energies Article
A Modified Bird-Mating Optimization with Hill-Climbing for Connection Decisions of Transformers Ting-Chia Ou 1, *, Wei-Fu Su 2 , Xian-Zong Liu 3 , Shyh-Jier Huang 3 and Te-Yu Tai 3 1 2 3
*
Institute of Nuclear Energy Research, Taoyuan 32546, Taiwan Department of Electrical Engineering, Kun Shan University, Tainan 71070, Taiwan;
[email protected] Department of Electrical Engineering, National Cheng Kung University, Tainan 70101, Taiwan;
[email protected] (X.-Z.L.);
[email protected] (S.-J.H.);
[email protected] (T.-Y.T.) Correspondence:
[email protected]; Tel.: +886-2-8231-7717 (ext. 6389)
Academic Editor: Issouf Fofana Received: 23 May 2016; Accepted: 18 August 2016; Published: 23 August 2016
Abstract: This paper endeavors to apply a hybrid bird-mating optimization approach to connection decisions of distribution transformers. It is expected that with the aid of hybrid bird-mating approach, the voltage imbalance and deviation can be mitigated, hence ensuring a satisfactory supplying power more effectively. To evaluate the effectiveness of this method, it has been tested through practical distribution systems with comparisons to other methods. Test results help confirm the feasibility of the approach, serving as beneficial references for the improvement of electric power grid operations. Keywords: bird-mating optimization; voltage imbalance; and voltage deviation
1. Introduction Three-phase and single-phase loads are sometimes supplied by transformers in the distribution system [1–3]. However, different connections of transformers may cause severe phase voltage imbalance, resulting in a larger ground current and bringing extra power losses. With consideration of transformer costs and loss reduction, the connection of transformers and negative sequence (N-Seq) current injection into utility generators have been deemed a feasible alternative to improve such system imbalance [4,5]. A systematic study with an effective solution approach is crucial to maintain a good quality of supplying power, thereby motivating the study made in this paper. Several improved schemes such as an energy storage system [6], static compensator (STATCOM) control [7,8], feeder cross-section increment, capacitor installation [9], flexible AC transmission system (FACTS) devices [10], and network reconfiguration [11] were proposed to deal with this three-phase imbalance problem [12–14]. Compared to the additional investment for equipment purchasing, network reconfiguration became an economically feasible alternative, which can be performed by solely changing the connection of distribution transformers. The phase-switching work can be practically incorporated below: (a) Choose the transformer to be ready for the change of phase connection; (b) Perform the fuse link to disconnect the regional power supply; (c) Ensure the attachment of the grounding copper rod; (d) Execute the phase-switching work following the confirmation of the above steps; and (e) Restore the power supply with the operation of fuse link, and complete the phase-changing work. It is also worth noting that the limitations in changing the connection should be taken into consideration since the load information varies with time, yet the phase-changing work is not real-time because it needs field labors. Previously, by formulating the phase-connection problem as a linear objective function, classical methods of using mixed-integer programming were employed to solve such imbalance problems [15,16]. The results were proved effective, yet it is arguable since the problem was handled as a linear function with approximation. Energies 2016, 9, 671; doi:10.3390/en9090671
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In view of aforementioned issues, several heuristic methods were previously suggested [17–19]. An intelligent approach of hybrid bird-mating optimization is also proposed in this study to solve the transformer connection problem. By mimicking the courtship behavior observed in the mating process of birds, different strategies of conventional bird-mating optimization was developed [20]. Feasibility of such a method was validated yet failed to locate the global minima for complex multi-minima functions because of limited capability of exploiting more areas. To improve such a demerit, this paper further embeds the bird-mating optimization with a local random search procedure and diversity measurement, by which the connection work in a distribution grid is anticipated with a higher confidence. Moreover, with the systematic computation of the proposed method, it can be included with commercial software for industry applications, creating a potential for extending to distribution automations. 2. Problem Description In this paper, the objectives of connection adjustment of transformers are to improve the voltage imbalance of each node and to minimize the voltage deviation while satisfying equality and inequality constraints of network operation. All functions and constraints are expressed as a multi-objective optimization problem, which are detailed below. Connections of distribution transformers in a distribution network of Taiwan can be largely divided into ‘single-phase three-wired’ and ‘three-phase four-wired’. When the single-phase three-wired connection is made, transformers with mid-tap grounded are often adopted for lighting loads. With a three-phase four-wired connection, a considerable number of transformers are utilized to supply three-phase and single-phase loads for economic benefits and space-saving. The objective functions of this study are formulated so as to minimize the total voltage imbalance ratio and deviation ratio. These functions and constraints are investigated as follows. Firstly, the minimization of voltage imbalance ratio helps improve the voltage profile. A lower value of voltage imbalance ratio implies a system with a better balance. By summing up voltage imbalance ratios of all nodes, an objective function can be expressed below N
Minimize f 1 (x, u) = ∑ VURi i = 1 N max |Vi xy |−Vi avg , |Vi yz |−Vavg , |Vi zx |−Vi avg × 100% = ∑ Vi avg
(1)
i =1
where VURi is the voltage imbalance ratio of i-th bus, Vi xy , Vi yz , and Vi zx are three-phase line voltages of i-th bus, Vi avg is the average line voltage among Vi xy , Vi yz , and Vi zx , and N is the number of nodes in a distribution system [21,22]. The vector of dependent variables x is expressed as xT = [V1 , ..., Vi , ..., VN , I1 , ..., Ij , ...INl ]
(2)
