Stochastic wind energy integrated multi source power system control via a novel model predictive controller based on Harris Hawks optimization

ABSTRACT

Combined voltage and frequency control is a critical control problem of modern power system to avoid blackouts. This paper discusses the simultaneous voltage and frequency control for an interconnected multi-source multi-area power system having two areas of equal generating capacity, each containing thermal, diesel, and wind units. A centralized model predictive controller (MPC) scheme is suggested to minimize voltage and frequency fluctuations. For effective control, a normalized performance criterion has been considered, and recently appeared Harris hawks optimization (HHO) algorithm has been integrated for the optimal tuning of MPC weights for the first time. The effectiveness of the proposed MPC-HHO controller has been verified after comparing its transient response performance indices with that of various existing controllers available in the literature. Quantitatively, the proposed controller yields a minimum performance index value, i.e. 0.000741, and it has been observed that the proposed MPC-HHO controlled system has 79.28%, 68.89%, 77.19%, and 81.96% better settling time for frequency deviation in area 1 when compared with PIλDF-LSA, FOIDF-LSA, MFO-FOPID, and PID-FA controllers, respectively. Further, the stochasticity in wind power generation has been considered with the help of Monte Carlo simulation of Autoregressive Integrated Moving Average model (ARIMA) model for practical wind speed data from National Renewable Energy Laboratory. The stability of the proposed controller has been verified using eigenvalues and Bode plot analysis, where the MPC-HHO controlled system was having more gain and phase margin values as compared to the PID controlled system. Furthermore, the robustness of the approach has been successfully evaluated by considering the nonlinearities, and parameter sensitivity analysis has been conducted after varying the parameters of voltage and frequency control loops and reevaluating the transient performance of the controlled system. Besides this, a separate case study wherein the most recent concepts like Electric Vehicle (EV) integration with grid and Virtual Inertia (VI) have been applied in addition to the proposed controller to provide auxiliary control support in the system. It has been validated that EV-VI coordinated MPC-HHO controller provides quality transient response under different scenarios including reduced inertia and stochastic load variations.

KEYWORDS:

• Automatic Voltage Control
• meta-heuristic optimization algorithm
• load frequency control
• model predictive controller
• wind power plant

Acknowledgment

The study was financially supported by Council of Scientific and Industrial research (CSIR), New Delhi, India underneath Human Resources Development Group project grant 22(0815)/19/EMR-II accredited to second and fourth author.

Disclosure statement

No potential conflict of interest was reported by the author(s)

Nomenclature

T	=	Simulation time
$T_{w1i},T_{w2i}$	=	Time constants of hydraulic pitch actuator model in area i
$K_{w1i}$	=	Gain-1 of hydraulic pitch actuator in area i
$K_{w2i}$	=	Gain-2 of hydraulic pitch actuator in area i
$G_{Bi}$	=	Gain of blade characteristics of wind turbine in area i
$K_{dii}$	=	Diesel power generator gain in ith area
$T_{gi}$	=	Time constant of the thermal governor model in area i
$T_{ti}$	=	Thermal plant turbine time constant in ith area
$T_{ri}$	=	Re-heat turbine time constant in area i
$K_{ri}$	=	Gain of the re-heat turbine in area i
$T_{12}$	=	Tie-line coefficient
$B_i$	=	Frequency-bias coefficient in ith area
$R_i$	=	Governor droop characteristic in ith area
$D_i$	=	Load change with respect to frequency in area i
$T_{pi}$	=	Time-constant of load model = $2H_i/f{D}_i$
$\mathrm{\Delta }{T}_{p12}$	=	Incremental tie-line power error between area 1 and 2
$H_i$	=	Load inertia constant in area i
$\mathrm{\Delta }{f}_i$	=	Incremental frequency deviation in ith area
$V_i$	=	Voltage in ith area
$\mathrm{\Delta }{V}_i$	=	Voltage deviation of ith area
$V_{ref}$	=	Reference voltage in both areas
$AC{E}_i$	=	Area control error in ith area
$f$	=	Nominal frequency of the system
$K_{Ai}$	=	Amplifier gain in ith area
$T_{Ai}$	=	Amplifier time constant of ith area
$K_{ei}$	=	Gain of exciter in ith area
$T_{ei}$	=	Time constant of exciter in ith area
$K_{fi}$	=	Field circuit gain in ith area
$T_{fi}$	=	Time constant of field circuit in ith area
$K_{si}$	=	Sensor gain in area i
$T_{si}$	=	Sensor time constant in area i
$K_1$$K_2$, $K_3$$K_4$	=	Coupling constants between AVR and LFC loops
$P_s$	=	Synchronizing power coefficient
$K_{VI}$	=	Virtual Inertia gain value
$T_{VI}$	=	Virtual Inertia time-constant value
$K_{EVi}$	=	Gain of EV in area i
$T_{EVi}$	=	EV time-constant in ith area
$R_{EVi}$	=	Regulation coefficient of EV in area i

Additional information

Funding

The work was supported by the Council of Scientific and Industrial research (CSIR), New Delhi, India [22(0815)/19/EMR-II].