Risk-Based Long Term Integration of PEV Charge Stations and CHP Units Concerning Demand Response Participation of Customers in an Equilibrium Constrained Modeling Framework

Abstract

Distribution networks are going toward the integration of distributed generators (DGs) to delivering the electrical energy in a cleaner and reliable manner to the customers. Additionally their implementation can yield the improvement in voltage profile and reduction in lost power for distribution companies (DISCO). Along with development of RESs, plug-in electric vehicles (PEVs) with a clean energy have an acceptable growth in both the number and technology. This chapter introduces the planning of PEV charge station and CHP units in distribution networks in the presence of long term demand response (DR) for interested customers. Since these DR customers seek to attain a higher profit by participating in DR and mutually the DISCO seeks to lessen the planning cost, the problem is modelled in a leader-follower Stackelberg framework. To this end, the bi-level planning problem is converted into a single-level problem using the KKT condition and implementing the equilibrium constrained concept for the lower level problem. Furthermore due to the existence uncertainties in the network, the risk management is considered in this chapter by modelling the payoff function of DR customers with conditional value at risk (CvaR).

Appendix A

The nomenclature is shown below.

ΩL	Set of buses
ΩS	Set of scenarios
NT	Number of hours in a day
Ny	Integration horizon
${\upsilon}_i^{Dr}$	Binary parameter that is 1 if ith customer is participated in DRP
${\upsilon}_i^{Du}$	Binary parameter that is 1 if ith customer is not interested in DRP
${P}_{i,y,h,\omega}^{Dr}$	Demand of ith DR customer in year y, hour h and scenario ω
${P}_{i,y,h,\omega}^{Du}$	Demand of ith DU customer in year y, hour h and scenario ω
CCCHP	Capital cost of CHP ($/MW)
MCCHP	Maintenance cost of CHP ($/MWh)
FCCHP	Fuel cost of CHP ($/MWh)
CCCS	Capital cost of charge station ($/PEV number)
MCCS	Maintenance cost of charge station ($/PEV number)
${\Theta}_i^{CS}$	PEV capacity of each charge station selected to be installed in bus i
${\xi}_i^{CHP}$	Binary decision variable that is 1 if a CHP is installed in bus i
${\xi}_i^{CS}$	Binary decision variable that is 1 if a WT is installed in bus i
${P}_i^{CHP}$	Rated power of CHP in bus i (MW)
Vi, y, h, ω	Voltage of bus i in year y, hour h and scenario ω (pu)
${\rho}_h^0$	Selling energy price to the entire customers in hour h
${\rho}_h^g$	Energy price bought from upstream network in hour h
${E}_{i,y}^{Min}$	Minimum energy consumption of ith DR customer in year t
${E}_{i,y}^{Max}$	Maximum energy consumption of ith DR customer in year t
πω	Probability of scenario ω
PWy	Present worth factor in year y
inf _ r	Inflation rate
int _ r	Interest rate
rij	Resistance between bus i and j
xij	Reactance between bus i and j
Td	Total number of days in a year
pfi	Power factor of CHP unit connected to bus i
γk	CVaR risk level of DR customer k
βk	Risk aversion strategy of DR customer k
Φk, y, h, ω	Penalty/incentive function of DR customer k
ηk	Value at Risk of DR customer k
ζk	CVaR auxiliary variable of DR customer k
Xk, b, y, h, ω	Piecewise demand of DR customer k, in block b, in year y, in hour h and in scenario ω
Sk, b, y, h, ω	Piecewise benefit curve slope of DR customer k, in block b, in year y, in hour h and in scenario ω
${P}_{i,y,h,\omega}^L$	Active power demand of load point in bus i, in year y, in hour h and in scenario ω