where Vi is the average phase voltage of the i-th node, and Ij is the current on the j-th branch. The subscript N defines the number of nodes, and Nl represents the number of branches. The vector of control variables u is written as single
uT = [χOYOD , ..., χOYOD , ..., χOYOD , χ1 Nk 1 i single
single
, ..., χ j
single
, ...χ Ns
]
(3)
where χOYOD and χ j are connections of the i-th transformer bank for each phase and the i j-th single-phase transformer, Nk is the number of transformer banks, and Ns is the number of single-phase transformers. Secondly, considering that the voltage profile may drift up and exceed the upper limit, the connection reconfiguration of a system with a better balance is suggested to help reduce the line
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current and lower the voltage deviation, hence preventing jeopardization of the system. Based on this minimization of voltage deviation, an objective function is formulated as follows N
Minimize f 2 (x, u) =
∑ VDRi
(4)
i =1
where VDRi is the voltage deviation of the i-th node. By considering both voltage imbalance and voltage deviation, the paper is devoted to perform the connection of transformers while satisfying the operating constraints. Equality constraints consist of three-phase imbalanced power flow equations of a distribution system. For each state variable, the inequality constraints are expressed as follows. Imbalanced three-phase voltages not only result in extra line losses, but also affect the lifetime of electrical equipment. The voltage imbalance ratio of each node needs to be restricted as VURi ≤ VURmax , where VURmax is the limit of voltage imbalance ratio, which is set at 2% in this study for a rigorous concern [23]. Next, a larger voltage deviation not only causes the load fluctuation, but also affects facility equipment. The voltage deviation needs to be regulated within a permissible range, VDRi ≤ VDRmax , where VDRmax is the limit of voltage deviation ratio, which is set at 2.5% [24]. Since the over-voltage may jeopardize the customer, the voltage of each load bus should be operated within the interval of 1.05 and 0.95, respectively. 3. Proposed Approach This section introduces the hybrid bird-mating optimization with local random search and diversity measurement. The bird-mating optimization and its hybrid one are both detailed below. 3.1. Bird-Mating Optimization The framework of bird-mating optimization is composed of bird species and their mating procedures. In this method, each bird represents a feasible solution for the problem, and genes of each bird are regarded as decision variables. The mating behaviors considered for female birds are parthenogenetic and polyandrous ones, and the promising genes gained through the process are solutions containing better objectives. This study considers the mating behaviors including monogamous, polygynous, and promiscuous processes. The corresponding computation mimicking each kind of bird-mating is discussed. Monogamy is a form of relationship in which a male bird tends to copulate with a female bird. Polygyny is a form of plural marriage in which a male bird has a tendency to pair two or more female birds. As for the promiscuity, it refers to an unstable relationship between a male bird and his preferred female partner in the society. In this computation method, promiscuous birds are produced using stochastic process. Subsequently, concerning the polyandry, it is a form of relationship where a female bird tends to copulate with two or more male birds, and the offspring is simulated to be the same as polygynous birds generate in the method. Figure 1 shows the mating behaviors of all species of birds representing the location of distribution transformer, in which each bird string represents a set of primary phase-connections of distribution transformers. To confirm the search space, a bird string is encoded as [0, 1, 2], representing the phase-connection of [a, b, c] for single-phase transformers, and [ab, bc, ca] for three-phase transformer banks, respectively.
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Figure 1. Mating process of all species of birds. Figure 1. Mating process of all species of birds. Figure 1. Mating process of all species of birds.
Different from the above mating, the parthenogenesis refers to an asexual reproduction in Different from the above mating, the parthenogenesis refers to an asexual reproduction in which which a female bird without mating with refers any one male. Considering all of Different from the raises above brood mating, the parthenogenesis to an asexual reproduction in a female bird raises brood without mating with any one male. Considering all of monogamous, monogamous, polygynous, promiscuous, and polyandrous birds, Figure 2 conclusively shows their which a female bird raises brood without mating with any one male. Considering all of polygynous, promiscuous, and polyandrous birds, Figure 2 conclusively shows their operation, operation, meaning that the state of a bit is from 0 to 1 or 2, or vice versa. In the proposed method, monogamous, polygynous, promiscuous, and polyandrous birds, Figure 2 conclusively shows their meaning that the state of a bit is from 0 to 1 or 2, or vice versa. In the proposed method, each each parthenogenetic bird represents the better solution, attempting to pass her better genes to her operation, meaning that the state of a bit is from 0 to 1 or 2, or vice versa. In the proposed method, parthenogenetic bird represents the better solution, attempting to pass her better genes to her brood brood with a smaller probabilistic disturbance. For the phase adjustment application in this paper, each parthenogenetic bird represents the better solution, attempting to pass her better genes to her with a smaller probabilistic disturbance. the phase‐connection, phase adjustment application in 1 this the“bc” lower the lower bound of 0 stands for the For “ab” the value of is paper, for the brood with a smaller probabilistic disturbance. For the phase adjustment application in this paper, bound of 0 stands for the “ab” phase-connection, the value of 1 is for the “bc” phase-connection, and phase‐connection, and the upper bound of 2 is for the “ca” phase‐connection. the lower bound of 0 stands for the “ab” phase‐connection, the value of 1 is for the “bc” thephase‐connection, and the upper bound of 2 is for the “ca” phase‐connection. upper bound of 2 is for the “ca” phase-connection.
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Figure 2. Mutation process of all species of birds. Figure 2. Mutation process of all species of birds. Figure 2. Mutation process of all species of birds.
