Accurate estimation of the dynamic states of a synchronous machine (e.g., rotor's angle and speed) is essential in monitoring and controlling transient stability of a power system. It is well known that the covariance matrixes of process noise (Q) and measurement noise (R) have a significant impact on the Kalman filter's performance in estimating dynamic states. The conventional ad-hoc approaches for estimating the covariance matrixes are not adequate in achieving the best filtering performance. To address this problem, this paper proposes an adaptive filtering approach to adaptively estimate Q and R based on innovation and residual to improve the dynamic state estimation accuracy of the extended Kalman filter (EKF). It is shown through the simulation on the two-area model that the proposed estimation method is more robust against the initial errors in Q and R than the conventional method in estimating the dynamic states of a synchronous machine.Index Terms-Kalman filter, dynamic state estimation (DSE), innovation/residual-based adaptive estimation, process noise scaling, measurement noise matching.
Power system dynamic state estimation (DSE) remains an active research area. This is driven by the absence of accurate models, the increasing availability of fast-sampled, timesynchronized measurements, and the advances in the capability, scalability, and affordability of computing and communications. This paper discusses the advantages of DSE as compared to static state estimation, and the implementation differences between the two, including the measurement configuration, modeling framework and support software features. The important roles of DSE are discussed from modeling, monitoring and operation aspects for today's synchronous machine dominated systems and the future power electronics-interfaced generation systems. Several examples are presented to demonstrate the benefits of DSE on enhancing the operational robustness and resilience of 21st century power system through time critical applications. Future research directions are identified and discussed, paving This work was partially supported by US Department of Energy under Advanced Grid Modernization Program.
A solar panel tilt angle plays a great role in the performance of the solar panel which is either fixed at an optimal tilt angle or continuously adjusted using a solar tracking system. Solar tracking systems are not cost efficient especially for residential usage. On the other hand, a fixed tilt angle results in a huge loss of solar energy. One resort to solve this problem is to adjust the tilt angle a limited number of times. In this paper, a novel procedure is proposed to select the number of intervals and their durations by solving an optimisation problem. The proposed algorithm is consisted of four major steps. First, the solar radiation of the next year is predicted using historical data. Second, using a bee algorithm the optimal tilt angle of each interval is computed. Third, an optimisation problem is solved to get new periods for each interval. Finally, a stopping criterion is checked to decide whether the previous step should be repeated or the algorithm has been converged. The effectiveness of the proposed approach is studied at nine different locations across the US. The results show improvement of the solar power generation by using the optimal intervals.
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