# Stochastic-Based Energy Procurement

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## Abstract

In this section, the uncertainty of the pool price and load demand in the power procurement problem of a large consumer is modeled using the stochastic programming. Based on the deterministic formulation of the problem, which was introduced in Chap. 2, the stochastic formulation is presented to solve the problem.

Then, using normal distribution, uncertainties of the problem as the load, solar irradiance, temperature, and power price in the market are modeled generating 100 discrete scenarios considering the output power of photovoltaic panels. Furthermore, the uncertainty of the output power of the wind turbine is modeled using the Weibull distribution, which is used to model the wind speed by 100 scenarios.

Two different cases as without and with considering demand response programs are assumed to solve the problem and investigate the impact of demand response programs. To do so, the time-of-use rate of demand response is applied to reduce the total power procurement cost of the large consumer.

The problem is formulated as a mixed-integer linear program, which is solved by the CPLEX solver under GAMS optimization software.

## Keywords

Power procurement of large consumer Uncertainty modeling Stochastic programming Normal distribution Weibull distribution Bilateral contracts Demand response programs## References

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