Scenario-based stochastic framework for coupled active and reactive power market in smart distribution systems with demand response programs


A stochastic coupled energy and VAr market for distribution networks is developed.

The loads and wind power generation uncertainties are considered.

A demand buyback program is considered in the proposed market.

The contribution of the demand buyback program to the voltage control is evaluated.


In this paper, an efficient stochastic framework is proposed to develop a coupled active and reactive market in smart distribution systems. Distributed Energy Resources (DERs) can offer active powers to the market and also offer their reactive powers via a multi-component bidding framework constructed based on their reactive power capability diagrams. Distribution Company (Disco) buys active and reactive powers from a wholesale market and sells them via this market. Aggregators on behalf of responsive loads can participate in the market using a demand buyback program (DBP). The uncertainties of forecasted loads and wind power generation are considered in the proposed framework. To model the stochastic variables, the scenario tree is created using the Weibull and the Gaussian probability density functions (PDFs). The cost objective function of the stochastic coupled market clearing consists of the expected costs of energy and reactive power purchased from the DERs and Disco, the expected penalty cost of CO2 emissions of DERs and the main grid as well as the expected cost of running DBP. The proposed market is cleared through a mixed-integer nonlinear optimization problem solved in GAMS software. The effectiveness of the proposed method is investigated based on a 22-bus 20-kV radial distribution test system.


  • Coupled active and reactive market;
  • CO2 emission;
  • Demand buyback program;
  • Distributed Energy Resources;
  • Stochastic programming;
  • Scenario-based uncertainty modeling

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