A Sollin Algorithm Based Strategy in Enabling Power System Island Recognition with Distributed Gener

www.ijape.org International Journal of Automation and Power Engineering (IJAPE) Volume 3 Issue 1, January 2014 DOI: 10.14355/ijape.2014.0301.12

A Sollin Algorithm Based Strategy in Enabling Power System Island Recognition with Distributed Generations Lin Lu*1, Lingzhu Zhang2 School of Electrical Engineering and Information, Sichuan University School of Electrical Engineering and Information, Sichuan University

1 2

Chengdu, China *1

lvlin@scu.edu.cn; 2emmazlz1988@gmail.com

Abstract Considering a system contains DGs and loads which are connected to the distribution network using feeders, which can be simplified according to the concept of T node. Then based on bus‐nodes and feeders, a minimum tree can be formed. Finally in the premise of guarantee that the power balances in the island, the loads can be added to the tree in ascending order based on their weights. In terms of separating isolated islands, Sollin algorithm has been involved due to its fast convergence. The experimental results indicated that the proposed strategy is suitable for the distribution network with various voltages, moreover, it works perfectly for the distribution network with same voltage.

Keywords Distributed Generation; T Node; Feeder; Island Separation; Minimum Spanning Tree; Sollin Algorithm

Introduction Distributed generation can work in both independent way and grid‐connected way. When accidents occur, distributed generation can work in island mode by supplying power for the downstream load independently, which increases the reliability of power supply. Therefore, achieving the division of island separation is the topic of this paper.

At present, many researchers have made wide and deep studies on island separation. According to the premier standards for distributed generation, when a fault or disturbance occurs in power system, DG should quit from system rapidly. So to some extent, it affects the benefits of distributed generation companies while also reducing the utilization of distributed generation. This point militates against the development of distributed generation technologies.

The scheduled islanding operation can improve the reliability of the power supply system effectively.

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However, the planned islanding operation may deviate.

Zhao Jingjing et al. presented an algorithm on DG island separation by forming the power circle diagram with the radius of rated capacity. However, the algorithm has its own limitation such as high switch frequency and only suits for the DG with small capacity in distribution system. Dong Xiao‐feng et al. focused on involving minimum spanning tree in solving the problem of island separation. However, the disadvantage is that the algorithm cannot adapt to the distribution network system which consists of DGs and load connected with feeders and node T. Su Lin et al. researched the island operation modes and the control strategies from the perspective of the micro grid. They regarded all controllable loads as uncontrollable ones. Consequently, our work adopted the advantages of related researches by considering both controllable load and uncontrollable loadby significantly simplifying the system that contains DGs and loads connected to the distribution network using feeder according to the concept of T node. Based on the experimental results, the algorithm can overcome the defects in previous paper while also maximizing the utilization of distributed generation.

Tree Model of Distribution System with DGs Access Forms of DGs and Load Access forms of DGs have two ways: one is connected through the bus as DG1 shown in Fig. 2; while the other is connected through the feeders as DG2 shown in Fig. 2.

There are two kinds of load access ways in distributed network. The first is load directly connecting to the bus, as shown in Fig. 2. The load L1 L2 is connected to

International Journal of Automation and Power Engineering (IJAPE) Volume 3 Issue 1, January 2014 www.ijape.org

load can be divided into two parts including controllable and uncontrollable load. The model can be restored to the original condition after the end of island separation. The circuit is shown in Fig. 2. The simplified model of the circuit is shown in Fig. 3 in which the load and switches are omitted.

bus 2 while the load L3 L4 is connected to bus 3 directly.

The second access way is load connected to the feeders ,which forms the T node, as shown in Fig. 2; while the load L5 L6 L9 L10 is connected to the feeders, which forms the T node. According to the work done

by Wang xu‐dong, load is divided into controllable and uncontrollable one.

Spanning Tree Model Distribution systems are usually designed with closed‐ loop structure and operated with open‐loop structure.

A radial network is configured during the runtime, and the distribution system is similar to a forest with the power supply being the root node. Thus the distribution network with DGs can be simplified to the rooted tree T(V, E, W)with node‐weight and edge‐ weight where T represents the tree, V represents the node, E represents the edge, W represents the weight.

Therefore the downstream distribution network of failures can be simplified to the tree model below:

Busi

Wi

FIG.3 CONNECED GRAPH OFDISTRIBUTION SYSTEM WITH DGS

It can be seen from the graph that all the DGs and load are connected with the buses 2 3 4 5 or feeders F1 F2 F3.

So if the power supply path which is equivalent to the spanning tree could be connected, all the DGs and load can be formed to a connected graph. Therefore, the problem is transformed into searching the spanning tree of the graph.

The Determination of Connected Graph Edge Weight In our search, a collection of nodes V={vi | 0≤i≤n‐1,n ≥0}contains DG nodes, bus nodes and load nodes. vi represents the value of node i. The value of DG and load node are nonnegative real number representing the active power produced and the active power absorbed respectively. The bus nodes have no numerical significance. The set of edges E={eij | 0≤i,j≤ n‐1,i ≠ j }has mainly three following types: the edge between buses (feeders) and DGs, the edge between buses, and the edge between the bus (feeders) and load. In the set of weight W={wij | 0≤i,j≤n‐1,i≠j }, the value of wij represents the weight of edge eij. How to define the weights is described below.

