## 2 Modeling of Novel Electrical Load Resources in UDNs
### 5G Base Stations  
When 5G base stations serve as internal regulation resources of a VPP, load curtailment is primarily achieved by adjusting the number of activated terminals and data traffic [23]. This paper employs a dynamic model to characterize the power consumption of 5G base stations. Assuming that the number of terminals remains constant within a scheduling time interval \(\Delta t\), the power variation of the 5G base station can be represented by the increase or decrease in the number of activated terminals, which is expressed as follows:  
\[P_{\text{5G}}^{t}=P_{i,\text{AAU}}^{t}+P_{b,\text{AAU}}^{t}+P_{b,\text{BBU}}^{t} \tag{1}\]  
where \(P_{\text{5G}}^{t}\) represents the total power consumption of the 5G base station at time \(t\); \(P_{i,\text{AAU}}^{t}\) denotes the incremental power consumption of the Active Antenna Unit (AAU) in the 5G base station; \(P_{b,\text{AAU}}^{t}\) is the rated power of the AAU; and \(P_{b,\text{BBU}}^{t}\) is the rated power of the Baseband Unit (BBU) in the 5G base station. The \(P_{i,\text{AAU}}^{t}\) consists of the power consumption generated by downlink data \(P_{\text{idd,AAU}}^{t}\) and the power consumption generated by downlink signaling \(P_{\text{ids,AAU}}^{t}\). The power of the 5G base station can also be regulated by reducing or increasing the data transmission volume of the 5G base station, which is expressed as follows:  
\[P_{i,\text{AAU}}^{t}=P_{\text{idd,AAU}}^{t}+P_{\text{ids,AAU}}^{t} \tag{2}\]  
\[P_{\text{idd,AAU}}^{t}=\frac{P_{\text{max,AAU}}-P_{b,\text{AAU}}}{D_{\text{dd }_{\text{max}}}}\cdot D_{\text{dd}}^{t} \tag{3}\]  
\[D_{\text{dd}}^{t}=A_{RE}\cdot R_{\text{ds}}^{t} \tag{4}\]  
\[P_{\text{ids,AAU}}^{t}=\frac{P_{\text{max,AAU}}-P_{b,\text{AAU}}}{R_{\text{ dsge}}+R_{\text{ddge}}}\cdot D_{\text{dd}}^{t} \tag{5}\]  
where \(P_{\text{max,AAU}}\) is the maximum power of the AAU; \(D_{\text{ddmax}}\) is the maximum downlink data rate of the 5G base station; \(D_{\text{dd}}^{t}\) is the downlink data rate at time \(t\) (This parameter is related to the hardware equipment, communication protocol and network environment of the base station, and can be obtained through the technical specifications of the base station equipment or determined according to the relevant communication standards and test results in practical applications); \(A_{RE}\) is the average data carried by each signaling resource element; \(R_{\text{ds}}^{t}\) is the downlink signaling resource element at time \(t\). where \(R_{\text{dsge}}\) represents the total number of signaling resource elements used for the downlink; and \(R_{\text{ddge}}\) represents the total number of data resource elements used for the downlink. Nevertheless, during regular operation, the 5G base station must maintain performance indicators such as data transmission rate and delay at a basic level. Therefore, it is  
Figure 1: The UDN architecture with VPP. necessary to consider the downlink data rate constraints and downlink signaling resource constraints to ensure the essential service quality of the 5G base station, which is expressed as follows:  
\[\left\{ \begin{array}{l}D_{\text{dd}}^{t}\leq D_{\text{dd}_{\text{max}}}\\ R_{\text{ds}}^{t}\leq R_{\text{ds}_{\text{max}}}\end{array} \right. \tag{6}\]  
where \(D_{\text{dd}_{\text{max}}}\) represents the maximum downlink data rate and \(R_{\text{ds}_{\text{max}}}\) represents the maximum downlink signaling resource. By regulating the number of activated terminals and data traffic, the load regulation power expression of the 5G base station is as follows:  
\[P_{\text{5G,DR}}^{t}=(P_{\text{max,AAU}}-P_{\text{b,AAU}})\Bigg{(}\frac{D_{ \text{dd}}^{t}-{D^{\prime}}_{\text{dd}}^{t}}{D_{\text{dd}_{\text{max}}}}+\frac {R_{\text{ds}}^{t}-{R^{\prime}}_{\text{ds}}^{t}}{R_{\text{ds}_{\text{BE}}}+R_ {\text{dd}_{\text{BE}}}}\Bigg{)} \tag{7}\]  
where \(R_{\text{ds}_{\text{BE}}}\) represents the total number of signaling resource elements used for the downlink and \(R_{\text{dd}_{\text{BE}}}\) represents the total number of data resource elements used for the downlink.