## 4 Case Study
### Actual Power Grid System in a Certain Region
#### 4.3.2 Analysis of Planning Scheme
\begin{tabular}{c c c c} \hline \hline
**Type** & **Symbol** & **Definition** & **SI _Unit_ \\ \hline \multirow{8}{*}{Sets} & \(N_{Y}\) & Set of planning years & / \\  & \(N_{p}\) & Set of candidate lines & / \\  & \(N_{ess}\) & Set of candidate installation nodes for energy storage & / \\  & \(N_{wind}\) & Set of wind farms and solar plants & / \\  & \(N_{solar}\) & Set of wind farms and solar plants & / \\  & \(N_{s}\) & Set of typical scenarios for load and variable energy output & / \\  & \(\mathbf{A^{y}}\) & Node-branch incidence matrix for new lines in year \(y\) & / \\  & \(\mathbf{A^{o}}\) & Node-branch incidence matrices for the initial lines & / \\  & \(\mathbf{A^{p}}\) & Node-branch incidence matrices for the candidate lines & / \\ \hline \multirow{8}{*}{Sets} & \(c_{p}\) & Unit power capacity cost & CNY/MW \\  & \(c_{E}\) & Unit energy capacity cost & CNY/MWh \\  & \(c_{0}\) & Maintenance cost of the energy storage & CNY/MW \\  & \(\sigma\) & Self-discharge rate of the energy storage station & \% \\  & \(\eta_{c}\) & Charging efficiency of the energy storage station & \% \\  & \(\eta_{d}\) & Discharging efficiency of the energy storage station & \% \\  & \(\Delta t\) & Dispatch time interval & h \\  & \(SOC_{min}\) & Lower percentage limits of the state of charge of the energy & \% \\  & \(SOC_{max}\) & Upper percentage limits of the state of charge of the energy & \% \\  & \(T\) & Dispatch period & h \\  & \(\lambda\) & Annual discount rate & \% \\  & \(f_{line}\) & Transmission investment cost & CNY \\  & \(f_{ess}\) & Energy storage investment cost & CNY \\  & \(f_{wind}\) & Wind curtailment penalty cost & CNY \\  & \(f_{solar}\) & Solar curtailment penalty cost & CNY \\ Parameters & \(c_{ij}\) & Unit investment cost of the line & CNY/km \\  & \(L_{ij}\) & Length of the line & km \\  & \(\alpha\) & Energy storage cost coefficient & \% \\  & \(d_{s}\) & Total number of days in scenario \(s\) & days \\  & \(c_{wind}\) & Unit penalty costs for wind curtailment & CNY/MWh \\  & \(c_{solar}\) & Unit penalty costs for solar curtailment & CNY/MWh \\  & \(x_{mes}^{\max}\) & Maximum number of energy storage installations allowed by & / \\  & \(x_{line,ij}^{\max}\) & Maximum number of new lines between nodes \(i\) and \(j\) & / \\  & \(n_{line,ij}^{\max}\) & Number of initial lines & / \\  & \(n_{line,ij}^{\max}\) & Number of candidate lines & / \\  & \(p_{ii}^{\max}\) & Maximum transmission power of a single line between nodes \(i\) & MW \\  & \(\omega_{\text{u,g}}\) & Ramp-up rates of conventional generator \(g\) & MW/h \\  & \(\omega_{\text{d,g}}\) & Ramp-down rates of conventional generator \(g\) & MW/h \\  & \(p_{sm,s}^{\max}\) & Maximum output limits of conventional generator \(g\) & MW \\  & \(p_{sm,g}^{\max}\) & Minimum output limits of conventional generator \(g\) & MW \\  & \(p_{less}^{\max}\) & Charging efficiency of the energy storage device & \% \\  & \(\eta_{ess}^{\max}\) & Discharging efficiency of the energy storage device & \% \\ \hline \multirow{8}{*}{Variables} & \(P\) & Planned charge/discharge power & MW \\  & \(S\) & Planned capacity of the energy storage & MWh \\  & \(e_{t}\) & Remaining energy at time \(t\) in the energy storage station & MWh \\  & \(P_{c,t}\) & Charging power at time \(t\) in the energy storage station & MW \\  & \(P_{d,t}\) & Discharging power at time \(t\) in the energy storage station & MW \\  & \(v_{c,t}\) & Charging states of the energy storage station & / \\  & \(v_{d,t}\) & Discharging states of the energy storage station & / \\ \hline \hline \end{tabular}