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Impact of Low Rotational Inertia on Power System Stability and Operation
Andreas Ulbig, Theodor S. Borsche, Göran Andersson
TL;DR
High shares of inverter-connected wind and PV displace synchronous-generator inertia, making frequency dynamics faster and challenging stability and operation. The paper models these effects in one- and two-area systems, analyzes their consequences, and identifies faster control and synthetic inertia as mitigations. Reduced inertia amplifies frequency deviations and transient tie-line exchanges, with transient power-flow magnitudes increasing by more than 50% and abruptness by up to 300%.
Problem
High inverter-connected RES shares invalidate the assumption of a sufficiently high, nearly constant grid inertia and raise challenges for frequency stability and power-system operation.
Method
The paper uses swing-equation-based one-area and two-area power-system models to analyze how reduced inertia affects frequency dynamics, stability, and operation.
Results
Transient tie-line power-flow magnitudes increase by more than 50%, while their abruptness increases by up to 300% under lower inertia levels.
Takeaways & Limitations
Faster primary frequency control and synthetic rotational inertia from wind, PV, or storage are identified as mitigation options, with BESS especially well-suited to fast responses.
Abstract
from arXiv · showhide
Large-scale deployment of RES has led to significant generation shares of variable RES in power systems worldwide. RES units, notably inverter-connected wind turbines and PV that as such do not provide rotational inertia, are effectively displacing conventional generators and their rotating machinery. The traditional assumption that grid inertia is sufficiently high with only small variations over time is thus not valid for power systems with high RES shares. This has implications for frequency dynamics and power system stability and operation. Frequency dynamics are faster in power systems with low rotational inertia, making frequency control and power system operation more challenging. This paper investigates the impact of low rotational inertia on power system stability and operation, contributes new analysis insights and offers mitigation options for low inertia impacts.
I. INTRODUCTION
Rising inverter-connected RES shares are displacing synchronous generators and reducing the traditionally stable inertia base. This makes frequency dynamics faster and challenges frequency stability and operation.
- Inverter-connected wind and PV units normally provide no rotational inertia, unlike conventional synchronous generators whose stored kinetic energy supports frequency dynamics.Synchronous-generator inertia reduces the rate of frequency change and increases response time after disturbances.
- Low rotational inertia makes frequency dynamics faster, potentially leaving traditional frequency-control schemes too slow to prevent large frequency deviations.Larger deviations can damage synchronous machines, trigger load shedding, and contribute to fault cascades or blackouts.
- Germany illustrates the trend: wind and PV covered around 50% of overall load demand during several hours in 2012, coinciding with unusually low regional inertia.The temporary lack of dispatched conventional generators reduced the rotating machinery contributing inertia.
- The paper examines how reduced inertia affects power-system stability and operation and discusses mitigation options for its impacts.The paper is organized around RES impacts, inertia modeling, stability, operation, and mitigation-oriented conclusions.
III. TIME-VARIANCE OF GRID INERTIA
The paper introduces the modeling concepts used to represent rotational inertia and synchronous power systems before analyzing time-varying grid inertia.
- The section presents basic modeling concepts for rotational inertia in power systems and synchronous power systems generally.
A. Modeling Inertial Response
Rotational inertia represents stored kinetic energy in synchronous generators and moderates frequency changes after power imbalances. The paper models these dynamics with the swing equation and frequency-dependent load damping.
- Stored kinetic energy in rotating generator masses is released after a frequency deviation, slowing frequency dynamics and making regulation easier.
- The inertia constant H is the duration for which a synchronous machine can supply rated power using only stored kinetic energy; typical values are 2–10 s.
- The classical swing equation relates changes in synchronous-generator rotational frequency to a power imbalance between mechanical input and electrical demand.Pm denotes mechanical generator power and Pe denotes electric power demand.
- The linearized model adds frequency-dependent load damping to the swing equation around reference frequency f0 and nominal mechanical power Pm, 0.Dload is the frequency-dependent load damping constant.
- As inverter-connected penetration increases, rotational inertia is reduced and becomes highly time-variant because wind and PV shares fluctuate over time.This is especially concerning for small networks with high shares of generation capacity that contribute no inertia.
B. Aggregated Swing Equation Model
The aggregated swing-equation framework models frequency dynamics and stability in interconnected power systems. It shows that inertia and damping shape shock responses and stability regions, while increasing inverter-based RES makes inertia lower, time-variant, and operationally more challenging.
- Model formulation: The Aggregated Swing Equation models interconnected generators, loads, and tie-lines using an aggregate representation of system frequency dynamics.The model uses Center of Inertia frequency and assumes a highly meshed grid with small load-frequency disturbances and negligible changes in transmission losses.
- Operational implications: Increasing inverter-based RES displaces controllable conventional plants and rotating masses, diminishing control reserves while making system inertia reduced, nonuniform, and markedly time-variant.These changes are associated with faster frequency dynamics and more challenging operational practices.
