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Challenges and opportunities of inertia estimation and forecasting in low-inertia power systems

Evelyn Heylen, Goran Strbac, Fei Teng

arXiv:2008.12692v1eess.SYcs.SY

TL;DR

Accurate inertia estimates and forecasts matter for operating low-inertia power systems, but existing estimation methods had not been surveyed. This paper surveys inertia-estimation approaches in relation to operational practice and identifies shortcomings and future research needs.

  • Problem

    Although many inertia-estimation methods exist, they had not been surveyed, despite the importance of accurate estimates and forecasts for low-inertia system operation.

    Source: §1 · pp. 1–2

  • Method

    The paper surveys inertia-estimation approaches and relates their development to operational practice to identify shortcomings.

    Source: §1 · p. 2

  • Results

    The paper identifies shortcomings in existing methods and highlights testing and validation of continuous estimation and development of inertia-forecasting models as future research needs.

    Source: §1 · p. 2, §4 · p. 19

  • Takeaways & Limitations

    Accuracy and reliability of continuous inertia-estimation techniques remain inadequately proven, motivating their testing and validation against situations where inertia is accurately known.

    Source: §4 · p. 19

    The accuracy and reliability of continuous inertia-estimation techniques have not been adequately proven because ground-truth data are limited.

    Source: §4 · p. 19

Abstract

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Accurate inertia estimates and forecasts are crucial to support the system operation in future low-inertia power systems. A large literature on inertia estimation methods is available. This paper aims to provide an overview and classification of inertia estimation methods. The classification considers the time horizon the methods are applicable to, i.e., offline post mortem, online real time and forecasting methods, and the scope of the inertia estimation, e.g., system-wide, regional, generation, demand, individual resource. Shortcomings of the existing inertia estimation methods have been identified and suggestions for future work have been made.

1. Introduction

As power systems move toward lower inertia, accurate estimates and forecasts are important for reliable operation, yet existing operator estimates can be approximate and inertia-estimation methods had not been surveyed. This paper reviews and classifies those methods, relates their development to operational practice, and identifies shortcomings and future research pathways.

1. Introduction

  • Converter-interfaced generation, consumption, and transmission are reducing inertia and challenging the maintenance of acceptable frequency profiles.Inertia has been especially low during periods of low demand and high renewable production.Source: §1 · p. 1
  • System operators would benefit from accurate real-time inertia estimates and forecasts, while current estimates based on part of the resource or simplified empirical relations are approximate.The cited approaches are based on part of the resource or a simplified empirical relation.Source: §1 · p. 1
  • Although inertia-estimation methods are numerous, they had not been surveyed; prior reviews instead addressed inertia emulation, inertia sources, or broader low-inertia challenges and solutions.The broader review focus included transient and frequency stability and converter control.Source: §1 · p. 2
  • The paper surveys and classifies inertia-estimation methods by applicable time horizon and estimation scope, relating their development to operational practice to identify shortcomings and future research pathways.The authors state that they put forward pathways for future research.Source: §1 · p. 2

2. Operational practice with respect to inertia

This section examines operational practices for managing low-inertia frequency risks, including how operators use inertia, demand, and largest-infeed-loss information to set response requirements. It covers constraints on operational options and measures such as frequency-response procurement, faster-acting services, virtual-inertia markets, and coordinated scheduling.

2.1. Operational constraints

  • Inertia helps limit ROCOF and frequency nadir, but COI frequency cannot be measured directly and pilot-node measurements vary with location and neighbouring generators.In Great Britain, inertial response is defined as the first second after a generation or demand loss, before primary frequency response activates.Source: §2.1 · pp. 3–4

2.2. Contributors to the power system inertia

  • Synchronous-machine response is declining; emulated inertia faces regulatory, dynamic-behaviour and energy-buffer uncertainty constraints.Emulated response has limited penetration, and zero-inertia systems remain difficult to implement because existing devices expect frequency to change relatively slowly.Source: §2.2 · p. 4

2.3. Operational measures to limit the risk of ROCOF and underfrequency relay tripping

  • Reduced instantaneous inertia raises relay-tripping risk; reducing the largest loss is typically 10 times cheaper than bringing additional generators online, though its effectiveness is questionable with smaller, variable generation.Operators can also increase inertia by replacing converter-interfaced generation with synchronous generation ahead of real time, accounting for synchronization time.Source: §2.3 · pp. 5–6
  • Operators should procure frequency response ahead of real time, and faster-acting services can contain frequency within limits and avoid underfrequency load shedding with relaxed ROCOF limits.Frequency response can prevent underfrequency-load-shedding relay tripping on a seconds-scale.Source: §2.3 · p. 6
  • Markets for virtual inertia from converter-interfaced resources have been suggested, and inertia is especially valuable when it reduces wind curtailment.Source: §2.3 · p. 6
  • National Grid ESO uses five-minute response-requirement tables based on demand, inertia, and largest infeed loss to optimize requirements and guide residual real-time procurement.The tables are built using a frequency simulation engine and combined with contractual arrangements per settlement period to inform control-room engineers.Source: §2.3 · pp. 6–7
  • Real-time coordination of multiple frequency-response services has been investigated, while stochastic unit commitment can schedule multiple services and dynamically reduce the largest loss to support secure operation.Source: §2.3 · p. 7