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3.2. Hybrid Bird‐Mating Optimization Approach 3.2. Hybrid Bird‐Mating Optimization Approach The Bird-Mating bird‐mating Optimization optimization Approach offers advantages of a simple concept, fewer parameters, and 3.2. Hybrid easy implementation. This approach is a good way of locating some promising areas with a better The bird‐mating optimization offers advantages of a simple concept, fewer parameters, and The bird-mating optimization offers advantages of a simple concept, fewer parameters, and solution, yet it may fail to locate global minima because of limited capability of exploiting more areas. easy implementation. This approach is a good way of locating some promising areas with a better easy implementation. This approach is a good way of locating some promising areas with a better Mechanisms of diversity increment and local search are hence suggested to add, anticipating enhancing solution, yet it may fail to locate global minima because of limited capability of exploiting more areas. solution, yet it may fail to locate global minima because of limited capability of exploiting more the solution performance of phase‐connection of distribution transformers. A simple way of calculating Mechanisms of diversity increment and local search are hence suggested to add, anticipating enhancing areas. Mechanisms of diversity increment and local search are hence suggested to add, anticipating the standard deviation of objective function values is adopted here in order to increase the diversity the solution performance of phase‐connection of distribution transformers. A simple way of calculating enhancing the solution performance of phase-connection of distribution transformers. A simple way of of the bird group. This standard deviation quantifies the amount of variation or dispersion of a set of the standard deviation of objective function values is adopted here in order to increase the diversity calculating the standard deviation of objective function values is adopted here in order to increase the data. When such a value decreases, it signals the promiscuous birds to generate more offspring to of the bird group. This standard deviation quantifies the amount of variation or dispersion of a set of diversity of the bird group. This standard deviation quantifies the amount of variation or dispersion of increase the diversity of the solution set, thus ensuring a sufficient diversity in the search space. data. When such a value decreases, it signals the promiscuous birds to generate more offspring to the When original parthenogenetic are regarded as solutions with a offspring higher a set of In data. suchapproach, a value decreases, it signalsbirds the promiscuous birds to generate more increase the diversity of the solution set, thus ensuring a sufficient diversity in the search space. possibility of evolving to be better ones. Yet, considering that the exploitation around these solutions In the parthenogenetic birds are regarded diversity as solutions a higher to increase the original diversityapproach, of the solution set, thus ensuring a sufficient in thewith search space. may be thoroughly performed, a local random search is added to the original approach [25]. possibility of evolving to be better ones. Yet, considering that the exploitation around these solutions In not the original approach, parthenogenetic birds are regarded as solutions with a higher possibility may not be performed, a local random search is added around to the original approach [25]. of Such a local search has been adopted in several methods with different formulations. The new work evolving to thoroughly be better ones. Yet, considering that the exploitation these solutions may not of this study is to combine the hill climbing with the bird‐mating optimization. Namely, if the Such a local search has been adopted in several methods with different formulations. The new work be thoroughly performed, a local random search is added to the original approach [25]. Such a local current best solution has no improvement through local exploitations, then a hill climbing method is of this is to combine the hill climbing the bird‐mating optimization. Namely, if study the search hasstudy been adopted in several methods withwith different formulations. The new work of this activated to assist in the solution search. By combining these modifications, a hybrid bird‐mating current best solution has no improvement through local exploitations, then a hill climbing method is is to combine the hill climbing with the bird-mating optimization. Namely, if the current best solution optimization approach is proposed. Computation procedures are detailed below. activated to assist in the solution search. By combining these modifications, bird‐mating has no improvement through local exploitations, then a hill climbing methoda ishybrid activated to assist in optimization approach is proposed. Computation procedures are detailed below.
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the solution search. By combining these modifications, a hybrid bird-mating optimization approach is proposed. Computation procedures are detailed below. Energies 2016, 9, 671 4. Computation of the Method
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4. Computation of the Method Figure 3 shows the flowchart of the proposed hybrid bird-mating optimization approach. Main blocks ofFigure 3 shows the flowchart of the proposed hybrid bird‐mating optimization approach. Main the method are discussed as follows. The computation starts with the data retrieval of blocks of the method are discussed as follows. The computation starts with the data retrieval of distribution transformers, customer information, and line impedance. The parameters of bird society distribution transformers, customer information, and line impedance. The parameters of bird society size, the initial mating probability, and the maximum number of iterations are all initialized. size, the initial mating probability, and the maximum number of iterations are all initialized.
Figure 3. Flowchart of hybrid bird‐mating optimization approach.
Figure 3. Flowchart of hybrid bird-mating optimization approach. A society of N birds is formed and each bird is composed of M genes. A matrix of B = [B1 B2 B3 … Bi … BN]T is used to represent such a society, where Bi = [βi,1 βi,2 …βi,j …βi,M], and βi,j is the j‐th gene of the i‐th A society of N birds is formed and each bird is composed of M genes. A matrix of B = [B1 B2 B3 bird. In the society, each bird represents a potential solution to the problem, and each gene of a given . . . Bi . . . society in matrix B is randomly assigned. Bird species are prescreened based on the objective value BN ]T is used to represent such a society, where Bi = [βi,1 βi,2 . . . βi,j . . . βi,M ], and βi,j is the of fthe obj(Bi-th i) to eliminate those with lower potentials. The standard deviation of all objective function is j-th gene of bird. In the society, each bird represents a potential solution to the problem, and calculated. If the current standard deviation σ(t) is smaller than the previous one σ(t − 1), then the each gene of a given society in matrix B is randomly assigned. Bird species are prescreened based on promiscuous birds are randomly generated to increase the diversity of the solution set. These new the objective value of fobj (Bi ) to eliminate those with lower potentials. The standard deviation of all set of solutions are next generated in the mating process. Next, the local random search is added objective function is calculated. If the current standard deviation σ(t) is smaller than the previous one such that the promising area can be better exploited. During the exploitation, if the objective value of the current best solution f (Bbest,neware ) is equal to the previous f obj(Bbest,old ), it implies that the current best σ(t − 1), then the promiscuousobjbirds randomly generated to increase the diversity of the solution set. These solution has no improvement. The local random search is then carried out in anticipation of finding new set of solutions are next generated in the mating process. Next, the local random search a better one. This optimization process is terminated after concluding with no better solution is added such that the promising area can be better exploited. During the exploitation, if the objective occurred within a predefined number of iterations.