- Model formulation: Inertia constants mitigate the frequency impact of sudden power shocks, while damping has a stabilizing effect; both are vital for power system stability.The stabilizing effect of damping also depends on the ratio involving inertia and damping parameters.
- Stability analysis: The two-area stability region is shaped directly by inertia and damping, determining how shocks are absorbed and how close trajectories approach the stability boundary.The region is unbounded and centered at the origin, with axes for frequency-angle difference and frequency deviation.
- Stability analysis: Rotational inertia reduces the direct impact of regional power faults on frequency, whereas damping increases the stability region, particularly along the frequency-deviation axis.Additional damping can be emulated by fast primary frequency control.
A. Experiments with a One-Area Power System Model
The one-area model analyzes how a 3000 MW fault affects grid frequency under different inertia and primary-control conditions. It highlights faster primary frequency control as a key mitigation option for low-inertia systems.
- Model and scenarios: A 3000 MW abrupt power fault is applied to an aggregated Continental European system model under realistic parameters and a 230 GW summer load.The analysis compares different inertia constants while retaining nominal primary and secondary frequency-control schemes.
- Mitigation: Fast primary control, fully activated within 5 s after a fault, is presented as a powerful mitigation option for low inertia and faster frequency dynamics.The paper identifies battery energy storage and temporary primary control from variable-speed wind turbines as possible sources of fast response.
- Control representation: Primary-frequency-control damping is time-variant because of control delays and power ramp-rate limitations.The control response depends on its reaction time and ramping constraints, so its stabilizing effect is most relevant in the first seconds after a fault.
- Model and scenarios: The swing dynamics identify two principal mitigation options: increasing rotational inertia H or augmenting frequency damping through fast primary frequency control.The control contribution is represented as an additional damping term kprim.(t).
- Model and scenarios: The study compares high inertia (H = 6 s), low inertia (H = 3 s) with nominal reserves, and low inertia with fast control reserves.The scenarios correspond respectively to no wind&PV feed-in, a 50 % wind&PV feed-in share, and faster reserves.
B. Experiments with a Two-Area Power System Model
The two-area simulations examine how reduced rotational inertia changes inter-area dynamics after a 3000 MW fault. Lower inertia amplifies swing dynamics and transient tie-line power flows, while better meshing reduces but does not eliminate these effects.
- Model and setup: The model represents two loosely coupled, equal-sized grid areas using realistic continental European system parameters and varying inertia in Grid Area II.The simulations use HII = {1 s, 3 s, 6 s}, while Grid Area I remains nominal at HI = 6 s and each area has a 115 GW base power.
- Dynamic response: Lower inertia in Grid Area II produces more amplified swing dynamics between the two regions after the 3000 MW fault.The fault occurs after 100 s in the simulation runs.
- Tie-line effects: Transient tie-line power-flow magnitude increases by more than 50%, while its abruptness increases by up to 300% under lower-inertia conditions.Both the transient power flow and its time-derivative become significantly larger and more abrupt.
- Protection implications: Large transient tie-line flows and their time-derivatives can trigger automatic protection devices designed to clear short circuits by tripping tie-lines.The resulting protection action may occur when the system is already in a sensitive state.
- Network topology: Three-area experiments show that better meshing diminishes and better damps swing dynamics and transient tie-line flows, although they remain significant.A triangular connection performs better than a string connection because it provides more tie-lines between areas.
VI. CONCLUSION AND OUTLOOK
The paper concludes that high shares of inverter-connected generation make inertia heterogeneous and time-variant, amplifying frequency and inter-area stability challenges. It identifies faster control and synthetic inertia as mitigation options, while noting that more realistic control dynamics require further analysis.
- Conclusions: High shares of inverter-connected generation significantly affect power system stability and operation by making rotational inertia heterogeneous across grid areas.Each area’s inertia depends on the mix of converter-connected and conventional units online.
- Conclusions: Rotational inertia becomes time-variant because power dispatch varies, causing frequency dynamics to become differently fast across individual grid areas.The conclusion describes this as a departure from using one global, constant inertia value.
- Conclusions: Reduced rotational inertia leads to faster frequency dynamics, larger frequency deviations, and greater transient power exchanges over tie-lines during faults.These effects may produce false protection errors and unexpected tie-line tripping, further aggravating critical conditions.
- Outlook and mitigation: The analyses use idealized primary and secondary frequency-control dynamics, so further work must include realistic delays and inverse-response behavior.The paper identifies these control characteristics as necessary for more detailed frequency-response analysis.
- Outlook and mitigation: Faster primary frequency control and synthetic rotational inertia from wind, PV, or storage units are proposed as mitigation options.Battery energy storage is identified as especially suitable because of its very fast response.