Source Inductance Effect

In a practical power converter, the AC supply lines are never purely resistive. Every supply transformer and feeder cable has an associated source inductance (also called line inductance or commutation inductance), typically denoted Ls. When a thyristor switches from one phase to another during commutation, this inductance prevents the current from transferring instantaneously. The finite time taken for current to transfer from one thyristor to another is called the commutation overlap, and it has significant effects on converter performance including output voltage reduction and waveform distortion.

Core Concept Explanation

In an ideal converter, current commutation from one thyristor to the next happens instantaneously when the incoming thyristor is triggered. In reality, each supply line has an inductance Ls due to transformer leakage reactance and cable inductance. When thyristor T2 is fired at angle α, the current through T1 cannot drop to zero instantly because the source inductance opposes any change in current. Instead, the current in T1 decreases gradually while the current in T2 builds up, and during this transition period, both T1 and T2 conduct simultaneously.

This simultaneous conduction period is called the commutation overlap angle μ (mu), also sometimes called the commutation notch angle u. During the overlap, the two conducting thyristors short circuit the two supply phases through the source inductances. The output voltage during this period is not equal to either phase voltage but is the average of the two phase voltages (for a simple two thyristor commutation). This average is lower than the expected output voltage, creating a depression or notch in the output waveform.

The voltage notch during commutation appears as a sudden dip in the converter output voltage waveform. Each commutation event produces one such notch. For a 6-pulse bridge, there are 6 commutations per cycle, so 6 notches appear at 60° intervals. These notches are a form of harmonic distortion that affects the output voltage waveform and the supply current waveform. They also cause electromagnetic interference (EMI) in sensitive equipment connected to the same supply bus.

Mathematical Expression

The commutation overlap angle μ is determined by the energy balance during commutation. For a single phase full wave or 6-pulse three phase converter, the governing equation is cos(α + μ) = cos α - (2 × ω × Ls × Id) / Vm, where Vm is the peak voltage driving commutation (peak phase voltage for 3-pulse, peak line voltage for 6-pulse), Id is the DC load current, ω is the angular supply frequency, and Ls is the per-phase source inductance.

The voltage drop due to commutation is given by ΔV = (ω × Ls / π) × Id = (Xs / π) × Id, where Xs = ω × Ls is the commutation reactance. For a p-pulse converter, the total voltage drop is ΔV = (p × Xs) / (2π) × Id. This voltage drop is also called the commutation voltage drop or reactive voltage drop. The actual output voltage including commutation effect is Vdc_actual = Vdc_ideal - ΔV = Vdo × cos α - (p × Xs) / (2π) × Id.

The commutation voltage drop has a very important characteristic: it behaves like an equivalent internal resistance in series with the DC output, even though Ls is a purely reactive element. This is because the voltage drop is proportional to Id but lags the current by 90°, and after integration over the commutation interval, the net effect is a resistive-like DC voltage drop. This equivalent commutation resistance is Rc = (p × Xs) / (2π) for a p-pulse converter.

Practical Understanding

In large industrial drives, source inductance is not negligible. The transformer supplying a large rectifier typically has a leakage reactance of 4 to 8 percent. For a 1 MVA transformer at 415 V, this corresponds to a significant Ls value. The commutation voltage drop at full load can be several percent of the rated output voltage, reducing efficiency and requiring higher firing angle to compensate, which in turn worsens power factor.

The commutation notches also affect the supply voltage at the point of common coupling (PCC). Because both thyristors short circuit their respective phases through Ls during overlap, the PCC voltage dips during each commutation. This voltage notching can cause malfunctions in sensitive loads such as programmable logic controllers, variable frequency drives, and communication equipment connected to the same supply bus. IEEE 519 standards define limits on the depth and duration of voltage notches.

To mitigate source inductance effects, engineers add series AC line reactors intentionally in some applications to improve the current waveform and limit di/dt. However, this also increases the commutation voltage drop. A trade-off must be made between harmonic reduction and output voltage regulation. In high power HVDC converters, commutation inductance is a major design consideration and is carefully modeled in simulation.

Given:
3-phase 6-pulse fully controlled bridge rectifier
Line voltage VL = 415 V (rms), f = 50 Hz
Firing angle α = 30°
Source inductance per phase Ls = 2 mH
Load current Id = 100 A

Why this formula applies:
Commutation voltage drop = (p × Xs / 2π) × Id
For 6-pulse converter, p = 6
Xs = ωLs = 2π × 50 × 0.002 = 0.628 Ω

Formula:
ΔV = (p × Xs / 2π) × Id
Vdc_actual = Vdo × cosα - ΔV
Vdo = 2.34 × VL_rms = 2.34 × 415 = 970.5 V

Substitution:
ΔV = (6 × 0.628 / (2π)) × 100
ΔV = (3.768 / 6.283) × 100 = 0.5996 × 100 = 59.96 V
Vdc_actual = 970.5 × cos30° - 59.96
Vdc_actual = 970.5 × 0.866 - 59.96 = 840.4 - 59.96

Final Answer: Vdc_actual = 780.4 V (vs ideal 840.4 V, drop = 60 V)

Exam Tip: The commutation voltage drop formula ΔV = (p × Xs)/(2π) × Id behaves like a resistance Rc = p×Xs/(2π) in series with the DC output. For GATE, remember that source inductance does NOT affect the firing angle α but reduces the actual output voltage. Also: larger Id or larger Ls means larger μ and larger voltage drop.

Effects of Source Inductance - Summary

• Overlap angle μ increases with load current Id and source inductance Ls. It decreases with higher supply voltage.
• During overlap, both commutating thyristors conduct simultaneously. Output voltage equals average of two phase voltages.
• Voltage notches appear in output waveform: one per commutation event. For 6-pulse, 6 notches per cycle.
• Commutation voltage drop: ΔV = (p × Xs)/(2π) × Id. Equivalent to a resistance Rc = p×Xs/(2π) in series with DC output.
• Supply current waveform is altered: current transitions are sloped instead of rectangular, reducing harmonic content slightly.
• For μ approaching 60° in 6-pulse bridge, commutation fails: next thyristor fires before previous commutation completes.

Quick Revision

• Source inductance Ls causes finite commutation time, described by overlap angle μ.
• During overlap: both thyristors ON, output voltage = average of commutating voltages (less than ideal).
• Overlap angle: cos(α + μ) = cosα - (2ωLs × Id)/Vm. Larger Id or Ls → larger μ.
• Commutation drop: ΔV = (p × Xs)/(2π) × Id. Acts like a series resistance in DC circuit.
• Actual output: Vdc = Vdo × cosα - (p × Xs × Id)/(2π). Always less than ideal.
• Voltage notching at PCC affects sensitive equipment. Governed by IEEE 519 standards.
• Exam trap: Source inductance reduces output voltage but does NOT change the firing angle α of the thyristors.