Modern power systems face a constant threat. Demand for electricity continues to rise, but our infrastructure cannot always keep up. During the evening hours, energy consumption spikes dramatically. This phenomenon creates dangerous stress on local substations. Engineers call this the “peak load.” If the grid cannot handle this surge, the result is often a voltage collapse or a total blackout. Therefore, finding an efficient solution is critical for grid reliability. In this comprehensive project breakdown, we explore a robust strategy for optimal generator dispatch using MATLAB.
We will simulate a realistic scenario on the standard IEEE 33-bus radial distribution system. Our goal is straightforward yet challenging. We must prevent a substation overload. To achieve this, we will employ quadratic programming to control backup diesel generators. This approach ensures safety while minimizing fuel costs.
Understanding the Peak Shaving Challenge
The concept of peak shaving is simple in theory but complex in execution. Imagine a city that typically consumes low power during the day. However, at 7:00 PM, everyone returns home. Air conditioners turn on. Electric vehicles plug in. Suddenly, the demand skyrockets.
In our MATLAB simulation, we model this exact behavior. We use a 24-hour load profile applied to the IEEE 33-bus system. The total demand reaches a massive 3.7 Megawatts (MW) during the peak. Here lies the problem. We assume our main substation has a strict physical limit of only 2.5 MW. Without intervention, the transformer would fail.
This gap between demand (3.7 MW) and supply capacity (2.5 MW) must be filled. We cannot simply cut power to customers. Instead, we use distributed generation. We placed three diesel generators at heavy load buses within the network. The challenge is not just turning them on. We must determine exactly how much power each unit should produce. This is the core definition of optimal generator dispatch.
Why We Choose Quadratic Programming
You might wonder why we don’t use simple logic to run the generators. Why not just run them at full power? The answer comes down to economics. Diesel fuel is expensive. Every liter counts.
Real-world diesel generators do not have a linear cost. Their efficiency changes based on how much power they output. Engineers represent this fuel cost using a quadratic equation:
Cost=aP2+bP+c
Because the cost function is a curve, linear solvers are not accurate enough. Furthermore, heuristic algorithms like Genetic Algorithms can be slow. Consequently, we utilize MATLAB’s built-in quadprog solver. This tool is designed specifically for quadratic objective functions. It finds the mathematical minimum cost instantly. By using this method, our optimal generator dispatch strategy becomes both fast and financially efficient.
You can learn more about the specifics of the quadprog function logic here.
The Engineering “Secret Sauce”: Reactive Power
Early versions of this simulation faced a critical error. The code calculated the correct active power (MW) to shave the peak. However, the simulation still failed. The grid voltage collapsed to near zero.
Why did this happen?
Power grids require two things to remain stable: Active Power and Reactive Power. Active power does the actual work, like lighting a bulb. Reactive power supports the magnetic fields in transformers and lines. It keeps the voltage “pressure” high.
Initially, our generators acted like simple batteries. They provided only active power. As a result, the current increased, but the voltage sagged dangerously. We fixed this by updating the generator logic. We forced the generators to operate at a 0.9 Power Factor.
In the code, we added a specific line:Â q_gen = p_gen * 0.48. This equation ensures that for every megawatt of power injected, a specific amount of reactive power supports it. This addition stabilized the entire network.
Implementing Optimal Generator Dispatch in MATLAB
Let’s break down the actual implementation. The project consists of three main script files. Each plays a vital role in the simulation.
1. The Database (ieee33_data.m)
First, we need a map of the grid. This file contains the standard data for the IEEE 33-bus system. It lists every bus connection. It also defines the resistance and reactance of every wire. Accurate data is the foundation of any good simulation. Without this, our loss calculations would be meaningless.
2. The Physics Engine (run_radial_power_flow.m)
Next, we need a way to check the grid’s health. We used the Backward-Forward Sweep algorithm. This is a standard iterative method for radial distribution systems.
Crucially, we implemented a “Per Unit” (p.u.) conversion system. Mixing raw Megawatts with Ohms often leads to calculation errors. By converting all values to a normalized per-unit system, the math remains stable. This function returns the minimum voltage of the grid. It also calculates the total power losses in the lines.
3. The Main Logic (main_dg_dispatch.m)
Finally, we have the execution script. This is where the optimal generator dispatch logic lives. The script runs a loop for every hour of the day.
Inside this loop, the code performs a calculation. It compares the current load against the 2.5 MW grid limit. If the load is too high, it calculates the deficit. This “gap” becomes a constraint for the quadprog solver.
The solver then looks at the three diesel generators. It checks their cost coefficients (a,b,c). It automatically assigns more work to the most efficient generator. Once the dispatch is determined, the script calls the physics engine. It verifies that the voltage remains safe.
Analyzing the Simulation Results
The output of our updated code confirms the strategy works. We can analyze the success through three distinct figures generated by MATLAB.
Visualizing Peak Shaving
The first figure displays the load curve. You see a black dashed line representing the city’s raw demand. It rises sharply in the evening. However, the blue shaded area shows the power drawn from the substation.
The result is visually perfect. The blue area rises until it hits the 2.5 MW red limit line. Then, it flattens out completely. It looks like a flat table top. This proves that the optimal generator dispatch successfully prevented the substation from overloading.
Generator Activity
The second figure explains the source of the extra power. It shows a stacked bar chart. During the morning, the chart is empty. The generators are off to save fuel.
However, as the evening peak approaches, the bars appear. The solver dispatches the generators exactly when needed. You can see the load being shared among the three units. This minimizes the total operational cost while ensuring reliability.
Voltage Stability
The third figure is perhaps the most important for safety. In power systems, voltage must stay between 0.90 and 1.10 per unit. In our failed runs, this dropped to 0.70, which signifies a blackout.
With our reactive power fix, the blue voltage line stays healthy. It fluctuates but never drops below 0.93. This confirms that local generation does more than just provide energy. It also acts as a voltage booster for the end of the line.
For further reading on distribution system stability, you can explore resources on IEEE Xplore.
Conclusion
This project demonstrates the power of combining mathematical optimization with electrical engineering physics. We took a standard grid problem and applied a modern solution. We did not rely on expensive hardware upgrades. Instead, we used smart software.
By utilizing MATLAB’s quadprog, we achieved a mathematically precise solution. We satisfied the strict grid limits. We minimized fuel consumption. Most importantly, we maintained voltage stability through reactive power support.
This simulation proves that optimal generator dispatch is not just a theoretical concept. It is a practical necessity for modern smart grids. As electric vehicles and home appliances increase demand, strategies like this will become the standard for utility companies worldwide.