Optimal Operation in Power Systems

Introduction

Optimization is the decision-making of how we can utilize the limited amount of resources in the best way (optimally!) such that we achieve our desired goal (objective) while also respecting any given conditions (constraints).

For example, in a power system, if we have three generators each with its own cost function and a 24-hour demand forecast for the next day, then day-ahead decision-making involves deciding how to operate those generators so that:

• The total system cost is minimized.
• Supply and demand remain balanced.
• Network security and resource constraints are never violated.

This way, we run the generators optimally to meet tomorrow’s demand at the lowest possible cost!

Microgrid Overview

Microgrids are the small scale power grid, that has there own distributed generation resources and demand. It can be connected to the external grid while it can also operate in the islanded mode.

Optimization Model

The optimization problem has the following components:

• Objective Function:
  Minimize:
     e.g. cost, load shedding.
  Maximize:
     e.g. profit.
• Decision Variables:
  Continuous:
     e.g. generator power, load-shedding amount.
  Binary:
     e.g. on/off status of line or battery charging/discharging status.
  Discrete integers:
     e.g. number of generators to install.
• Constraints:
  Power balance constraints.
  Limiting constraints:
     e.g. generators minimum and maximum limits.
  Operational constraints:
     e.g. state of charge of the battery.
  Binary constraints:
     e.g. controlling that the charging and discharging don't happen at the same time.

Economic Dispatch (Optimal Operations)

Economic dispatch refers to determining the operational schedules of dispatchable generators, energy storage systems, and external grid exchanges so that the total operational cost of the system is minimized, subject to all operational and limit constraints.

Consider The Below System As An Example

The above system has 5lines, 4buses, 2DGs, 2Load, 1BESS, 1RES, and an external grid connection.

Centralized Approach

To determine the operational schedule of the system we solve the optimization model. The centralized approach assumes that there is a central controller (energy management system EMS) that performs optimization.

Mathematical Model

The objective of microgrid is to minimize the cost while maintaining supply and demand balance. The optimization model is as follows:

Operation Results Figure

Operation Results Data Table

Optimal Power Flow

In optimal power flow, we consider network constraints—such as limits of line and bus voltages—and determine both power flows and dispatch schedule. linear power flow model assumes “linear mathematical formulation”, consider only each line susceptance and buses voltage angles.

Changes in Mathematical Model

The nodal power balance equation is:

While the objective function and other constraints remains the same as in centralized mathematical modelling.

Optimal Power Flow Results

Power Flow Heatmap

Code Implementation

Conclusion

This project models and solves the optimal operation of a microgrid over 24 hours. It highlights the importance of MILP in energy management, showcasing how economic dispatch, storage operation, and optimal power flow constraints are handled in a centralized framework.