## 3 Preventive Control Policy Construction
### Construction Method
\tag{3}\]  
where \(P_{Gi}\) and \(Q_{Gi}\) denote the active power and the reactive power of a power generator node \(n_{Gi}\), respectively, \(P_{Li}\) and \(Q_{Li}\) denote the active power and the reactive power of a load node \(n_{Li}\), respectively, \(v_{i}\) denotes the voltage of a node \(n_{i}\) in the PN, \(freq\) denotes the frequency of an ADN, and \(P_{Gi}\), \(Q_{Gi}\), \(P_{Li}\), \(Q_{Li}\), \(v_{i}\), \(I_{Pi}\), and \(freq\) are all defined in Definition 1. To be safe, it is necessary to limit the value ranges of variables. Correspondingly, \(P_{Gi\_min}\) and \(P_{Gi\_max}\) denote the lower and the upper active power bound of a power generator node \(n_{Gi}\), respectively, \(Q_{Gi\_min}\) and \(Q_{Gi\_Max}\) denote the lower and the upper reactive power bound of a power generator node \(n_{Gi}\), respectively. Similarly, \(\Delta P_{Gi\_min}\) and \(\Delta P_{Gi\_max}\) denote the lower and the upper control action bound, \(P_{Li\_min}\) and \(P_{Li\_max}\) denote the lower and the upper active power bound of a load node \(n_{Li}\), respectively, \(Q_{Li\_min}\) and \(Q_{Li\_max}\) denote the lower and the upper reactive power bound of a load node \(n_{Li}\), respectively, \(v_{i\_min}\) and \(v_{i\_max}\) denote the lower and the upper voltage bound of a node \(n_{i}\) in the PN, \(I_{Pi\_max}\) denotes the upper current bound of a node \(n_{i}\) in the PN. \(freq_{min}\) and \(freq_{max}\) denote the frequency limits of an ADN. \(NON_{P}\) is the number of nodes in the PN. \(\zeta_{i}\) denotes the voltage phase angle of a node \(n_{i}\) in the PN. \(Y_{ij}\) and \(\alpha_{ij}\) denote the admittance and admittance phase angle between a node \(n_{i}\) and a node \(n_{j}\), respectively, in the PN. In order to get the fitted PCP, the objective function and inequality constraints shown in Formulas (1) and (2) are integrated into the infinite horizon discounted expected cumulative reward, and then the immediate reward \(r\) of a transition should be given. The immediate reward \(r\) is composed of a reward \(r_{1}\) reflecting voltage stability, a reward \(r_{2}\) for preventing the CCF caused by the current overload, a reward \(r_{3}\) reflecting the frequency stability, a reward \(r_{4}\) reflecting the control cost, and a reward \(r_{5}\) reflecting robustness against CCF. The reward \(r_{1}\) is shown in Formula (4). \[r_{1}=\sum_{i\in\mathcal{V}_{p}}w_{ni}r_{ni\_1} \tag{4}\]  
where \(r_{1}\) is the weighted sum of \(r_{ni\_1}\), and the definition of \(r_{ni\_1}\) is shown in Formula (5). \(w_{ni}\) is the weight (proportional to the importance of a node) of a node \(n_{i}\), \(V_{P}\) is the set of nodes in the PN. \(r_{1\_ni\_1}\) (greater than zero) and \(r_{1\_ni\_2}\) (less than zero), respectively, denote the specific immediate reward value when the voltage value of the node \(n_{i}\) is in different ranges, \(\|\bullet\|\) denotes the norm, \(v_{i\_normal}\) is the reference voltage value of a node \(n_{i}\), \(v_{ni}=\min\{\|v_{i\_normal}-v_{i\_min}\|,\|v_{i\_max}-v_{i\_normal}\|\}\) is the voltage threshold of a node \(n_{i}\). \[r_{ni\_1}=\left\{ \begin{array}{ll}r_{1\_ni\_1}&\|v_{i}-v_{i\_normal}\|\leq v _{ni}\\ r_{1\_ni\_2}&\|v_{i}-v_{i\_normal}\|>v_{ni}\end{array} \right. \tag{5}\]  
The reward \(r_{2}\) is shown in Formula (6). \[r_{2}=\sum_{i\in E_{P}}w_{ni}r_{ni\_2} \tag{6}\]  
where \(r_{2}\) is the weighted sum of \(r_{ni\_2}\), and the definition of \(r_{ni\_1}\) is shown in Formula (7). \(E_{P}\) is the set of edges in the PN, \(r_{2\_ni\_1}\) (greater than zero) and \(r_{2\_ni\_2}\) (less than zero), respectively, represent the specific reward value when the current value of the node \(n_{i}\) is in different ranges, \(l_{i\_normal}\) is the reference current value of a node \(n_{i}\) in an ADN, \(l_{ni}=lP_{i\_max}\) is the current threshold value of the node \(n_{i}\). \[r_{ni\_2}=\left\{ \begin{array}{ll}r_{2\_ni\_1}&\|I_{i}-I_{i\_normal}\|\leq I _{ni}\\ r_{2\_ni\_2}&\|I_{i}-I_{i\_normal}\|>I_{ni}\end{array} \right.