Grid-Forming Inverter: Fault Current, Synthetic Inertia & SCR

Three-phase bases are $I_b=S_n/(\sqrt{3}U_n)$ and $Z_b=U_n^2/S_n$, with explicit unit conversions. External-grid quantities are $|Z_g|=U_n^2/S_{sc}$, $I_g=S_{sc}/(\sqrt{3}U_n)$ and $SCR=S_{sc}/P_r$. The MW-denominator definition and independent 717 MVA / 300 MW = 2.39 example are from NYISO's 2021–2030 Comprehensive Reliability Plan, appendices, printed p. 111. A separate $S_{sc}/S_n$ value prevents confusion when the ratings differ.

The balanced-sag model is derived here from Kirchhoff's voltage law. At the pre-sag PCC voltage $1\angle0$ pu, take exported current $p_0-jq_0$ and lossless reactance $jx_{eff}$. The held internal source is $\underline E=1+x_{eff}q_0+jx_{eff}p_0$. At imposed residual voltage $u_f\angle0$, the demand is $i_{dem}=\sqrt{p_0^2+[q_0+(1-u_f)/x_{eff}]^2}$. The magnitude screen is $i_f=\min(i_{dem},k_I)$ and $I_f=i_fI_b$. It supplies no prediction of current angle after limiting. ENTSO-E (3 October 2025), pp. 60–66, discusses effective-reactance and magnitude-limit behaviour; Masenge et al. (2025), pp. 3–4, supplies an independent simulated 1.2 pu limited-current plateau, not a validation of this entire reduced model.

For the prescribed ramp, $\Delta P_{req}=-2HS_n\dot f/f_n$ and $E_{req}=|\Delta P_{req}|T$. This uses the nominal-frequency linear inertia relation. ENTSO-E (2025), p. 26, equations (6)–(8), and Appendix F pp. 71–72 provide power/energy relations and worked inertia examples. On the plant MW base, $T_M=2HS_n/P_r$; only for equal numerical MW/MVA bases is $T_M=2H$.

At nominal voltage with fixed $q_0$, the rated-current active-power bound is $P_c=S_n\sqrt{1-q_0^2}$. Intersect $[-P_c,P_c]$ with the entered source limits. Select upward or downward headroom according to RoCoF, then limit the magnitude of support to the least of requested power, directional headroom and $E_{buf}/T$. Effective H is reduced in the same proportion as the power response. The power reduction is uniform over the full ramp, rather than full response followed by energy exhaustion.

The entered charging limit is independent of the generating rating P_r. P_r limits the upper generating bound and remains the SCR denominator. Charging is bounded by the entered P_min and the inverter apparent-power capability. EPRI's OpenDSS parameter-mapping documentation states that charging ratings may differ from generating ratings.

• All ratings are aggregate three-phase quantities referred to the stated PCC voltage. Inverter per-unit values and H use S_n; SCR uses rated plant MW, not dispatch.
• The fault screen assumes balanced positive-sequence fundamental RMS quantities, initially nominal PCC voltage, a lossless fixed coupling reactance and an internal source held at its initial phasor. The sag is imposed independently of the network fault level.
• The fault and inertia calculations are separate scenarios. Inertia headroom assumes nominal PCC voltage, fixed reactive power and rated apparent power, with no temporary overload credit.
• The same S_n apparent-power bound is used in both directions. The entered charging limit may exceed the generating MW rating, or impose a tighter charging bound. P_r is the generating rating only.
• Power-source bounds are available for the entire ramp. The energy reserve is incremental, directional and already adjusted for losses, baseline energy use and state of charge.
• The ramp is prescribed, not calculated from a disturbance. Response is immediate and constant during it. There is no damping, droop, delay, recovery or energy replenishment model. A zero RoCoF gives zero response; effective H then retains the setting by convention.

Use for preliminary comparisons and teaching. A clipped fault-current magnitude is a screening estimate, not a guaranteed waveform or minimum protection current. Obtain vendor data for current priority, RMS time window, overshoot, sustained duration and recovery; use sequence or EMT models for unbalanced faults and detailed studies. Deep-sag results are particularly sensitive to controller behaviour and neglected resistance.

External-grid bolted-fault current is a separate reference result and is not the grid current at the selected residual voltage. Do not add current magnitudes to infer total fault duty. This plant's current contribution is excluded from the input fault level used for SCR. Closely coupled multiple inverter plants need a suitable multi-infeed assessment; SCR alone cannot establish stability.

Frequency excursion is restricted to ±10% of nominal as a modelling guard, not a grid-code limit. The feasible H result describes only the entered ramp and energy budget, not an independently verified controller inertia or predicted frequency nadir. This calculator applies no national grid-code compliance test. The cited ENTSO-E report is dated 3 October 2025; check any applicable requirements against the standard in force.