Event-Trigger Dynamic State Estimation for Practical WAMS Applications in Smart Grid

This chapter provides the detailed description on the constitution of wide-area measurement systems (WAMS) and its system topology, covering the synchronization of WAMS based on the phasor measurement unit (PMU) as well as the network communication system from the local sensor to the remote control center. Based on the clear understanding on WAMS, the critical dynamic state estimation (DSE) technique, which plays an important role in power system planning and control, is specified regarding the practical operating environment. Although the DSE technique is well developed in the field of control theory, few considerations are taken into the practical design for WAMS application. For the further DSE design, it is divided into the event triggered strategy as the prior stage and nonlinear filtering development as the post stage and both are further reviewed separately.

This chapter introduces the commonly used event triggered sampling strategies for linear system, which are divided into the deterministic one such as Send-on-Delta, innovation based condition, covariance based condition, and stochastic one, including stochastic open loop condition and stochastic innovational condition. The detailed comparison among them is further given regarding the critical characteristics for the further practical application. Based on this, the design procedure of event triggered linear filter will be used as the fundamental to design the event-triggered nonlinear counterpart. Finally, the intermittent Kalman filter design is given as an evaluation reference of filtering performance, which can also deal with the filtering problem for the communication reduction.

This chapter develops an event triggered cubature Kalman filter (ETCKF) to reduce the communication rate while ensuring the estimation accuracy. The ETCKF uses the innovation based event triggered sampling strategy in the sensor node to reduce the data transmission of measurements. Based on the developed nonlinear event triggered strategy, the cubature Kalman filter (CKF), using the third degree spherical-radial cubature rule, is further applied to ensure the estimation accuracy. Furthermore, the stochastic stability of ETCKF is analyzed using the stochastic Lyapunov stability lemma. The ETCKF is proven to be stochastically stable if a sufficient condition, which is composed of offline parameters, is satisfied. Moreover, the average communication rate of ETCKF is derived and only related to design parameters in innovation condition. The feasibility and performance of the developed filterings are verified based on the IEEE 39 bus system.

The WAMS application always requires the determined arrival rate due to the limited network capacity. To address this issue, this chapter designs an event triggered particle filter in order to satisfy the need of determined arrival rate. An arrival rate guaranteed event triggered strategy is firstly established by utilizing Monte Carlo method in order to approximate the prior conditional distribution of observations. Furthermore, an event triggered particle filter (ET-PF) filtering algorithm is developed by making full use of the information from the event triggered strategy to enhance the performance of estimation. The feasibility and performance of the developed filterings are verified based on the IEEE 39 bus system.

The constraints including both the communication and computation power at sensor nodes are widely encountered in the practical WAMS application. This chapter designs an event triggered heterogeneous nonlinear Kalman filter (ET-HNF). The ET-HNF utilizes the unified filtering of unscented transformation with particle filter theories so that the accuracy and the relief of communication burden can be guaranteed at the same time. An unscented transformation based event triggered UKF (ET-UKF) is firstly designed at the sensor node to supply the event triggered strategy. Furthermore, a Monte Carlo based filtering algorithm is designed in the estimation center to provide the accurate filtering results. The feasibility and performance of the developed filterings are verified based on the IEEE 39 bus system.

This chapter designs the stochastic event triggered robust cubature Kalman filter (SETRCKF) in order to deal with the non-Gaussian or unknown noises. Firstly, to overcome the deficiency of ETCKF in this chapter, the stochastic event triggered cubature Kalman filter (SETCKF) is developed based on the stochastic innovation based event triggered sampling strategy, which can maintain the Gaussian property of the conditional distribution of the system state. Based on SETCKF, the SETRCKF is further designed by using the moving-window estimation method and the adaptive method to estimate the measurement noise covariance matrices and the process noise covariance matrices. The Huber function is used to make SETCKF more robust. Moreover, the stochastic stabilities of these two proposed filters are analyzed by deriving the sufficient conditions regarding the stochastic stability of the filtering error. The feasibility and performance of the developed filterings are verified based on the IEEE 39 bus system.

Chapter 7 develops the stochastic event triggered cubature suboptimal filter (SETCF) in order to tackle the presence of packet dropout when using the stochastic innovation based event triggered sampling strategy. Firstly, the cubature suboptimal filter (CF) is designed for periodic sampling system by modeling the packet dropout as a Bernoulli process and inspired by the linear suboptimal filter. Based on CF and the stochastic innovation based event triggered sampling strategy, SETCF is developed to address the suboptimal nonlinear filtering for packet dropout condition. Moreover, the stochastic stability of the two proposed filters is analyzed by using the Lyapunov stability lemma. The feasibility and performance of the developed filterings are verified based on the IEEE 39 bus system.

Considering that CPS is vulnerable to cyber attack and has limited bandwidth, the event triggered cubature Kalman filters under these two typical attack types, which are the data tampering attack and the deviation control command forgery attack, are established in this chapter. Aiming at the data tampering attack problem, the anomaly data detector is designed by using the projection statistics method. After the attack is detected, the weight matrix is constructed by using the detection result to correct the measurement value in order to ensure the filtering accuracy, which completes the filter design. For the deviation control command forgery attack problem, the problem is transformed into the problem that the system is with unknown input at first. Based on this transformation, the Bayesian inference method is further used to derive the event triggered cubature Kalman filtering algorithm. The feasibility and performance of the developed filterings are verified based on the IEEE 39 bus system.

The dynamic state estimation has become more and more important as the fundamental and critical factor to guarantee the efficient and stable operation of WAMS in power system. However, with booming size of power grid, although PMUs facilitate the DSE to capture the dynamics of power system, the communication network is easily congested due to the PMU data transmission to the WAMS application in center.