Source-linked AI summary
On the Local and Global Nature of Frequency and Voltage Dynamics
Taulant Kerci, Federico Milano
TL;DR
The paper examines how inverter-based resources may blur conventional distinctions between local voltage and global frequency dynamics. It applies autocorrelation to measurements across buses and supports its real-world analysis with simulations; the results show local behavior at short timescales and more global behavior at longer ones, with a shared voltage dynamic around one second.
Problem
It remains unclear how coupling from fast inverter-based dynamics changes the local-versus-global properties of frequency and voltage, which are conventionally treated as global and local, respectively.
Source: §I · p. 1Method
Results
Frequency and voltage both show local dynamics at about 100 ms, while long-term frequency is mostly global and voltage magnitude remains local; around 1 s, voltage dynamics appear common across the system.
Source: §V · p. 3Takeaways & Limitations
Autocorrelation provides a metric for quantifying local and global frequency and voltage dynamics across timescales.
Source: §II · p. 2, §V · p. 3
Abstract
from arXiv · showhide
This paper utilizes the autocorrelation of frequency and voltage measurements to identify, quantify and classify local and global properties of power system dynamics. The analysis is based on measurements with various resolutions (20 ms, 1 s, and 1 min) from several nodes of the Irish All-Island Power System (AIPS). Simulations based on stochastic differential algebraic equations on an IEEE benchmark system support conclusions drawn from real-world data.
I. INTRODUCTION
The paper asks how inverter-based resources affect the local or global character of frequency and voltage dynamics, which may overlap over short timescales. It applies autocorrelation to measurements at multiple grid nodes to identify the timescales of those dynamics.
I. INTRODUCTION
- Fast inverter-based controls may make local frequency and voltage dynamics overlap over timescales of tens to hundreds of milliseconds.The paper identifies how this coupling changes local versus global dynamics as an unresolved question.Source: §I · p. 1
- The paper addresses the unresolved local-versus-global question for frequency and voltage dynamics.Conventional assumptions treat voltage dynamics as local and frequency dynamics as global.Source: §I · p. 1
- The study applies frequency autocorrelation (ACF) and voltage autocorrelation (ACV) across diverse buses in Ireland’s IBR-based All-Island Power System, then uses stochastic simulations to support observations from real-world measurements.The objective is a metric that identifies the timescales of local and global dynamics.Source: §I · p. 1
II. AUTOCORRELATION FUNCTION
The paper uses autocorrelation to distinguish signal behavior across time lags and to identify modes that are bus-specific or shared across buses. A signal model and its autocorrelation decomposition explain how slow baseline behavior and damped oscillations appear in the metric.
II. AUTOCORRELATION FUNCTION
- Autocorrelation can reveal repeating cycles in noisy signals because exponential decay retains its time constant and periodic signals retain periodicity in their average autocorrelation.The paper uses this property to separate dynamics at different timescales.Source: §II · p. 1
- The modeled signal combines a slowly varying baseline with a damped harmonic transient whose parameters represent typical power-system transient modes.The transient amplitude is small relative to the baseline, which varies slowly compared with the oscillation period and decay time.Source: §II · p. 1
- The total autocorrelation expands into four terms, including baseline, transient, and cross-term contributions.The baseline autocorrelation is slowly varying; the cross-term is small under the stated conditions of small transient amplitude and typical oscillation frequency.Source: §II · pp. 1–2
- The transient autocorrelation contains damped oscillations with damping α and angular frequency ω0, and under α ≪ ω0 it has a simplified expression.The paper identifies this parameter regime as typical of electromechanical oscillations.Source: §II · p. 1
- The resulting autocorrelation has a slowly varying baseline and a decaying oscillatory component that characterizes the transient mode; pure white noise has zero correlation at non-zero lag.If residual autocorrelation approaches zero, the remaining variance represents noise.Source: §II · p. 2
- Bus-specific modes appear at individual buses, while system-common modes are visible across buses; autocorrelation behavior also indicates the timescales of local and global dynamics.Autocorrelation measures correlation between a signal and a delayed version of itself across time lags.Source: §II · pp. 1–2
III. REAL-WORLD DATA
The real-world analysis uses frequency and voltage measurements from geographically separated buses and several sampling resolutions. The data-based autocorrelation estimate is framed for a continuous stationary signal.
