Clusters partition and zonal voltage regulation for distribution networks with high penetration of PVs
2018; Institution of Engineering and Technology; Volume: 12; Issue: 22 Linguagem: Inglês
10.1049/iet-gtd.2018.6255
ISSN1751-8695
AutoresJinjin Ding, Qian Zhang, Hu Shijun, Qunjing Wang, Qiubo Ye,
Tópico(s)Microgrid Control and Optimization
ResumoIET Generation, Transmission & DistributionVolume 12, Issue 22 p. 6041-6051 Research ArticleFree Access Clusters partition and zonal voltage regulation for distribution networks with high penetration of PVs Jinjin Ding, Corresponding Author Jinjin Ding djinjin123@126.com Department of Electrical Engineering and Automation, Anhui University, Hefei, 230061 People's Republic of China Anhui Electric Power Science Research Institute, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorQian Zhang, Qian Zhang Department of Electrical Engineering and Automation, Anhui University, Hefei, 230061 People's Republic of ChinaSearch for more papers by this authorShijun Hu, Shijun Hu orcid.org/0000-0002-8071-4147 Anhui Electric Power Science Research Institute, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorQunjing Wang, Qunjing Wang Department of Electrical Engineering and Automation, Anhui University, Hefei, 230061 People's Republic of China Collaborative Innovation Centre of Industrial Energy-Saving and Power Quality Control, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorQiubo Ye, Qiubo Ye Department of Electrical Engineering and Automation, Anhui University, Hefei, 230061 People's Republic of China College of Information Engineering, Jimei University, Fujian, 361021 People's Republic of ChinaSearch for more papers by this author Jinjin Ding, Corresponding Author Jinjin Ding djinjin123@126.com Department of Electrical Engineering and Automation, Anhui University, Hefei, 230061 People's Republic of China Anhui Electric Power Science Research Institute, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorQian Zhang, Qian Zhang Department of Electrical Engineering and Automation, Anhui University, Hefei, 230061 People's Republic of ChinaSearch for more papers by this authorShijun Hu, Shijun Hu orcid.org/0000-0002-8071-4147 Anhui Electric Power Science Research Institute, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorQunjing Wang, Qunjing Wang Department of Electrical Engineering and Automation, Anhui University, Hefei, 230061 People's Republic of China Collaborative Innovation Centre of Industrial Energy-Saving and Power Quality Control, Anhui University, Hefei, 230601 People's Republic of ChinaSearch for more papers by this authorQiubo Ye, Qiubo Ye Department of Electrical Engineering and Automation, Anhui University, Hefei, 230061 People's Republic of China College of Information Engineering, Jimei University, Fujian, 361021 People's Republic of ChinaSearch for more papers by this author First published: 20 November 2018 https://doi.org/10.1049/iet-gtd.2018.6255Citations: 12AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Integration of distributed generation (DG) at large scale with high penetration challenges the radial structure of the traditional distribution networks and the effectiveness of the conventional voltage regulation methods. In this study, the clusters partitioning and voltage regulation are researched. The modified electrical distance is introduced. An effective method, based on spectral clustering algorithm, is proposed for the partitioning of the DG network via the judgement of critical load buses. Two-stage voltage regulation optimisation is realised in each sub-community. The optimal objects are the minimal voltage fluctuation and the network loss of the distributed network. The independent variables are reactive-power absorption and active-power curtailment for each controllable photovoltaic node. An advanced particle swarm optimisation algorithm is applied to the voltage regulation for the sub-communities. After a case study of the IEEE 33-bus system, a regional distribution network in Anhui province of China is analysed. Simulation results indicate that the node voltages are stabilised with the improvement of power quality employing the proposed clusters partitioning method and zonal power control scheme. 