value of the current best solution fobj (Bbest,new ) is equal to the previous fobj (Bbest,old ), it implies that the 5. Numerical Studies current best solution has no improvement. The local random search is then carried out in anticipation of finding a better one. This optimization process is terminated after concluding with no better solution In order to confirm the effectiveness of the proposed bird‐mating optimization for connection decision aof transformers, the operation data acquired from real distribution systems of Taiwan occurred within predefined number of iterations. 5. Numerical Studies
In order to confirm the effectiveness of the proposed bird-mating optimization for connection decision of transformers, the operation data acquired from real distribution systems of Taiwan Power
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Power Company Company (TPC) (TPC) and and the the Institute Institute of of Nuclear Nuclear Energy Energy Research Research (INER) (INER) are are served served for for Power validation. For all of tests, the results of using the proposed method are compared with those using validation. For all of tests, the results of using the proposed method are compared with those using Company (TPC) and the Institute of Nuclear Energy Research (INER) are served for validation. For all genetic algorithm algorithm (GA), particle particle swarm swarm optimization optimization (PSO), (PSO), and and bird‐mating bird‐mating optimization optimization (BMO) (BMO) genetic of tests, the results(GA), of using the proposed method are compared with those using genetic algorithm algorithm. In the evaluation, the number of birds in the society is set at 100, in which the number of algorithm. In the evaluation, the number of birds in the society is set at 100, in which the number of (GA), particle swarm optimization (PSO), and bird-mating optimization (BMO) algorithm. In the monogamous, polygynous, promiscuous, polyandrous, and parthenogenetic birds amount to 50, 30, monogamous, polygynous, promiscuous, polyandrous, and parthenogenetic birds amount to 50, 30, evaluation, the number of birds in the society is set at 100, in which the number of monogamous, 10, 5, and 5, respectively. The mating rate is set at 0.8, the mutation rate is 0.1, and the maximum 10, 5, and 5, respectively. The mating rate is set at 0.8, the mutation rate is 0.1, and the maximum polygynous, promiscuous, polyandrous, and parthenogenetic birds amount to 50, 30, 10, 5, and 5, number of allowed iterations is 1000. For both genetic algorithm and particle swarm optimization, number of allowed iterations is 1000. For both genetic algorithm and particle swarm optimization, respectively. The mating rate is set at 0.8, the mutation rate is 0.1, and the maximum number of allowed the population size is 100, the crossover probability is 0.8, the mutation rate is 0.1, and the cognitive the population size is 100, the crossover probability is 0.8, the mutation rate is 0.1, and the cognitive iterations is 1000. For both genetic algorithm and particle swarm optimization, the population size is and social parameters equal to 2. These parameter settings are considered suitable for the problem and social parameters equal to 2. These parameter settings are considered suitable for the problem 100, the crossover probability is 0.8, the mutation rate is 0.1, and the cognitive and social parameters concerned [26,27]. concerned [26,27]. equal to 2. These parameter settings are considered suitable for the problem concerned [26,27]. Figures 4 4 and 5 5 show the the load patterns patterns of feeders feeders measured in in an area area of TPC. TPC. Because of of Figures Figures 4 and and 5 show show the load load patterns of of feeders measured measured in an an area of of TPC. Because Because of capacitive effect caused by underground cables, the reactive power is fed to the secondary capacitive effect caused caused underground cables, the reactive fed to the secondary capacitive effect byby underground cables, the reactive powerpower is fed tois the secondary substation substation during some intervals, possibly bringing a higher voltage imbalance. Assumptions and substation during some intervals, possibly bringing a higher voltage imbalance. Assumptions and during some intervals, possibly bringing a higher voltage imbalance. Assumptions and descriptions of descriptions of following scenarios are listed below. Case 1 considers the voltage imbalance ratio, descriptions of following scenarios are listed below. Case 1 considers the voltage imbalance ratio, following scenarios are listed below. Case 1 considers the voltage imbalance ratio, case 2 considers case 2 considers the voltage deviation, and case 3 considers both of them. Each scenario along with case 2 considers the voltage deviation, and case 3 considers both of them. Each scenario along with the voltage deviation, and case 3 considers both of them. Each scenario along with its test results are its test results are examined as follows. its test results are examined as follows. examined as follows.
Active Active Power Power (kW) (kW)
Resedential Feeder Feeder Resedential 5000.0 5000.0 4500.0 4500.0 4000.0 4000.0 3500.0 3500.0 3000.0 3000.0 2500.0 2500.0 2000.0 2000.0 1500.0 1500.0 1000.0 1000.0 500.0 500.0 0.0 0.0
Industrial Feeder Feeder Industrial
Commercial Feeder Feeder Commercial
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Reactive Reactive Power Power (kVar) (kVar)
Figure 4. Active power curves of three test feeders. Figure 4. Active power curves of three test feeders. Figure 4. Active power curves of three test feeders. 1200.0 1200.0 1000.0 1000.0
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Figure 5. Reactive power curves of three test feeders. Figure 5. Reactive power curves of three test feeders. Figure 5. Reactive power curves of three test feeders.
