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Theoretical analysis of measurement Island merging in observability analysis of power system state estimation

1 Introduction

network observability analysis refers to that in power system state estimation, the range of electric state can be calculated correctly by using the existing measurement configuration [1], and the quality of its algorithm will directly affect the operation performance of state estimation, and even determine whether the state estimation software can run smoothly. In some cases, the calculation of state estimation does not converge because the network observability analysis algorithm is wrong, and this happens from time to time. There are two main types of observability analysis algorithms: numerical algorithm [2,3] and topological algorithm [4,5]. Topological algorithm is favored by many power researchers because of its fast computing speed and its ability to overcome the weakness of numerical algorithm that is easily affected by rounding errors. Generally, there are two typical ways to deal with the observability analysis problem with the topological method. One is to consider the whole and add pseudo measurements where the measurements are insufficient in order to make it fully observable. However, these pseudo measurements are often key measurements, and the addition of pseudo measurements seriously affects the accuracy of state estimation. Another approach does not require full observability, but looks for observable islands in the whole, and makes state estimation on these observable islands, which can make the most effective use of the existing measurement configuration and make the estimation results more accurate. The general way to form an observable island is to use the branch tide flow measurement to form an initial branch measurement Island, and then use the bus injection measurement to expand or connect the observable island [4]. How to use the bus injection measurement to expand the observable island is the key to the success of the topology algorithm. If you want to get an interior trim with low emission characteristics. The existing methods usually have problems. One of the problems is that the important role of voltage amplitude measurement in the combination of measurement islands is ignored. In addition, when the measurement islands are interconnected into a complex shape, there is a lack of effective means to deal with the problem of how to use injection measurement to expand the observation islands. For example, the island ring criterion proposed in document [4] to deal with problems such as those shown in Figure 1 is not applicable in some special cases

in Figure 1, each circle represents the tidal flow measurement island formed by the branch tidal flow measurement, and the arrow represents the injection measurement. If the six islands are judged according to the roundabout criterion, five of the six islands are injected for measurement, and according to article [4], it is considered that the six islands can be merged. However, when analyzing the injection measurements of the four islands on the right, it is found that the injections at N3 and N4 are connected with D3 and D4, and have no contribution to connecting d5 and D6 islands, while the injection equation at N7 cannot solve the unknown quantities on d5 and D6 islands. Therefore, in fact, only d1~d4 islands can be merged, while d3~d6 islands cannot be merged. The reason is that the injection measurement may also have local redundancy and local insufficiency. For example, one of the four injection measurements N1, N2, N3 and N4 is redundant, while the boundary injection measurement of the four islands on the right is insufficient. If the six islands in Figure 1 are considered to be merged, the subsequent state estimation will not converge, It is difficult to find the reason for this non convergence. Therefore, the roundabout criteria proposed in document [4] cannot judge the consolidation of roundabouts as a whole. Based on the full analysis of the observable conditions of branch measurement islands, this paper theoretically analyzes the merging conditions between measurement islands. 2 theoretical analysis of merging between measuring islands

2.1 definitions of several basic concepts

(1) branch measuring Island: it is the initial measuring island formed by using the tidal flow measurement of roads operated by most dealers in zhianyang for more than 10 years. The isolated nodes without branch measurement and connected to other nodes can also be used as an initial branch measurement island to participate in the next step of consolidation judgment

(2) measurement Island: refers to the branch measurement island or the new island formed by combining the branch measurement islands by injection measurement

(3) live Island: refers to the measurement island with voltage amplitude measurement in the island. Each live island is an independent observable Island, and state estimation can be carried out separately

(4) suction Island: in a live Island, given the voltage phase angle of a node, the island is a suction Island, and the combination of measurement islands starts from the suction island

(5) dead Island: refers to the measurement island without voltage amplitude measurement in the island. Dead Island cannot be used as an independent observable island for state estimation

(6) inter Island branch: it is a branch connecting different measuring islands

(7) boundary node: the endpoint of the inter Island branch is called the boundary node

(8) degree of boundary node: the number of other measuring islands connected to the boundary node with inter Island branches

(9) degree 1 node: the boundary node with degree 1, that is, the node is only connected with another measurement island

(10) degree 2 node: the boundary node with degree 2. The degree 2 node is connected with the other two measurement islands by the inter Island branch

(11) to be merged: the connected network composed of boundary nodes and inter Island interconnection branches is called to be merged, and the whole network to be studied in this paper may contain one or more such to be merged

(12) to be merged after splitting: refers to several smaller networks obtained by splitting without injecting measurement nodes in the process of analysis

2.2 analysis of the merging principle between measuring islands

property 1[6]: given the voltage at one end of the branch and the power at one end of the branch, the voltage at the other end of the branch can be calculated, that is, the branch voltage of the branch can be estimated

property 2[6]: the branch voltage of the network is a group of independent variables, which can be used to calculate the voltage of all nodes, and then calculate the power flow of the whole branch

branch tidal flow measurement supports all nodes on the branch measurement island. There must be a group of branch measurement sets on the island to form a tree on the branch measurement island. Given the voltage of any node of the tree, all tree branch voltages can be obtained from property 1, and then all node voltages can be obtained from property 2. The accuracy of the sensor will be affected by the low accuracy of the resistance strain gauge inside the sensor, the poor anti-aging ability of the glue used to fix the strain gauge, and the poor material of the sensor. From the above analysis, it can be seen:

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