Q: How is Q defined, calculated, and optimized for field testing?
A: Q = X_L / R = energy stored/energy dissipated × 2π. It determines voltage amplification and input power savings.
Components of total resistance R:
• Reactor copper: 40–60%. Core losses: 15–25%. Lead resistance: 5–10%.
• Load dielectric (tanδ): 10–25%. Corona/PD: 0–5%.
Typical Q values by load:
|
Load Type |
Capacitance |
Typical Q |
|
Power transformer |
5–20 nF |
30–60 |
|
GIS/substation |
1–50 nF |
40–100 |
|
MV cable (< 1 km) |
0.1–0.5 μF |
30–50 |
|
HV cable (> 5 km) |
1–5 μF |
15–30 |
|
Generator stator |
0.5–5 μF |
20–50 |
|
Capacitor bank |
10–100 μF |
10–20 |
Q vs. Input Power (for 500 kVA output):
Q=10 → 50 kW (large diesel) | Q=30 → 16.7 kW (medium gen)
Q=50 → 10 kW (small gen) | Q=80 → 6.25 kW (mains) | Q=100 → 5 kW (mains)
Factors affecting Q:
• Reactor: larger air gap → lower Q. Use grain-oriented steel. Litz wire > 200 Hz.
• Frequency: higher f → lower Q (skin effect).
• Load: higher C → lower Q. Voltage: higher V → lower Q (corona loss).
Field estimate: Q_est ≈ 1/(tanδ_specimen + tanδ_reactor).
If tanδ_specimen = 0.005 and tanδ_reactor = 0.02 → Q ≈ 40.
⚠ Always assume Q 20% lower than nominal for generator sizing.