## 3 Aggregation Model Based on Multi-Scenario and Multi-Objective  
### Objective Functions  
In order to deal with the uncertainty when establishing the aggregation model, this paper describes the output of WP and PV through multiple probability scenarios. (1) The lowest daily average cost of RA  
The daily average cost is mainly composed of generation cost, energy storage cost and response cost, which correspond to DG, ES and DR in DERs respectively. The objective function is as follows:  
\[\min f_{1}=\sum_{k=1}^{K}p_{k}\sum_{n=1}^{N}C_{n,k}^{DG}X_{n}^{DG}+\sum_{n=1}^ {N}C_{n}^{ES}X_{n}^{ES}+\sum_{n=1}^{N}C_{n}^{DR}X_{n}^{DR} \tag{3}\]  
where \(K\) is the number of multiple scenarios, \(N\) is the number of aggregated regions, \(P_{k}\) is the probability of the \(k\)-th scenario, \(C_{n,k}^{DG}\) is the average daily generation cost of DG in the \(n\)-th region under the \(K\)-th scenario, \(X_{n}^{DG}\) represents whether there is DG in the \(n\)-th region, which is 1 and vice versa, \(C_{n}^{ES}\) is the charge-discharge cost of energy storage in the \(n\)-th region, \(X_{n}^{ES}\) represents whether there is ES in the \(n\)-th region, \(C_{n}^{DR}\) is the response cost of DR in the \(n\)-th region, and \(X_{n}^{DR}\) represents whether there is DR in the \(n\)-th region. DG includes WP and PV, and its cost mainly includes investment cost and operation- maintenance costs [20]. The generation cost is as follows:  
\[C_{n}^{DG}(k)=\sum_{t=1}^{T}\left(1+M_{n}^{DG}\right)\frac{\beta_{n}^{DG}I_{n} ^{DG}}{P_{t,n,k}^{DG}} \tag{4}\]  
where \(t\) is the time series with an interval of 1 h, \(M_{n}^{DG}\) is the maintenance rate of DG in the \(n\)-th region, \(\beta_{n}^{DG}\) is the annual investment rate of DG in the \(n\)-th region, \(I_{n}^{DG}\) is the initial investment of DG in \(n\)-th region, \(P_{t,n,k}^{DG}\) is the DG output at the \(t\)-time in the \(n\)-th region under the \(K\)-th scenario. The energy storage cost is expressed as the product of the battery loss rate \(\gamma_{d}\) of the unit power and the actual charge-discharge power:  
\[C_{n}^{ES}=\sum_{t=1}^{T}\gamma_{d}P_{t,n}^{ES} \tag{5}\]  
where \(\gamma_{d}\) is the battery loss rate of the unit power, \(P_{t,n}^{ES}\) is the charge-discharge power at the \(t\)-time in the \(n\)-th region. When users actively participate in demand response and reduce the load at a specific time according to the agreement requirements, the company will provide compensation to users [21]. The response cost is as follows;  
\[C_{n}^{DR}=\sum_{t=1}^{T}c_{n}P_{t,n}^{DR} \tag{6}\]  
where \(c_{n}\) is the compensation cost of DR in the \(n\)-th region, \(P_{t,n}^{DR}\) is the response capacity at the \(t\)-time in the \(n\)-th region. (2) The optimal generation characteristics of RA  
Daily average output and curve volatility are used to measure the generation characteristics of RA. DG belongs to generation resources; although DR cannot generate electricity directly, it can reduce load and provide the virtual output at a specific time; ES is the energy-consuming resources for RA. The objective function of the maximum daily average output is as follows:  
\[\max f_{2}=\sum\limits_{k=1}^{K}p_{k}\sum\limits_{t=1}^{T}\sum\limits_{n=1}^{N }P_{t,n,k}^{DG}X_{n}^{DG}-\sum\limits_{t=1}^{T}\sum\limits_{n=1}^{N}P_{t,n}^{ ES}X_{n}^{ES}+\sum\limits_{t=1}^{T}\sum\limits_{n=1}^{N}P_{t,n}^{DR}X_{n}^{DR} \tag{7}\]  
The curve \(L\) is used to represent the difference between the virtual output curve of RA and the electric load curve. The volatility of curve \(L\) is defined as the ratio of the standard deviation of the output force to the geometric mean at each time [22]. The smaller the fluctuation rate is, the smoother the curve \(L\) is, the better the fitting degree between the virtual output curve and the electric load curve is. The objective function is as follows:  
\[\left\{