Mike Dolt Enterprises
Mike Dolt Enterprises
User: ish1284, Location: Arlington Heights, IL, USA
Asked on: Friday, May 2, 2025 at 2:40 pm EDT
Answered on: Friday, May 2, 2025 at 2:41 pm EDT
Question: I have a transformer test report where the %Z is given along with the load losses broken down into I2R losses and then stray losses, and then it totals them together in a third column as total load losses.I need to use this information to calculate the X/R ratio of the transformer. Is the correct way to determine the "R" component of X/R to consider the I2R losses only or both the I2R plus the stray losses?Note that there is a separate column for no-load losses which I know not to include. In the example provided, the I2R losses are 159.68kW, stray losses 15.93kW, and total load losses as 175.6kW.
You should use the total load losses to calculate the "R" component for the X/R ratio. Here's why: Total Load Losses Represent the Equivalent Resistance
The percentage impedance (%Z) represents the total opposition to current flow in the transformer at rated current. This opposition is made up of both resistive (R) and reactive (X) components. The total load losses (I2R + stray) represent the total power dissipated due to the equivalent resistance of the transformer winding and core under load conditions.
Stray Losses are Part of the Effective Resistance
Stray losses are caused by eddy currents in the core, tank, and other structural parts of the transformer due to the leakage flux produced by the load current. These losses are dependent on the load current and are a legitimate component of the effective resistance presented by the transformer under load.
X/R Calculation Needs Total Equivalent Resistance
When calculating the X/R ratio, you're trying to determine the relative importance of the reactive and resistive elements in limiting the current flow during a fault. Using only the I2R losses would underestimate the total resistive component and lead to an incorrect X/R ratio.
Calculation Steps
Calculate the Rated Impedance (Z)
You need to know the %Z from your test report. Assume you have the transformer's rated voltage (V) and rated apparent power (S). Then, the base impedance (Zb) can be calculated as:Zb = (V^2)/SThe impedance (Z) is then:Z = (%Z/100) Zb2.
Calculate the Resistance (R)
Convert the total load losses (Pload) to a per-unit or percentage value based on the rated power (S).R = Pload/SAlso, the effective resitance (R) can be found from the total load loss as follows:R = (Pload)/I^2Where Pload is the total load losses in watts, and I is the rated current.3.
Calculate the Reactance (X)
Use the impedance (Z) and resistance (R) to find the reactance (X) using the Pythagorean theorem:X = sqrt(Z^2 - R^2)4.
Calculate the X/R Ratio
X/R = X / R
Example
Let's say: Total Load Losses (Pload) = 175.6 kW = 175600 W %Z = 5% Rated Power (S) = 1000 kVA = 1000000 VA Rated Voltage (V) = 11 kV = 11000 V Rated current (I) = 1000000/11000 = 90.91 Amps1. Zb = 11000^2 / 1000000 = 121 ohmsZ = (5/100) 121 = 6.05 ohms2. R = 175600/(90.91^2) = 21.275 ohms3. X = sqrt(6.05^2 - 21.275^2) - complex numberThe error is because the %Z is very small, and the total load losses are comparatively high. The correct formula for resistance (R) is the percentage of the base impedance (Zb).R = (Pload/S) Zb = (175600/1000000) 121 = 21.248 ohms4. X = sqrt(6.05^2 - 0.021248121^2) = 5.735. X/R = 5.73/ 0.021248121 = 2.22
In summary: Use the total load losses (I2R + stray) to calculate the "R" component for the X/R ratio. This will give you a more accurate representation of the transformer's behavior under fault conditions. Flag for review