3. Classification of inertia estimation methods

This section classifies inertia-estimation methods by time horizon and geographical scope, including system-wide and zonal estimates and the inertia contributors estimated. It covers online estimation approaches and forecasting, along with limitations related to data, measurement, coverage, and validation.

3. Classification of inertia estimation methods

  • Methods are classified by time horizon and estimation scope, with Table 1 organizing them by horizon in rows and scope in columns.The paper introduces this framework as a way to organize the literature for systems with increasing variability in inertia.Source: §3 · p. 7, Table 1 · p. 8

3.1. Classification of inertia estimation methods according to the time horizon of interest

  • The time-horizon categories are offline post-mortem, online real-time, and forecast methods, respectively assessing past disturbances, current conditions, and expected future inertia.Methods spanning multiple scopes are listed once in the table under the smallest scope to which they apply.Source: §3.1 · p. 7

3.1.1. Offline, post-mortem inertia estimation

  • Post-mortem methods estimate system inertia after large disturbances using known power imbalance and frequency measurements, but event-size uncertainty and infrequent events limit accuracy and continuity.Assuming damping and short-term frequency response are negligible becomes more challenging as fast response services shorten the pure inertial-response window; storing event estimates can support higher temporal resolution.Source: §3.1.1 · pp. 9–10

3.1.2. Online inertia estimation

  • Online methods may provide closer-to-real-time information about inertia in the system than post-mortem approaches, including SCADA/EMS lower-bound estimates, discrete PMU estimates during disturbances, and continuous PMU-based estimates.Source: §3.1.2 · pp. 10–11
  • Estimating inertia from generators’ online capacities and inertia constants has very low complexity, but underestimates total system inertia when embedded units are excluded, so it serves as a lower bound.Source: §3.1.2 · pp. 11–12
  • Online methods comprise lower-bound estimates, discrete disturbance-based estimates, and continuous estimates; discrete methods use time-series or modal-domain approaches.Continuous methods estimate inertia in the time, Laplace, or modal domain.Source: §3.1.2 · pp. 12–13
  • Discrete methods estimate inertia near real time from PMU frequency and power-imbalance estimates, using time-series or inter-area-oscillation modal approaches.They typically apply a linearised swing equation that ignores damping and frequency response, assuming estimation occurs before those slower dynamics take effect.Source: §3.1.2 · p. 12
  • Discrete disturbance-based performance depends on disturbance size; generator rescheduling can provide suitable events, but estimates remain 30–60 minutes apart and require extrapolation between them.Online detection of suitable disturbances and accurate estimation of their size from PMU measurements are also challenging.Source: §3.1.2 · pp. 12–13
  • Near-continuous inertia-estimation methods use PMU measurements and power-imbalance information, but estimating imbalance during normal operation is difficult because imbalances are small compared with measurement noise and cannot be measured directly.Source: §3.1.2 · p. 13
  • Continuous inertia-estimation accuracy and reliability remain unproven; Guo et al. found estimate accuracy decreases with larger measurement errors and accurate initial inertia guesses are required for convergence, while another method showed deficiencies.Empirical results did not correspond with ground-truth inertia; without ground truth or a calibration reference, swings are hard to attribute.Source: §3.1.2 · pp. 13–14
  • Microdisturbance-based online estimation needs validation in large, densely meshed, high-inertia systems, where the single-centre-of-inertia approximation may fail and small disturbances can be hard to distinguish from noise.Potential power-quality issues from inserted microdisturbances also require investigation.Source: §3.1.2 · p. 14