FIG. 1 THE FORMATION OF THE “T” NODE

The weight of edge between buses (feeders) and DGs is set to be 0. In order to form the island, DGs were merged into island firstly. The algorithm determining the weight of edges connected with the buses depends on if there are feeders:

FIG. 2 DISTRIBUTION SYSTEM WITH DGS

1). Processing on node load: treat node load as T node, create one line load controlled by a switch from the power on the node load, thus a T node is formed. As shown in Fig. 1, P1 P2 P3 represent the power on node load.

1). The value is 0 for the cases that there are feeders with the access to load.

2). Turn the circuit which contains T node load into graph shown in Fig. 3: The bus can be equivalent to node, the load and feeders can be equivalent to branches and trunks. According to previous paper, the

2). Second, if there were transformers without feeders, the value is 0.1. If there are no transformers, 0.5 is set for two winding transformer because of losses. And

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0.25 is set for three‐coil transformers in virtue of its higher efficient use.

The principle to determine the weight of edges connecting the buses with feeders is to guarantee the priority of the small load for reducing the operating times. So the weight is determined by two factors: load power and the levels of importance. If the two values obtained by formula (1) are equal, the importance of load should be taken into account by formula (1) and (2). wij   Pij  s j (1) 10 Pij  Pj (2) Pmax  Pmin

Where wij represents the weight of the edge connected the feeders with load: α, β represent the load power and a share of the importance of load, respectively. In this paper α=β=1, Sj represents the importance index of node load j, Sj={0,1,2}. The smaller the value is, the more important the load is, Pmax represents the maximum power needed for DG island separation, Pmin represents the minimum power required for DG island separation, Pj represents power of load node j, Pij represents the standardized power which is processed to 0~10 of load node j.

active power in the island without considering the reactive power, which can be adjusted by compensation condenser instruments with load. The second constraint condition is the voltage of node that should not exceed specified limits in 0.95~1.05 of normal voltage. The third constraint condition is the current of lines in the island that should not exceed specified limits.

The Sollin Algorithm Solving the Minimum Spanning Tree The aim is to obtain the tree with the minimum sum of weight in the graph from the equation (3). This paper has presented the sollin algorithm for solving the minimum spanning tree. Specifications are as follows: The pseudo code of the data selection Algorithm: Data Selection 1. Define Ni={i| i=0,1,2……n‐1}to any node i∈N，T* =φ 2. If there are n‐1 arcs in T*, T* is the minimum spanning tree of T. If not, calculate the minimum arc of the edge‐cut[Nk，/Nk] to the collection sub‐tree Nk of nodes in T*, which is W(ek*)= {minW(e)|e∈[Nk, /Nk]}, ek*=(ik,jk), ik∈Nk,jk∈/Nk, then continue.

3. To the collection sub‐tree Nk of nodes in T*and the minimum arc ek*=（ik,jk）, ik∈Nk,jk∈/Nk, Merge this subtree and the subtree contains jk. Take the smaller side of i+j if exists the same minimum arc. And T*= T*∪{(ik,jk)} , then continues the first step.

The Mathematical Model and Algorithm

Strategies in Island Separation

The Mathematical Model of Island Separation

The first step is to solve a minimum spanning tree with branch. The second step combines the DG to the minimum spanning tree. Under the power balance condition, the load is merged as leaf node with ascending counts of weight into the minimum spanning tree. The process is as follows:

On amount of the model of the graphs, the mathematical model of island separation is proposed: min



Wij

(i , j )T *

  PGi   Pj  0 (3) iT * jT *  s.t. Vmin  V j  Vmax  max  I ij  I ij  The objective function is to obtain the minimal spanning tree which is to calculate the minimal weight, T* represents the minimal spanning tree obtained. PGi represents the active power of DGs of the minimal spanning tree. Pj represents the active power of load of the minimal spanning tree. Local compensation is adopted as the reactive power that is not applicable at transmitting over long distances without considering the reactive power. Vj represents the normal voltage of node j, Vmin Vmax represents the voltage lower allowable limit and voltage upper l allowable limit of node j, Iij Iijmax represents the normal allowable current and the maximum allowable current of line eij. The first constraint condition is to guarantee the balance of

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1). Treat the bus as the node of the tree, adopt the sollin algorithm to get the minimum spanning tree T* (V*, E*), put the feeders in the set of edges E*, according to Fig. 2, join feeders connecting between the buses in the tree with a weight of 0, join feeders connecting only one bus in the tree directly in this paper. Where V* represents the bus node, E* represents the edge and feeder connecting between the buses.

2). Join all the DGs which need island separation in the minimum spanning tree T* (V*, E*). Add all the power of DGs in the island by calculating P   PGi , V* iT *

contains the bus nodes and DGs nodes, E* contains the edge connected between the buses and the edge connecting the bus with feeders.

