Abstract
In order to overcome the inaccurate proposal distribution along with the particle degeneracy problem of particle filter (PF), this paper proposed a state estimator based on cubature particle filter (CPF) and Markov chain Monte Carlo (MCMC) sampling, and applied it on unbalanced distribution system. The proposal distribution of PF is constructed by cubature Kalman filter (CKF). To preserve particle diversity, MCMC sampling is used to resample particles in CPF. Markov chain Monte Carlo cubature particle filter (MCMC-CPF) has both advantages of CKF and PF. MCMC-CPF is no longer limited by the types of systems and noises, and can effectively abate particle degeneracy, meanwhile, preserve particle diversity. Simulations results on the IEEE 33-node unbalanced distribution system proved the accuracy superiority of the MCMC-CPF compared with the CPF.
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Abbreviations
- \(k\)::
-
specific time point among the measurement period.
- \(w_{k}^{\alpha }\)::
-
importance weight at time \(k\) for particle \(\alpha\).
- \(\hat{\varvec{x}}_{k}\):
-
state estimation values at time \(k\).
- \(\hat{\varvec{x}}_{k|k - 1}\):
-
state prediction values at time \(k - 1\) for time \(k\).
- \(\hat{\varvec{x}}_{k}^{\alpha }\):
-
state estimation values at time \(k\) for particle \(\alpha\).
- \({\varvec{P}}_{k - 1}^{\alpha }\)::
-
covariance matrix at time \(k - 1\) for particle \(\alpha\).
- \(\chi_{i,k - 1}^{\alpha }\)::
-
cubature-points at time \(k - 1\) for particle \(\alpha\), cubature-point \(i\).
- \(\chi_{i,k|k - 1}^{\alpha }\)::
-
state prediction values at time \(k - 1\) for particle \(\alpha\), cubature-point \(i\).
- \(\hat{X}_{i,k|k - 1}^{\alpha }\)::
-
state prediction values at time \(k - 1\) for time \(k\), particle \(\alpha\).
- \(\hat{\varvec{P}}_{k|k - 1}^{\alpha }\):
-
prediction covariance matrix at time \(k - 1\) for time \(k\), particle \(\alpha\).
- \(\hat{\varvec{P}}_{k|k - 1}^{\alpha }\):
-
new covariance matrix at time \(k - 1\) for particle \(\alpha\).
- \(\chi_{i,k}^{\alpha }\):
-
estimation cubature-points at time \(k\) for particle \(\alpha\), cubature-point \(i\).
- \(Y_{i,k|k - 1}^{\alpha }\)::
-
theoretical measurement values at time \(k\) for particle \(\alpha\), cubature-point \(i\).
- \(Y_{k}\)::
-
actual measurement values at time \(k\).
- \(\hat{\varvec{P}}^{\alpha }_{{\varvec{YY,}k|k - 1}}\)::
-
covariance matrix of measurements at time \(k\).
- \(\hat{\varvec{P}}^{\alpha }_{{\varvec{XY,}k|k - 1}}\)::
-
covariance matrix of measurements and state values at time \(k\).
- \({\varvec{K}}_{k}\)::
-
Kalman gain at time \(k\).
- \(\hat{X}_{k}\):
-
state estimation values at time \(k\).
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Acknowledgement
This work was supposed by the National Natural Science Foundation of China under Grant 52077125.
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Wan, Y., Zhang, T., Zhang, W. (2023). Markov Chain Monte Carlo Cubature Particle Filter for Unbalanced Distribution System State Estimation. In: Zeng, P., Zhang, XP., Terzija, V., Ding, Y., Luo, Y. (eds) The 37th Annual Conference on Power System and Automation in Chinese Universities (CUS-EPSA). CUS-EPSA 2022. Lecture Notes in Electrical Engineering, vol 1030. Springer, Singapore. https://doi.org/10.1007/978-981-99-1439-5_56
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DOI: https://doi.org/10.1007/978-981-99-1439-5_56
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