1 Introduction With the objective of overcoming the financial, environmental, and availability issues of conventional energy power resources, renewable energy resources are involved to produce power at a large scale. Local grid integration of distributed generation (DG) unavoidably will change the radial structure of the distribution network and probably will lead to overvoltage, reverse power flow, loop network etc. Thus, there are technique challenges of power quality, protection, stability, and voltage regulation [1, 2]. Researchers and engineers, therefore, are paying attention to the analysis and improvement of distribution feeders [3–5], communication infrastructures [6–9], energy storage systems [10, 11], and voltage regulation algorithms [12–21]. On the basis of existing infrastructures, the optimisation of control schemes is an effective and economical solution for maintaining power quality, especially concerning the overvoltage issue. Many advanced methods have been proposed in the literature including centralised and decentralised schemes. Owing to high investment in communication and data processing, centralised control is possible to provide the best performance at small scale [8]. However, the disadvantages of the centralised control such as large computational burden, slow response speed, and numerical stability issues will become more and more obvious with the increase of DG penetration level and the scale-up of the distribution grid. In such circumstances, the decentralised control schemes attract attention in both academia and industry [21–30]. In recent years, there has been abundant research on this issue. Among them, the zonal voltage control based on the clusters partitioning is a key technique and research focus. In [27], an economical operation strategy is proposed based on load response and system partitioning, in which a two-stage optimisation schedule is proposed for post-contingency power systems incorporated with DGs. In [28], a community-detection-based optimal network partitioning is carried out based on an improved modularity index. A multi-objective optimisation problem is formulated for the sub-community reactive/active-power–voltage control, and solved by the particle swarm optimisation (PSO) algorithm. In [30], a novel Laplacian spectrum-based approach is constructed to solve bio-objective network partitioning problems, the resultant Pareto front of the voltage regulation solution is obtained. Even so, the clustering methodology and voltage regulation schemes of distribution networks are still in discussion and exploration. Conventional power grid partitioning usually is determined by the geographical environment or municipal governance, which is appropriate in the traditional radial grid structure. However, for the planning and operation of distributed networks with high penetration of renewable DGs, it is necessary to analyse the relation between the integration of renewable DGs and the distributed network's behaviour. Therefore, advanced partition techniques are proposed. The electrical distance [31], modularity index [26], and voltage sensitivity (VS) matrix [28, 32] are introduced as the indexes describing the relationships among nodes in the distributed network. Subsequently, the clustering methods such as K-means, self-organising mappings, fuzzy C-means, and agglomerative hierarchical clustering [32] can be applied to the clustering partition of distributed power systems. In this paper, the modified electrical distance is defined based on the impedance distance and VS index. The distributed network is divided into several sub-communities based on the spectral clustering algorithm. Considering the energy interaction among clusters, the zonal voltage regulation is constructed into a constrained optimisation problem. An advanced PSO is proposed to solve the obtained problem. The effectiveness and computational efficiency are verified through a case study of the IEEE 33-bus system. Finally, this approach is applied to an actual distributed grid system with high penetration of photovoltaics (PVs) located in Anhui Province, China. It is demonstrated that the clustering method and optimisation algorithm are capable of dealing with the overvoltage issue and improving the power quality. 2 Measurement indices for the distributed system partition In a power grid, large systems are divided into areas and zones for applications of planning and control schemes. Different partitions lead to various results; i.e. good partitioning reduces loop flows [31]. To formalise the notion of strong and weak connections, an electrical distance matrix is introduced. To understand the structure of power grids from a complex network perspective, it is necessary to study not only its topology, but also its electrical structure. Thus, a measure of electrical connectedness (or conversely distance) is introduced to clarify the electrical structure of a given power grid. Under this background, the electrical distance is applied extensively in the context of structural network analysis [22]. There are several variant measures of electrical distance for power networks. Here, the modified electrical distance has been proposed to describe the characteristic of distributed power systems. 