# Synchronous Remote Calibration for Electricity Meters: Application and Optimization
## 3 Methods
### System Model
#### 3.1.1 Network Model  
In the remote calibration process, the central laboratories and detection points are key components, with calibration tasks scheduled between them using remote technology. We model this process as a distributed remote calibration system, which facilitates task allocation between the server end and the client end. * **Server End:** It comprises metrology experts and essential communication facilities. Given that each expert's specialization and skill level vary, leading to differences in the types and quantities of calibration equipment they can handle, this variation is a key consideration in the scheduling process. Communication devices ensure real-time information exchange between the server and client ends, supporting online calibration operations. Although minimal transmission delays occur during this communication, their impact on the overall calibration process is negligible and can be largely disregarded. * **Client End:** It integrates electricity metering devices (the devices requiring calibration), standard equipment, operating personnel for the procedures, and communication technologies. The system's core components, the electricity metering devices and standard equipment, jointly execute the calibration process. Operating personnel follow remote guidance from experts to execute the actual calibration steps. This role has modest technical requirements and ample human resources, thus not posing a significant constraint in the scheduling strategy. Communication devices once again play a pivotal role in maintaining real-time communication between both ends, with minor delays having little effect on the overall smoothness of calibration activities and can be disregarded. Some parameters of the distributed remote calibration system are shown in Table 1. A distributed remote calibration network is depicted in Figure 2, where detection points are located within the overlapping coverage areas of several laboratory stations. The distributed remote calibration network model is described as \(\mathcal{I}=(\mathcal{N}_{K},N_{G})\), where \(\mathcal{N}_{K}\) and \(\mathcal{N}_{G}\) represent the set of detection points and the set of central laboratories, respectively. Specifically, the set \(\mathcal{N}_{K}=\{K_{1},K_{2},\ldots,K_{i}\}\) denotes the detection points. Each detection point \(K_{i}\in\mathcal{N}_{K}\) hosts multiple clients (standard equipments) and has a two-dimensional coordinate \(\big{(}x_{k_{i}},y_{k_{i}}\big{)}\). Similarly, the set \(\mathcal{N}_{G}=\big{\{}G_{1},G_{2},\ldots,G_{j}\big{\}}\) denotes the central laboratories. Each central laboratory \(G_{j}\in\mathcal{N}_{G}\) accommodates several servers (metrology experts) and is assigned a two-dimensional coordinate \(\big{(}x_{G_{j}},y_{G_{j}}\big{)}\). Additionally, each central laboratory has a coverage restriction denoted by \(G_{j}^{\prime}\). By combining the coordinates of the detection points and central laboratories, the matrix \(\mathbf{D_{KG}}\) represents the distances between them. These distances are calculated using the Euclidean distance Formula (1). \[D_{K_{i},G_{j}}=\sqrt{(x_{K_{i}}-x_{G_{j}})^{2}+(y_{K_{i}}-y_{G_{j}})^{2}} \tag{1}\]