Demand response program using incentive and dis-incentive based scheme

  • Kumar Raja GadhamEmail author
  • Tirthadip Ghose
Original Paper


Demand Response (DR) is becoming an effective tool to change consumption in order to maintain the balance between generation and consumption in real time. Demand Response Programs (DRPs) are employed for assisting the DR activities to encourage consumers to change their own load responding incentive/price based signal sent by the aggregator. Motivating the customers to change their consumption pattern poses a great challenge for the aggregator. In this paper, an incentive and dis-incentive based scheme has been designed for effective implementation of mandatory participation based incentive DR Program. This scheme is designed on the basis of social welfare concept calculating the expected gain of the generating utility and customers. While determining the benefit of generating utilities, this is observed that DR causes a loss for some costly units due to the reduction of the demand. The proposed scheme provides an incentive to such loss making generating utilities and responsive customers for playing their role in implementing the proposed DR program. Dis-incentive charge will then be imposed upon the non-responsive customers who are under the mandatory program but violate the agreement and still enjoy the monetary benefit in their energy bills due to price reduction. The effects on social welfare function due to different DR values show the importance of framing incentive prices for the participating utilities in DRP. Generation scheduling of 10 units is considered here to create different DR conditions and illustrate the effectiveness of the proposed scheme.


Demand response programs Demand response modeling Social welfare function Dis-incentive and incentive schemes 

List of symbols

A. Parameters


Index of hour


Index of generator


Percentage of customers who do violate the agreement in DR event


Percentage of customers who do fulfill the agreement in DR event


Minimum power generated by jth generator


Maximum power generated by jth generator

\( \uplambda \)min,j

Minimum price of jth generator

\( \uplambda \)max,j

Maximum price of jth generator

\( {\text{a}}_{\rm{j}} \)

Fixed cost of jth generator

\( {\text{b}}_{\rm{j}} \)

Coefficient of linear term of the variable cost function of the jth generator

\( {\text{c}}_{\rm{j}} \)

Coefficient of quadratic term of the variable cost function of the jth generator

B. Variables

\( {\text{Q}}_{\rm{o}}^{\rm{i}} \)

Power demand at ith hour before DR (MW)

\( {\text{Q}}_{\rm{DR}}^{\rm{i}} \)

Power demand at ith hour after implementing DRPs (MW)

\( \uplambda_{\rm{o}}^{\rm{i}} \)

Initial marginal price at ith hour ($/MWh)

\( \uplambda_{\rm{DR}}^{\rm{i}} \)

Marginal price at ith DR hour ($/MWh)

\( \uplambda_{\rm{NPC}}^{\rm{i}} \)

Non-participating customers’ price at ith DR hour

M\( \uplambda_{\rm{NPC}}^{\rm{i}} \)

Non-participating customers’ price at ith DR hour by MPBI scheme

P\( \uplambda_{\rm{NPC}}^{\rm{i}} \)

Non-participating customers’ price at ith DR hour by PBI scheme

E\( \uplambda_{\rm{NPC}}^{\rm{i}} \)

Non-participating customers’ price at ith DR hour by EBI scheme

\( {\text{IC}}_{\rm{PR}}^{\rm{i}} \)

Incentive price at ith hour ($/MWh)

\( {\text{IC}}_{\rm{T}}^{\rm{i}} \left( {\Delta {\text{Q}}^{\rm{i}} } \right) \)

Total incentive amount in DRPs at ith hour ($/h)

\( \epsilon \left( {{\text{i}},{\text{i}}} \right) \)

Demand-price elasticity at ith DR hour

\( {\text{IC}}^{\rm{MP}} \)

Marginal price based incentive price

\( {\text{IC}}^{\rm{PF}} \)

Profit based incentive price

\( {\text{IC}}^{\rm{EB}} \)

Elasticity-based incentive price

\( \Delta {\text{Q}}^{\rm{i}} \)

Change in demand at ith hour (MW)

\( \Delta \uplambda^{\rm{i}} \)

Change in marginal price at ith hour ($/MWh)

\( {\text{P}}_{\rm{gj}}^{\rm{i}} \)

j-Generators output at ith hour (MW)

\( {\text{C}}\left( {{\text{P}}_{\rm{gj}}^{\rm{i}} } \right) \)

j-Generators production cost at ith hour ($/h)

