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| Harmonic Source Location in the Partial Unobservable System Based on Interval Dynamic State Estimation |
| Shao Zhenguo1,2, Lin Hongzhou1,2, Chen Feixiong1,2, Lin Junjie1,2, Zhang Yan1,2 |
1. Fujian Smart Electrical Engineering Technology Research Center Fuzhou 350108 China;
2. College of Electrical Engineering and Automation Fuzhou University Fuzhou 350108 China |
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Abstract Due to the cost of measurement devices, it is impossible to directly monitor all nodes. Although some nodes can be indirectly monitored by optimizing the configuration of measurement devices, there may still be areas where harmonic information is unobservable in the system. At present, based on the sparse characteristics of harmonic source, the researches estimate harmonic state to locate the harmonic source in the partial unobservable system, but the accuracy of the results is easily affected by factors such as the position of the measurement devices. In addition, the current harmonic state estimation researches are all deterministic state estimation. In fact, due to changes in the field environment, operating status, and equipment aging, the line parameters may be deviated, making it difficult to calculate the accurate harmonic state for deterministic harmonic state estimation. To address the above shortcomings, a harmonic source location method based on interval dynamic state estimation is proposed for the partial unobservable system.
Firstly, the partial unobservable system is transformed into an equivalent observable system by using the multiport equivalence. Secondly, the interval Kalman filter algorithm, which is based on minimal upper bound of error covariance, is used for interval dynamic harmonic state estimation with considering the uncertainty of line parameters. Thirdly, the state variables with linear correlation between boundary nodes are screened out. Then, the linear regression at the midpoint of the interval is used to obtain the regression coefficients, which are applied to be matched with the nodes. The node with the highest matching degree is considered as the position of harmonic source in the unobservable region. Finally, the feasibility and accuracy of the proposed method are demonstrated by simulation and arithmetic case verification.
The simulation results show that, under the partial unobservable system, the traditional harmonic source location method based on compressed sensing incorrectly judges node 7 and node 16 as harmonic sources, but by using the proposed method to transform the system, the calculation results show that the harmonic sources are in the region between node 7 and node 16. Compared with the current solution method, the equivalent method is used to solve the partial unobservable system, which has better accuracy and stability. At the same time, the interval estimated values of equivalent harmonic current cover the actual values and track the dynamic change. Further, according to the harmonic source location strategy, the estimated values are divided into 6 windows, and its R2 is calculated for each window, where the results larger than 0.8 threshold are window 3 and window 6, and the corresponding R2 are 0.967 8 and 0.914 0 respectively. Through linear regression of the estimated values in the two windows, it can be seen that in the node matching degree curve a, the matching degree of node 9 is larger than that of other nodes, indicating that the main harmonic source is most likely to be located in node 9, so it is judged that the harmonic pollution is located at node 9, which is consistent with the setting. From the node matching degree curve b, it can be seen that in window 6, node 15 has the largest matching degree, indicating that the main harmonic source is the most likely to be located at node 15, so it is judged that harmonic pollution is located at node 15, which is also consistent with the setting.
The following conclusions can be drawn from the simulation analysis: (1) The proposed method using the multiport equivalence, can improve the accuracy of harmonic state estimation results, and identify the unobservable region containing harmonic source. (2) The Optimally bounded interval Kalman filter algorithm is used to estimate the dynamic harmonic state, which can characterize the uncertainty of the harmonic estimation state, and reflect the fluctuation characteristics of the harmonic state. (3) For the existence of harmonic sources in the unobservable region, this proposed method can accurately determine the position of harmonic sources in the unobservable region.
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Received: 23 December 2021
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2023, Vol. 38 
