Optimal scheduling for solar wind and pumped storage systems considering imbalance penalty

ABSTRACT

The safe and stable operation of the traditional power system has been tremendously affected by the large-scale integration of various renewable energy sources, which has tendency to deliver variable power. The coordinated operation of renewable energy sources has become a hot topic of research nowadays. Utilizing complementary characteristics of solar, wind, and pumped hydro, this paper presents a mixed-integer problem to find optimal scheduling of hydro plants to enhance the market profit. Considering the market schedule for the day ahead, a mathematical formulation has been developed for the operation of a hybrid system. For this problem, the pumping operation of the pumped storage plant has been done by using grid supply during low market price hours. The overall profit can be increased by using the stored energy when the market price is high. The mismatch in the demand and generation has been curtailed by including a penalty factor in the objective function. The results obtained depict reasonable improvement in terms of economic benefits when the coordinated operation suggested is utilized. The results show that the penalty cost has been reduced by a factor of $28\mathrm{\%}$, and profit earned during solar-wind alone was negative and whereas using the Solar-Wind-PSP system (SWPS) the profit has increased and was found to be approximately $29\mathrm{\%}$ of total revenue generated. The overall revenue saw an increase of nearly $38\mathrm{\%}$.

KEYWORDS:

• Solar
• Wind
• PSP
• Solar-Wind-PSP
• Optimal Scheduling
• Optimization
• Imbalance Penalty

Nomenclature

$\eta$	=	Conversion efficiency of SPV system
$\lambda (t)$	=	Market clearing price at $t^{th}hour$, $Rs/MWh$
$\nu$	=	Wind speed, m/s
${\nu }_r$	=	Rated wind Turbine speed, m/s
${\nu }_{in}$	=	Cut in wind Turbine speed, m/s
${\nu }_{out}$	=	Cut out wind Turbine speed, m/s
$\psi$	=	Penalty factor
$A$	=	Surface areas of SPV system, $m^2$
$E_{min}$,$E_{max}$	=	Reservoir stored energy limits, $MW$
$g_d$	=	Market deman, $MW$
$g_w$	=	Output power of wind generator, MW
$g_{pg}$	=	Power generated by PSP, $MW$
$g_{pg}^{min}$,$g_{pg}^{max}$	=	PSP power generated limits, $MW$
$g_{pp}$	=	Power consumed by PSP, $MW$
$g_{pp}^{min}$,$g_{pp}^{max}$	=	PSP power consumed limits, $MW$
$g_{PV}$	=	Solar PV (SPV) output, $kW$
$I_b$	=	Beam Solar radiation, $kWh/m^2$
$I_d$	=	Diffuse Solar radiation, $kWh/m^2$
$I_T$	=	Solar radiation on a tilted surface, $kWh/m^2$
$P_{rated}$	=	Rated output power of wind generator, m/s
$PS{P}_r(t)$	=	PSP revenue during generating mode at $t^{th}hour$, $Rs$
$P{V}_r(t)$	=	SPV revenue during $t^{th}hour$, $Rs$
$R_{Loss}(t)$	=	Revenue loss during $t^{th}hour$, $Rs$
$s(t)$,$sp(t)$	=	PSP’s control variable
$W_r(t)$	=	Wind revenue during $t^{th}hour$, $Rs$

Acknowledgments

The first author expresses sincere thanks to Department of Hydro and Renewable Energy and Quality Improvement program (QIP) Centre, IIT, Roorkee, India for providing research facilities and All India council for Technical Education (AICTE), Government of India for providing financial assistance in the form of research fellowship. He also expresses heartedly gratitude to National Institute Of Technology Hamirpur, Himachal Pradesh, India, for financially sponsoring him to pursue doctoral study and National Institute of Wind Energy, Chennai for providing the data for solar and wind.

Additional information

Funding

This work was supported by the All India Council for Technical Education [Financial assistance as research fellowship].

Notes on contributors

Rajesh Kumar

Rajesh Kumar received B. Tech. Degree in Electrical Engineering National Institute of Technology Hamirpur, India, M.E Degree in Power Systems from Punjab Engineering College, Chandigarh and is currently pursuing Ph.D. from IIT Roorkee. His research interests include Power system and Renewable energy.

Arun Kumar

Arun Kumar is Professor at Department of Hydro and Renewable Energy (formerly AHEC), IIT Roorkee and serving since 1981. He graduated from IIT Roorkee, post-graduated from the Indian Institute of Science, Bangalore, PG diploma in Hydropower development from NTNU Norway and Ph.D. from IIT Roorkee. His contribution in the field of small scale hydropower and environmental Management of Rivers and lakes is well recognized both within India as well as internationally. He has been awarded MNRE Chair Professor (Renewable Energy) in July 2013 and again in April 2015 by IIT Roorkee. He served as an independent director on the Board of NHPC Ltd, Govt. of India PSU during 2015-2019. He has over 38 years experience of research, development, extension, and teaching experience in the area of small hydropower and other renewable energy sources.