\( {\text{PF}}_{\rm{U}}^{\rm{i}} \left( {{\text{P}}_{\rm{gj}}^{\rm{i}} } \right) \)

Profit of generators before implementing DRPs at ith hour ($/h)

\( {\text{PF}}_{\rm{TC}}^{\rm{i}} \left( {{\text{Q}}_{\rm{DR}}^{\rm{i}} } \right) \)

Total customers profit after implementing DRPs at ith hour ($/h)

\( {\text{PF}}_{\rm{PC}}^{\rm{i}} ({\text{Q}}_{\rm{DR}}^{\rm{i}} ) \)

Participating customers profit after implementing DRPs at ith hour ($/h)

\( {\text{PF}}_{\rm{NPC}}^{\rm{i}} ({\text{Q}}_{\rm{DR}}^{\rm{i}} ) \)

Profit of non-participating customers for their consumption at ith DR hour ($/h)

\( {\text{NPF}}_{\rm{U}}^{\rm{i}} \left( {{\text{P}}_{\rm{gj}}^{\rm{i}} } \right) \)

Net profit of generators after implementing DRPs at ith hour ($/h)

\( {\text{NPF}}_{\rm{PC}}^{\rm{i}} \left( {{\text{Q}}_{\rm{DR}}^{\rm{i}} } \right) \)

Net profit of participating customers after implementing DRPs at ith hour ($/h)

\( {\text{NPF}}_{\rm{NPC}}^{\rm{i}} \left( {{\text{Q}}_{\rm{DR}}^{\rm{i}} } \right) \)

Net profit of non-participating customers after implementing DRPs at ith hour ($/h)

\( {\text{DIC}}_{\rm{PR}}^{\rm{i}} \)

Dis-incentive price at ith hour ($/MWh)

\( {\text{DIC}}_{\rm{T}}^{\rm{i}} \left( {{\text{Q}}_{\rm{DR}}^{\rm{i}} } \right) \)

Total collected dis-incentive payment at ith hour ($/h)

\( {\text{DIC}}_{\rm{NPC}}^{\rm{i}} \left( {{\text{Q}}_{\rm{DR}}^{\rm{i}} } \right) \)

Dis-incentive of non participating customers at ith DR hour

\( {\text{DIC}}_{\rm{U}}^{\rm{i}} \left( {{\text{P}}_{\rm{gj}}^{\rm{i}} } \right) \)

Dis-incentive of utility at ith DR hour

\( {\text{pf }}_{\rm{U}}^{\rm{i}} \)

Participation factor to generators at ith hour

\( {\text{pf}}_{\rm{NPC}}^{\rm{i}} \)

Participation factor to completely non-participating customers at ith hour

\( {\text{H}}\left( {{\text{Q}}_{\rm{DR}}^{\rm{i}} } \right) \)

Customers profit function at DR hour

\( {\text{Ho}}\left( {{\text{Q}}_{\rm{DR}}^{\rm{i}} } \right) \)

Customers profit function before DR hour

\( {\text{B}}\left( {{\text{Q}}_{\rm{DR}}^{\rm{i}} } \right) \)

Customers owned profit at DR hour

\( {\text{Bo}}\left( {{\text{Q}}_{0}^{\rm{i}} } \right) \)

Customers owned profit before DR hour


Demand ratio parameter

\( {\text{PF}}^{\rm{NPL}} \)

Profit of non-participating load

\( {\text{Rev(P}}_{\rm{gj}}^{\rm{i}} ) \)

Revenue of the jth generating unit at ith hour

\( {\text{PF}}_{{{\text{U}},\% {\text{S}}}}^{\rm{i}} ({\text{Q}}_{\rm{gj}}^{\rm{i}} ) \)

Profit of generating utility at sth loading condition

\( {\text{PF}}_{{{\text{TC}},\% {\text{S}}}}^{\rm{i}} \left( {{\text{Q}}_{\rm{DR}}^{\rm{i}} } \right) \)

Profit of customers at sth loading condition

\( {\text{SW}}_{{\% {\text{S}}}} \)

Social welfare at sth loading

C. Abbreviations


Incentive price with different schemes


Marginal price based incentive scheme


Profit based incentive scheme


Elasticity-based incentive scheme


Marginal price based dis-incentive price scheme


Elasticity-based dis-incentive price scheme


Incentive based programs


Market cleaning price



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical and Electronics EngineeringBirla Institute of Technology, MesraRanchiIndia

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