A Data-Driven Optimal Control Architecture for Grid-Connected Power Converters

This paper proposes "DeePConverters," a novel data-driven optimal control architecture based on DeePC that enables grid-connected power converters to implicitly learn grid characteristics from measured data and adaptively achieve robust, optimal performance without relying on simplified or inaccurate grid models.

The Gist

Imagine the electrical grid as a massive, bustling city. In this city, power converters are the smart traffic lights and intersection managers. They connect renewable energy sources (like solar panels and wind turbines) to the main grid, ensuring electricity flows smoothly without causing blackouts or traffic jams.

For decades, these "traffic lights" have been managed by PID controllers. Think of PID controllers as old-school, rigid traffic rules. They work well if the city is simple and predictable. But today's city is chaotic: the weather changes (wind/solar intermittency), the population grows and shrinks, and the road conditions vary wildly. The old rules were written based on a simplified map of the city that doesn't exist anymore. When the real city gets messy, these rigid rules start to fail, causing oscillations (traffic jams) or even total gridlock (instability).

The Problem: Driving with an Old Map

The authors of this paper point out a major flaw: traditional controllers try to control the grid based on a presumed model (an old map). But the real grid is a living, breathing entity that changes every second. It's like trying to drive a car through a city using a map from 1990 while the roads are being repaved in real-time. The result? The car swerves, stalls, or crashes.

The Solution: The "DeePConverter" (The Self-Learning Driver)

The authors propose a new kind of controller called a DeePConverter. Instead of relying on a pre-drawn map (a mathematical model of the grid), the DeePConverter is like a self-driving car that learns by driving.

Here is how it works, using simple analogies:

1. Learning from Experience (Data-Driven)

Instead of asking, "What does the theory say the road looks like?", the DeePConverter asks, "What actually happened when I turned the wheel last time?"

• The Analogy: Imagine a jazz musician. A traditional controller plays a song exactly as written in the sheet music (the model). If the audience changes the tempo, the musician gets confused. A DeePConverter is like a jazz improviser. It listens to the crowd (the grid data) and instantly adjusts its melody (control strategy) to match the vibe, without needing a sheet of music.
• The Tech: It uses a mathematical concept called the "Fundamental Lemma," which basically says: If you record enough past inputs and outputs, you can predict the future without knowing the underlying physics. It looks at the history of voltage and current data to figure out how the grid is behaving right now.

2. The Modular "Lego" Design

The paper introduces a modular architecture. Think of a traditional power converter as a custom-built, one-piece statue. If you want to change one part, you have to break the whole thing.

• The Analogy: The DeePConverter is like a set of Lego bricks. You can swap out specific blocks (like the synchronization block or the power regulation block) without rebuilding the whole car.
• Why it matters: This means engineers can upgrade just the "brain" of the system while keeping the "muscles" (the hardware) the same. It allows the system to switch between different driving modes (like "Grid-Following" which follows the grid's lead, or "Grid-Forming" which acts like a strong anchor) just by changing the software settings.

3. The "Integral" Memory (Fixing the Drift)

Sometimes, even smart drivers make small mistakes that add up over time, like a car slowly drifting to the left.

• The Analogy: The authors added an Integral feature, which acts like a memory of past mistakes. If the car has been drifting left for 10 seconds, the system doesn't just say, "Oops, I'm off by 1 inch." It says, "I've been off for a while; I need to steer harder to the right to fix the accumulated error." This ensures that over the long run, the power output is perfectly accurate, with zero drift.

4. Adapting to the Storm (Online Adaptation)

What if the city suddenly changes? What if a new highway opens or a bridge collapses?

• The Analogy: A rigid controller would keep driving on the old map and crash. The DeePConverter has two ways to adapt:
  • Recursive Update: It constantly tweaks its map in real-time, like a GPS that updates every second as you drive.
  • Batch Reconstruction: If the changes are huge, it stops for a moment, gathers fresh data, and redraws the whole map instantly.
    This allows the system to handle sudden storms, equipment failures, or changes in the grid's strength without losing control.

The Results: A Smoother Ride

The paper tested this new system in two ways:

1. High-Fidelity Simulations: Like a flight simulator, they tested it in a virtual world with extreme weather and traffic. The DeePConverter handled voltage drops and frequency changes much better than the old controllers, staying stable when others crashed.
2. Hardware-in-the-Loop (HIL): This is like putting the new autopilot in a real car chassis connected to a supercomputer. The results showed the DeePConverter was faster, smoother, and more robust.

The Bottom Line

The DeePConverter is a paradigm shift. It stops trying to guess how the grid works with complex math models and starts learning directly from the data.

• Old Way: "I think the grid is like X, so I will do Y." (Often wrong).
• New Way: "The grid just did Z, so I will do Y to match it." (Always right).

By turning power converters into self-learning, adaptable, and modular systems, this technology promises a future where our electrical grid is more resilient, can handle more renewable energy, and won't crash when the weather gets weird. It's the difference between driving with a paper map and driving with a self-learning AI.

Technical Summary

1. Problem Statement

Modern power systems are increasingly dominated by renewable energy sources connected via power electronics converters. Unlike traditional synchronous generators (SGs), these converters have low physical inertia and interact complexly with the grid.

• Limitations of Conventional Control: Traditional control relies on multiple nested PID loops tuned based on simplified, presumed grid models (e.g., infinite bus assumptions).
• The Core Issue: The real power grid is highly complex, time-varying, and often unknown. This leads to model mismatch, causing degraded performance, oscillations, and even instability (e.g., small-signal instabilities in wind farms) when the actual grid dynamics differ from the design model.
• Challenges with Existing Advanced Methods: Robust control, adaptive control, and Model Predictive Control (MPC) require accurate system models or reliable retuning strategies, which are difficult to maintain in power electronics-dominated systems due to uncertain grid impedance and proprietary device details.

