phase permanent magnet synchronous motor. The algorithm has been employed successfully in this paper in the dynamic state estimation of the highly non ...
ASIAN JOURNAL OF ENGINEERING, SCIENCES & TECHNOLOGY, VOL. 4, ISSUE 1
MARCH 2014
State Space Least Mean Fourth Algorithm for State Estimation of Synchronous Motor Arif Ahmed, Ubaid M. Al-Saggaf, Muhammad Moinuddin
adaptive filtering algorithms are highly computationally complex and requires more number of computations per iterations. Moreover, they don’t always have the upper hand as will be presented in this paper. In this paper we deal with the state estimation of a permanent magnet synchronous motor. For effective control of the motor it is essential to know as best representation as possible of the true states of the motor. Which demands effective and efficient estimation algorithms giving us the cost benefit of not having sensors. The synchronous motor is a highly non linear system and it is common practise to use non linear Kalman filtering algorithms like Extended Kalman filter (EKF), and Unscented Kalman filter (UKF) ([12],[13],[14],etc.). We work on the the proposed state space least mean square (SSLMS) and the state space normalized least mean square (SSNLMS) by Malik et al. ([4],[5]) which have only been applied to linear time varying systems to derive and propose the state space least mean fourth (SSLMF) algorithm. In this paper we propose and implement the SSLMF algorithm for non linear synchronous motor state estimation and compare it’s performance with the EKF. The proposed algorithm is superior due to the fact that it requires lesser computations per iteration compared to the existing non linear model based algorithms. The performance of the algorithms in presence of Gaussian noise is investigated.
Abstract—The most common estimation algorithms used today for power system static and dynamic state estimation are the variants of Kalman filter (KF) like Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). These model based estimation algorithms are well known for their accuracies. However, it is a well known fact that EKF requires fine tuning and good initial guess for optimum performance. Moreover, these adaptive filters generally employed for estimation purposes require high computational power when it comes to real time estimation. Therefore, in this paper we propose a computationally light yet effective estimation algorithm based on state space model which have not yet been applied to the problem of power system dynamic state estimation. We derive and propose the use of state space least mean fourth algorithm for the purpose of dynamic state estimation considering the problem of a two phase permanent magnet synchronous motor. The algorithm has been employed successfully in this paper in the dynamic state estimation of the highly non linear synchronous motor. The problem has been investigated in the presence of Gaussian noise to show the effectiveness of the algorithm. Moreover, the algorithm is also compared with the performance of the EKF. Index Terms—SSLMF, State Space Least Mean Fourth, Power System Dynamic State Estimation, Synchronous Motor Dynamic State Estimation.
I. I NTRODUCTION DAPTIVE filters are now widespread due to advancements in computational speed, complexity and power efficiency of digital processors. An adaptive filter adapts by self adjusting filter parameters according to the optimization algorithm utilized ([1],[2]). Two of the most widely used adaptive filtering algorithms are the least mean squares (LMS) algorithm ([1],[2],[3]) and the recursive least squares (RLS) algorithm ([1],[2],[3]). The state space (SS) version of these algorithms have been developed and presented by Malik et al. ([4],[5],[6],[7]) along with different analyses.
A
The paper is organized as such, Section II of the paper introduces the SS model along with the two phase permanent magnet synchronous magnet model. Then in Section III the proposed SSLMF algorithm is derived following Section IV presenting simulation results and discussion of the comparison of the proposed algorithm. And finally we conclude the paper in Section V. II. S TATE -S PACE M ODEL We begin by defining the general state-space model of a linear time varying system.
One of the important uses of adaptive filtering algorithms is in the area of power systems. State estimation has become an essential part of power system ([8],[9],[10],etc.) which requires the use of adaptive filtering algorithms like the Kalman filter, its variants and other algorithms ([11],[12],[13],etc.). However, these model based non linear
x[k + 1] = A[k]x[k] + B[k]u[k] + w[k], y[k] = C[k]x[k] + D[k]u[k] + v[k]
(1a) (1b)
where x ∈
