Chance-Constrained Optimization of Demand Response to Price Signals

Household-based demand response is expected to play an increasing role in supporting the large scale integration of renewable energy generation in existing power systems and electricity markets. While the direct control of the consumption level of households is envisaged as a possibility, a credible alternative is that of indirect control based on price signals to be sent to these end-consumers. A methodology is described here allowing to estimate in advance the potential response of flexible end-consumers to price variations, subsequently embedded in an optimal price-signal generator. In contrast to some real-time pricing proposals in the literature, here prices are estimated and broadcast once a day for the following one, for households to optimally schedule their consumption. The price-response is modeled using stochastic finite impulse response (FIR) models. Parameters are estimated within a recursive least squares (RLS) framework using data measurable at the grid level, in an adaptive fashion. Optimal price signals are generated by embedding the FIR models within a chance-constrained optimization framework. The objective is to keep the price signal as unchanged as possible from the reference market price, whilst keeping consumption below a pre-defined acceptable level.