2. Methodology

The authors propose DeePConverters, a novel control architecture based on Data-Enabled Predictive Control (DeePC). This approach leverages the Fundamental Lemma of Behavioral Systems Theory, which states that the dynamics of a controllable Linear Time-Invariant (LTI) system can be fully characterized by its input/output trajectories without identifying a parametric model.

Key Methodological Components:

• Data-Driven Formulation: Instead of identifying a transfer function or state-space model, the controller uses historical input/output data (voltage, current, power) to construct Hankel matrices. These matrices implicitly capture the closed-loop converter-grid dynamics.
• Integral DeePC: To address steady-state tracking errors caused by system nonlinearities (common in converters), the authors introduce an integral action into the DeePC framework. This is achieved by optimizing the difference of control inputs ($\Delta u$) rather than the inputs themselves, effectively adding a discrete-time integrator to eliminate steady-state errors.
• Modular Architecture: The paper proposes a "plug-and-play" architecture allowing for five distinct configurations where DeePC can replace specific control layers:
  1. Full DeePConverter: Replaces synchronization, outer, and inner loops.
  2. Power/Voltage-regulated: Replaces only the outer loop.
  3. Current-regulated: Replaces outer and inner loops.
  4. Self-synchronized: Replaces synchronization and outer loops.
  5. Hybrid-synchronized: Replaces only the synchronization unit.
• Unified GFL/GFM Framework: The architecture unifies Grid-Following (GFL) and Grid-Forming (GFM) behaviors. By designing specific cost functions (weighting matrices and coupling terms), the same DeePC structure can emulate PLL-based synchronization (GFL) or swing-equation-based inertia (GFM).
• Online Adaptation: To handle time-varying grid conditions, two strategies are introduced:
  • Recursive Update: Continuously shifts data in the Hankel matrix to adapt to rapid changes.
  • Batch Reconstruction: Periodically reconstructs the matrix using a fresh data window when significant parameter changes or performance degradation are detected.

3. Key Contributions

1. Modular Data-Driven Architecture: Proposes a flexible framework that allows selective replacement of control loops (synchronization, power regulation, current control) with DeePC, facilitating practical implementation in existing industrial standards.
2. Integral Formulation for Nonlinearities: Introduces an integral DeePC formulation that eliminates steady-state tracking errors, a critical improvement over standard DeePC when applied to nonlinear converter systems.
3. Generalized GFL/GFM Synthesis: Demonstrates how to systematically design cost functions to emulate both GFL and GFM control paradigms within a single data-driven structure, effectively bridging the gap between these two distinct control philosophies.
4. Inherent Robustness and Adaptability: Analyzes and validates the controller's robustness against measurement noise, communication delays, and model uncertainties through regularization. It also provides mechanisms for online adaptation to time-varying dynamics.
5. Efficient Implementation: Develops closed-form solutions for scenarios where constraints are inactive, significantly reducing computational burden for real-time execution.

4. Results

The effectiveness of DeePConverters was validated through high-fidelity simulations and Hardware-in-the-Loop (HIL) experiments.

• Performance vs. Conventional Control:
  • GFL Mode: DeePConverters demonstrated superior active power tracking and significantly reduced oscillations during Short-Circuit Ratio (SCR) variations compared to conventional PID-based GFL and Subspace Predictive Control (SPC) emulations.
  • GFM Mode: DeePConverters successfully emulated virtual inertia and damping, providing better transient power support and faster voltage recovery during grid faults compared to conventional GFM converters.
• Transient Stability:
  • Under severe voltage sags (down to 0.5 p.u.), conventional GFL converters lost synchronization, and GFM converters experienced temporary loss of synchronism. DeePConverters remained stable throughout the fault and recovery process.
  • In frequency disturbance tests, DeePConverters with configured inertia/damping parameters provided effective primary frequency response.
• Adaptability:
  • Tests involving unbalanced voltage and sudden changes in PLL bandwidth showed that non-adaptive DeePConverters suffered from oscillations, while those using recursive updates or batch reconstruction quickly adapted and restored stable performance.
• Multi-Converter Systems: In a two-area test system, replacing a converter with a DeePConverter (PV or PQ mode) effectively suppressed oscillations caused by weak grid interactions, outperforming both pure GFL and GFM setups.
• HIL Validation: Real-time experiments on an OP5700 simulator confirmed that the DeePC algorithm (using closed-form solutions) meets real-time constraints (approx. 0.001 ms computation time) and achieves faster reference tracking and smoother mode switching (PQ to PV) than benchmarks.

5. Significance

This paper represents a paradigm shift in power converter control by moving from model-based to data-centric design.

• Mitigating Model Mismatch: It solves the critical issue of model mismatch in complex, unknown grids by "learning" the grid dynamics directly from operational data.
• Unified Control Paradigm: It unifies GFL and GFM control, offering a single framework that can be tailored to specific grid needs via cost function design rather than structural changes.
• Resilience: The inherent robustness and adaptability of DeePConverters make them highly suitable for future power systems characterized by high renewable penetration, weak grids, and rapidly changing operating conditions.
• Practicality: The modular design and efficient computational implementation address the "black box" concerns of data-driven control, making it a viable candidate for industrial deployment in renewable energy integration and grid stabilization.