III. REAL-WORLD DATA
- The study analyzes three hours of frequency and voltage measurements from five geographically distant AIPS buses at 20 ms, 1 s, and 1 min resolutions.The selected normal-operation period had no major contingency and the buses represent different grid areas and types of loads and generators.Source: §III · p. 2
- The autocorrelation can be estimated from a continuous stationary signal with mean μ and variance σ² without knowing the signal’s analytical expression.The expectation operator is denoted E(·).Source: §III · p. 2
A. Autocorrelation of Bus Voltage Frequency (ACF)
At 20 ms resolution, frequency autocorrelation differs across five buses at short lags, indicating local frequency components during normal operation. The curves substantially coincide after 550 ms, while a slope change around 30 minutes is attributed to market operations.
A. Autocorrelation of Bus Voltage Frequency (ACF)
- The first 500 ms of the five-bus ACFs show small but distinct differences that are not attributed to PMU vendor or type.Measurements were collected during a period without a major system disturbance.Source: A. Autocorrelation of Bus Voltage… · p. 2, Figure 1 · p. 2
- After 550 ms, the five-bus ACFs substantially coincide, following bus differences in the first 500 ms that indicate local frequency components during normal operation.The slow frequency component is substantially the same throughout the grid beyond 500 ms.Source: A. Autocorrelation of Bus Voltage… · p. 2, Figure 1 · p. 2
- A change in ACF slope around 30 minutes is attributed to market operations in the AIPS.Source: A. Autocorrelation of Bus Voltage… · p. 2
B. Autocorrelation of Bus Voltage Magnitude (ACV)
Voltage autocorrelations distinguish bus-local long-term behavior from faster dynamics that become similar across buses. Measurement resolution also determines which time scales are captured.
B. Autocorrelation of Bus Voltage Magnitude (ACV)
- Long-term ACVs differ by bus, indicating that voltage magnitude variations are essentially driven by local dynamics.At short time scales, voltage-rate autocorrelations show fast local modes around 100 ms, but by 1 s their behavior is similar across locations.Source: B. Autocorrelation of Bus Voltage… · p. 2, Figure 2 · p. 2, Figure 3 · p. 3
- The autocorrelation of voltage-rate changes has 1 Hz cycles attributed to data centers connected to the AIPS.Source: B. Autocorrelation of Bus Voltage… · p. 2, Figure 3 · p. 3
- Higher-resolution measurements capture faster dynamics, while ACVs for a given bus eventually overlap across resolutions.This allows sampling time to be tuned to the time frame of interest; the 20 ms and 1 s measurements also show a ripple linked to 60 s data-center duty cycles.Source: B. Autocorrelation of Bus Voltage… · p. 2, Figure 4 · p. 3
IV. CASE STUDY
Stochastic simulations on the IEEE 9-bus system compare three wind-plant voltage-control scenarios. They agree with measurements in the long term, while fast voltage control produces faster initial ACV decay.
IV. CASE STUDY
- The study uses three-hour dynamic stochastic simulations of the IEEE 9-bus system, replacing the bus 3 synchronous generator with a wind plant providing primary frequency and voltage control.The voltage-control scenarios are no control, slow control, and fast control.Source: §IV · p. 3
- The simulations show good long-term agreement with measurements.Source: Figure 5 · p. 3, §IV · p. 3
- Fast voltage control leads to faster initial ACV decay than slow or no voltage control, consistent with real-world observations.Fast control quickly compensates voltage variations, so voltage changes more quickly.Source: Figure 6 · p. 3, §IV · p. 3
V. CONCLUSIONS
Autocorrelation of frequency and voltage quantifies local and global dynamics. Results distinguish very short-term local behavior from slower dynamics, where frequency is mostly global and voltage remains local, with a system-common regime around 1 s.
V. CONCLUSIONS
- The paper proposes autocorrelation as a metric for quantifying local and global dynamics of frequency and voltage using operational data from the IBR-based AIPS.Source: §V · p. 3
- At the 100 ms time scale, both frequency and voltage are driven by local dynamics during normal operation, not only after large disturbances.Source: §V · p. 3
- For dynamics above 1 s, frequency is mostly global over minutes to hours, whereas voltage magnitude remains local.The conclusion applies to relatively slow dynamics.Source: §V · p. 3
- Around 1 s, voltage dynamics include system-common modes and both quantities are global.Simulations show faster voltage control during normal conditions yields faster initial ACV decay, with the same conclusion for fast frequency control.Source: §V · p. 3
- Future work will apply the autocorrelation metric to other variables to compare relevant dynamics across real-world power systems.Source: §V · p. 3