2.1 Impedance distance Defining the equivalent impedance as the impedance between a generation bus i to a load bus j [1], the electrical distance between these two nodes is expressed as below [3, 7]: (1)The superposition principle is illustrated in Fig. 1, where is the current entering the node i and is the voltage across nodes i and j. Fig. 1Open in figure viewerPowerPoint Computing the impedance distance between buses in a power grid 2.2 Modified electrical distance According to the physical significance of the local voltage stability index, the modified electrical distance is defined. As a result, the load buses of a specific power system are mapped into the multivariate load space. In a multi-attribute network partitioning problem, this mapping relates the network topology and active-power sensitivities. To achieve the goal of voltage control, it is necessary to quantify the node power injection/absorption. The VS coefficient is introduced to specify the change in the voltage at node j for a variation of the injected active power and absorbed reactive power at the node i. Two sensitivity matrices and in the operating state are defined as below: (2)where is the VS coefficients from node i to j; is the voltage of the node j; and are the active and reactive powers generated by the PV individual units. The voltage influence factor (VIF) is the ratio of a given VS coefficients and the scalar sum of all VS coefficients. Following equations define two VIFs for the injected active power and absorbed reactive-power transmission from node i to node j in the operating state (3)For the purpose of considering effects of both the active and reactive powers of PV nodes simultaneously, these two matrices are merged into a single one as expressed in (4) and (5), which is defined as the modified electrical distance matrix (4)with (5)The electrical distance between pairs of nodes is calculated according to the superposition principle, based on the information contained in the characteristics of the power network. 2.3 Quality measures for zonal boundaries Conventional partitioning algorithms such as spectral and K-means approaches are computationally efficient, but are not easily adapted to the optimal solutions with respect to objectives of maximising between-cluster distances and minimising within-cluster distances [31]. For this reason, we construct some quality measures for zonal boundaries. Considering the above-defined electrical distance as the quantification of distance between node i and node j in the distributed network for clustering partition, we then assume that there are N nodes in the distributed network, which are divided into n clusters/sub-communities/zones without overlap. The sub-communities are denoted as . Taking the sub-community , for example, the resultant clustering is detailed as follows. The total number of nodes in is . As the centroid in the cluster has the higher VS and the more important structure characteristic than the other nodes, it is judged to be the critical node . The remaining nodes are normal nodes in this cluster. Controllable PV units are settled at the critical node to get the best voltage regulation with the minimum financial cost. The definition of the modified electrical distance forms the basis of the measures for the clustering of the electronic power system with DGs. To optimise the clustering result, various indices are investigated to present adequate information. 2.3.1 Normalised mean square error The normalised mean square error (NMSE) expresses the normalised sum of the unweighted electrical distance of each normal node from the critical node within the same cluster as defined in the equation below: (6)The MSE is a popular function widely used in clustering algorithms. The normalisation is for the purpose of combination with other indexes. 2.3.2 Davies–Bouldin index This index was first proposed in [33], and it identifies clusters with high intra-connectivity and low inter-connectivity as expressed below: (7) (8)where is the modified electrical distance between the critical nodes in clusters i and j, , and are the average electrical distances between all normal nodes in clusters i and j to their critical nodes. A smaller Davies–Bouldin index (DBI) value indicates compact clusters and large electrical distances between critical nodes. 2.3.3 Silhouette index The silhouette width of the node is a confidence indicator for its membership in the cluster as expressed below: (9) (10) (11)where is the average electrical distance between the node and all other nodes in the same cluster , while is the minimum average electrical distance between the node and all nodes in the different clusters. The average Silhouette width represents the heterogeneity of the given cluster [34]; the overall Silhouette index (SI) is defined below: (12)The cluster partition with larger SI value has greater heterogeneity. 