5.1. Case 1 5.1. Case 1 5.1. Case 1 In this test, the proposed method is applied to an industrial feeder in the TPC test system. This In this test, the proposed method is applied to an industrial feeder in the TPC test system. This In this test, the proposed method is applied to an industrial feeder in the TPC test system. feeder consists of seventeen seventeen 25 kVA, kVA, thirty‐eight 50 kVA, kVA, forty‐six 100 kVA, and nine 167 kVA feeder consists of 25 thirty‐eight 50 forty‐six 100 kVA, This feeder consists of seventeen 25 kVA, thirty-eight 50 kVA, forty-six 100 kVA,and andnine nine167 167kVA kVA distribution transformers. The total feeder load is 4.36 MW and 2.22 MVar. There are 11 high‐voltage distribution transformers. The total feeder load is 4.36 MW and 2.22 MVar. There are 11 high‐voltage distribution transformers. The total feeder load is 4.36 MW and 2.22 MVar. There are 11 high-voltage customers connected to three‐phase transformers. customers connected to three‐phase transformers. customers connected to three-phase transformers. Figure 6 shows the voltage imbalance ratio at each node before and after the phase adjustment Figure 6 shows the voltage imbalance ratio at each node before and after the phase adjustment Figure 6 shows the voltage imbalance ratio at each node before and after the phase adjustment considering minimizing the summation of voltage imbalance ratio at all nodes. It indicates that the considering minimizing the summation of voltage imbalance ratio at all nodes. It indicates that the considering minimizing the summation of voltage imbalance ratio at all nodes. It indicates that the voltage imbalance ratio ratio can be be decreased decreased through through the the reconfiguration reconfiguration work. work. Figure Figure 7 shows the voltage reconfiguration work. voltage imbalance imbalance ratio can can be decreased through the Figure 7 7 shows shows the the convergence characteristics of different methods. Both bird‐mating optimization (BMO) and hybrid convergence characteristics of different methods. Both bird‐mating optimization (BMO) and hybrid
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convergence characteristics of different methods. Both bird-mating optimization (BMO) and hybrid Energies 2016, 9, 671 7 of 12 bird-mating optimization (HBMO) have similar convergence features, which are better than Energies 2016, 9, 671 7 of 12 other Energies 2016, 9, 671 7 of 12 bird‐mating optimization (HBMO) have similar convergence features, which are better than other approaches. Because of added diversity and local search, the HBMO method is further improved. approaches. Because of added diversity and local search, the HBMO method is further improved. bird‐mating optimization (HBMO) have similar convergence features, which are better than other have similar convergence which are better than other Figurebird‐mating optimization (HBMO) 8 shows the daily voltage imbalance of initial connectionfeatures, and reconfiguration, where the largest Figure 8 shows the daily voltage imbalance of initial connection and reconfiguration, where the approaches. Because of added diversity and local search, the HBMO method is further improved. approaches. Because of added diversity and local search, the HBMO method is further improved. imbalance often happens near the peak load in a day. Since the reconfiguration work is usually made largest imbalance often happens the peak load in a day. Since reconfiguration work is Figure 8 the daily voltage imbalance of connection and the reconfiguration, where the Figure 8 shows shows the daily voltage near imbalance of initial and reconfiguration, where the around the peak load, the significant improvement occurs at hours 9–18 as the plot reveals. Table 1 usually made around the peak load, the significant improvement occurs at hours 9–18 as the plot largest imbalance often happens near the peak load in a day. Since the reconfiguration work is largest imbalance often happens near the peak Since the reconfiguration work is shows that the proposed method can obtain the lowest Max.VUR%. Comparing the Max.VUR% of the reveals. Table 1 shows that the proposed method can obtain the lowest Max.VUR%. Comparing the usually made around the peak load, the significant improvement occurs at hours 9–18 as the plot usually made around the peak load, the significant improvement occurs at hours 9–18 as the plot regulation algorithms the proposed method with those prior to improvement, it to can be Max.VUR% of the obtained regulation by algorithms obtained by the proposed method with those prior reveals. Table 1 shows that the proposed method can obtain the lowest Max.VUR%. Comparing the reveals. Table 1 shows that the proposed method can obtain the lowest Max.VUR%. Comparing the seen Max.VUR% that the Max.VUR% fall by up to 34.5%. improvement, it can be seen that the Max.VUR% fall by up to 34.5%. proposed method method with with those those prior prior to to Max.VUR% of of the the regulation regulation algorithms algorithms obtained obtained by the proposed improvement, it can be seen that the Max.VUR% fall by up to 34.5%. improvement, it can be seen that the Max.VUR% fall by up to 34.5%. Initial Connection
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Initial Connection Connection Initial
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11 1 88 8 15 15 15 22 22 22 29 29 29 36 36 36 43 43 43 50 50 50 57 57 57 64 64 64 71 71 71 78 78 78 85 85 85 92 92 92 99 99 99 106106 106 113113 113 120120 120 127127 127 134134 134 141141 141 148148 148 155155 155 162162 162
Voltage Unbalance Ratio (%) Voltage Unbalance Ratio Voltage Unbalance Ratio (%)(%)
2.0 1.8 2.0 2.0 1.6 1.8 1.8 1.4 1.6 1.6 1.2 1.4 1.4 1.0 1.2 1.2 1.0 0.8 1.0 0.8 0.6 0.8 0.6 0.4 0.6 0.4 0.2 0.4 0.2 0.0 0.2 0.0 0.0
1 11 414141 818181 121 121 121 161 161 161 201 201 201 241 241 241 281 281 281 321 321 321 361 361 361 401 401 401 441 441 441 481 481 481 521 521 521 561 561 561 601 601 601 641 641 641 681 681 681 721 721 721 761 761 761 801 801 801 841 841 841 881 881 881 921 921 921 961 961 961
11 1 171717 333333 494949 656565 818181 979797 113 113 113 129 129 129 145 145 145 161 161 161 177 177 177 193 193 193
Objective Function Value Objective Function Value Objective Function Value
Node Number Node Number Node Number Figure 6. Comparison of the improvement in the voltage imbalance ratio for each node of the Taiwan Figure 6. Comparison of the improvement in the voltage imbalance ratio for each node of the Taiwan Figure 6. Comparison of the improvement in the voltage imbalance ratio for each node of the Taiwan Power Company (TPC) 162‐node system. Figure 6. Comparison of the improvement in the voltage imbalance ratio for each node of the Taiwan PowerPower Company (TPC) 162‐node system. Company (TPC) 162-node system. Power Company (TPC) 162‐node system. 85 85 80 85 80 80 80 70 80 80 75 70 60 70 75 60 75 50 70 60 50 70 50 70 65 65 GA PSO 65 GA PSO 60 BMO HBMO GA PSO 60 BMO HBMO 60 55 BMO HBMO 55 55 50 50 50 Number of Iterations Number of Iterations Number of Iterations Figure 7. Comparison of convergence characteristics among methods. Figure 7. Comparison of convergence characteristics among methods. Figure 7. Comparison of convergence characteristics among methods. Figure 7. Comparison of convergence characteristics among methods. Max. Voltage Unbalance Ratio (%)(%) Max. Voltage Unbalance Ratio (%) Max. Voltage Unbalance Ratio
2.0 2.0 1.8 2.0 1.8 1.6 1.8 1.6 1.4 1.6 1.4 1.2 1.4 1.2 1.0 1.2 1.0 0.8 1.0 0.8 0.6 0.8 0.6 0.4 0.6 0.4 0.2 0.4 0.2
Initial Connection Initial Connection Initial Connection
Reconfiguration Reconfiguration Reconfiguration
0.0 0.2 0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time (Hour) Time 1 2 3 4 5 6 7 8 9 10 11 12 (Hour) 13 14 15 16 17 18 19 20 21 22 23 24 Time (Hour)
Figure Max. voltage voltage imbalance imbalance ratio ratio for for the the industrial industrial Figure 8. 8. Comparison Comparison of of the the improvement improvement in the Max. feeder on a daily scale. feeder on a daily scale. Figure 8. Comparison of the improvement in the Max. voltage imbalance ratio for the industrial
Figure 8. Comparison of the improvement in the Max. voltage imbalance ratio for the industrial feeder feeder on a daily scale. on a daily scale.
