Stochastic Model Predictive Fault Tolerant Control Based on Conditional Value at Risk for Wind Energy Conversion System

Abstract

Abstract:Wind energy has been drawing considerable attention in recent years. However, due to the random nature of wind and high failure rate of wind energy conversion systems (WECSs), how to implement fault-tolerant WECS control is becoming a significant issue. This paper addresses the fault-tolerant control problem of a WECS with a probable actuator fault. A new stochastic model predictive control (SMPC) fault-tolerant controller with the Conditional Value at Risk (CVaR) objective function is proposed in this paper. First, the Markov jump linear model is used to describe the WECS dynamics, which are affected by many stochastic factors, like the wind. The Markov jump linear model can precisely model the random WECS properties. Second, the scenario-based SMPC is used as the controller to address the control problem of the WECS. With this controller, all the possible realizations of the disturbance in prediction horizon are enumerated by scenario trees so that an uncertain SMPC problem can be transformed into a deterministic model predictive control (MPC) problem. Finally, the CVaR object function is adopted to improve the fault-tolerant control performance of the SMPC controller. CVaR can provide a balance between the performance and random failure risks of the system. The Min-Max performance index is introduced to compare the fault-tolerant control performance with the proposed controller. The comparison results show that the proposed method has better fault-tolerant control performance.

Stochastic Hybrid Estimator Based Fault Detection and Isolation for Wind Energy Conversion Systems with Unknown Fault Inputs

“…. , T), then divided into different intervals according to the wind speed ( Figure 1) [5]. The state transition probability p ij of the wind speed is the probability that the state of wind speed is S i in time t (i.e., v t = S i ), and is S j in time t + 1 i.e., v t+1 = S j , t ∈ (0, T − 1):…”

“…The one-step Markov transition matrix of the wind speed can be estimated by a statistical method. In order to obtain the Markov chain transition matrix of the wind speed, the wind speed is discretized into , ∈ (0,1,2, … , ), then divided into different intervals according to the wind speed ( Figure 1) [5]. The state transition probability of the wind speed is the probability that the state of wind speed is in time (i. e. , = ), and is in time + 1 (i. e. , +1 = ), ∈ (0, − 1):…”

“…A tracking control algorithm with augmented state variables in model (4) [34] is implemented. It has been used in the previous studies [5], which can be described as follows:…”

“…However, in recent years, the accidents of wind turbines and power grid disturbances (such as voltage sag mitigation [2,3] to which wind energy conversion systems (WECSs) are highly sensitive) caused by loss of control in the design, manufacture, installation, operation and maintenance of intermediate links have threatened the safe operation of wind farms. The probability of failure of actuators and sensors is very high, and maintenance costs are enormous [4,5]. Therefore, fault detection and diagnosis of wind turbines have become a vital and stiff topic.…”

“…The WECS is a complex stochastic switching nonlinear dynamic system, which is integrating mechanisms, electricity and liquid. Therefore, the traditional control methods have difficulty in achieving satisfactory performance [5]. In these features of WECSs, the stochastic switching, which is caused by the randomness of the wind, is the most important feature of the WECS.…”