2.3.4 Aggregate clustering fitness To evaluate the quality of a given clustering partition conveniently, an aggregate fitness function is calculated as the weighted product of the above three quality measures below: (13)where represent the importance of NMSE, DBI, and SI. The multiplicative form of the fitness function is given whenever any cluster is not fully connected [31]. For the contracture and essence of the index formulas, the priorities of these three indexes NMSE, DBI, and SI are equal in our research. After several experiments, the trade-off parameters are chosen as λ 1 = λ 2 = λ 3 = 1, which should be readjusted in the other research. 3 Zonal partition using a spectral clustering method K-means [31] and spectral clustering [27, 28, 30] methodologies are proved to be effective in solving the problem of power network partition. However, the K-means algorithm has disadvantages of dependence on the initial set of partition and result randomness. In our research, the spectral clustering is selected to solve for distributed network zonal division. On the basis of graphic theory, a generalised electric power network can be described by an undirected weighted graph , where is the set of nodes in the distributed network and E is the set of all nodes and branches. An average edge weight is introduced as a symmetric weight matrix as a set of edge weights defined below: (14)Then a diagonal degree matrix is constructed as (15)The normalised Laplacian matrix is calculated as (16)Next, eigenvalues and eigenvectors of the normalised Laplacian matrix are calculated. eigenvalues are chosen, and their corresponding eigenvectors are normalised to form a feature matrix . Each row of is regarded as a spectral data point and mapped to the corresponding node in the electrical network. The Laplacian treatment effectively reduces the dimensionality in this problem. In the next step, the classical K-means method is applied to the cluster spectral data points thus yielding network partitioning, with (4) as the distance and (13) as its clustering fitness. The process flowchart is illustrated in Fig. 2. Fig. 2Open in figure viewerPowerPoint Flowchart of spectral clustering method for the power network partition 4 Two-stage zonal voltage control scheme Suppose that there is sufficient active/reactive-power supply at the controllable PV nodes. The control objects are minimal voltage deviation and the minimisation of network loss. 4.1 Problem formulation The zonal voltage control problem can be summarised as a constrained multi-objective non-linear optimisation problem (CMOP) as expressed below: (17) (18)s.t. (19) (20) (21) (22) (23) where is the expected node voltage of the distributed system, and are, respectively, the active- and reactive-power losses of the controllable PV unit, and are, respectively, the active and reactive powers generated by PV units, and are, respectively, the load active and reactive demons, and are, respectively, the susceptance and conductance of the branch consisting of nodes i and j, is the phase difference of node i and node j, is the curtailed active power of the controllable PV unit, and are the minimum and maximum values of , is the absorbed reactive power of the controllable PV unit, and are the minimum and maximum values of , and is the power factor angle of the controllable PV's inverter. The two objective functions are linearly combined, with adaptive weighting coefficients, forming an optimisation problem with single objective function. 4.2 Advanced PSO algorithm For the solution of this class of CMOP issue, the heuristic algorithms such as PSO and genetic algorithm are widely used. The traditional PSO is an evolutionary algorithm that adjusts and updates the position and velocity of each particle according to the global best position and particle best position . In our research, the swarms correspond to the curtailed active power and the absorbed reactive power . The number of swarms in one particle is . There are particles in the D-dimensional searching space. The PSO algorithm is formulated below: (24) (25) (26)where t is the iterative generation, the particle's position and velocity in the generation are and , rand is a uniform random value in the range of [0, 1], and are the acceleration constants, and w is the inertia weight which changes from to . To improve the searching performance of the conventional PSO, the elimination mechanism, which is originally proposed in the cuckoo search algorithm, is introduced to form an advanced PSO algorithm. In the advanced PSO, a set of the worst performing particles are chosen with a friction . These particles are abandoned and replaced by randomly generated ones within the specified search space. In our research, it is found that the advanced PSO has the ability to deal with the multi-objects, constrains, and non-linearity of the CMOP. However, with the implementation of this algorithm in every control cycle, computation times are very long. To overcome this deficiency, a two-stage intelligent control strategy is proposed. 