Mike Dolt Enterprises
Mike Dolt Enterprises
User: Grouch1980, Location: New York, NY
Asked on: Sunday, January 5, 2025 at 5:35 pm EST
Answered on: Thursday, March 6, 2025 at 6:58 am EST
Question: Gents,I attached a one-line diagram that I'm looking at. It's from GE's white paper on short circuit calculations.The 2nd attachment shows how they derive the per unit X and R values at each piece of equipment (transformers, motors, the cables, and the utility). The base power value throughout is 15000 kVA.My questions are how they derived the X and R values where I highlighted in blue in the 2nd attachment.For the utility (top blue rectangle): the equation to solve for the per unit impedance (Z)... shouldn't it be actual power / base power? The equation that they are using seems to be base power / actual power. The utility power is 1500 MVA. Base power as I mentioned above is 15000 KVA.For Motor M1 (the bottom blue rectangle): what equation are they using to solve for the motor impedance X? The equation includes an X"d of 15% (sub-transient reactance) and a horsepower of 4000. I'm not familiar with the equation though. What equation is this?Thanks!
Okay, let's break down these calculations. I'll assume you've provided the diagrams and data correctly and address your questions.
Utility Impedance (Top Blue Rectangle)
You are correct! The equation used in the GE whitepaper for the utility impedance appears to be inverted. Correct Formula
`Z_pu = (Base MVA) / (Utility MVA)`
GE Whitepaper Formula
`Z_pu = (Utility MVA) / (Base MVA)`Therefore, the calculation in the white paper for the utility impedance is incorrect, as the calculation should be:
The calculated value for the utility Z is 0.01 pu.Then the X/R ratio of the utility impedance is 20, which means that the utility impedance consists of the real value, R, and the imaginary value, X. We know Z = sqrt (R^2 + X^2) and also X/R = 20. This means X = 20RSo, Z = sqrt (R^2 + (20R)^2) = sqrt(R^2 + 400R^2) = sqrt(401R^2) = R sqrt (401)Z = R sqrt (401)R = Z / sqrt (401) = 0.01 pu / sqrt (401) = 0.0005 puX = 20R = 20 0.0005 pu = 0.01 puZ_pu = (15 MVA) / (1500 MVA) = 0.01 pu
Important Note
Using the inverse formula is a common shortcut method only when dealing with very large power sources relative to the base power. It essentially provides the approximate impedance of the utility expressed on the base. However, it is conceptually and technically more accurate to calculate it the correct way as outlined above, using the correct formula as I mentioned above.
Motor M1 Impedance (Bottom Blue Rectangle)
The equation used here is a simplified approach for estimating the motor's subtransient reactance based on its nameplate horsepower and subtransient reactance (X"d). It's derived from typical motor characteristics and empirical data. The equation isn't a fundamental electrical law but rather a practical approximation used in short-circuit studies. Here's the breakdown:1. The Foundation
This method uses the motor's nameplate kVA as a starting point. The X"d (subtransient reactance) is the key parameter because it dominates the motor's impedance during the initial moments of a short circuit.2.
Approximation & Derivation
While I don't know the exact derivation used by GE, the equation is likely based on these concepts:
Motor kVA
Estimated as approximately = `HP 0.746 / Power Factor / Efficiency`. Typical Power Factor and Efficiency are assumed based on motor size and type.
Base kVA
Your defined base of 15000 kVA.
Per-Unit Impedance
X"d is often given as a percentage (e.g., 15%). To express it per-unit on the motor's own base, you would divide the percentage by 100. Then, to shift it to your system base (15000 kVA), you use the following: `X"_pu (system base) = X"_pu (motor base) (Motor kVA / System Base kVA)`.3.
General Form
The equation in the white paper is likely a simplified version that combines these steps into a direct calculation:
Where 'Factor' combines typical Power Factor, Efficiency, and the conversion from HP to kVA.4. X_pu ≈ (Base kVA) / (HP Factor) (X"d / 100)
Applying to Your Case
Base kVA = 15000 kVA HP = 4000 HP X"d = 15% = 0.15 From what I can tell, 'Factor' is approximately 2.2 `X_pu ≈ 15000 / (4000 2.2) (0.15) = 0.255 pu`5.
Important Considerations
Motor Data
The actual motor nameplate data is always preferred. If you have the actual motor kVA, Power Factor, and Efficiency, use those to calculate the motor's kVA and then calculate X"d on the system base. This will be more accurate than the simplified formula.
Motor Type
This formula is generally more applicable to induction motors. Synchronous motors have different characteristics.
Short-Circuit Software
Modern short-circuit software will have motor models that account for more detailed parameters.
In Summary Utility
The utility impedance calculation appears inverted in your excerpt. Use `(Base MVA) / (Utility MVA)` for the correct per-unit value.
Motor M1: The equation is a simplification, but you can approximate it by estimating the motor nameplate kVA and using the change-of-base formula. Ideally, get the actual motor nameplate data.Let me know if you have any other questions. Flag for review