Demand response (DR) is proven to be very efficacious for load mitigation especially in peak time period. On the other hand, DR benefits both consumers and system operators to reduce their payment and system operating cost, respectively. Offer cost minimization is currently used as the clearing mechanism with locational marginal pricing scheme to determine the consumers' payment. These clearing and pricing mechanisms are inconsistent as the system cost is being minimized, but the final payments are calculated based on marginal prices. Payment cost minimization (PCM) auction as a price-based clearing mechanism is envisaged to be an effective alternative to solve the issue. This paper shows how to include DR in PCM mechanism to further reduce the consumers' payment. It facilitates utilizing price responsive consumers for load shifting DR (LSDR) in a PCM auction. The optimization problem is modeled as a mixed-integer nonlinear bi-level programming. Duality theorem, Karush-Kuhn-Tucker conditions and integer algebra are used to convert such a problem to a single level mixed-integer linear programing problem. This problem is then solved by CPLEX solver in GAMS. The impacts of LSDR are studied by implementing the proposed formulation to solve the clearing problem in the case studies deriving promising numerical results.
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