4.3 Two-stage control strategy In this section, based on the clustering partition result and the advanced PSO algorithm, the two-stage intelligent control strategy is proposed for the regulation of a distributed power system. The optimisation process of voltage control is divided into two stages. The first stage is a non-linear optimisation process using the advanced PSO algorithm. Considering the computational burden, it may be performed only in a 24 h control period. The node voltage updating is undertaken in each step for real-time optimisation. The details of this scheme is expressed below: Step 1 : Select a pre-set period in advance. The update frequency can be set as 4, 12 h per time etc., depending on the requirement of control accuracy and the consideration of calculation burden. When the iteration satisfies the pre-set period, proceed to Step 2; otherwise, go to step 7. Step 2 : Set the parameters of the advanced PSO such as , D, , , and . Initialise the swarms in particles . While or another stop criterion. Step 3 : Calculate the fitness as below: (27) Moreover, find the and . Step 4 : Choose a friction of the worst performing swarm in terms of the fitness function. These particles should be abandoned and replaced by randomly generated ones within the specified search space. Step 5 : Update the position X and velocity V. Step 6 : Determine the suitable values of VS coefficients and VIFs from (3). Step 7 : The increment of the node voltage is deduced from the equation below: (28) Step 8 : Output the best operation of the controllable PVs , and the final node voltage. End. In the first stage, the sensitivity matrix is rolling optimised using the Newton–Raphson method and advanced PSO algorithm during a pre-set period. Reasonable values of and in working state are determined. In the second stage, linear regulation is processed in each control cycle. The termination conditions of the PSO algorithm are specified, so that the deviation of fitness function is <1 × 10−3 or the generation meets its maximum. The flowchart of the two-stage voltage control scheme is illustrated in Fig. 3. Fig. 3Open in figure viewerPowerPoint Flowchart of the two-stage control strategy 5 Case studies 5.1 IEEE 33-bus case system The topology of the conventional IEEE 33-bus system is shown in Fig. 4. The original total nominal load is 3.715 MW + j2.3 MVar along the feeder. Fig. 4Open in figure viewerPowerPoint Topology of the IEEE 33-bus network In our research of PV integration, an extreme scenario is assumed, i.e. PV units are connected to all nodes. It is no doubt that there will be the overvoltage phenomena. We want to regulate the node voltage with the least number of controllable PV units. Values of , , , , and are calculated in particular working situations . The spectral clustering algorithm is applied. As a result, the IEEE 33-bus system with PV is divided into five sub-communities as shown in Fig. 5. Fig. 5Open in figure viewerPowerPoint Partition result of the IEEE 33-bus network Since the dimension of the aforementioned coefficient matrices is all , we only enumerate some nodes data. Take cluster 2, for example, and of nodes in the work state are listed as Tables 1 and 2. In our research, some other work conditions are also considered. Total and of node i are defined as and as below: (29) Table 1. matrix of nodes in cluster 2 under working state Nodes 6 7 8 9 10 11 12 26 27 6 2.396814 2.425133 2.466553 2.506396 2.512028 2.521668 2.564686 1.7319 1.839659 7 2.420325 2.713366 2.763963 2.812655 2.819671 2.831681 2.884092 1.748889 1.857705 8 2.451566 2.748389 3.639057 3.703206 3.71245 3.728275 3.797321 1.771463 1.881683 9 2.480694 2.781044 3.682294 4.59556 4.607045 4.626706 4.712469 1.792511 1.904041 10 2.485007 2.785879 3.688696 4.603549 4.689203 4.709507 4.797812 1.795627 1.907351 11 2.492558 2.794344 3.699904 4.617537 4.703451 4.865696 4.95882 1.801083 1.913146 12 2.523663 2.829215 3.746076 4.67516 4.762146 4.926416 6.366558 1.823559 1.937021 26 1.716553 1.741501 1.776653 1.810492 1.815445 1.823924 1.860255 2.013319 2.141623 27 1.757256 1.782796 1.818781 1.853423 1.858493 1.867173 1.904366 2.061059 3.272102 Table 2. matrix of nodes in cluster 2 under work state Nodes 6 7 8 9 10 11 12 26 27 6 2.585915 2.575164 2.571268 2.567304 2.565234 2.561696 2.55922 2.347205 2.360281 7 2.592479 3.450889 3.450122 3.449115 3.44709 3.443631 3.444793 2.351948 2.365319 8 2.580326 3.437265 4.718608 4.717233 4.714464 4.709734 4.711325 2.343167 2.355991 9 2.569595 3.425234 4.702678 6.031593 6.028067 6.022045 6.024172 2.335412 