Voltage THD
0.0%
✓ NOMINAL
System Resonance
h = 4.8
PEAK FREQUENCY
Bank Current
0.0 A
Total RMS
PCC Impedance
0.0 Ω
At Critical Harmonic
1. Impedance Calculations
The system is analyzed using complex frequency-dependent impedance. For any harmonic order h, the individual components are modeled as:
Grid Capacitance: Z_C(h) = R_c - j(X_C / h)
Filter Path: Z_filter(h) = R_f + j(h · X_Lf - X_Cf / h)
The Grid Path impedance depends on the selected Grid Topology mode:
Series Resonance (L–C): Z_grid(h) = Z_L(h) + Z_C(h)
Parallel Resonance (L ∥ C): Z_grid(h) = (Z_L(h) · Z_C(h)) / (Z_L(h) + Z_C(h))
The total impedance seen by the VFD source is the parallel combination of the Grid Path and the local Filter Branch:
2. VFD as a Harmonic Current Injector
In power system modeling, a Variable Frequency Drive (VFD) is represented as a Norton Equivalent current source. Unlike a battery or utility grid (which are voltage sources), a VFD's rectifier bridge behaves as a non-linear load that "injects" harmonic currents into the system regardless of the system impedance (to a first approximation).
Mathematically, the drive is a source of current pulses. The current injection for each harmonic ($I_h$) is calculated from the user-defined percentage of the fundamental ($I_1$):
This injected current travels through the system impedance ($Z_{total}$). The resulting voltage distortion at the bus is a direct consequence of Ohm's Law for each harmonic: $V_h = I_h · Z_{total}(h)$. High impedance at a specific harmonic (Parallel Resonance) results in severe voltage "notching" or "peaking".
3. Parallel vs. Series Resonance
Parallel Resonance: Occurs when the grid's inductive reactance matches the local capacitor's capacitive reactance. At this frequency, the denominator of the total impedance equation approaches zero, causing the impedance magnitude to skyrocket. This results in massive voltage deviations ($V_h = I_h · Z_{total}$).
Series Resonance: Occurs within a single branch (e.g., the detuned filter). When the L and C reactances cancel each other out, the impedance drops to its minimum. This creates a "harmonic sink" where current flows freely into that branch instead of the grid.
4. Detuning & IEEE 519
By adding a detuning reactor, we shift the parallel resonance frequency downward (typically below the 5th order). This prevents amplification and creates a series resonant trap for 5th, 7th, etc. The toolkit references IEEE 519-2022, recommending a maximum Voltage THD of 5.0%.