Problem constraints

Problem LP constraints.¶

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Linear programming constraints¶

Linear programming constraints (LP constraints) are the rules that gouverne the problem optimization process. They are fondamentally set of equations, they might be either inequality equations ( example : $a + b \leq c$ ) or equality equations ( example : $a + b = c q$ ) constructed based on the LP variables quantities and problem parameters. (See. Problem LP variables and Problem LP constraints).

Set of problem LP constraints¶

Load requirements :

\begin{aligned} L_{k} = P_{k}^{load} + η^{from_Bat} {\cdot P}_{k}^{from_Bat} & \forall k = 1, \dots, n \end{aligned}

Power split :

\begin{aligned} P_{k} = P_{k}^{load} {+ P}_{k}^{to_Bat} & \forall k = 1, \dots, n \end{aligned}

Charge balance constraints :

\begin{aligned} Q_{k} = Q_{k - 1} + η^{to_Bat} \cdot P_{k}^{to_Bat} Δ t - P_{k}^{from_Bat} Δ t \\ Q_{0} = Q_{init} \\ Q_{n} = Q_{final} & \forall k = 1, \dots, n \end{aligned}

Genset constraints :

\begin{aligned} P_{k} \leq {0.9 P}_{\max} {\cdot y}_{k} & \forall k = 1, \dots, n \\ P_{k} \leq {0.2 P}_{\max} {\cdot y}_{k} & \forall k = 1, \dots, n \end{aligned}

Battery logical constraints :

\begin{aligned} y_{k}^{to_Bat} + y_{k}^{from_Bat} \leq 1 & \forall k = 1, \dots, n \\ P_{k}^{to_Bat} \leq 0.9 P_{\max} {\cdot y}_{k}^{to_Bat} & \forall k = 1, \dots, n \\ P_{k}^{from_Bat} \leq 0.9 P_{\max} {\cdot y}_{k}^{from_Bat} & \forall k = 1, \dots, n \end{aligned}

Fuel consumption :

\begin{aligned} {F C}_{k} = {a P}_{k} + b - {f c}_{o f f s e t} \cdot (1 - y_{k}) & \forall k = 1, \dots, n \end{aligned}

Objective linearization :

\begin{aligned} z_{k} \geq y_{k} - y_{k - 1} & \forall k = 2, \dots, n \end{aligned}