A robust MPC design concerning on battery variables for frequency regulation and saving battery life collaborating with demand response for a multi-source integrated power system

Abstract

The present work has taken a challenge to design a model predictive controller (MPC) for automatic load frequency control (ALFC) of two-area, wind-integrated thermal power system equipped with battery energy storage system (BESS) and demand response (DR) for frequency regulation task. Primarily, the incremental BESS model employs a new state of charge (SOC)-based strategy to regulate the power from battery for saving battery life. Then, DR, along with the SOC-based BESS, is employed in ALFC for frequency regulation. A modified state space model of MPC incorporating all BESS variables is developed and employed in ALFC of the studied power system. The performance of the designed MPC is examined for inertia issues arising from wind in the conventional two-area power system. Furthermore, the capability of BESS for frequency regulation and effect on the life of BESS with the proposed control strategy are measured through MPC-based ALFC and results are compared with system performance when integral controller in ALFC and inertia controller from wind are present. In addition to DR and BESS in ALFC, double-fed induction generator-based proportional derivative (PD) inertia controller also contributes in the power system for frequency support from wind energy section to avoid inertia issues. So, all the controllers of the test power system such as integral controller in ALFC and PD controller in wind are tuned concurrently for smooth frequency control. However, performance of MPC is tested for smooth frequency regulation by tuning PD controller gain of wind only while keeping MPC gain parameters as available in the literature. Particle swarm optimization is used to tune the integral controller gain of ALFC for the studied power system to compare the results with MPC-based ALFC. A transfer function model of wind-integrated two-area thermal power system is taken into consideration in the present study to verify the effectiveness of the battery variable concerning MPC design for ALFC collaborating with DR for smooth frequency control and provide safe battery life. Finally, results confirm the effectiveness of the designed MPC-based ALFC, collaborating with DR- and SOC-based incremental BESS through various case studies.

Appendix A

BESS parameters
$Battery \, voltages = 1755 - 2925V \, DC$	$C_{bp} = 52597F$	$K_{BESS} = 100kv/pu.mw$
$R_{bs} = 0.013\Omega$	$X_{CO} = 0.0274\Omega$	$\alpha^{ \circ } = 15^{ \circ }$
$R_{bt} = 0.0167\Omega$	$I_{BESS}^{0} = {0}{\text{.02213}}$ p.u	$\begin{gathered} Base \, voltage = 10KV, \hfill \\ \, Base \, current = 200KA \hfill \\ \end{gathered}$
$R_{b} = 0.001\Omega$	$R_{bp} = 10k\Omega$	$C = 40MWh$
$C_{b} = 1F$	$T_{BESS} = 0.026\sec$	$SOC_{ref} = 0.5$

Power system parameters $(Base \, power \, = 2000MW)$
Area no	KP (Hz/pu.MW)	K r	Tr (sec)	Tp (sec.)	f (Hz)	Tg(sec)	Tt (sec)	R (Hz/pu.MW)	H	D (pu.MW/Hz)	B (pu.MW/Hz)
1	120	0.5	10	20	60	0.08	0.3	3	4.7104	8.33 × 10–3	0.3417
2	120	0.5	10	20	60	0.08	0.3	3	4.7104	8.33 × 10–3	0.3417

MPC Parameters:prediction horizon = 10,control horizon = 2,weights on manipulated variables = 0.8,weights on manipulated variable rates = 0.10, weight on output signals = 0.10

PSO Parameter:number of particles = 20,maximum inertia weight = 0.9,minimum inertia weight = 0.4,acceleration factor (c1& c2 are): c1 = 2; c2 = 2,maximum number of steps = 20,dimension of the problem = 3