3.1.2. Objective function of power plant

The profit of the power plant under the risk-sharing model is described below:

In objective function (5), the first term represents the revenue from selling electric power to consumers. It is estimated based on the minimum value of the output capacity of the power plant and the energy consumption demand of consumers because COVID-19 has affected both the supply and demand sides. The parameter ϕ in the range [0; 1] reflects the impact of COVID-19 on the total output capacity of the power plant from RE generation units i. A higher value of ϕ indicates a higher impact of the COVID-19 pandemic. The second term is the amount of subsidy from the government. This subsidy will cover losses of energy prices and provide financial support to the power plant when allowing customers to delay payment. The third term calculates the fixed cost and variable operating cost of the power plant based on the amount of electric power generated and stored at RE generation units. Because the performance-based risk-sharing model is applied to stimulate energy consumption during the pandemic, consumers postpose electricity bill payments for the period h. Then, the RE generation units will suffer a loss of financial costs based on the revenue and interest rate during the deferral period. This is expressed in the final term of the objective function.

The constraints of the RRESN are presented in Eqs. (6)–(14). The inequality constraint (6) ensures that the amount of generated and stored electric power at the RE generation units is larger than the demand loads of all consumers during the planning time. Eqs. (7) and (8) are the capacity limitation constraints of the storage devices and RE generation units, respectively. Constraint (7) states that the stored power amount cannot exceed the limited capacity of the storage device. Constraint (8) ensures that the amount of electric power generated and stored cannot exceed the total output capacity of the power plant. To guarantee the minimum electricity bill of consumers according to the proposed risk-sharing model, Eqs. (3)–(4) in Section 2.2.1 become constraints (9) and (10) in the power plant optimization model. Eq. (9) is applied to calculate the price adjustment coefficient for each consumer under the COVID-19 effects. Constraint (10) is established to ensure that the energy consumption cost of consumers in the objective function (2) is a concave function of the optimal value of the risk-sharing effort index. Constraint (11) limits the range of energy consumption demand reduction of consumers because of the COVID-19 pandemic. Constraint (12) guarantees that subsidies cannot exceed the government's budget. Constraint (13) guarantees the nonnegativity of the decision variable regarding the amount of generated and stored electric power. Constraint (14) is the condition for the risk-sharing model to be applied. When the value of φ_m equals 1, it indicates that the risk-sharing model has not been applied to enhance the resilience of the supply network.

S.t.