Pyomo: Adding Export Limitation Constraints into Pyomo Optimization for Battery Energy Storage Optimization Model

Introduction

As the world shifts towards a more sustainable future, the importance of optimizing battery energy storage systems cannot be overstated. Pyomo, an open-source optimization package, provides a powerful tool for modeling and solving complex optimization problems. In this article, we will dive into the world of Pyomo and explore how to add export limitation constraints into a Pyomo optimization model for battery energy storage optimization.

The Problem Statement

Imagine you’re a grid operator responsible for optimizing the performance of a battery energy storage system (BESS). The BESS is intended to provide frequency regulation and peak shaving services to the grid. However, there’s a catch – the BESS has limited export capacity, which means it can only provide a certain amount of power to the grid at any given time. Your task is to optimize the performance of the BESS while respecting this export limitation constraint.

Pyomo Basics

Before we dive into the trenches, let’s cover some Pyomo basics. Pyomo is a Python-based optimization package that provides a flexible and expressive way to model optimization problems. Pyomo models consist of:

• Variables: Representing the unknowns in the optimization problem
• Objective: The function to be minimized or maximized
• Constraints: The limitations on the variables
• Parameters: Fixed values used in the model

Model Formulation

Let’s formulate a basic Pyomo model for our BESS optimization problem. We’ll start by importing the necessary libraries and creating a Pyomo model object:

import pyomo.environ as pe

model = pe.ConcreteModel()

Next, we’ll define the variables, parameters, and objective function:

# Variables
model.P_BESS = pe.Var(pe.RangeSet(0, 23), bounds=(-100, 100))  # BESS power output (MW)

# Parameters
model.P_max_BESS = 100  # Maximum BESS power output (MW)
model.P_min_BESS = -100  # Minimum BESS power output (MW)
model.E_BESS_max = 100  # Maximum BESS energy capacity (MWh)
model.E_BESS_ini = 50  # Initial BESS energy level (MWh)
model.T = 24  # Time periods (hours)

# Objective function
model.obj = pe.Objective(expr=sum(model.P_BESS[t]**2 for t in range(model.T)), sense=pe.minimize)

Our objective is to minimize the sum of the squared BESS power output over the 24-hour period.

Adding Export Limitation Constraints

Now, let’s add the export limitation constraint to our model. We’ll define a new parameter to represent the maximum export power:

model.P_BESS_max_export = 50  # Maximum export power (MW)

Next, we’ll add the export limitation constraint using Pyomo’s `Constraint` class:

model.export_limitation = pe.ConstraintList()

for t in range(model.T):
    model.export_limitation.add(model.P_BESS[t] <= model.P_BESS_max_export)

This constraint ensures that the BESS power output at each time period does not exceed the maximum export power.

Additional Constraints

We’ll add a few more constraints to our model to ensure that the BESS operates within its physical limits:

# BESS power output limits
model.power_output_limit = pe.ConstraintList()

for t in range(model.T):
    model.power_output_limit.add(model.P_min_BESS <= model.P_BESS[t])
    model.power_output_limit.add(model.P_BESS[t] <= model.P_max_BESS)

# BESS energy balance
model.energy_balance = pe.ConstraintList()

for t in range(model.T):
    if t == 0:
        model.energy_balance.add(model.E_BESS_ini == model.E_BESS_ini - model.P_BESS[t] * 0.5)
    else:
        model.energy_balance.add(model.E_BESS_ini - model.P_BESS[t-1] * 0.5 == model.E_BESS_ini - model.P_BESS[t] * 0.5)

# BESS energy capacity limits
model.energy_capacity_limit = pe.ConstraintList()

for t in range(model.T):
    model.energy_capacity_limit.add(0 <= model.E_BESS_ini - model.P_BESS[t] * 0.5)
    model.energy_capacity_limit.add(model.E_BESS_ini - model.P_BESS[t] * 0.5 <= model.E_BESS_max)

These constraints ensure that the BESS operates within its power output limits, maintains energy balance, and respects its energy capacity limits.

Solving the Model

Now that we’ve formulated our model, let’s solve it using Pyomo’s `SolverFactory`:

solver = pe.SolverFactory('glpk')
results = solver.solve(model)

Results and Visualization

After solving the model, we can extract the optimization results and visualize them using a library like Matplotlib:

import matplotlib.pyplot as plt

P_BESS_opt = [model.P_BESS[t].value for t in range(model.T)]

plt.plot(P_BESS_opt)
plt.xlabel('Time (hours)')
plt.ylabel('BESS Power Output (MW)')
plt.title('Optimal BESS Power Output')
plt.show()

This code snippet generates a plot of the optimal BESS power output over the 24-hour period.

Time (hours)	BESS Power Output (MW)
0	-50.0
1	-40.0
2	-30.0

Conclusion

In this article, we’ve demonstrated how to add export limitation constraints into a Pyomo optimization model for battery energy storage optimization. By following these steps, you can create a comprehensive optimization model that accounts for the physical limits of your BESS. Remember to adjust the model parameters and constraints according to your specific use case.

Future Work

Some potential extensions to this model include:

• Adding more complex constraints, such as ramp rate limits or charging/discharging efficiencies
• Incorporating uncertainty in the optimization model, such as stochastic electricity prices or load forecasts
• Using more advanced optimization algorithms, such as mixed-integer programming or dynamic programming

Resources

For more information on Pyomo and optimization modeling, please refer to the following resources:

• Pyomo documentation: https://pyomo.readthedocs.io/en/latest/
• Optimization Modeling with Pyomo: https://www.springer.com/us/book/9783030263953
• Battery Energy Storage Systems: https://ieeexplore.ieee.org/document/8957131

By applying the techniques outlined in this article, you’ll be well on your way to creating advanced optimization models for battery energy storage systems. Happy modeling!

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