Programming for supplying electricity in these regions is performed by developing the global electricity system and using islanded microgrids (MGs). Herein, a probabilistic model for simultaneous programming of energy and reserve of an islanded MG is proposed by considering demand-response (DR) programs and security constraints using a developed water wave search algorithm. Since the above problem has many nonlinear constraints, in order to avoid early convergence and not be located in local points, an additional operator is provided to improve the search performance in the feasible space of the problem. In the proposed method, the weak waves are eliminated, and the waves that are close to the optimal answer are strengthened; so that the unworthy answers are removed from the population and worthy answers are created in their place. The objective function aims to maximize the MG operator's profit by considering several security-related and operational constraints, e.g., voltage and frequencies. In the proposed method, the conditional value at risk (CVaR) method is adopted to evaluate and manage the risk of problem uncertainties. An effort is made to coordinate the variables of the problem, such that their generation capacity can be determined based on the created scenarios. In this method, the operator's profit sensitivity and the safety margins of the MG with and without the participation of responsive loads are evaluated concerning the risk index. This method enables the operators to select the proper risk coefficient, maximize their profit and improve the safety margin, voltage, and frequency of the MG. Finally, the proposed method and model have been discussed and investigated on the studied system on different scenarios. The numerical results show that with the participation of customers in the DR program, the expected profit of the operator and the security margin of voltage and frequency increase. In periods of low load, production units have more free capacity. Therefore, even at a low-risk factor, the operator has purchased enough storage capacity, and as a result, the frequency deviation in these hours is low in both cases with and without DR.
- Demand-side management
- Economic programming
- Energy and reserve scheduling
- Probabilistic renewable energy sources model
- Risk system
- Water wave optimization algorithm