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Mitigating Forced Oscillations in Power Systems via Data-Enabled Predictive Control
Soraya Daabak, Verena Häberle, Gabriela Hug, Gustavo Valverde
TL;DR
Sustained forced oscillations challenge conventional PSSs because their parameters are fixed and seldom retuned. The paper evaluates DeePC, which predicts directly from measured trajectories, across input-output configurations and in combination with PSSs. DeePC reduces local active-power oscillations, while its effectiveness varies with output selection and can increase terminal-voltage oscillations.
Problem
Sustained forced oscillations, including those induced by large data-center AI workloads, are difficult to mitigate with conventional PSSs that are not self-adaptive and are seldom retuned.
Method
The paper applies DeePC using Hankel matrices built from measured trajectories and evaluates alternative input-output configurations and coordination with a PSS.
Results
DeePC can reduce local active-power oscillations more effectively than a PSS, but output selection affects performance and terminal-voltage oscillations can increase.
Takeaways & Limitations
The combination of DeePC and PSS yields the best results reported in the conclusions, while including terminal voltage as an output reduces the transient peak but can interfere with active-power damping.
Takeaways & Limitations
DeePC can increase terminal-voltage oscillations because its signal is injected into the machine’s terminal-voltage control loop.
Abstract
from arXiv · showhide
Sustained forced oscillations in power systems, driven by large cyclic loads such as data centers, pose a challenge to conventional power system stabilizers (PSSs), which rely on fixed tuned parameters and limited adaptability. This paper investigates the use of Data-Enabled Predictive Control (DeePC) as a data-driven alternative for damping such oscillations. DeePC constructs control actions directly from measured trajectories without requiring an explicit system model, enabling adaptation to changing operating conditions. We evaluate the performance of DeePC on a multi-machine two-area system subject to forced oscillations and compare it against a conventional PSS. The study examines the impact of different input-output configurations and the role of representative historical data in the Hankel matrix construction. Results show that DeePC can achieve superior damping. However, its effectiveness depends critically on the quality and representativeness of the underlying dataset. These findings highlight the potential of data-driven predictive control to complement or outperform conventional stabilizers in modern power systems with evolving and uncertain dynamics.
I. INTRODUCTION
The paper motivates DeePC as a data-driven approach for damping forced oscillations that challenge fixed-parameter PSSs. It investigates input-output configurations, PSS coordination, and the importance of informative historical data.
- Conventional PSSs are typically not self-adaptive and are seldom retuned after offline parameter studies and manual adjustments.
- Sustained forced oscillations from large cyclic loads, including data-center AI workloads, can be difficult to mitigate with PSSs alone.
- DeePC constructs predictions directly from measured trajectories in Hankel matrices, avoiding explicit model identification.
- The study evaluates whether DeePC damps forced oscillations more effectively than a conventional PSS and examines single- versus multiple-input configurations.
- The evaluation also considers alternative outputs and the feasibility of operating DeePC alongside a PSS in a synchronous-machine voltage-regulation loop.
- The paper emphasizes that informative historical data are critical for closed-loop DeePC performance.
A. Offline Construction of the Hankel Matrix
Offline DeePC construction organizes historical input-output trajectories into Hankel matrices partitioned into past and future segments. The construction depends on persistently exciting, representative data and assumes fixed dynamics during operation.
- Historical input and output trajectories are arranged in Hankel matrices that capture admissible system behaviors under persistency of excitation.
- The Hankel matrices are partitioned into past and future segments for subsequent DeePC prediction and control.
- The construction uses Tini greater than the system lag, horizon N, Hankel depth L = Tini+N, and total data length T.
- Persistency of excitation requires a full-row-rank HL(u) and T ≥ L, making the input sufficiently rich to produce representative system behavior.
- The offline Hankel matrix remains fixed during online operation under the assumption that system dynamics do not change.
B. Online Optimization-based Controller
DeePC uses measured historical trajectories and recent input-output measurements to solve a regularized online optimization problem without an identified state-space model. Its receding-horizon implementation updates the past-data window after each applied input and new output measurement.
- DeePC infers system behavior directly from measured input-output data instead of identifying a parametric model.
- The online optimization includes input and output constraints and regularization terms to address noise and limited historical data.
- The output-cost matrix Q penalizes deviations from the reference, while R is the control-cost matrix.
- The decision vector g forms a linear combination of Hankel-matrix columns, yielding predicted future inputs and outputs consistent with behavioral data and past measurements.
- At each time step, DeePC applies only the first optimized input, then appends the resulting measurement and removes the oldest past entry.
- This rolling update implements a receding-horizon strategy analogous to model predictive control while relying only on measured data.
III. RESULTS
This section assesses DeePC in the voltage-regulation loop of a synchronous machine. The assessment focuses on using DeePC to mitigate forced oscillations in that loop.
- The section evaluates DeePC in the voltage-regulation loop of a synchronous machine.
- The evaluated control setting is a synchronous-machine regulation loop rather than a standalone generic controller.
