Stabilizing HVDC Links With Adaptive Controls

Modern power systems continue to increasingly rely on interconnection and integration of renewable energy sources, making high-voltage direct current (HVDC) links important in facilitating efficiency in long-distance power transmission. HVDC links not only offer precision in power flow control but also reduce losses, allowing for a flexible grid integrated with a range of energy sources. However, with the increased volatility of renewable energy sources and the decentralization of power generation, there is some complexity in these grid systems that directly affect the HVDC technology, which has to adapt to the dynamic of AC grids.

Figure 1. A substation with power converters that handle high voltage. Image used courtesy of Pixabay

Overview of HVDC Systems and AC Grid Disturbances

In asynchronous grids, HVDC systems are often used for interconnection and power transfers over long distances by converting alternating current (AC) to direct current (DC), transmitted at high voltage. At the receiving end, the HVDC is converted back to AC by converter stations available at both ends of the link. Compared to traditional AC lines, HVDC systems feature less resistance, reduced reactive power issues, and are less prone to charging currents.

The stability of HVDC links can, however, be affected by transient faults, voltage sags, and frequency changes in AC grids. These grid disturbances, if not managed correctly, risk causing disruptions in power distribution. Traditional control methods have often depended on the use of fixed parameter controllers like proportional-integral (PI) controllers, feedback loops, and droop control schemes that work by adjusting the output of the converter to maintain a steady operation in response to voltage and current changes. These traditional control methods are, however, less adaptable in the event of grid disturbances as they cannot quickly adjust power to dynamically respond to grid changes. Designed with linear systems assumption, the conventional control methods cannot handle non-linear dynamics in power systems, evident during disturbances.

Advanced Converter Control Strategies

One of the most common inverter control methods is the adaptive control technique that continuously changes response based on the condition of the grid in real-time. Using algorithms like Kalman filtering or recursive least squares, the adaptive method can estimate parameters in the HVDC links dynamically, identifying variations in aspects like voltage, current, and frequency of the power in the grid. For grid stability, this control method allows for gain setting. For instance, the controller might adjust to tackle transient faults by increasing damping for oscillation suppression and later reverting to the standard working state when the condition of the grid is steady. This ensures resilience in HVDC links even in fluctuations in the condition of the grid.

Another converter control approach is known as a droop scheme, which allows for decentralized regulations of power systems. This involves adjusting the output voltage of the converter and its frequency to respond to reactive and active power flow. By intentionally allowing the output voltage to “droop” (decrease) about a preset characteristic curve, power can be proportionally shared among multiple converters without centralized control. Operating on a fixed characteristic curve, the droop scheme is not an ideal choice to tackle all disturbances in the grid. Therefore, this scheme can be integrated with adaptive control for dynamic adjustments of droop parameters in real-time. The integration of the two control methods offers a coordinated response system that balances the need for the rejection of rapid disturbances with the sharing of steady-state power, creating a more resilient HVDC system.

To better understand and ensure the stability of HVDC links, it is essential to consider quantitative analysis frameworks like Eigenvalue analysis and Bode plot evaluations. For linearization of nonlinear HVDC converter's dynamic equations, Eigenvalue analysis is done around steady state operating point by considering state vectors (x) such as current, control states, and voltages. Other than the input state, the input vector (u) is also considered in representing the linearized model, as shown below, where the state matrix that handles the dynamics in the system is defined by (A), and the input matrix is represented by (B). This analysis helps power engineers assess instabilities in the HVDC links. In this case, all Eigenvalues can have negative real parts, and the system is considered stable in this state. However, if any of the Eigenvalues have a positive real part, the system might be unstable. When the value nears the imaginary axis, it could suggest oscillatory behavior sensitive to changes in parameters.

\[x^{\cdot}=Ax+Bu\]

Bode plot, on the other hand, is a quantitative tool that works well in assessing the stability of the control systems of the HVDC links. Offering a frequency-domain perspective on a system’s dynamic, Bode plots visually represent the system's reaction to sinusoidal inputs across different frequencies. Components of a Bode plot include the gain margin (GM) in the magnitude plot, which assesses the point of instability, and the phase margin in the phase plot, which depicts the phase shift in the system. From the sample bode plot of an HVDC system in Figure 2 below, it can be noted that there is a large phase margin, indicating the converter control system can handle additional phase lags from grid disturbances or delay without risking oscillations or instabilities. On the same note, when the gain margin is okay, the controller can withstand deviation in parameters and grid disturbances without facing runaway amplifications. Analysis of these margins can aid in fine-tuning adaptive and droop control methods to ensure HVDC system stability amid grid disturbances.

Figure 2. The Bode plot of the HVDC converter control system reveals a significant peak in the magnitude response near 10 rad/s and a sharp phase shift from -90° to -180°. These features indicate crucial frequency ranges that demand careful management to ensure system stability. Image used courtesy of Bob Odhiambo

Fault Ride-Through Capabilities and Modern MMC Technologies

In HVDC links, fault ride-through (FRT) forms one of the systems that allows the links to remain functional during transient faults in the AC grids. This FRT works to prevent disconnection or power shutdowns in conventional HVDC systems resulting from problems like voltage drop, fluctuations in frequencies, or short circuits. To implement FRT, strategies like rapid current limiting to protect the semiconductor devices in the HVDC system, support for dynamic reactive power for a stable AC voltage, and the integration of energy storage to handle imbalances in transient power can be considered for a more resilient HVDC link.

HVDC links modeled on the modular multilevel converter (MMC) feature enhanced FRT compared to those with two- or three-level converters. This is because MMC's multiple submodules provide redundancy by allowing the bypass of faulty modules, preventing a total system shutdown. For controlled fault recovery, MMC’s decentralized energy storage capacitors in its submodules and gradual power restoration after a fault to reduce inrush current makes its use for stability common in modern HVDC links.

As the technology in HVDC links improves, it's essential to understand how to create resilient and future-proof power systems. Engineers can design stable and secure modern power grids with efficient HVDC links through adaptive control strategies.