3). Arrange the load in ascending counts of weight, if there is the same weight, the degree of importance is

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Results and Discussions

considered. Join the tree T* (V*, E*) from the minimum weight in sequence one at a time, calculate P=P‐PLi. PLi represents the power of load Li. If the P is greater than 0, continue joining the next load until P is less than or equal to 0 or after all the loads are searched.

The 69‐buses distribution system integrated with DGs is shown in Fig. 5. Node 49, 50 contain 40% controllable load. The remaining parameters are the same as the work done by DONG Xiaofeng. The island can be obtained through the island separation in our work by switching off all the load of node 61 and the controllable load of node 49 and 50 restored. The advantage is only one island generated with minimum operations of switch and one load cut‐off. The final island separation is shown in Fig. 5.

4). Island optimization: optimize the minimum spanning tree T* (V*, E*), remove the bus node or feeders unconnected the load, calculate the power flow to verify if it meets the constraint condition. The minimum spanning tree is shown in Fig. 4.

Busi

Wi

The optimal island separation strategy of the typical distribution network system which consists of DGs from previous paper is shown in Fig. 6. The power load connecting the switches 6, 7, 23, 44, 65, 59, 72 is the first kind of load, while the power load connecting the switches 5 , 21 , 33 , 70 is the third kind of load, and the rest is the second kind of load. Nearly one‐third of the load connecting the switch 21 is controllable load. One eighth of the load connecting the switch 80 is also controllable load. The final island after the power flow calculation is shown in Fig. 6: switching off the load of 52, 16, 70, 5, the controllable load of 21 and 80 can be recovered.

FIG. 4 THE CHART OF MINIMUM SPANNING TREE

FIG.5 SIXTY NINE‐BUSES DISTRIBUTION SYSTEM INTEGRATED WITH DGS 1

Bus1 2

Bus14 1.51

1.32 0.73

5

110kV

25

28

67

48 Bus4

Bus5 68

49

Bus15

4

6

9 29 30 35kV Bus6 Bus7 31 32 33 11

8

7 10 10kV

2

12

0.9

Bus10

15Bus 36 17

18 19

1.33 1.21 20

21 22 23 24 2.5

0.61 0.83 42 Bus21

Bus12

59

60 61

1.4

64

1

78 Bus19

79

62

80

81 82

0.77

10kV

1.6 Bus23 84

85

0.65 3

71

72 10kV

58

66

65

0.71 1.34

74 Bus9 75

77

2

0.55 63 Bus22

1.1 1.2

76 Bus13

2

55 56

2

43 44 45

0.74 0.5

73

54

57 37 Bus 1810kV

38 39 40 41

2

Bus8

35kV 35kV

53

1.3

Bus11

10kV

Bus20

1.09 0.91

52

35

14

51

50

0.7

34

13

Bus16 10kV16 17

70

69

35kV

1.11

46 47

27

Bus3

Bus2

3

26

0.97

83

86

2 0.72

FIG.6 ISLAND PARTITION OF SCHEME OF THE DISTRIBUTION SYSTEM WITH DGS AT REF.

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In comparison with the work done by Dong Xiaofeng:

islanding strategies of distributed generation based on

1). The algorithm proposed in this paper adapts to the distribution network system which consists of DGs and load under various voltage classes or the same voltage class. The computational example in Fig. 5 does not adapt in previous paper.

rooted tree[J]. Proceedings of the CSEE, 2008，28(25): 62‐

2). The sollin algorithm organizes all the nodes in an independent tree, and the sub‐trees is joined to an entire tree according to the optimum condition for edge cut, which shortens the searching time dramatically. The previous work proposed a distributed islanding algorithm based on prim algorithm, and the idea gradually expands the tree with node by node according to the optimum condition for edge cut, which cannot adapt to the large distribution network of multiple nodes obviously.

3). The algorithm generating the spanning tree in previous work needs three times calculation based on Prim algorithm. However, the algorithm in our work needs only one‐time calculation based on sollin algorithm on account of getting only one spanning tree of bus node.

4). The restorability power in previous work is 18.38 MW, while the restorability power in our work is 18.42 MW by involving controllable load and uncontrollable load, which improves the efficiency of DGs. Conclusions This paper proposed an algorithm in which the bus is treated as node, and feeders as trunk to obtain the minimum spanning tree. Under the conditions to ensure power balance, the algorithm added the load based on their weight to the minimum in ascending order. Then it checked the power flow to guarantee that the line parameters did not exceed any specified limit. The experimental results showed that the algorithm has a series of advantages including easy faulty recovery, low frequency of switch operation, high utilization of DGs, easy adaption to arbitrary scale of distribution network.

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Lin Lu, Professor of School of Electrical Engineering and Information, Sichuan University. His researches mainly focus on the analysis and control of power system and automation of distribution network. Heʹs been sponsored by National Natural Science Foundation of China, and with his team a number of papers indexed by SCI and EI have been published.

Lingzhu Zhang, Master student of School of Electrical Engineering and Information, Sichuan University. Her researches mainly focus on the analysis and control of power system.