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Table 1. Comparison of algorithms considering the Max. voltage imbalance ratio as the single objective. Energies 2016, 9, 671 Energies 2016, 9, 671
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Max. VUR%
GA
PSO
BMO
1.74% PSO PSO 1.16% 1.74% 1.74% 1.16% 1.16%
1.74% BMO BMO 1.14% 1.74% 1.74% 1.14% 1.14%
HBMO
Table 1. Comparison of algorithms considering the Max. voltage imbalance ratio as the single objective. Table 1. Comparison of algorithms considering the Max. voltage imbalance ratio as the single objective.
Origin 1.74% Max. VUR% GA Max. VUR% GA Result 1.16% Origin 1.74% Origin 1.74% Result 1.16% Result 1.16%
5.2. Case 2
1.74% HBMO HBMO 1.14% 1.74% 1.74% 1.14% 1.14%
5.2. Case 2 In5.2. Case 2 this case, the proposed method is applied to commercial feeders in a TPC test system. In this case, the proposed method is applied to commercial feeders in a TPC test system. The The feeders consists of nineteen 25 kVA, thirty-eight 50 kVA, fifty-three 100 kVA, and four 167 kVA In this case, the proposed method is applied to commercial feeders in a TPC test system. The feeders consists of of nineteen nineteen 25 kVA, kVA, thirty‐eight 50 kVA, kVA, voltage fifty‐three 100 kVA, kVA, at and four 167 kVA kVA distribution Figure 9 shows the maximum deviation each node with and feeders transformers. consists 25 thirty‐eight 50 fifty‐three 100 and four 167 distribution transformers. Figure 9 shows the maximum voltage deviation at each node with and distribution transformers. Figure 9 shows deviation the maximum at each node with and without the reconfiguration. The voltage mayvoltage occur deviation due to the inclusion of renewable without the reconfiguration. The voltage deviation may occur due to the inclusion of renewable energy. energy.without the reconfiguration. The voltage deviation may occur due to the inclusion of renewable energy. The equivalent loads become more evenly distributed among phases after the reconfiguration. The equivalent loads become more evenly distributed among phases after the reconfiguration. The The equivalent loads become more evenly distributed among phases after the reconfiguration. The The line currents are reduced along with the mitigation of voltage rise. Figure 10 shows the daily line currents are reduced along with the mitigation of voltage rise. Figure 10 shows the daily voltage line currents are reduced along with the mitigation of voltage rise. Figure 10 shows the daily voltage voltage deviation gained fromfield fieldmeasurements. measurements. After reconfiguration, increased voltage deviation gained from After the the reconfiguration, these these increased voltage deviation gained from field measurements. After the reconfiguration, these increased voltage deviations can be effectively restricted. deviations can be effectively restricted. 2.5 2.5 Initial Connection Initial Connection
2.0 2.0
Reconfiguration Reconfiguration
1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0
11 99 17 17 25 25 33 33 41 41 49 49 57 57 65 65 73 73 81 81 89 89 97 97 105 105 113 113 121 121 129 129 137 137 145 145 153 153 161 161 169 169 177 177 185 185 193 193 201 201
Voltage VoltageDeviation DeviationRatio Ratio(%) (%)
deviations can be effectively restricted.
Node Number Node Number
Figure 9. Comparison of voltage deviation for each node of the TPC test system. Figure 9. Comparison of voltage deviation for each node of the TPC test system. Figure 9. Comparison of voltage deviation for each node of the TPC test system.
Max. Max.Voltage VoltageDeviation DeviationRatio Ratio(%) (%)
2.5 2.5 2.0 2.0
Initial Connection Initial Connection
Reconfiguration Reconfiguration
1.5 1.5 1.0 1.0 0.5 0.5 0.0 0.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time (Hour) Time (Hour)
Figure 10. Daily voltage deviation ratio of initial connection and reconfiguration in the test feeder. Figure 10. Daily voltage deviation ratio of initial connection and reconfiguration in the test feeder.
