A probabilistic approach for power system injection shift factor estimation

• A novel probabilistic estimation approach for ISF is proposed.
• Only the measurement data are necessary for the proposed approach.
• There is no need to set a reference node in the estimation process.
• The estimation results reflect the probability distribution information of the ISFs.
• The estimated ISFs can be used to calculate probabilistic active branch power flow.

The data-based power system injection shift factor (ISF) estimation approaches can automatically adapt to the changes of power system operating situation and provide more accurate ISF estimation results. However, because of the linearization assumption and the measurement errors, the data-based ISF estimation approaches still have significant estimation errors, which may degenerate the usefulness of the estimated ISFs. For this reason, predicting the deviation of the ISF estimation error is necessary for developing robust power system operational analysis and control approaches. In this paper, a novel probabilistic approach for ISF estimation is proposed. Using the samples obtained from the online measurements, the posterior probability distribution estimation model of ISFs is established according to the Bayesian linear regression (BLR) rules. Additionally, a numerical method named Gibbs sampling is adopted to solve the posterior probability distribution model and to avoid complicated analytical derivation. The proposed approach has the following distinguished features: (1) The proposed approach makes use of the measurement data, rather than the element parameters, to estimate the ISFs. Therefore, the estimation errors resulting from possible inaccurate element parameters are avoided, and the approach can adapt to the system topology and operating point changes automatically; (2) It is not necessary to set a reference node in the estimation process, and this avoids the estimation error from the inconsistency of the reference node setting between the theoretical calculation and the practical operational situation; (3) The approach can provide probabilistic ISF estimation results, which can quantify the degree of ISF deviation caused by the linearization assumption and the random measurement errors. Tests on a real transmission network in central China demonstrate the feasibility and effectiveness of the proposed approach.