2.347754 10 2.570973 3.426779 4.704723 6.034145 6.284814 6.278807 6.281966 2.336408 2.348812 11 2.573203 3.429279 4.708034 6.038277 6.289022 6.769355 6.774478 2.338019 2.350524 12 2.556823 3.410916 4.68372 6.007933 6.258114 6.737381 8.672774 2.326184 2.337952 26 2.405053 2.400045 2.402291 2.404277 2.403335 2.401729 2.405333 2.974069 2.995258 27 2.414711 2.409843 2.412287 2.414463 2.41355 2.411991 2.415799 2.985396 4.32494 It is found in the analysis of the calculated result that nodes 13 and 29 have two largest values among 33 nodes. Values of and of nodes 13 and 29 in work states and are also listed in Table 3. Table 3. VIF of nodes 13 and 29 under various working states Work states Nodes Node13 Node29 Node13 Node29 1 0.0016 0.0017 0.0012 0.0013 2 0.0102 0.0106 0.0079 0.0080 3 0.0165 0.0172 0.0128 0.0130 4 0.0231 0.0241 0.0179 0.0182 5 0.0404 0.0422 0.0304 0.0310 6 0.0491 0.0425 0.0354 0.0312 7 0.0593 0.0429 0.0438 0.0315 8 0.0782 0.0434 0.0578 0.0319 9 0.0972 0.0439 0.0718 0.0323 10 0.0999 0.0439 0.0741 0.0323 11 0.1052 0.0441 0.0784 0.0324 12 0.1328 0.0446 0.0984 0.0328 13 0.1458 0.0448 0.1070 0.0329 14 0.1461 0.0449 0.1073 0.0330 15 0.1465 0.0450 0.1076 0.0331 16 0.1470 0.0452 0.1080 0.0333 17 0.1471 0.0452 0.1080 0.0333 18 0.0016 0.0017 0.0012 0.0013 19 0.0016 0.0017 0.0013 0.0013 20 0.0016 0.0017 0.0013 0.0013 21 0.0016 0.0017 0.0013 0.0013 22 0.0102 0.0107 0.0079 0.0081 23 0.0104 0.0108 0.0080 0.0082 24 0.0104 0.0109 0.0081 0.0082 25 0.0405 0.0457 0.0305 0.0337 26 0.0407 0.0506 0.0307 0.0374 27 0.0417 0.0732 0.0314 0.0532 28 0.0423 0.0902 0.0319 0.0652 29 0.0426 0.0987 0.0321 0.0718 30 0.0430 0.0995 0.0324 0.0723 31 0.0430 0.0996 0.0324 0.0724 32 0.0431 0.0997 0.0325 0.0725 33 0.0000 0.0000 0.0000 0.0000 From Table 3, it is found that the relationship between the active/reactive-power injections and the VIFs (, ) is almost linear with the increase of active/reactive power. The linear relationship between the active/reactive-power injections and modified electrical distance can be deduced from (4). Thus, the dynamic zonal partition is not needed. After the effective clustering partition, the two-stage zonal voltage regulation is realised. In the first stage of zonal voltage regulation, parameters in the advanced PSO are set as follows: , , , , , , , , , and . In the second stage, the voltage is rolling optimised around the identified working state according to (27). Node voltages under three scenarios are illustrated in Fig. 6. The red curve is the node voltages without PV integration, and the blue one is the data after PV integration without control. PV penetration is about 100% in the assumed scenarios, in which the PV is merged into each node. It is obvious that this causes the overvoltage problem. When the proposed two-stage control scheme is applied with the aforementioned parameters, the expected node voltage is set as 1.05 pu. Following the application of the two-stage control scheme with clustering partitioning, the green curve is obtained as the optimised result. It is demonstrated in Fig. 6 that the proposed method can deal with the overvoltage problem effectively. Fig. 6Open in figure viewerPowerPoint Voltage profiles under different scenarios of the IEEE 33-bus network 5.2 Practical case study system The network of Jinzhai County at China's Anhui province is studied for this research. An operational three-phase balanced 10 kV radial feeder in Jinzhai is chosen to be analysed in our study. There are 61 load nodes in this DG system with a total nominal load of 1.16 MW + j0.69 MVar along the feeder. Each node represents a low-voltage transformer area. Among them, there are 27 PV units installed, the nodes number and corresponding capacities are listed in Table 4. The PV penetration is up to 143%. The line type and length are listed in Table 5. There are overvoltage issues reported in the past operations under this situation. In the future, a total increase of 5.01 MW PV capacity will be installed at this feeder. Capacities of currently installed PV infrastructures and the transformers for future PV installation are shown in Fig. 7. Table 4. Current PV installation and capacity at the Jinzhai radial feeder PV location PV capacity, kW PV location PV capacity, kW 9 90 33 6 11 27 34 30 14 18 35 30 15 105 38 66 5 3 39 126 17 30 41 90 18 27 44 9 19 21 45 6 23 9 47 75 26 54 48 12 27 21 53 18 28 24 57 660 30 45 60 51 31 9 / / Table 5. Parameter of 10 kV racial feeder From To Line impedance, Ω Type Length, m 1 2 0.13212 + j1.386 SZ115000/35 — 2 3 0.085 + j0.04 LGT-35 100 3 4 0.6461 + j0.304 LGT-35 760.09 4 5 0.2019 + j0.095 LGT-35 237.58 5 6 0.2019 + j0.095 LGT-35 237.58 6 7 0.1978 + j0.093 LGT-35 232.73 7 8 1.7645 + j0.8304 LGT-35 2075.9 3 9 0.05183 + j0.0215 JKLGYJ-50 83.61
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