nicomignoni/Smart-Grid-Centralized-Opt

Scripts for a university project, a simple centralized/cooperative smart grid energy cost minimization problem.

Brief formulation

The smart grid topology is depicted in the figure on the left, while on the right the single prosumer energy flow.

The tensor of variables is

$\boldsymbol{\Phi}_{tn} = [p_{tn}^{R \to D}, p_{tn}^{R \to E}, p_{tn}^{S \to D}, p_{tn}^{S \to E}, p_{tn}^{S \to R}, p_{tn}^{E \to D}, p_{tn}^{E \to R}, e_{tn}] \in \mathbb{R}^{\Phi \times T \times N}$

where $D$ is the domestic demand, $S$ is the PV generator, $E$ is the storage and the notation $p_{tn}^{X \to Y}$ stands for the energy dispatched from device $X$ to device $Y$ at time $t$ for prosumer $n$ . The storage charge state is $e_{nt}$ for prosumer $n$ at time $t$ .

The optimization problem is

$\displaystyle \min_{\boldsymbol{\Phi}_{tn}}{\sum_{t}{} \Big(C_t \sum_{n}{} (p_{tn}^{R \to D} + p_{tn}^{R \to E}) - R_t \sum_{n}{} (p_{tn}^{S \to R} + p_{tn}^{E \to R})\Big)}$

subject to

$\begin{cases} p_{tn}^{S \to D} + p_{tn}^{S \to E} + p_{tn}^{S \to R} = S_{tn}, \ \forall t \ \forall n \\ p_{tn}^{S \to D} + p_{tn}^{E \to D} + p_{tn}^{R \to D} = D_{t}, \ \forall t \ \forall n \\ e_{tn} = e_{n,t-1} + \eta^{\uparrow}(p_{tn}^{R \to E} + p_{tn}^{S \to E}) - \eta^{\downarrow}(p_{tn}^{E \to D} + p_{tn}^{E \to R}), \ \forall n\, \ \forall t \\ e_{tn} = E^{\text{init}}, \ \forall n\\ e_{tn} \leq E^{\text{max}}, \ \forall t \ \forall n \\ p_{tn}^{R \to E} + p_{tn}^{S \to E} \leq P^{\text{max}}, \ \forall t \ \forall n \\ p_{tn}^{E \to R} + p_{tn}^{E \to D} \leq P^{\text{max}}, \ \forall t \ \forall n \\ \boldsymbol{\Phi}_{tn} \geq \boldsymbol{0}, \ \forall t \ \forall n \end{cases}$

References

N. Vespermann, T. Hamacher and J. Kazempour, "Access Economy for Storage in Energy Communities," in IEEE Transactions on Power Systems, https://doi.org/10.1109/TPWRS.2020.3033999.

N. Vespermann, T. Hamacher, and J. Kazempour, "Electronic companion: Access economy for storage in energy communities", Technical University of Munich, Tech. Rep., 2020. [Online], https://bitbucket.org/nivesp/marketdesign_energycommunities/.

Paul Neetzow, Roman Mendelevitch, Sauleh Siddiqui, "Modeling coordination between renewables and grid: Policies to mitigate distribution grid constraints using residential PV-battery systems", Energy Policy, Volume 132, 2019, https://doi.org/10.1016/j.enpol.2019.06.024.

nicomignoni / Smart-Grid-Centralized-Opt

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Brief formulation

References