I want to formulate a decentralized model for my centralized model, I’m not sure how will be the formulation.

My centralized model is energy management model for 4 houses, has import/export power cost term, battery degradation cost and peer to peer cost term.

I know that the model is coupled with the peer to peer term and not sure how to formulate it using ADMM.

this is the objective function of my centralized model for 96 time step(24 hours , 15 mins time period):
I’m using pyomo solver in python

def objective_rule(model):
    return sum(
        sum(
            sum(
                p2p_cost[m] * delta_t * (model.Pe[n, m, t])**2    # P2P trading cost with delta_t
                for n in M if n != m
            )  # Inner loop for peer-to-peer exchanges
            +p2p_cost[m]*delta_t *(sum((model.Pe[m,n, t]) for n in M if n != m))**2
            + tou[t] * model.P_import[m, t] * delta_t  # Cost for grid imports
            - rho_md[m] * model.P_export[m, t] * delta_t  # Revenue for grid exports
            + rho_battery[m] * (model.P_charge[m, t] + model.P_discharge[m, t]) * delta_t  # Battery cost
            for m in M  # Middle loop for each house
        )
        for t in T  # Outer loop for each time step
    )

model.objective = pyo.Objective(rule=objective_rule, sense=pyo.minimize)

I tried to formulate the model using local problem and global problem.

the local problem will calculate the local variable needed to do the update for the global variable which needed to maintain the consisus between the peer to peer term.