Optimal charging of electric vehicles for cost minimization in re-configurable active distribution network considering conservation voltage reduction

ABSTRACT

This paper presents a coordinated plug-in electric vehicle (PEV) charging scheme in the presence of conservation voltage reduction (CVR) with a possibility of network re-configuration in a half-hourly based tariff environment. The information of the arrived PEVs in time slot “t” are gathered in a centralized manner, including initial and desired state of charge (SOC), rating of PEV charger, and arrival and departure times. In addition, the load forecasted data of all the nodes are also collected. A linear programming (LP) based intelligent charging framework is developed whereby an optimal global solution for EV charging is obtained that tends to minimize the charging cost, and the schedule is dispatched to all the PEVs. At first, PEV charging cost is minimized using the existing time of use (TOU) based tariff structure. After that, the charging schedule is carried out under the same TOU tariff structure but on a re-configured network with and without CVR deployment. The proposed charging strategy through re-configuration of the distribution network under CVR is implemented on a modified IEEE-33 bus test system. The results obtained from the simulation show that the proposed PEV charging scheme through network re-configuration under a TOU-based tariff structure considerably reduces the charging cost by 55.8% compared to uncoordinated charging. However, a 50.2% cost reduction is achieved in the absence of network re-configuration. Therefore, the proposed PEV charging through network re-configuration under a TOU-based tariff is more effective in cost reduction. Further, investigations were carried out on EV charging through network re-configuration under TOU-based tariff and CVR deployment. It was observed that the PEV charging cost was reduced by 51.3% compared to uncoordinated charging, where higher cost benefits were obtained through the reduction in energy consumed by constant impedance loads. It has been further observed that the proposed scheme effectively flattens the load profile by clipping the peak and filling the valley load.

KEYWORDS:

• Plug-in electric vehicles (PEVs)
• State of charge (SOC)
• time of use (TOU)
• active distribution network (ADN)
• network re-configuration
• conservation voltage reduction (CVR)

Nomenclature

Symbol	=	Description
${\left(X^{+}\right)}_t^n$	=	Charging rate of $n^{th}$ PEV in $t^{th}$ time interval
${\left(X^{-}\right)}_t^n$	=	Discharging rate of $n^{th}$ PEV in $t^{th}$ time interval
$C_t$	=	Cost of energy in $t^{th}$time interval
$L_{ET}$	=	Energy throughput of the battery
$L_c$	=	Charge/discharge cycle life of the battery
$E$	=	Energy stored in the battery
$DOD$	=	Depth of discharge of battery at specified $L_c$
$c_{bat}$	=	Capital cost of the battery
$c_d^n$	=	Battery degradation cost of $n^{th}$ PEV
$n^{th}$ PEV	=	${\left(X^{+}\right)}_{max}^n$:Maximum charging rate of
${\left(X^{-}\right)}_{max}^n$	=	Maximum discharging rate of $n^{th}$ PEV
$T_a$	=	Arrival time of PEV
$T_d$	=	Indicated departure time of PEV
$SO{C}^n$	=	State of Charge of the battery of $n^{th}$ PEV
$SO{C}_{min}^n$	=	Minimum allowable SOC of the battery of $n^{th}$ PEV
$SO{C}_{max}^n$	=	Maximum allowable SOC of the battery of $n^{th}$ PEV
$SO{C}_d^n$	=	Indicated SOC as desired by the PEV owner
$SO{C}_i^n$	=	Initial SOC of the battery of $n^{th}$ PEV at the time of plug-in
${\eta }_{charging}^n$	=	Charging efficiency of $n^{th}$ PEV charger
${\eta }_{discharging}^n$	=	Discharging efficiency of $n^{th}$ PEV charger
$V_t^i$	=	Voltage at $i^{th}$bus in $t^{th}$ time instant
$V_{min}^i$	=	Minimum voltage limit at $i^{th}$bus
$V_{max}^i$	=	Maximum voltage limit at $i^{th}$bus
$E_{CVRoff}$	=	Energy consumed by the loads without CVR
$V_{CVRoff}$	=	System voltage without CVR
$E_{CVRon}$	=	Energy consumed by the loads with CVR
$V_{CVRon}$	=	System voltage with CVR
$Z_p$	=	Constant impedance coefficient of ZIP load model
$I_p$	=	Constant current coefficient of ZIP load model
$P_p$	=	Constant power coefficient of ZIP load model
$P$	=	Power consumed by the load at operating system voltage $V$
$P_0$	=	Power consumed by the load at nominal system voltage $V_0$
$V$	=	Operating system voltage
$V_0$	=	Nominal system voltage

Author contributions

The authors confirm their contributions to the paper as follows: study conception and design: Shailendra Singh, Akhilesh K. Barnwal; analysis and interpretation of results: Shailendra Singh, Mitresh K. Verma; draft manuscript preparation: Shailendra Singh, Akhilesh K. Barnwal, Mitresh K. Verma. All authors reviewed the results and approved the final version of the manuscript.

Disclosure statement

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