Coordinated Optimization of Grid-Forming Control in LCC-MMC Hybrid DC Transmission Systems Considering Virtual Power Angle Evolution Mechanism

Imagine the electrical grid as a massive, invisible ocean of energy, constantly churning to power our lights, phones, and cities. In this ocean, there are two main types of "boats" that help keep the water calm and moving in the right direction. Some boats, called "Grid-Following" boats, are like diligent rowers who simply watch a lighthouse (a signal from the main grid) and row in perfect sync with it. They are great when the ocean is calm, but if a storm hits and the lighthouse flickers, they can get lost or panic. Other boats, called "Grid-Forming" boats, are like the captains of the fleet. They don't just follow the light; they generate their own rhythm and voltage, acting like a virtual engine that helps stabilize the whole ocean, even when the storm is raging. This is crucial as we add more wind and solar power, which are a bit unpredictable, to our energy mix. However, these "Grid-Forming" captains have a tricky secret: when the storm gets too violent, they sometimes get scared and switch into a "current-source" mode, where they stop steering and just push as hard as they can, which can actually make the ship capsize.

This paper tackles exactly that scary moment for a specific type of super-high-voltage power line that connects a sending station to a receiving station. The researchers, working with a model of a ±800 kV system, discovered that when a fault (like a short circuit) hits the receiving end, the "Grid-Forming" converters can get stuck in a dangerous loop where they lose control of the angle that keeps them synchronized with the grid. They call this angle the "virtual power angle," which you can think of as the steering wheel's position relative to the wind. If this angle swings too far, the boat spins out. The authors used computer simulations (specifically on a platform called PSCAD/EMTDC) to prove that by watching the "surplus power" (the extra energy piling up because the storm blocked the exit), they could dynamically tell the captain to slow down just enough to keep the steering wheel from spinning out of control. Furthermore, if the storm gets so bad that slowing down isn't enough, they designed a "smooth switch" that lets the captain hand the wheel over to a "Grid-Following" rower instantly, without jolting the ship, ensuring the boat survives the worst storms.

The Story of the Virtual Steering Wheel

In the world of high-voltage power transmission, engineers are constantly trying to move massive amounts of electricity from where it's made (like giant wind farms) to where it's needed (like big cities). One popular way to do this is using a "hybrid" system: a Line-Commutated Converter (LCC) at the start and a Modular Multilevel Converter (MMC) at the end. Think of the LCC as a sturdy, old-school truck that's cheap and tough, and the MMC as a fancy, flexible sports car that can handle tricky roads.

The problem arises at the destination. Sometimes, the local power grid is "weak," meaning it doesn't have much inertia (like a heavy flywheel) to keep things stable. To fix this, engineers use "Grid-Forming" (GFM) control on the sports car. Instead of just following the grid's rhythm, the GFM control acts like a virtual synchronous generator, creating its own voltage and frequency to hold the grid steady. It's like a captain who can steer the ship even if the compass is broken.

But here's the catch: when a massive fault hits the grid (like a three-phase short circuit), the GFM captain gets overwhelmed. The system tries to limit the current to protect the equipment, and in doing so, the converter switches from acting like a voltage source (a steady captain) to a current source (a frantic pusher). In this state, the "virtual power angle"—the angle between the converter's internal voltage and the grid voltage—starts to swing wildly. If it swings too far, past a specific "Critical Clearing Angle" (CCA), the system loses synchronization and crashes. It's like a pendulum that swings so high it hits the ceiling and gets stuck.

The Two-Part Rescue Plan

The authors of this paper proposed a two-part strategy to save the ship when the storm hits.

1. The "Surplus Power" Brake
The first part of their plan is a smart way to slow down before the crash. They realized that when a fault happens, the sending end keeps pushing power, but the receiving end can't let it out. This creates "surplus power," which causes the DC voltage to spike. The authors used this spike as a warning signal.

Instead of just slamming the brakes or keeping the power setting fixed (which is like driving with cruise control stuck on), they created a "Dynamic Power Reduction" strategy. They calculated the exact amount of unbalanced power and used it to instantly lower the power setpoint of the GFM controller.

• How it works: By lowering the power target, they effectively shrink the "acceleration area" (the force pushing the steering wheel away) and increase the "deceleration area" (the room to stop). This makes the Critical Clearing Angle larger, giving the system more time to recover before it spins out.
• The Result: In their simulations, when they tested a fault that cleared after 5.7 seconds, a fixed power reduction scheme failed to stabilize the system. However, with their dynamic strategy, the system recovered smoothly. The virtual power angle didn't swing as wildly, and the DC voltage and active power returned to normal much faster (around 8 seconds instead of dragging on).

2. The "Smooth Switch" to a Backup Rower
But what if the storm is so severe that even slowing down isn't enough? What if the virtual power angle is already past the point of no return?
The authors' second strategy is a "Smooth Switching" mechanism. If the angle gets too dangerous, the system instantly switches the converter from "Grid-Forming" mode to "Grid-Following" (GFL) mode.

• The Challenge: Usually, switching modes is like yanking the steering wheel from one driver to another while the car is moving at 100 mph. It causes a jolt that can crash the car.
• The Solution: They designed a "feedforward compensation" system. This acts like a co-pilot who watches the main driver and pre-calculates exactly what the backup driver needs to do. Before the switch happens, the backup system (the GFL controller) is already tracking the main system's output. When the switch happens, the inner-loop current references (the actual commands to the motors) remain continuous. There is no jolt, no spike, and no loss of control.
• The Result: In simulations of a severe fault (voltage dropping to 0.1 p.u.), the system that used this smooth switch recovered in about 7.5 seconds. Without the switch, the system struggled to recover, and the current references took much longer to settle.

What the Simulations Showed

The researchers tested these ideas on a detailed computer model of a ±800 kV, 4,000 MW hybrid DC transmission system. They simulated three-phase short-circuit faults on the high-end converter AC bus.

• The Danger Zone: They confirmed that if the fault lasts too long, the virtual power angle exceeds the Critical Clearing Angle, and the system becomes unstable. Specifically, when the fault clearing time was extended to 5.9 seconds, the fixed power reduction scheme failed completely, causing the virtual power angle to keep rising and the system to lose stability. In contrast, the dynamic strategy kept the system stable.
• The Dynamic Advantage: When they compared their dynamic power reduction against a fixed power reduction for the 5.9-second fault test, the dynamic method showed significantly smaller disturbances. The active power dropped to 380 MW but began recovering at 8.5 seconds, whereas the fixed scheme saw the DC voltage continue to rise to 690 kV and the power oscillate severely without recovering.
• The Switching Advantage: When they tested the smooth switching on a severe fault (0.1 p.u. voltage), the system with the switch recovered 1 second faster than the system without it. Crucially, it prevented the converter from getting "locked" in the dangerous current-source mode.

The Bottom Line

This paper doesn't claim to have solved every problem in the world of power grids, but it offers a very specific and clever solution for a known weakness in Grid-Forming converters. By treating the "virtual power angle" like a steering wheel that needs careful management, the authors showed that:

1. Dynamic braking based on surplus power is better than static braking. It gives the system a bigger safety margin.
2. Smooth switching to a Grid-Following mode is a viable emergency exit if the storm gets too big, provided you don't jerk the wheel.

The authors suggest that this approach combines the best of both worlds: the stability of a Grid-Forming captain in calm weather and the reliability of a Grid-Following rower in a hurricane. While these results are based on simulations and not yet tested on a real-world power line, they provide a strong theoretical and modeled foundation for making future high-voltage DC systems safer and more resilient against the inevitable storms of the electrical grid.