Abstract
Energy consumption with recovery of surplus production and availability at peak times is desirable for sustainable environments. The objective of the present paper is to plan storage systems based on battery banks in electrical distribution systems having distributed resources. In particular, wind-based power is considered, and the goal is to determine the quantity, location and capacity of batteries, as well as their operation conditions considering investment and operating costs. In this sense, a three-stage method is proposed. The first one determines candidate buses for battery allocation by applying a proposed sensitivity index that seeks to improve the quality and computational efficiency, obtained from an optimal power flow model. The second stage comprises a metaheuristic algorithm to optimize quantity and location of batteries and an optimal power flow to determine the batteries’ capacity, where the power injected or absorbed by batteries is modeled as an optimization variable. Finally, the optimal power flow of the third stage seeks to optimize the batteries and system operation. Four case studies are presented with different test systems. The proposed approach proved to be applicable for these systems, since it provides a reduction in the total planning and operating cost considering grid reliability and gives results that have good cost reduction from comparison with other solutions of literature. The main motivation is to show the applicability of a novel approach based on optimization procedure and sensitivity index to investigate issues that are relevant for planning storage systems in distribution networks.
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Abbreviations
- \({\text{CSE}}\) :
-
Energy cost from the grid
- \({\text{CINEB}}\) :
-
Investment cost in battery energy storage capacity
- \({\text{CINPB}}\) :
-
Investment cost in battery power capacity
- \({\text{COM}}\) :
-
Operational and maintenance cost associated with battery systems
- \({\text{CONF}}\) :
-
Network reliability cost
- \({\text{CUE}}_{t}\) :
-
Unit cost of energy from the substation at time period \(t\), in $/kWh
- \({\text{PSE}}_{t}\) :
-
Power supplied by the substation at \(t\), in kW
- \(nb\) :
-
Number of system buses
- \(nh\) :
-
Number of time periods in a day
- \(ny\) :
-
Number of years in the planning horizon (25 years)
- \(ns\) :
-
Number of batteries
- \({\text{EBAT}}_{is}\) :
-
Nominal energy storage capacity of battery \(is\), in kWh
- \({\text{CINEB}}_{is}\) :
-
Unit cost related to the energy storage capacity of battery \(is\), in $/kWh
- \({\text{CINPB}}_{is}\) :
-
Unit cost for power capacity of battery \(is\), in $/kVA
- \({\text{SBA}}_{is,t}\) :
-
Power of battery \(is\) at time \(t\), in kVA
- \({\text{COM}}_{is}\) :
-
Operation and maintenance unit cost of battery \(is\), in $/kW
- \({\text{NA}}\) :
-
Number of distribution feeders
- \({\text{CENS}}_{ia}\) :
-
Cost of energy not supplied (ENS) in feeder \({ia}\)
- \(N_{ba}\) :
-
Number of buses supplied by feeder \(ia\)
- \(\lambda_{ib}\) :
-
Annual failure rate associated with bus \(ib\), in failure/year
- \({\text{FD}}_{ib}\) :
-
Damage function to clients at bus \(ib\)
- \({\text{CIR}}, {\text{CIC}}, {\text{CII}}\) :
-
Interruption costs for residential, commercial and industrial consumers, respectively, in $/kW
- \({\text{LR}}_{ib} ,{\text{LC}}_{ib} ,{\text{LI}}_{ib}\) :
-
Percentages of residential, commercial and industrial loads, respectively, at bus \(ib\)
- \(V_{{{\text{SE}},t}}\) :
-
Voltage of the EEDS substation at period \(t\)
- \(V_{{{\text{min}}}} ,V_{{{\text{max}}}}\) :
-
Lower and upper voltage limits, respectively
- \(V_{ib,t}\) :
-
Nodal voltage of bus \(ib\) at period \(t\)
- \({\text{PG}}_{ib,t} ,{\text{QG}}_{ib,t}\) :
-
Active and reactive powers, respectively, generated at bus \(ib\) and period \(t\) by non-distributed resources
- \(P_{ib,t}^{{{\text{wind}}}}\) :
-
Wind power at bus \(ib\) and period \(t\)
- \(P_{ib - m,t} ,Q_{ib - m,t}\) :
-
Active and reactive power flows, respectively, in section \(ib - m\), period \(t\)
- \({\Omega }ib\) :
-
Set of buses connected to bus \(ib\) through distribution branches
- \({\text{PBA}}_{is,t} ,{\text{QBA}}_{is,t}\) :
-
Active and reactive powers, respectively, developed by battery \(is\) at period \(t\)
- \(S_{ib}\) :
-
Set of batteries at bus \(ib\)
- \(P_{ib,t}^{{{\text{load}}}} ,Q_{ib,t}^{{{\text{load}}}}\) :
-
Active and reactive load demands, respectively, at bus \(ib\) and period \(t\)
- \(x_{ib}\) :
-
Integer variable related to the decision of battery allocation at bus \(ib\)
- \(x_{ib}^{*}\) :
-
Optimal values of \(x_{ib}\) from Stage 2;
- \(v_{t}\) :
-
Wind speed at period \(t\);
- \(\lambda p_{ib,t}\) :
-
Lagrange multiplier associated with the active power balance constraint of the OPF for bus \(ib\) and period \(t\);
- \({\text{SI}}_{ib}\) :
-
Sensibility index for bus \(ib\);
- \(E_{ib}\) :
-
Set of equipment connected to bus \(ib\)
- \(\lambda_{ie}\) :
-
Annual failure rate of equipment \(ie\)
- \({\text{SOC}}_{is,t}\) :
-
State of charge of battery \(is\) in period \(t\)
- \(\eta_{is,t}\) :
-
Operating efficiency of battery \(is\) at period \(t\)
- \(a_{is} ,b_{is}\) :
-
Recharging constants inherent to battery \(is\)
- \(I_{is,t}\) :
-
Current in terminals of battery \(is\) at period \(t\)
- \(I_{10}\) :
-
Battery rated discharge current
- \(it, it_{{{\text{max}}}} ,nt_{{{\text{est}}}}\) :
-
Generation counter, maximum number of generations and number of generations without improvement in the best solution of the AIS algorithm
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Appendix A: Type of Consumers
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de Oliveira, L.W., de Oliveira, J.G., Dias, B.H. et al. Optimal Allocation of Battery in Electrical Distribution Systems with Distributed Resources. J Control Autom Electr Syst 32, 1289–1304 (2021). https://doi.org/10.1007/s40313-021-00732-x
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DOI: https://doi.org/10.1007/s40313-021-00732-x