Research on Voltage Unbalance in Shared Transmission Corridors Based on Capacitance Parameter Matrix Asymmetry

Imagine a world where electricity travels on giant, high-speed highways stretching across the sky. These are the transmission lines, carrying massive amounts of power from where it's made to where it's needed. But sometimes, to save space and money, these giant highways have to share the same narrow path, or "corridor," with smaller, local roads—the distribution lines that actually deliver power to your home. Think of it like a supersonic jet flying just a few feet above a quiet neighborhood street. While the jet is doing its job, its sheer size and speed create a powerful wind that can rattle the windows and knock over trash cans on the street below. In the world of electricity, this "wind" is a strong electric field. When the high-voltage line and the low-voltage line get too close, this electric field can push and pull on the electricity in the smaller line, making the power wobble. This wobble is called "voltage unbalance," and if it gets too bad, it can mess up the sensitive electronics in our homes or even cause the power grid to trip and shut down.

This paper dives into a specific, tricky version of this problem found in Northwest China, where 750 kV ultra-high-voltage lines run dangerously close to 35 kV distribution lines. The researchers wanted to understand exactly why this happens and how to predict it. They discovered that the culprit isn't just the distance between the lines, but the way the lines are arranged in space. Because the lines aren't perfectly symmetrical (like a triangle vs. a flat line), the electric field creates an uneven "push" on the three phases of electricity. The team built a detailed computer model to measure these invisible forces, tested how different distances and lengths change the problem, and even created a smart computer program (a neural network) that can predict the wobble with incredible accuracy. Their goal was to give engineers a simple tool to design safer power lines that don't rattle the neighborhood.

The Electric Tug-of-War

Let's break down what the researchers found. Imagine the three wires of a distribution line as three friends holding hands in a circle, trying to keep their balance. Normally, they are perfectly equal. But when a giant, high-voltage line flies overhead, it acts like a giant magnet pulling on them. Because the friends are standing in different spots relative to the magnet, one friend gets pulled harder than the others. This is the "capacitance matrix asymmetry" the paper talks about. It's just a fancy way of saying the electric "pull" isn't the same for all three wires because of their geometry.

The researchers used a powerful simulation tool called the Finite Element Method (FEM) to map out this invisible electric landscape. They treated the wires like a complex web of springs and pulls. Their model showed that when the distribution line is empty (no-load), the electric pull from the high-voltage line causes one specific phase (the "B" phase) to get a voltage boost, while the others lag behind. It's like one friend in the circle suddenly getting taller, throwing off the whole group's balance.

The Rules of the Game

The team then ran a series of experiments in their computer world to see what makes this wobble better or worse. They looked at four main factors:

1. How far apart are they? (Coupling Distance)
   The closer the lines are, the worse the wobble. But here's the good news: the effect drops off very quickly. The researchers found that once the lines are more than 100 meters apart, the electric pull becomes so weak that it barely causes any trouble. It's like standing far enough away from a loud speaker that the music just becomes a faint hum.

2. How long are they side-by-side? (Coupling Length)
   If the lines run parallel for a long time, the wobble gets worse. In their simulations, when the lines ran together for 18 km, the voltage unbalance was significant. As they extended the parallel section from 2 km to 20 km, the unbalance grew from about 5% to 10%. The longer the "tug-of-war" lasts, the more the balance is disturbed.

3. How much of the line is actually touching? (Coupling Ratio)
   Sometimes the lines don't run parallel for the whole trip. The researchers found that if the distribution line spends more of its time running parallel to the high-voltage line (a higher "coupling ratio"), the problem gets worse. When the parallel section went from 10% to 90% of the total length, the unbalance jumped from 1% to nearly 10%.

4. Is the line busy? (Load Power)
   This is the most interesting part. When the distribution line is empty (no load), the wobble is at its worst. But as soon as you start using power—like turning on lights or appliances—the wobble shrinks! The researchers saw that as the load increased from 0 to 200 kW, the unbalance dropped sharply from nearly 10% down to about 2.5%. If you keep adding power up to 1000 kW, the wobble stabilizes and stays below 1%. It's as if the "friends" holding hands got stronger and more stable once they started doing work together, making them less sensitive to the giant magnet overhead.

The Crystal Ball

Finally, the researchers wanted to know if they could predict this wobble without running a full, complex simulation every time. They built a "neural network," which is a type of computer brain that learns from patterns. They fed it data on the distance, length, ratio, and load, and asked it to guess the voltage unbalance.

The result? The computer brain was incredibly accurate. When they tested it on new scenarios it hadn't seen before, the predictions were almost perfect. The difference between the computer's guess and the actual simulation was less than 1% on average (specifically, the average relative error was 0.464%). In fact, for one test case, the error was only 0.27%. This means engineers can now use this simple, fast tool to check if a new power line design will be safe, without needing to do hours of heavy math.

The Bottom Line

This paper doesn't just say "voltage unbalance is bad." It explains exactly why it happens in these shared corridors: the uneven electric pull caused by the lines' geometry. It proves that while the problem is real, it can be managed. By keeping the lines 100 meters apart, keeping the parallel sections short, or ensuring the lines have a decent load, the voltage wobble can be kept under control. The authors have provided a reliable, fast way to predict these issues, helping engineers design power grids that are both efficient and safe for everyone living nearby.