- The section’s assessment concerns the use of DeePC within that voltage-regulation loop.
A. Simulation Setup
DeePC is evaluated on a multi-machine two-area system with a cyclic-load forced oscillation, using generator, AVR, and PSS models based on established system parameters.
- DeePC is tested on the two-area system during a forced oscillation induced by a cyclic load at bus 9.
- The test system includes synchronous generators, exciters, AVRs, and PSSs represented by the classical STAB1 model.The PSS uses rotor speed as input and sends its output to the AVR summing point.
- The cyclic load at bus 9 fluctuates by ± 50 MW around 88.35 MW at 0.55 Hz, near the system’s inter-area mode frequency.
B. Application of DeePC
DeePC is applied at generator G1 through the AVR using measured outputs and historical trajectories, with configurations and weighting choices selected for forced-oscillation mitigation.
- DeePC receives measured system outputs and computes VDeePC, which is added at generator G1’s AVR summing point.Candidate outputs include rotor speed, active and reactive power, and terminal voltage.
- The Hankel matrices are built offline from AVR-reference excitation data collected during cyclic-load operation.The dataset uses zero-mean white noise with standard deviation 0.005 pu sampled every 0.01 s, with T = 4490, Tini = 40, and N = 100.
- The reported output configurations are P1 alone and P1 together with V1, while other single-output tests were also performed.P1 alone gave the best single-output performance, whereas P1 and V1 gave the best result among output combinations.
- All scenarios use the same Hankel-matrix values, changing only its structure with the number of outputs.
- DeePC penalizes deviations from pre-disturbance references, with output weights of 5000 for P1 and 5 for V1.This corresponds to an output-weight ratio QP1/QV1 of 1000.
C. Simulation Results
The simulation compares DeePC alone and DeePC combined with the PSS at G1 while the PSSs at the other generators remain active.
- The study analyzes system responses for two output choices using DeePC alone and DeePC combined with the PSS at G1.
- The PSSs at generators G2, G3, and G4 remain active in every scenario.
1) DeePC Alone:
Without the G1 PSS, DeePC substantially reduces active-power oscillations, but this improvement trades off against terminal-voltage regulation and depends on output weighting.
- DeePC Alone: 20.19 MW falls to 0.55 MW with DeePC using P1 alone, compared with 2.12 MW using P1 and V1.The combined-output controller balances active-power damping and terminal-voltage regulation, reducing responsiveness to P1 oscillations.
- DeePC Alone: 7.5 × 10^-3 pu and 7.0 × 10^-3 pu are the steady-state voltage oscillation amplitudes with P1 alone and P1 with V1, respectively, versus 2.6 × 10^-3 pu before activation.Including V1 better mitigates the transient voltage peak after DeePC activation.
- DeePC Alone: Injecting VDeePC into the terminal-voltage control loop makes improved electrical-torque damping counterproductive for terminal-voltage regulation.
- DeePC Alone: Reducing the QP1/QV1 weight ratio substantially worsens active-power damping while only slightly changing steady-state voltage oscillation amplitude.The lower ratio reduces the transient voltage peak when DeePC is activated.
2) DeePC and PSS:
With a PSS at G1, DeePC further reduces local active-power oscillations, while output selection affects damping performance and voltage behavior across machines.
- The PSS reduces the initial oscillation amplitudes relative to the base case before DeePC is added.
- 0.27 MW with P1 alone and 1.03 MW with P1 and V1 are the active-power oscillation amplitudes achieved by DeePC with a PSS.The PSS baseline has a 68.3% inter-area-mode damping ratio, and DeePC is evaluated alongside it.
- Across machines, DeePC at G1 outperforms the PSS at G1 for active-power damping of P1 and P4, but not for the remaining machines.For rotor-speed oscillations, DeePC alone reduces amplitudes in G1 but not in the other machines.
- All voltage-magnitude oscillation amplitudes are slightly larger when DeePC is present, while reactive-power damping is sometimes better than with the PSS alone.
- P1 and V1 are the system-output configurations represented in the steady-state oscillation-amplitude comparisons.The corresponding tables report results for P1 alone and for P1 together with V1.
IV. CONCLUSIONS
The paper evaluates DeePC in a synchronous-machine AVR for forced oscillations caused by a cyclic load. DeePC reduces local active-power oscillations, while combining it with a PSS gives the best reported results and output selection creates a voltage-versus-active-power trade-off.
- DeePC in the AVR of a synchronous machine is used to mitigate forced oscillations induced by a cyclic load.
- DeePC reduces local active-power oscillation amplitudes more effectively than a PSS, but increases oscillations in the machine’s terminal voltage.
- Including terminal voltage as a system output reduces the transient peak when DeePC is activated but can interfere with active-power amplitude reduction.
- The combination of DeePC and PSS yields the best results, while future work will study multiple DeePC agents.The proposed agents include conventional machines or inverter-based resources for increasing system damping.