Handle start conditions with battery SOC below minimal SOC

openapi.yaml

@@ -63,7 +63,8 @@ paths:
               $ref: "#/components/schemas/OptimizationInput"
             example:
               batteries:
-                - s_min: 5000
+                - s_capacity: 52000
+                  s_min: 5000
                   s_max: 50000
                   s_initial: 15000
                   s_goal: [0, 0, 40000, 0, 0, 0]
@@ -207,6 +208,12 @@ components:
               - True: The battery can discharge to the grid at any time. The actual decision is
                 subject to the optimization.
               - False: (default) The battery cannot be discharged while power is exported to the grid.
+        s_capacity:
+          type: number
+          minimum: 0
+          description: |
+            The capacity at 100% SOC in Wh. If not specified s_capacity will be set to s_max.
+            s_initial must be less or equal s_capacity, otherwise the optimization will return an error.
         s_min:
           type: number
           minimum: 0

src/optimizer/app.py

@@ -67,6 +67,7 @@ def handle_validation_error(error):
 battery_config_model = api.model('BatteryConfig', {
     'charge_from_grid': fields.Boolean(required=False, description='Controls whether the battery can be charged from the grid.'),
     'discharge_to_grid': fields.Boolean(required=False, description='Controls whether the battery can discharge to grid.'),
+    's_capacity': fields.Float(required=False, description='Battery capacity at 100% state of charge (Wh)'),
     's_min': fields.Float(required=True, description='Minimum state of charge (Wh)'),
     's_max': fields.Float(required=True, description='Maximum state of charge (Wh)'),
     's_initial': fields.Float(required=True, description='Initial state of charge (Wh)'),
@@ -156,6 +157,7 @@ def post(self):
                 batteries.append(BatteryConfig(
                     charge_from_grid=bat_data.get('charge_from_grid', False),
                     discharge_to_grid=bat_data.get('discharge_to_grid', False),
+                    s_capacity=bat_data.get('s_capacity', bat_data['s_max']),
                     s_min=bat_data['s_min'],
                     s_max=bat_data['s_max'],
                     s_initial=bat_data['s_initial'],

src/optimizer/optimizer.py

@@ -25,6 +25,7 @@ class GridConfig:
 class BatteryConfig:
     charge_from_grid: bool
     discharge_to_grid: bool
+    s_capacity: float
     s_min: float
     s_max: float
     s_initial: float
@@ -83,6 +84,7 @@ def __init__(self, strategy: OptimizationStrategy, grid: GridConfig, batteries:
         # scaling for penalty parameters. Make sure goal_penalty is always positive
         self.prc_e_goal_pen = np.min([self.max_import_price, 0.1e-3]) * 10e1
         self.prc_p_goal_pen = np.min([self.max_import_price, 0.1e-3]) * np.max(self.time_series.dt) / 3600 * 10e1
+        self.prc_soc_exc_pen = np.min([self.max_import_price, 0.1e-3]) * 10e2
 
         # penalty for exceeding grid import limit. Result shall not become infeasible but report the violation
         # with helpful information
@@ -136,7 +138,7 @@ def _setup_variables(self):
         self.variables['s'] = {}
         for i, bat in enumerate(self.batteries):
             self.variables['s'][i] = [
-                pulp.LpVariable(f"s_{i}_{t}", lowBound=bat.s_min, upBound=bat.s_max)
+                pulp.LpVariable(f"s_{i}_{t}", lowBound=0, upBound=bat.s_capacity)
                 for t in self.time_steps
             ]
 
@@ -157,6 +159,10 @@ def _setup_variables(self):
                 for t in self.time_steps:
                     self.variables['p_demand_pen'][i][t] = pulp.LpVariable(f"p_demand_pen_{i}_{t}", lowBound=0)
 
+        # penalty variable for staying above max SOC and below min SOC
+        self.variables['s_max_pen'] = [[pulp.LpVariable(f"s_max_pen_{i}_{t}", lowBound=0) for t in self.time_steps] for i in range(len(self.batteries))]
+        self.variables['s_min_pen'] = [[pulp.LpVariable(f"s_min_pen_{i}_{t}", lowBound=0) for t in self.time_steps] for i in range(len(self.batteries))]
+
         # Grid import/export variables [Wh]
         self.variables['n'] = [pulp.LpVariable(f"n_{t}", lowBound=0) for t in self.time_steps]
         self.variables['e'] = [pulp.LpVariable(f"e_{t}", lowBound=0) for t in self.time_steps]
@@ -248,6 +254,12 @@ def _setup_target_function(self):
         if self.is_grid_demand_rate_active:
             objective += - self.grid.prc_p_exc_imp * self.variables['p_max_imp_exc']
 
+        ############################################################################
+        # Penalties for exceeding battery SOC limits at start
+        for i, bat in enumerate(self.batteries):
+            for t in self.time_steps:
+                objective += - self.prc_soc_exc_pen * (self.variables['s_max_pen'][i][t] + self.variables['s_min_pen'][i][t])
+
         ############################################################################
         # Penalties for goals that cannot be met
         for i, bat in enumerate(self.batteries):
@@ -275,7 +287,8 @@ def _setup_target_function(self):
             # penalty for exceeding the grid export limit
             if self.grid.p_max_exp is not None:
                 # negative target function contribution in a maximizing optimization
-                objective += - self.prc_e_grid_exp_pen * self.variables['e_exp_lim_exc'][t]
+                # decrease penalty slightly over time to push limit exceeding to late times
+                objective += - self.prc_e_grid_exp_pen * (1.0 - t * 1e-5) * self.variables['e_exp_lim_exc'][t]
 
         #############################################################################
         # Secondary strategies to implement preferences without impact to actual cost
@@ -311,8 +324,6 @@ def _add_energy_balance_constraints(self):
         Add constraints related to the energy balance to the model.
         """
 
-        self.time_steps = range(self.T)
-
         # Constraint (2): Power balance for each time step:
         # - solar yield
         # - household consumption
@@ -396,6 +407,13 @@ def _add_battery_constraints(self):
         """
         Add constraints related to battery behavior to the model.
         """
+        # constraint for the max and min SOC. If the battery starts with an initial SOC
+        # greater than the maximum SOC or lesser than min SOC, maximum discharging is forced until the max.
+        # SOC is reached or max. charing will be forced until min SOC is reached.
+        for i, bat in enumerate(self.batteries):
+            for t in range(0, self.T):
+                self.problem += (self.variables['s_max_pen'][i][t] >= self.variables['s'][i][t] - bat.s_max)
+                self.problem += (self.variables['s_min_pen'][i][t] >= bat.s_min - self.variables['s'][i][t])
 
         # Constraint (3): Battery dynamics
         for i, bat in enumerate(self.batteries):