Modern power systems face increasing stress. Demand peaks are higher than ever. Consequently, distribution networks often operate near their stability limits. When a grid becomes overloaded, the voltage can drop rapidly. If this drop goes unchecked, it leads to a total system collapse. Therefore, engineers must design robust strategies for emergency voltage recovery. In this post, we explore a sophisticated MATLAB project that solves this critical problem. We will compare traditional load shedding against modern Electric Vehicle (EV) integration.
Understanding the Crisis Scenario
Voltage collapse is a nightmare for utility operators. It happens when the power demand exceeds what the lines can deliver. In our MATLAB simulation, we model this exact scenario using the IEEE 33-bus system. We artificially increase the system load by a factor of three.
The results are immediate and alarming. The simulation shows the minimum voltage dropping to roughly 0.55 per unit (p.u.). Standard safety limits usually require voltage to stay above 0.90 p.u. Therefore, a value of 0.55 represents a complete blackout. Standard power flow equations often fail at these low levels. However, our project uses a robust physics engine to model this crisis accurately. This sets the stage for implementing our recovery strategies.
Strategy 1: Optimal Load Shedding
The traditional method to save a crashing grid is load shedding. This is a “last resort” demand response technique. The utility company deliberately cuts power to specific areas to prevent the entire grid from failing. While effective, it causes significant disruption to customers.
In this project, we treat load shedding as a mathematical optimization problem. We do not want to cut power randomly. Instead, we want to calculate the minimum amount of load to shed. This ensures the grid recovers to 0.90 p.u. while keeping as many lights on as possible.
We utilize MATLAB’s linprog solver for this task. Linear Programming is fast and efficient. It minimizes the total kilowatts (kW) removed from the system. However, the relationship between power and voltage is non-linear. Therefore, we cannot solve this in one step. We implemented a process called Successive Linear Programming (SLP). The code calculates the sensitivity of the grid, makes a small correction, and repeats. This iterative process finds the precise solution to the emergency voltage recovery problem.
Strategy 2: Electric Vehicle V2G Support
Smart grids offer a better alternative to blackouts. Electric Vehicles (EVs) are essentially large batteries on wheels. Vehicle-to-Grid (V2G) technology allows these cars to send power back into the network.
In our second simulation scenario, we deploy EV fleets at the weakest points of the grid. Instead of cutting customer load, we inject active power at specific buses. The results are remarkable. The simulation proves that injecting power at just four locations—Buses 18, 25, 32, and 33—stabilizes the entire network.
Furthermore, EVs can provide reactive power support. This acts as a voltage booster. Consequently, the grid voltage recovers to the safe target of 0.90 p.u. The most significant advantage here is customer satisfaction. Unlike load shedding, V2G support keeps the power flowing for everyone.
Breaking Down the MATLAB Code
This project relies on four interconnected MATLAB scripts. Each file performs a specific function to ensure the simulation is accurate and robust.
The Database:Â ieee33_data.m
First, we need a map of the electrical network. This file contains the standard IEEE 33-bus data. It defines the connections between buses. It also lists the resistance and reactance of every wire. This data forms the foundation of our physical model.
The Physics Engine:Â run_radial_power_flow.m
Simulating a blackout is mathematically difficult. Standard algorithms often crash when voltage drops below 0.7 p.u. Therefore, we built a custom physics engine using the Backward-Forward Sweep method. Additionally, we coded everything using the Per-Unit (p.u.) system. This normalization keeps the math stable. It allows us to simulate voltages as low as 0.55 p.u. without errors.
The Sensitivity Logic:Â calc_voltage_sensitivity.m
To optimize the grid, we need to know how it reacts to changes. This script calculates the Jacobian Matrix (dV/dP). It runs a loop that perturbs every bus by 1 kW. Then, it measures the resulting voltage change. This matrix tells the linprog solver exactly where to cut load or inject power for maximum effect.
The Master Controller:Â main_voltage_recovery_pro.m
Finally, the main script ties everything together. It compares the crisis scenario against the two solutions. This script demonstrates the power of iterative design in engineering.
Analyzing the Visualization Results
The code generates three professional figures to visualize the data. These plots make the complex math easy to understand.
Figure 1: Voltage Profiles
This graph compares the three states of the grid. The black line shows the deep voltage sag of the crisis. The red line shows the profile after load shedding. It hugs the 0.90 safety line perfectly. The green line shows the recovery using EVs. Both recovery methods work, but they achieve the result differently.
Figure 2: Corrective Actions
This bar chart reveals the cost of each strategy. The red bars appear at almost every bus. This indicates that load shedding affects the entire city. Conversely, the green bars appear at only four locations. This highlights the efficiency of targeted EV injection.
Figure 3: Power Balance
This stacked bar chart summarizes the total energy impact. In the shedding scenario, the chart shows that we lost over 60% of the total load. We had to shut down the majority of the city to save the grid. In the EV scenario, the chart is full. We served 100% of the customer demand. This visual evidence proves that V2G is the superior strategy for emergency voltage recovery.
For more details on linear programming applications, you can check the MathWorks Optimization Toolbox documentation.
Why Linearization Matters
You might wonder why we use a linear solver for a non-linear grid. The answer is speed. In an emergency, decisions must be made in milliseconds. Linear programming is computationally efficient.
However, accuracy is also vital. This is why we use the Successive Linear Programming (SLP) approach. By recalculating the sensitivity matrix in every loop, we combine the speed of linear solvers with the accuracy of non-linear physics. The code usually converges to the optimal solution within four to five iterations. This technique is widely used in professional power system software.
Conclusion
This MATLAB project provides a comprehensive look at modern grid stability. We successfully modeled a severe voltage collapse. We demonstrated that while load shedding works, it comes at a high cost to the consumer.
Alternatively, integrating EV fleets offers a smart solution. It maintains grid stability without disrupting service. This project serves as an excellent resource for electrical engineering students and researchers. It bridges the gap between theoretical power flow analysis and practical optimization techniques. Mastering these concepts is essential for building the resilient smart grids of the future.
For further reading on distribution system challenges, the IEEE Power and Energy Society offers numerous resources.