3.1.3. Estimation of expected inertia: Forecasting

  • A 30-minute forecast resolution is currently acceptable given generator contracting intervals, though renewable variability may require higher resolution.Forecast accuracy depends on historical inertia-estimate accuracy and resolution; discrete-event estimates may leave too little data for accurate forecast modeling, while near-continuous estimates may be inaccurate or unvalidated.Source: §3.1.3 · pp. 14–16
  • Existing inertia forecasts are mainly explanatory point forecasts using exogenous-variable forecasts, but omitting demand inertia can underestimate total system inertia.Some approaches combine forecast generator status and capacity with demand multiplied by an empirical constant; generator status may not be available day ahead to all operators.Source: §3.1.3 · pp. 14–15
  • ERCOT week-ahead forecasts based on generator reports typically overestimate real-time inertia during periods with low energy prices.Greater variability from renewables is expected to make day-ahead generator statuses less accurate, further hampering forecasts.Source: §3.1.3 · p. 15
  • Forecasting improvements include modeling generator online capacity from operator-accessible variables and developing probabilistic forecasts to assess ROCOF and underfrequency-relay risk.Probabilistic models can represent future inertial energy conditional on system state, but current regression approaches assume independent, constant-variance, normally distributed errors; accurate models also need more inertia data than current methods often provide.Source: §3.1.3 · pp. 15–16

3.2. Scope of inertia estimation methods

  • Methods differ in spatial resolution, estimating total-system or regional inertia, or focusing on contributors such as synchronous generators, demand, and virtual inertia resources.Source: §3.2 · p. 16

3.2.1. Geographical scope

  • A single centre-of-inertia value captures generation, demand, and virtual inertia, but lower inertia increases the risk of inter-area angle swings and oscillations, motivating zonal or spatial-profile estimates.A single system value is acceptable in strong transmission systems with limited frequency variation between locations; zonal estimates are more flexible.Source: §3.2.1 · p. 17
  • Zonal estimates can be aggregated to obtain total system inertia, but a system-wide estimate cannot reveal zonal or individual contributions.Source: §3.2.1 · p. 17
  • Zonal estimates may guide procurement of very fast frequency response and coordinated frequency control.Source: §3.2.1 · p. 17
  • Approaches define zones by network constraint boundaries or by closely coupled angles and frequency, with the latter preferred physically.Source: §3.2.1 · p. 17

3.2.2. Contributors to the system inertia

  • As total inertia declines, unmonitored demand and embedded units become more important, while direct estimation of their contributions remains challenging.Source: §3.2.2 · p. 17
  • Forecasts of demand and embedded-unit inertia can support advanced unit commitment that schedules energy and frequency response [77] or determine inertia-market procurement.Source: §3.2.2 · p. 17
  • Demand and embedded-unit inertia contributions have been estimated at 8%–25% of total system inertia, averaging 18.18%.Source: §3.2.2 · p. 17
  • Demand and embedded-unit inertia can be inferred by subtracting synchronous-generator contributions from system estimates during large disturbances, while PMU-based dynamic methods estimate generator or virtual-resource inertia constants.Source: §3.2.2 · pp. 17–18
  • With limited estimates of inertia contributions from embedded units and demand during large disturbances, explanatory models relate them to total system demand and have predictive capabilities; limited data led to simple, few-parameter structures such as linear regression to avoid overfitting.Source: §3.2.2 · p. 18

4. Conclusion and the future of inertia estimation methods

Secure, cost-effective operation of low-inertia systems requires accurate, reliable inertia estimates, including near-continuous regional estimates. Future work focuses on validating these methods, accounting for inertia contributors, and improving forecasts.

4. Conclusion and the future of inertia estimation methods

  • Near-continuous estimates are important for monitoring frequency-response profiles in strong regions interconnected by long links.The paper calls for estimates on a close-to-continuous and regional basis.Source: §4 · pp. 18–19
  • The accuracy and reliability of continuous inertia-estimation techniques remain inadequately proven because reliable system-inertia ground truth is limited.The paper identifies this as a reason for further research.Source: §4 · p. 19
  • Near-continuous estimation methods need validation against known-inertia situations and testing for stability impacts to improve estimate accuracy.Suggested test cases include a single generator or a large frequency event.Source: §4 · p. 19
  • Future models should forecast total-system or zonal inertia and contributions from individual resources, including demand and unmonitored embedded units.Source: §4 · p. 19
  • Demand and embedded-unit estimates currently rely on large-disturbance events because reliable, high-temporal-resolution total-system inertia estimates are limited.Estimating these contributions depends on subtracting monitored transmission-connected generator inertia from total inertia.Source: §4 · p. 19
  • Current inertia forecasting is limited to explanatory linear regression with few exogenous variables and point forecasts; probabilistic models could support operator decisions.The paper suggests developing probabilistic models when reliable, high-resolution inertia estimates become available.Source: §4 · p. 19
  • An alternative is to forecast predictive distributions of rate of change of frequency and frequency deviation directly, rather than inertia itself.These forecasts could be used to estimate the probability of frequency-response issues.Source: §4 · p. 20
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