An optimized fuzzy sliding based active disturbance rejection control for simultaneous cyber‐attack tolerant and demand response participation program

Abstract

The simultaneous investigation of false data injection cyber-attack (FDICA) and demand response (DR) participation in smart power systems are dealt with in this paper. For this purpose, simultaneous and separate detection of FDICA and determination of the changes in the power consumption for participation in DR (P DR ) are necessary. To balance between generation and consumption, P DR must be equal to the load disturbances (LDs). Activedisturbance rejection control (ADRC) with the extended state observer (ESO) is implemented to detect FDICA and LDs. But, ESO only detects the sum of FDICA and LDs without the ability to separate them. Therefore, a nonlinear sliding mode observer (NSMO) is implemented to detach FDICA from LDs. In order to improve the NSMO estimation accuracy, the modified salp swarm algorithm (SSA) is implemented to design NSMO parameters. Moreover, to achieve better performance of ADRC, a fuzzy tuner is applied to the online tuning of controller parameters. The proposed optimized fuzzy sliding-based modified active-disturbance rejection control (FSADRC) is tested for load frequency control of the IEEE 9 bus standard test system and the 10 machines List of Symbols and Abbreviations: FDICA i t ð Þ, false data injection cyber-attack in the area i; LDs i , load disturbances in the area i; Δω i , frequency deviation in area i; Δω j , frequency deviation in area j; ΔP tie,ij , transferred power between areas i and j; β i , frequency bias in the area i; D i , equivalent damping in the area i; R, droop coefficient; T ij , the synchronizing power coefficient between areas i and j; H i , equivalent inertia constant in the area i; T t,ji jth, time constant of turbine in the area i; T G,ji jth, time constant of governor in the area i; R j,i jth, droop coefficient in the area i; ΔP c , input signals to the primary control loop; ΔP valve,i , deviation in the valve of the governor in the area i; ΔP mech,i , deviation in the mechanical power of the turbine in the area i; T G , governor time constant; T t , turbine time constant; ΔP tie,i , transferred power in the area i; A s,i , system matrix for the area i; A s,ij , relation matrix between states in the areas i and j; B s,i , known input matrix in the area i; B Ld , LDs matrix; C s,i , output matrix in the area i; u s,i , system inputs (the controller output) in the area i; y s,i , system output in the area i; x s,i , system states in the area i; x s,j , system states in the area j; A s , system matrix for a multi area AGC; B s , known input matrix for a multi area AGC; B Ld , LDs matrix for a multi area AGC; C s , output matrix for a multi area AGC; D AT , FDICA distribution matrix for a multi area AGC; P DR , changing in the power consumption due to the participation in DR program; P AGG , available DR power; B AGG , DR matrix; D ATÀi , FDICA distribution matrix for the area i; D AT_decom , FDICA distribution matrix after decomposition; ν s,n t ð Þ, discontinuous output error injection term to retain a sliding motion; δ s , a small positive number; X 1 k , ...

Adaptive barrier function‐based fractional‐order chattering‐free finite‐time control for uncertain chaotic systems

“…Despite the nonlinearity and uncertainty of the model in most real systems, the main step is to be careful in choosing a control method capable of applying to these types of systems [1–3]. Chaotic systems are of this class.…”