3.2.5. Emission Constraints

The proposed CEED problem takes into account maximum emission constraints to prevent air pollution. If the MGOs violate emission constraints, they will have to pay a fee for the volume of excess.

$$em(t) \le em^{\max}(t) \tag{26}$$

#### **4. Environment-Based Demand Response Program**

This paper proposes a new type of incentive DR program called EBDR with emission control measures by including emission constraints. Generally, aiming to reduce peak demand, the MGO uses DR programs to adjust consumer behavior and manage power demand. The DR program includes the modification of electricity consumption patterns and incentives to promote this change. Demand and pollutant emission are directly related during MG operation. Thus, when solving the CEED problem, the EBDR is used to control pollutant emissions as well as reduce peak demand for economic benefits. By utilizing EBDR, MGOs can operate the MGs in an ecofriendly manner.

## *4.1. Price Elasticity of Demand*

The EBDR includes the concept of elasticity based on market price. Elasticity is a measure used in economics to assess the percentage of change in demand caused by price fluctuations. In terms of power consumption, this percentage changes as the power demand varies with the changes in market prices, which is defined as an increase in price over time and not an absolute value. Elasticity is expected to be negative because higher power prices can cause demand reductions. The elasticity of the demand for electricity is calculated as follows:

$$E(t\_1, t\_2) = \frac{MP\_0(t\_2)}{D\_0(t\_1)} \times \frac{\partial D(t\_1)}{\partial MP(t\_2)}, \quad t\_1, t\_2 = 1, 2, \dots, 24 \tag{27}$$

Two types of elasticity of demand exist: self-price elasticity and cross-elasticity [34,35]. Self-price elasticity disregards the shift in demand from one period to another and considers changes in consumption over a given period. In this case, increments in market price lead to demand reduction, and self-elasticity always has a negative value. Meanwhile, cross-elasticity is the transferred demand from the peak period to the off-peak demand period within a day. When *t*<sup>1</sup> is not equal to *t*2, the price drop at *t*<sup>2</sup> causes a demand reduction at *t*1. Thus, cross-elasticity always has a positive value.

$$\begin{cases} \ E(t\_1, t\_2) \le 0 & \text{if } |t\_1 = t\_2| \\ \ E(t\_1, t\_2) > 0 & \text{if } |t\_1 \ne t\_2| \end{cases} \tag{28}$$