Figure 10. Daily voltage deviation ratio of initial connection and reconfiguration in the test feeder. 5.3. Case 3 5.3. Case 3 5.3. Case 3 In this case, the composite of maximum voltage imbalance ratio and voltage deviation ratio is In this case, the composite of maximum voltage imbalance ratio and voltage deviation ratio is concerned. The voltage imbalance of the the system system may become worse worse because of the the deviation connected ratio Inconcerned. this case,The thevoltage composite of maximum voltage imbalance ratiobecause and voltage imbalance of may become of connected renewable resources. Now for the case where the maximum voltage deviation ratio of 2.75%, it can renewable resources. Now for the case where the maximum voltage deviation ratio of 2.75%, it can is concerned. The voltage imbalance of the system may become worse because of the connected be controlled to be 2.5% after the reconfiguration. However, it is also suggested that if the voltage be controlled to be 2.5% after the reconfiguration. However, it is also suggested that if the voltage renewable resources. Now for the case where the maximum voltagestorage deviation ratio of 2.75%, it can imbalance continues increasing, continues increasing, then then the the equipment equipment such as such as energy energy storage system installation installation or or imbalance system be controlled to be 2.5% after the reconfiguration. However, it is also suggested that if the voltage additional transformer installation may be further required. It is worth mentioning that the suitable additional transformer installation may be further required. It is worth mentioning that the suitable imbalance continues increasing, then the equipment such as energy storage system installation or connection of transformers can be served as an alternative for utility engineers when the supplying connection of transformers can be served as an alternative for utility engineers when the supplying quality is concerned. additional transformer installation may be further required. It is worth mentioning that the suitable quality is concerned.
connection of transformers can be served as an alternative for utility engineers when the supplying quality is concerned.
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Figure 11 shows the daily voltage profile. In view of this voltage profile, the degree of imbalance Figure 11 shows the daily voltage profile. In view of this voltage profile, the degree of Energies 2016, 9, 671 9 of 12 is significant the night because the because peak load thisload feeder occurs at 22:00. Through imbalance during is significant during the night the of peak of this feeder occurs at 22:00. the reconfiguration, dailythe voltage and deviation be subsequently Through the reconfiguration, both daily voltage imbalance and deviation curve can be subsequently Figure both 11 shows daily imbalance voltage profile. In view curve of this can voltage profile, the ameliorated degree of at each ameliorated at each hour, hence supporting the feasibility of the proposed method. hour, hence supporting the feasibility of the proposed method. imbalance is significant during the night because the peak load of this feeder occurs at 22:00.
2.5 2.0 2.5 1.5 2.0 1.0 1.5 0.5 1.0 0.0 0.5
5.4. Case 4
5.4. Case 4
0.0
Max. Voltage Unbalance Ratio of Reconfiguration Max. Voltage Deviation Ratio of Initial Connection Max. Voltage Voltage Deviation UnbalanceRatio RatioofofReconfiguration Initial Connection Max. Max. Voltage Unbalance Ratio of Reconfiguration Max. Voltage Deviation Ratio of Initial Connection Max. Voltage Deviation Ratio of Reconfiguration
5.0
4.0 5.0 3.0 4.0 2.0 3.0 1.0 2.0 0.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1.0 Time (Hour) 0.0 1 2 3 4 5 Figure 11. Daily voltage profile. 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Figure 11. Daily voltage profile. Time (Hour)
Voltage Deviation Ratio (%) Voltage Deviation Ratio (%)
Voltage Unbalance Ratio (%) Voltage Unbalance Ratio (%)
Through the reconfiguration, both daily voltage imbalance and deviation curve can be subsequently Max. Voltage Unbalance Ratio of Initial Connection ameliorated at each hour, hence supporting the feasibility of the proposed method.
Figure 11. Daily voltage profile.
A distribution network with renewable generation systems [28–30] in the Institute of Nuclear 5.4. Case 4 A distribution with renewable generation systems [28–30] in the Institute of Nuclear Energy Research network (INER) was taken into account to perform the phase adjustment of distribution transformers in this case. shows the one‐line diagram the real 11.4 kV distribution Energy Research (INER) wasFigure taken12 into account to perform the of phase adjustment of distribution A distribution network with renewable generation systems [28–30] in the Institute of Nuclear network in the INER. This system consists of 30 buses along with several hybrid energy resources, in Energy Research (INER) was 12 taken into account to perform phase of distribution transformers in this case. Figure shows the one-line diagramthe of the realadjustment 11.4 kV distribution network which includes battery energy storage system (BESS), micro turbine generator (MTG), diesel transformers in this case. Figure 12 shows the one‐line diagram of the real 11.4 kV distribution in the INER. This system consists of 30 buses along with several hybrid energy resources, in which generator photovoltaic system (PV), micro high turbine concentration photovoltaic system (HCPV), (DG), network in the INER. This system consists of 30 buses along with several hybrid energy resources, in includes battery(DG), energy storage system (BESS), generator (MTG), diesel generator vanadium redox battery (VRB), sodium sulfur fuel cell (SOFC), and wind turbine (WT), which are which includes battery energy storage system (BESS), micro turbine generator (MTG), diesel photovoltaic system (PV), high concentration photovoltaic system (HCPV), vanadium redox battery connected at Bus 18 in Figure 12. It is worth noting that all loads are supplied through open wye‐open generator (DG), photovoltaic system (PV), high concentration photovoltaic system (HCPV), (VRB), sodium sulfur fuel cell (SOFC), and wind turbine (WT), which are connected at Bus 18 in delta transformers in this simulation system. vanadium redox battery (VRB), sodium sulfur fuel cell (SOFC), and wind turbine (WT), which are Figure 12. It is worth noting that all loads are supplied through open wye-open delta transformers in connected at Bus 18 in Figure 12. It is worth noting that all loads are supplied through open wye‐open this simulation system. delta transformers in this simulation system.
Figure 12. Single line diagram of 11.4 kV substation of the Institute of Nuclear Energy Research (INER) 30‐Bus system. Figure 12. Single line diagram of 11.4 kV substation of the Institute of Nuclear Energy Research
Figure 12. Single line diagram of 11.4 kV substation of the Institute of Nuclear Energy Research (INER) (INER) 30‐Bus system. 30-Bus system.
