maximum number of iterations (Itermax). The flowchart of the proposed CSA for DNR problem is given in Fig. 1.
Numerical results in 69-Node system
To demonstrate the performance and effectiveness of the proposed method using CSA to medium-scale distribution networks, it is applied to standard IEEE test systems consisting of 69-node and compared the results with those of PSO as well as Continuous Genetic Algorithm (CGA). In CGA, arithmetic crossover, Gaussian mutation and roulette wheel selection are used as described in [13]. The CSA based methodology was developed by MATLAB R2014a in 2 GHz, i3, personal computer. The threshold value of power flow analysis is 0.005. Moreover, the upper and lower voltage ranges are set as Vmin = 0.9 p.u. and Vmax = 1 p.u.
currents should be in their premising range.
^min — — ^rnax 1,2, ... ,Nbus
0 — ¡I — Imax ,i>ï 1,2, .■■,
max ,i '
(15)
(16)
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Initialize population of host nests Xt = roundiSWUj + rand x (SW^ - W^)]
i
Run the radial system checking algorithm and the load flow to calculate the power loss and voltage deviation
I
Set A", to Xbesh for each nest and the best of all Xbest, to
Gbest- Iteration = 1, Pa - 0.25 ►
V 1
Generate new solution via I.ovy flights X?'w = roundlXbesti + a x rand x AJrens"'l
I
Run the radial system checking algorithm and the load flow to calculate the power loss and voltage deviation Evaluate fitness function to get new Xbesij and Gbest
1
Discover alien egg and randomize X™w = round[Xbesti + Kx AX?ew\
1
Run the radial system checking algorithm and the load flow to calculate the power loss and voltage deviation
Evaluate fitness function to get new Xbest, and Gbest i
Iter - Iter I
Return best nest Gbest (network configuration has minimum power loss and voltage deviation)
Fig. 1. Flowchart of proposed algorithm based on CSA
Values of these parameters can be different in each optimal problem. In this case, the optimal values of control parameters of the algorithms have been obtained by numerous trial simulations. In addition, to analyse the performance of CSA in DNR problem, the value of discovering probability Pa will be adjusted in the range from 0.1 to 0.9 with a step 0.1 with the same initial population set.
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The 69-node distribution system, which is a medium-scale system, includes 69 nodes, 73 branches. There are 68 sectionalizing switches and 5 tie switches and total loads are 3.802MW and 3.696 MVAr [14]. The schematic diagram of the test system is shown in Fig. 2. In a normal operation, switches {69, 70, 71, 72, 73} are opened. After performing the proposed reconfiguration problem based on CSA, switches {14, 57, 61, 69, 70} are opened and the network losses are reduced from 224.95 kW to 98.568 kW. Fig. 3 shows the voltage profile improvement achieved by the proposed CSA algorithm. As shown, most of the bus voltages have been improved after reconfiguration. The minimum bus voltage before reconfiguration was equal to 0.9092 p.u. and after reconfiguration; it is raised to 0.9495 p.u.
Fig. 2.IEEE 69-bus test system
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Fig. 3. Voltage profile for the 69-node system before and after reconfiguration
Reconfiguration results are given in Table 4 while a comparison is made with previous study. It can be observed that using the proposed CSA algorithm, the final power loss after reconfiguration is 98.568 kW and the minimum bus voltage is 0.9495 p.u. These results are identical to the results obtained by the methods proposed in Ref. [11] and are better than the results obtained by the method proposed in Refs. [5,8]. In Ref. [5], the optimum configuration is obtained by opening the switches {14, 56, 61, 69, 70}, which causes a power loss of 98.59 kW which is 0.022 kW higher than the optimum solution obtained from CSA. The minimum power loss so far reported in literature is 99.35 kW Ref. [8] which is 0.79 kW higher than the optimum solution obtained from CSA. Also the minimum bus voltage is 0.9428 which is 0.0067 p.u. lower than the proposed method.
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Table 4. Comparison of simulation results for 69-node network
Method Openswitches Fitness (Fig. 3.) AP(kW) AVd Vmin(p.u)
Initial 69, 70, 71, 72, 73 1.09080 224.95 0.0908 0.9092
CSA 14, 57, 61, 69, 70 0.48879 98.5680 0.0505 0.9495
PSO 14, 57, 61, 69,70 0.48879 98.568 0.0505 0.9495
CGA 14, 57, 61, 69, 70 0.48879 98.568 0.0505 0.9495
In the 69-node network system, the proposed CSA method can obtain optimal solution for the values of Pa from 0.1 to 0.9 when adjusting the value of the probability Pa. The convergence behaviours are presented Fig. 4.
Fig. 4. Effect of adjusting discovered probability on the 69-node system
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Fig. 5. Comparison of 69-node system indices for CSA, CGA and PSO
From Fig. 5, it is clear that the CSA has outperformed PSO with the fitness function settles at the minimum after 29 iterations with the CSA, while with the CGA and PSO algorithm settles at the minimum after 25 and 97 generations, respectively. The power loss characters and deviation index DVD characters of the 69-node system are shown in Figs. 6 and 7. The membership functions for real power loss reduction and voltage deviation index also tend to find the optimal values.
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Fig. 6. Comparison of 69-node system indices for CSA, CGA and PSO in power loss
Fig. 7. Comparison of 69-node system indicesfor CSA, CGA and PSO in deviation index
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Conclusion
In this paper, the CSA method has been successfully applied for distribution network reconfiguration problem. The objective is to minimize the active power loss and voltage profile enhancement of power distribution systems. The radial topology of the network is maintained by the new algorithm based on the movement of each load node to the set of power nodes when it is connected to a node in the set of power nodes. The effectiveness of proposed method is demonstrated 69-node distribution networks. The numerical results verify that the proposed algorithm is capable of finding optimal solution and found to be better than the PSO and some other compared methods in literature.
In addition, it has been shown that the potential of using the CSA in distribution network reconfiguration because it needs a few parameters to be tuned, the global solution obtained by using Levy flight is not sensitive to the parameters used. The simulated results on the large-scale system like 69-node distribution systems have shown that the applicability of CSA is more noticeable. Thus, the proposed method can be applied to any medium-scale and large-scale practical radial distribution networks.
References
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ОПТИМИЗАЦИЯ РЕЖИМОВ РАБОТЫ РАСПРЕДЕЛИТЕЛЬНОЙ СЕТИ С МИНИМИЗАЦИЕЙ АКТИВНОЙ МОЩНОСТИ ПОТЕРЬ И УРОВИЯ НАПРЯЖЕНИЕ С ИСПОЛЬЗОВАНИЕМ АНГОРИТМА «ПОИСК КУКУШКИ» Ха Дык Нгуен, Чан Ван Тханг,НгуенТханьТхуан, Валеев И.М.
Изложен алгоритм "Поиск кукушки" (АПК) являющийся перспективным и эффективным способом по минимизации потерь активной мощности и уровня напряжения в распределительных электрических сетях. Приведены результаты моделирования по изменению топологии распределительных сетей для 69 узлов с определением параметров и режимов работы.
Ключевые слова: реконфигурация распределительной сети, алгоритм «Поиск кукушки», оптимизация методом роя частиц, алгоритм генетический непрерывный, снижение потерь мощности.
Дата поступления 05.02.2016.
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