From 3336eaf13ae2a92e84cf9755e44cb823ba9f0023 Mon Sep 17 00:00:00 2001 From: Juliette-Gerbaux <130555142+Juliette-Gerbaux@users.noreply.github.com> Date: Tue, 12 Nov 2024 11:09:19 +0100 Subject: [PATCH] Fix documentation for hydro heuristic (#2488) Co-authored-by: Juliette-Gerbaux --- docs/user-guide/solver/06-hydro-heuristics.md | 46 ++++++++++--------- 1 file changed, 25 insertions(+), 21 deletions(-) diff --git a/docs/user-guide/solver/06-hydro-heuristics.md b/docs/user-guide/solver/06-hydro-heuristics.md index 78ff065933..9a684926d9 100644 --- a/docs/user-guide/solver/06-hydro-heuristics.md +++ b/docs/user-guide/solver/06-hydro-heuristics.md @@ -33,7 +33,7 @@ not be confused with those of the document "optimization problem formulation" The hydro storage energy monthly and weekly profiles of each zone $z$ do not depend at all on the local demand and must-run generation in $z$ - $L_{z.}^+$ Time-series of "net" load for zone $z$, defined as: $L{z.}^+ = L{z.} - M{z.}$ -- $L_{z.}$ Time-series of "weighted" load for zone $z$, defined as:_ $L_{z.} = A^t L_{z.}^+$ +- $L_{z.}$ Time-series of "weighted" load for zone $z$, defined as: $L_{z.} = A^t L_{z.}^+$ All following parameters are related to the generic zone $z$: @@ -47,9 +47,9 @@ not be confused with those of the document "optimization problem formulation" - $S$ Reservoir size -- $\overline{S_d}$ Reservoir maximum level at the end of day d, expressed as a fraction of $S$ (rule curve) +- $\overline{S_d}$ Reservoir maximum level at the end of day d (rule curve) -- $\underline{S_d}$ Reservoir minimum level at the end of day d, expressed as a fraction of $S$ (rule curve) +- $\underline{S_d}$ Reservoir minimum level at the end of day d (rule curve) - $S_0$ Reservoir initial level at the beginning of the first day of the "hydro-year" @@ -72,18 +72,18 @@ not be confused with those of the document "optimization problem formulation" - $W_m^k$ Energy to generate on month m, at the end of stage k of pre-allocation -Following variables and parameters are local to linear optimization problems $M$ & $D(Tm)$ +Following variables and parameters are local to linear optimization problems $M$ & $D(m)$ solved within the heuristic. For the sake of clarity, the same generic index is used for all time steps, -knowing that in $M$ there are 12 monthly time-steps, while in $D(m)t$ there are from 28 to 31 daily +knowing that in $M$ there are 12 monthly time-steps, while in $D(m)$ there are from 28 to 31 daily time-steps. Costs $\gamma_{Var}$ given to these variables are chosen to enforce a logical hierarchy of penalties (letting the reservoir overflow is worse than violating rule curves, which is worse than deviating from the generation objective assessed in stage 1, etc.) -- $Y$ Generation deficit at the end of the period, as compared to the objective aimed at +- $W$ Generation deficit at the end of the period, as compared to the objective aimed at (positive variable) -- $O_t$ Overflow from the reservoir on time step $t$ +- $O_t$ Overflow from the reservoir on time step $t$ (positive variable) -- $G_t, \overline{G_t}$ Optimal generation and maximum generation on time step $t$ +- $G_t, \overline{G_t}, \underline{G_t}$ Optimal generation, maximum and minimum generation on time step $t$ - $T_t$ Generation objective assessed in the first stage, for time step t ( $W_m^1$ or $W_d^1$) @@ -95,9 +95,9 @@ from the generation objective assessed in stage 1, etc.) - $\Delta$ Maximum deviation throughout the period -- $V_t^+$ Amplitude of the violation of the upper rule curve at time step $t$ +- $V_t^+$ Amplitude of the violation of the upper rule curve at time step $t$ (positive variable) -- $V_t^-$ Amplitude of the violation of the lower rule curve at time step $t$ +- $V_t^-$ Amplitude of the violation of the lower rule curve at time step $t$ (positive variable) - $Y$ Maximum violation of lower rule curve throughout the period @@ -117,17 +117,20 @@ $$else: \text{for } m\in [1, 12]: \{W_m^1 \leftarrow I_m\}$$ _M2:_ -$$\text{for } m\in [1, 12]: W_m^2 \leftarrow \text{Solution of linear problem M}$$ +$$if (\mu) : \text{for } m\in [1, 12]: W_m^2 \leftarrow \text{Solution of linear problem M}$$ + +$$else : W_m^2 \leftarrow W_m^1$$ _D1:_ $$if (j): \text{for } d\in [1, 31]: W_d^1 \leftarrow \frac{L_d^{\beta}. (W_m^2)}{(\sum_{d\in m}{L_d^{\beta}})}$$ -$$else: \text{for } d\in [1, 31]: W_d^1 \leftarrow \frac{I_d . (W_m^2)} {(\sum_{d\in m}{I_d})}$$ +$$else: \text{for } d\in [1, 31]: W_d^1 \leftarrow I_d $$ _D2:_ -$$\text{for } m \in [1, 12]: W_{d\in m}^2 \leftarrow \text{Solution of linear problem D(m)}$$ +$$if(\mu) : \text{for } m \in [1, 12]: W_{d\in m}^2 \leftarrow \text{Solution of linear problem D(m)}$$ +$ else : \text{for } m \in [1, 12]: W_{d\in m}^2 \leftarrow$ Solution of a simplified version of linear problem $D(m)$ without reservoir levels _End_ @@ -146,9 +149,9 @@ $$S_t \geq 0$$ $$S_t \leq S$$ -$S_t + G_t - S_{t-1} = I_t$ (see note [^monthly_allocation]) +$G_t \geq \underline{G_t} $ and $G_t \leq \overline{G_t} $ -$$\sum_{t}{G_t} = \sum_{t}{T_t}$$ +For $t\in [1,12], S_{t} + G_{t} - S_{t-1} = I_{t}$ (see note [^monthly_allocation]) and $S_{12} = S_{0}.$ $$G_t - D_t \leq T_t$$ @@ -160,27 +163,28 @@ $$V_t^+ - S_t \geq -\overline{S_t}$$ $$Y - V_t^- \geq 0$$ +$$\Delta - D_t \geq 0$$ **Optimization problems $D(m)$** -$$\min_{G_t, S_t, ...}{\gamma_{\Delta}\Delta + \gamma_Y Y + \sum_{t}{(\gamma_D D_t + \gamma_{V-} V_t^- + \gamma_{O} O_t + \gamma_S S_t)}}$$ +$$\min_{G_t, S_t, ...}{\gamma_{\Delta}\Delta + \gamma_Y Y + \gamma_{W}W+ \sum_{t}{(\gamma_D D_t + \gamma_{V-} V_t^- + \gamma_{O} O_t + \gamma_S S_t)}}$$ s.t $$S_t \geq 0$$ $$S_t \leq S$$ -$$G_t \geq 0$$ +$$G_t \geq \underline{G_t}$$ $$G_t \leq \overline{G_t}$$ -$S_t + G_t + O_t - S_{t-1} = I_t$ (see note [^daily_allocation]) +$S_t + G_t + O_t - S_{t-1} = I_t$ (see note [^daily_allocation]) (initial level of the period is either $S_0$ if $m=1$ or the final level found in solving $D(m-1)$) -$\sum_{t}{G_t + Y} = \sum_{t}{T_t} + Y_{m-1}$ (value of Y previously found in solving **$D(m-1)$**) +$\sum_{t}{G_t + W} = \sum_{t}{T_t} + W_{m-1}$ (0 if $m=1$ else value of $W$ previously found in solving **$D(m-1)$**) -$$G_t - D_t \leq T_t$$ +$$G_t - D_t \leq T_t + \frac{W_{m-1}}{|d \in m|}$$ -$$G_t + D_t \geq T_t$$ +$$G_t + D_t \geq T_t + \frac{W_{m-1}}{|d \in m|}$$ $$\Delta - D_t \geq 0$$