The Application of Demand Response Program on the Dynamic Planning of Energy Storage System Allocation in Distribution Networks

  • Alireza Akbari-DibavarEmail author
  • Amir Farahmand-Zahed
  • Sayyad Nojavan
  • Kazem Zare


This chapter proposes an optimization framework for dynamic planning of sizing and siting of energy storage systems (ESSs) in an AC microgrid (MG) in the presence of different kinds of distributed generators. Considering the high capital cost of ESS units, it is an economical way to invest ESS capacities according to each year situation. An AC optimal power flow is formulated as mixed-integer nonlinear programming with the objective of minimizing the total operational cost of the MG and the investment cost of the ESS. Three case studies are considered. An optimal power flow calculation without ESS and demand response program (DRP) has been done in case 1 to create a baseline for comparison. In other cases, the optimal sizing and siting of ESS have been done for each year of the planning horizon, where the effects of DRP on the ESS allocation problem are studied in the last case.


Dynamic planning Optimal sizing and siting Energy storage system Optimal power flow Demand response program Time of use 



i, j

Indices of bus


Index of time


Index of year

Set of buses with wind turbine


Set of buses with the diesel generator


Set of buses with solar PV source


Set of buses with ESS


\( {P}_{{\mathrm{sub}}_{t,h}} \)

Active power injected by the upstream grid at time t in year h

\( {Q}_{{\mathrm{sub}}_{t,h}} \)

Reactive power injected by the upstream grid at time t in year h

\( {P}_{{\mathrm{loss}}_{t,h}} \)

Active power losses due to flowing active power at time t in year h

\( {P}_{i,t,h}^{\raisebox{1ex}{$c$}\!\left/ \!\raisebox{-1ex}{$d$}\right.} \)

Power charged or discharged by ESS at bus i at time t in year h

\( {P}_{{\mathrm{DG}}_{i,t,h}} \)

Power produced by the diesel generators at bus i at time t in year h

ui, t, h

State of diesel generator unit at bus i at time t in year h

yi, t, h

If the diesel generator unit will turn on at time t, it is 1; otherwise, it is 0

zi, t, h

If the diesel generator unit will turn off at time t, it is 1; otherwise, it is 0

\( {P}_{{\mathrm{wind}}_{i,t,h}} \)

Produced active power by wind turbines at bus i at time t in year h

\( {P}_{p{v}_{i,t,h}} \)

Produced active power by PV systems at bus i at time t in year h

TOUi, t, h

Amount of additional or reduced load (load shifting), in bus i at time t in year h

Di, t, h

Supplied load in at bus i at time t (considering shifted load), in year h

Pi, j, t, h

Active power exchanged between bus i and j at time t in year h

Qi, j, t, h

Reactive power exchanged between bus i and j at time t in year h

Vi, t, h

Voltage amplitude at bus i at time t in year h

δi, t, h

Voltage angle at bus i at time t in year h

SOCi, t, h

State of charge at bus i at time t in year h

\( {C}_{{\mathrm{ess}}_{i,h}} \)

Nominal ESS capacity installed at bus i in year h

\( {P}_{{\mathrm{ess}}_{i,h}} \)

Nominal ESS power installed at bus i in year h

Parameters Network

\( {P}_{i,{j}_{\mathrm{max}}} \)

Maximum capacity of active power flow at line i-j

\( {Q}_{i,{j}_{\mathrm{max}}} \)

Maximum capacity of reactive power flow at line i-j

\( {P}_{{\mathrm{sub}}_{\mathrm{max}}} \)

Rated active power of the upstream grid’s transformer

\( {Q}_{{\mathrm{sub}}_{\mathrm{max}}} \)

Rated reactive power of the upstream grid’s transformer

Vmin, Vmax

Minimum and maximum amounts of voltage amplitude

Zi, j

Line impedance amplitude (between buses i and j)

Gi, j

Line conductance amplitude (between buses i and j)

θi, j

Line impedance angle (between buses i and j)

\( {P}_{\mathrm{load}- DR{P}_{i,t,h}} \)

Active load at bus i at time t in year h

\( {Q}_{{\mathrm{load}}_{i,t,h}} \)

Reactive load at bus i at time t in year h


The maximum amount of participated loads in DRP

Renewable Resources (PV and Wind)


Rated power of PV installed at bus i


Time availability of PVs at time t

\( {P}_{{\mathrm{wind}}_i}^{\mathrm{max}} \)

The maximum rate of a wind turbine at time t

VC − I

The cut-in speed of wind turbines

VC − O

Cutout speed of wind turbines


The rated velocity of wind turbines

\( {V}_{{\mathrm{wind}}_t} \)

Wind velocity



Minimum state of charge for storage units


A constant value related to the minimum state of charge of ESS


A constant value related to power charge and discharge of ESS


Charge and discharge efficiency of ESS

Diesel Generator

ag, bg, cg

Cost coefficients of diesel generators

\( {P}_{D{G}_i}^{\mathrm{max}} \)

Maximum limit of power production by the diesel generators

\( {P}_{D{G}_i}^{\mathrm{min}} \)

The minimum limit of power production by the diesel generators


The ramp up rate of diesel generators unit at bus i


The ramp down rate of diesel generators unit at bus i


Minimum uptime of diesel generators unit at bus i


Minimum downtime of diesel generators unit at bus i

Economic Parameters and Variables

CostIn. C

The investment cost of ESS capacity

CostIn. P

The investment cost of ESS power


The cost related to contracted power from the upstream grid


The loss payment


The purchased power cost from diesel generator units

πt, h

Energy price at time t in year h


Cost factor


Inflation rate


Interest rate


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Alireza Akbari-Dibavar
    • 1
    Email author
  • Amir Farahmand-Zahed
    • 1
  • Sayyad Nojavan
    • 2
  • Kazem Zare
    • 1
  1. 1.Faculty of Electrical and Computer EngineeringUniversity of TabrizTabrizIran
  2. 2.Department of Electrical EngineeringUniversity of BonabBonabIran

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