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VoltageUnbalance UnbalanceRatio Ratio(%) (%) Voltage
Figure 13 shows the voltage imbalance ratio at each bus with and without the reconfiguration. Figure 13 shows the voltage imbalance ratio at each bus with and without the reconfiguration. Figure 13 shows the voltage imbalance ratio at each bus with and without the reconfiguration. The test shows that the voltage imbalance ratio of each bus not only decreases significantly after the The test shows that the voltage imbalance ratio of each bus not only decreases significantly after The test shows that the voltage imbalance ratio of each bus not only decreases significantly after the rearranging phase of distribution transformers, but also satisfies the rearranging phase of distribution transformers, but also satisfiesthe thelimit limitof of allowable allowable voltage voltage rearranging phase of distribution transformers, but also satisfies the limit of allowable voltage balance ratio. Meanwhile, the total loss is also lowered down from 265.70 kW to 247.31 kW after the balance ratio. Meanwhile, the total loss is also lowered down from 265.70 kW to 247.31 kW after balance ratio. Meanwhile, the total loss is also lowered down from 265.70 kW to 247.31 kW after the employment of the suggested approach. It is also the employment of the suggested approach. It is alsoworth worthnoting notingthat thatthe the aforementioned aforementioned phase phase employment of the suggested approach. It is also worth noting that the aforementioned phase adjustment of distribution transformer is implemented as a human machine interface (HMI) to assist adjustment of distribution transformer is implemented as a human machine interface (HMI) to assist adjustment of distribution transformer is implemented as a human machine interface (HMI) to assist utility engineers in monitoring system operation. Figure 14 shows the display of HMI made by this utility engineers in monitoring system operation. Figure 14 shows the display of HMI made by this utility engineers in monitoring system operation. Figure 14 shows the display of HMI made by this paper. The functions functions ofof HMI include single diagram of kV 11.4 kV substation the 30-Bus INER paper. The HMI include thethe single lineline diagram of 11.4 substation of the of INER paper. The functions of HMI include the single line diagram of 11.4 kV substation of the INER 30‐Bus well as the with results and reconfiguration. without reconfiguration. The information of HMI system system as well as as the results andwith without The information of HMI including 30‐Bus system as well as the results with and without reconfiguration. The information of HMI including the voltage imbalance ratio of each bus, neutral line current, and total power loss are also the voltage imbalance ratio of each bus, neutral line current, and total power loss are also displayed including the voltage imbalance ratio of each bus, neutral line current, and total power loss are also displayed respectively. It is for engineer the utility supervise the grid with a higher respectively. It is suitable forsuitable the utility to engineer superviseto the grid with a higher convenience displayed respectively. It is suitable for the utility engineer to supervise the grid with a higher convenience and efficiency. and efficiency. convenience and efficiency. 1.0 1.0 0.9 0.9 0.8 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0
with configuration with configuration
without configuration without configuration
1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930 Bus Number Bus Number
Figure 13. Comparison of the improvement in the voltage imbalance ratio for the INER 30‐Bus system. Figure 13. Comparison of the improvement in the voltage imbalance ratio for the INER 30-Bus system. Figure 13. Comparison of the improvement in the voltage imbalance ratio for the INER 30‐Bus system.
Figure 14. Comparison of the results of each Bus for the INER 30‐Bus system considering reduction Figure 14. Comparison of the results of each Bus for the INER 30‐Bus system considering reduction Figure 14. Comparison of the results of each Bus for the INER 30-Bus system considering reduction of of voltage imbalance ratio and neutral line current with reconfiguration. of voltage imbalance ratio and neutral line current with reconfiguration. voltage imbalance ratio and neutral line current with reconfiguration.
6. Conclusions 6. Conclusions 6. Conclusions An approach using hybrid bird‐mating optimization is proposed to enhance the phase‐connection An approach using hybrid bird‐mating optimization is proposed to enhance the phase‐connection An approach using hybrid bird-mating is proposed to enhanceunder the phase-connection adjustment of distribution transformers in optimization a grid. Through tests performed three practical adjustment of distribution transformers in a grid. Through tests performed under three practical adjustment ofproposed distribution transformers in a grid. Through tests performed under imbalance three practical systems, this approach has exhibited its capability of improving voltage and systems, this proposed approach has exhibited its capability of improving voltage imbalance and deviation. This work is being done in cooperation with the Institute of Nuclear Energy Research deviation. This work is being done in cooperation with the Institute of Nuclear Energy Research (INER) in Taiwan. Through the project cooperation, we are endeavoring to implement the proposed (INER) in Taiwan. Through the project cooperation, we are endeavoring to implement the proposed
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systems, this proposed approach has exhibited its capability of improving voltage imbalance and deviation. This work is being done in cooperation with the Institute of Nuclear Energy Research (INER) in Taiwan. Through the project cooperation, we are endeavoring to implement the proposed method for the assessment of the phase adjustment performance through open wye-open delta transformers. The outcomes gained from this study validate the feasibility of the proposed approach for balancing the phase operation of a power system, making it effective for electric power operation improvement applications. Reliability of scenario assessment becomes the major concern at this time. Further validation of this practical system will be reported in the near future. Acknowledgments: The authors are greatly indebted to the Institute of Nuclear Energy Research for their valuable operating experience. Financial support of this paper under the contract number of MOST 104-3111-Y-042A-055 of Ministry of Science and Technology (MOST), Taiwan is appreciated. Author Contributions: Ting-Chia Ou made substantial contributions to conception and plan; give final approval of the version to be submitted and any revised version. Wei-Fu Su handled the project. Xian-Zong Liu performed the experiments and conducted simulations; analysis and interpretation of data. Shyh-Jier Huang supervised the research throughout. Te-Yu Tai assisted analysis of algorithm. Conflicts of Interest: The authors declare no conflict of interest.
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