Demand Response Application in Smart Grids pp 193-214 | Cite as

# Optimal Stochastic Planning of DERs in a Game Theory Framework Considering Demand Response and Pollution Issues

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## Abstract

Equipping the distribution network with distributed energy resources (DERs) provides a situation that can facilitate the energy delivery to the customers and cut a portion of the requirement to the energy purchased from upstream network. Furthermore, they have an essential effect on pollution reduction. Optimal DER planning under demand response programs (DRPs) can result in a cost-effective siting and sizing of these resources in the network. However, customers who participated in DRP follow their own motivation to increase their payoff. This issue leads to conflict between the planning decision of DisCo and consumption decision of customers. Therefore, by consideration of network uncertainties and modeling the problem in a Stackelberg framework, this paper introduces a new concept in probabilistic planning of distribution network. In addition, the planning in this paper has the concern of pollution and is in the perspective of CO_{2} emission reduction.

## Keywords

DER Distribution network planning Demand response Stackelberg CO_{2}emission

## List of Symbols

- Ω
_{L} Set of buses

- Ω
_{S} Set of scenarios

*N*_{T}Planning horizon (year)

*N*_{h}Number of hours in a day

- \( {\varsigma}_i^{Dr} \)
Binary parameter that is 1 if

*i*th customer is participated in DRP- \( {\varsigma}_i^{Du} \)
Binary parameter that is 1 if

*i*th customer is not interested in DRP- \( {P}_{i,t,h,\omega}^{Dr} \)
Demand of

*i*th DR customer in year*t*, hour*h*, and scenario*ω*- \( {P}_{i,t,h,\omega}^{Du} \)
Demand of

*i*th DU customer in year*t*, hour*h*, and scenario*ω*- CC
^{CHP} Capital cost of CHP ($/MW)

- MC
^{CHP} Maintenance cost of CHP ($/MWh)

- FC
^{CHP} Fuel cost of CHP ($/MWh)

- CC
^{WT} Capital cost of WT ($/MW)

- MC
^{WT} Maintenance cost of WT ($/MWh)

- CC
^{PV} Capital cost of PV ($/MW)

- MC
^{PV} Maintenance cost of PV ($/MWh)

- \( {\xi}_i^{CHP} \)
Binary decision variable that is 1 if a CHP is installed in bus

*i*- \( {\xi}_i^{WT} \)
Binary decision variable that is 1 if a WT is installed in bus

*i*- \( {\xi}_i^{PV} \)
Binary decision variable that is 1 if a PV is installed in bus

*i*- \( {P}_i^{CHP} \)
Rated power of CHP in bus

*i*(MW)- \( {P}_{r,i}^{WT} \)
Rated power of WT in bus

*i*(MW)- \( {P}_{r,i}^{PV} \)
Rated power of PV in bus

*i*(MW)- \( {P}_{i,t,h,\omega}^{WT} \)
Power of WT in bus

*i*, year*t*, hour*h*, and scenario*ω*(MW)- \( {P}_{i,t,h,\omega}^{PV} \)
Power of PV in bus

*i*, year*t*, hour*h*, and scenario*ω*(MW)- \( {P}_{t,h,\omega}^{\mathrm{G}} \)
Purchased power from upstream network in year

*t*, hour*h*, and scenario*ω*(MW)*ϕ*^{G}Penalty of CO

_{2}emission by conventional plants in the main grid ($/kWh)*ϕ*^{CHP}Penalty of CO

_{2}emission by CHP ($/kWh)*V*_{i, t, h, ω}Voltage of bus

*i*in year*t*, hour*h*, and scenario*ω*(pu)*δ*_{i, t, h, ω}Voltage angle of bus

*i*in year*t*, hour*h*, and scenario*ω*(rad)- \( {\lambda}_{i,t,h,\omega}^{Dr} \)
Energy selling price in year

*y*, hour*t*, and scenario*ω*for*i*th DR customer ($/MWh)- \( {\lambda}_h^0 \)
Selling energy price to the entire customers in hour

*h*- \( {\rho}_h^g \)
Energy price bought from upstream network in hour

*h*- \( {E}_{i,t}^{Min} \)
Minimum energy consumption of

*i*th DR customer in year*t*- \( {E}_{i,t}^{\mathrm{Max}} \)
Maximum energy consumption of

*i*th DR customer in year*t**π*_{ω}Probability of scenario

*ω*- PW
_{t} Present worth factor in year

*t*- inf _ r
Inflation rate

- int _ r
Interest rate

*Z*_{ij}Impedance between bus

*i*and*j**T*_{d}Total number of days in a year

*v*_{ci}Cut-in speed (m/s)

*v*_{r}Rated speed (m/s)

*v*_{co}Cut-out speed (m/s)

*ψ*_{max}Maximum solar irradiation (m/s)

- pf
_{i} Power factor of CHP unit connected to bus

*i**γ*Penalty multiplier for the Lagrangian function related to PCPM

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