Demand Response Optimization for Battery Energy Storage

docs/control/pyomo_controllers.md

@@ -58,3 +58,93 @@ tech_to_dispatch_connections: [
   ["battery", "battery"],
 ]
 ```
+
+# Optimized Demand Response Controller
+
+This controller optimizes the dispatch of a Battery Energy Storage System (BESS) based on a pre-defined supervisory signal. This signal could be the Locational Marginal Price (LMP), a demand profile, or a $LMP\times demand$ product depending on the application. The objective is to maximize incentive payments to the battery, subject to constraints on the maximum number of dispatch events per month and on the battery state of charge.
+
+## Definitions
+
+**Given:**
+- $\lambda_t$ := `supervisory_signal`: price, demand, or price $\times$ demand time series at time $t$
+- $\mathcal{W}$ := `peak_window`: set of hours eligible for dispatch (e.g., 12:00--19:00)
+- $\gamma$ := performance incentive (\$/kW per dispatch hour)
+- $\bar{P}$ := `max_charge_rate` (kW): maximum charge and discharge rate, used as deemed capacity since the battery is assumed to always dispatch at full rated power
+- $E_{\max} :=$ `max_capacity` $\times$ (`max_soc_fraction` $-$ `min_soc_fraction`): usable energy capacity (kWh)
+- $\eta_c$ := `charge_efficiency`, $\quad \eta_d$ := `discharge_efficiency`
+- $\overline{\text{SoC}}$ := `max_soc_fraction`, $\quad \underline{\text{SoC}}$ := `min_soc_fraction`
+- `n_control_window` := Horizon length for optimization
+- $\mathcal{T} := \{0, 1, \ldots, T\}$: hourly time steps over `n_control_window`
+- $\mathcal{M}_m$ := set of hours in month $m$, for $m = 1, \ldots, 12$
+
+## Decision Variables
+
+- $u_t \in \{0, 1\}$ := discharge binary: 1 if battery dispatches at hour $t$, 0 otherwise
+- $v_t \in \{0, 1\}$ := charge binary: 1 if battery charges at hour $t$, 0 otherwise
+
+## Optimization Problem
+
+This optimization is executed for each window, during which the performance model is invoked and the initial conditions are set.
+
+### Objective
+
+Maximize total annual incentive revenue:
+
+$$
+\max_{u_t,\, v_t} \quad \gamma \cdot \bar{P} \sum_{t \in \mathcal{T}} u_t
+$$
+
+### Constraints
+
+- Dispatch only within peak window:
+
+$$
+u_t = 0 \qquad \forall\, t \notin \mathcal{W}
+$$
+
+- Dispatch only on high supervisory signal:
+
+$$
+u_t = 1 \implies \lambda_t \geq \lambda^*_m \qquad \forall\, t \in \mathcal{M}_m
+$$
+
+where $\lambda^*_m$ is the threshold selecting the high LMP/peak load hours within month $m$.
+
+- Maximum $N_{max}$ events per month:
+
+$$
+\sum_{t \in \mathcal{M}_m} u_t \leq N_{\max} \qquad \forall\, m, \quad N_{\max}.
+$$
+
+- SoC evolution with charge and discharge:
+
+$$
+\text{SoC}_{t+1} = \text{SoC}_t + \frac{\eta_c \cdot v_t \cdot \bar{P}}{E_{\max}} - \frac{u_t \cdot \bar{P}}{\eta_d \cdot E_{\max}} \qquad \forall\, t \in \mathcal{T}
+$$
+
+- SoC bounds:
+
+$$
+\underline{\text{SoC}} \leq \text{SoC}_t \leq \overline{\text{SoC}} \qquad \forall\, t \in \mathcal{T}
+$$
+
+- No simultaneous charge and discharge:
+
+$$
+u_t + v_t \leq 1 \qquad \forall\, t \in \mathcal{T}
+$$
+
+- No charging during dispatch window (battery reserved for discharge):
+
+$$
+v_t = 0 \qquad \forall\, t \in \mathcal{W}
+$$
+
+- Binary variables:
+
+$$
+u_t \in \{0, 1\}, \quad v_t \in \{0, 1\}, \quad \text{SoC}_t \in [0, 1] \qquad \forall\, t, m
+$$
+Example 34 performs the optimization with a synthetic LMP signal. The look-ahead horizon is set to 10 hours. As this value increases, the computational complexity grows and the solver may take significantly longer to run or fail to converge. Care should be taken when choosing this parameter: a short horizon limits visibility, making it difficult for the optimizer to identify the best dispatch opportunities across the full month. See figure below for the results. 
+
+![](./figures/plm_optimized_dispatch.png)

docs/user_guide/model_overview.md

@@ -288,6 +288,7 @@ Below summarizes the available performance, cost, and financial models for each
     - `'SimpleStorageOpenLoopController'`: open-loop control; manages resource flow based on demand and input commodity
     - `'DemandOpenLoopStorageController'`: open-loop control; manages resource flow based on demand and storage constraints
     - `'HeuristicLoadFollowingStorageController'`: open-loop control that works on a time window basis to set dispatch commands; uses Pyomo
+    - `'PLMOptimizedStorageController'`: optimized controller for demand response that works on a time window basis. 
     - `'PeakLoadManagementHeuristicOpenLoopStorageController'`: open-loop control that reduces peaks rather than trying to meet a load
 - Optimized Dispatch:
     - `'OptimizedDispatchStorageController'`: optimization-based dispatch using Pyomo

examples/34_plm_optimized_dispatch/34_plm_optimized_dispatch.yaml

@@ -0,0 +1,5 @@
+name: H2Integrate_config
+system_summary: PLM MILP-optimized battery dispatch
+driver_config: driver_config.yaml
+technology_config: tech_config.yaml
+plant_config: plant_config.yaml