task: determine feasible steady-state operating points for joint gas-power networks while ensuring the maximal delivery of gas and power loads simultaneously
the MLD problem maximizes the amount of nongeneration gas load and active power laod simultaneously
- nongeneration gas load: gas demand uncommitted to electric power generators)
Objective term relating to the amount of nongeneration gas load be defined by:
\(\eta_G (d) := (\sum\limits_{i \in D^{'}}\beta_i d_i) (\sum\limits_{i\in D^{'}}\beta_i \bar{d}_i)^{-1}\)
-
where \(\mathcal{D}^{'}\) is the set of the delivery points in the gas network not connected to interdependent generators in the power network
-
\(\beta_i \in \mathbb{R}_+\) is a predefined restoration priority for delivery \(i \in \mathcal{D}^{'}, d_i\)
- \(d_i\) is the variable mass flow of gas delivered at \(i \in \mathcal{D}^{'}\) and \(\bar{d_i}\) is the maximum deliverable gas load at \(i \in \mathcal{D}^{'}\)
-
\(\beta_i \in \mathbb{R}_+\) is a predefined restoration priority for delivery \(i \in \mathcal{D}^{'}, d_i\)
Objective term relating to the amount of active power load can be defined by
\(\eta P(z^d) := (\sum\limits_{i\in \mathcal{L}} \beta_i z^d_i |\mathbb{R}(S^d_i)|)(\sum\limits_{i\in \mathcal{L}} \beta_i |\mathbb{R}(S^d_i)|)^{-1}\)
- \(\mathcal{L}\) is the set of loads in the power network
- \(\beta_i \in \mathbb{R}_+\) is the load restoration priority for load \(i \in \mathcal{L}\)
-
\(z_i \in |0,1|\) is a variable that scales the absolute maximum amount of active power load
- \(|\mathbb{R}(S^d_i)|\) , at load \(i \in \mathcal{L}\)