How to Calculate Grid-Forming Inverter Virtual Inertia
Grid-forming inverters are replacing synchronous machines as the source of system strength on weak and renewable-rich grids. Operators therefore need a transparent method to express how much virtual inertia these converters can provide, how that headroom translates into active power injection, and whether settings comply with grid codes. This walkthrough derives the core equations, defines units and variables, and shows how to validate estimates against electromagnetic transient (EMT) studies and commissioning tests.
The workflow complements adjacent resilience analytics. Combine inertia screening with the offshore wind cable thermal headroom guide when integrating export systems, or link it to fleet dispatch planning using the Virtual Power Plant Flexibility Value calculator. Together they frame how inverter settings propagate through thermal limits, contingency response, and commercial flexibility.
Definition and intent
Virtual inertia is the emulation of synchronous machine inertial response by a power electronic converter. A grid-forming controller synthesises the swing equation, using its DC-link energy buffer to inject active power proportional to the rate-of-change of frequency (RoCoF) or to the measured frequency deviation. Utilities specify a minimum inertia contribution per megawatt of converter capacity to maintain frequency stability after disturbances such as generator trips or HVDC pole blocking. Quantifying the virtual inertia margin tells system planners how much kinetic-like energy is available before control saturation.
We focus on a widely used parameterisation: the inertia constant H expressed in seconds, applied to the converter apparent power rating S. The resulting energy headroom equals 2HS. Translating that energy into instantaneous active power for a given frequency excursion provides an implementation-ready metric for plant settings, interconnection studies, and compliance submissions.
Variables and measurement units
Document every input using SI-consistent units. When using utility forms that mix unit systems, restate values explicitly in megawatts (MW), megavolt-amperes (MVA), hertz (Hz), and seconds (s) to avoid ambiguity during EMT model imports.
- S – Converter apparent power rating (MVA). For unity power factor during inertia response, this approximates MW capability.
- H – Virtual inertia constant (s). Controller parameter defining how many seconds of rated power are stored virtually.
- fN – Nominal system frequency (Hz). Use 50 or 60 depending on region.
- Δf – Magnitude of frequency deviation to be supported (Hz). Express as a positive value.
- Δt – Support window over which Δf occurs (s). Represents the time taken for the excursion; defaults to 1 s for initial RoCoF.
- Einertia – Inertia headroom (MW·s).
- Psupport – Approximate active power injection during the event (MW).
Capture additional metadata for traceability: firmware version, control mode (grid-forming versus grid-following), DC-link voltage limits, and whether fast frequency response (FFR) blocks run in parallel. These contextual notes simplify audits and ensure that later retuning aligns with the documented assumptions.
Governing formulas
The virtual inertia headroom mirrors synchronous machines: the stored energy equals twice the inertia constant times apparent power. When a frequency deviation unfolds over a known window, we approximate RoCoF as Δf ÷ Δt and scale by nominal frequency to estimate active power injection.
Einertia = 2 · H · S
RoCoF ≈ Δf ÷ Δt
Psupport ≈ (2 · H · S · RoCoF) ÷ fN
These expressions intentionally simplify converter dynamics. They assume the DC link and current limits permit the computed active power, and that any reactive current injection commanded by low-voltage ride-through does not constrain the active channel. For interconnection studies, the calculated power should be compared with converter short-term overload capability and the plant-level energy storage buffer (if present).
Step-by-step calculation workflow
1. Confirm nameplate and settings
Gather the converter's grid-forming rating and the configured inertia constant from site controller files or the vendor's parameter sheet. Verify that the value applies to the relevant operating mode and firmware. If the plant derates apparent power during curtailment or high temperature, document the lower rating for conservative calculations.
2. Select the representative event
Choose Δf based on grid code thresholds (for example, 0.2 Hz for 50 Hz systems) or the worst credible contingency identified in the system impact study. Set Δt equal to the time over which that deviation is expected to occur; 1–2 s covers most primary frequency events, while slower ramps may be used for islanding transitions.
3. Compute inertia headroom
Multiply 2 · H · S to obtain Einertia in MW·s. This value represents the kinetic-like energy that the inverter can exchange with the grid without violating the configured inertia constant.
4. Estimate active power injection
Calculate RoCoF as Δf ÷ Δt and plug it into the Psupport expression. Compare the result with converter current limits and any plant-level constraints such as transformer thermal headroom. If Psupport exceeds the converter's overload capability, flag the need to lower H or cap active power during events.
5. Document and review
Summarise the inputs, outputs, and assumptions in a commissioning memo. Cross-reference with EMT plots and relay settings. Share the summary with the protection engineer to ensure under-frequency load shedding or synchronous condensers are coordinated.
Validation and sanity checks
Validate Einertia by comparing with EMT simulations: run a disturbance that produces the chosen Δf and confirm the inverter delivers Psupport without voltage instability. Cross-check the energy draw against DC-link capacitance or battery state of charge if the inverter is DC-coupled. For plants paired with storage, reconcile results with the grid-interactive building flexibility index methodology to ensure the control stack can prioritise inertia versus other services.
Perform boundary testing by halving and doubling Δt: shorter windows raise Psupport, revealing whether current limits trigger. Also test extreme Δf values specified in the interconnection agreement to confirm that anti-windup logic handles saturation. If measured field tests deliver less power than calculated, inspect PLL settings, current limiters, and DC-link voltage droop curves.
Limits and interpretive cautions
The simplified formula ignores coupling between active and reactive current during voltage dips. In practice, low-voltage ride-through may pre-empt active current injection, reducing available inertia response. Likewise, harmonic filters and transformer saturation can constrain current at high RoCoF, especially on weak grids. Treat the calculation as a planning upper bound, not a guaranteed delivery commitment.
Finally, virtual inertia is one piece of stability. System strength also depends on short-circuit ratio, control-loop tuning, and mechanical inertia from any remaining synchronous fleets. Periodically refresh H based on post-event analysis and hardware upgrades, and align the chosen value with compliance testing intervals set by the transmission operator.
Embed: Grid-forming inverter inertia calculator
Use the embedded calculator to turn nameplate data and target frequency events into an inertia headroom estimate and power response figure ready for interconnection submissions.