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Calculation No.: Calc-001
Revision: A
Description:
Created By: Engineer Name
Project: Project Name
Project No.: P001
Client: Client Name

Input Parameters

The following motor and electrical parameters were used for this calculation:
Parameter Symbol Value Notes
Motor Active Power P 90 kW Rated motor power
Supply Voltage Vpp 400 V Phase-to-phase voltage
Power Factor PF 0.85 cos(φ)
Motor Efficiency η 97 % Motor efficiency

Calculations

All calculations were performed in accordance with three-phase AC motor theory and Australian Standards (AS).

Motor Line Current (I)

The motor line current is calculated using the three-phase power equation: This represents the current drawn by the motor from the three-phase supply.

Formula: $$ \begin{aligned} I &= \frac{P/\eta}{\sqrt{3} \times V_{pp} \times PF} \times 1000 \\ &= \frac{90/0.97}{\sqrt{3} \times 400 \times 0.85} \times 1000 \\ &= 157 \; \text{A} \end{aligned} $$

Apparent Power (S)

The apparent power is calculated from voltage and current: Apparent power represents the total power supplied to the motor.

Formula: $$ \begin{aligned} S &= \frac{\sqrt{3} \times V_{pp} \times I}{1000} \\ &= \frac{\sqrt{3} \times 400 \times 157}{1000} \\ &= 109 \; \text{kVA} \end{aligned} $$

Reactive Power (Q)

The reactive power is calculated using the power triangle, where P_elec is the electrical input power (shaft power ÷ efficiency): Reactive power represents the non-productive power component due to motor inductance.

Formula: $$ \begin{aligned} Q &= \sqrt{S^2 - P_{elec}^2} \\ &= \sqrt{(109)^2 - (92.8)^2} \\ &= 57.5 \; \text{kVAr} \end{aligned} $$

Phase Angle (θ)

The phase angle between voltage and current is calculated from the power factor: Phase angle indicates the lag between voltage and current due to motor inductance.

Formula: $$ \begin{aligned} \theta &= \cos^{-1}(PF) \times \frac{180}{\pi} \\ &= \cos^{-1}(0.85) \times \frac{180}{\pi} \\ &= 31.7 \; ^\circ \end{aligned} $$

Power Triangle Relationships

The relationship between active, reactive, and apparent power follows the power triangle: These fundamental relationships define the power characteristics of AC systems.

Formula: $$ \begin{aligned} S^2 &= P^2 + Q^2 $$ \\ &= \frac{P}{S} = \cos(\theta) $$ \\ &= S \times \sin(\theta) \end{aligned} $$

Summary of Results

Below is the summary of calculated motor electrical parameters:
Parameter Symbol Value Notes
Line Current I 157 A Motor line current
Apparent Power S 109 kVA Total apparent power
Reactive Power Q 57.5 kVAr Reactive power component
Phase Angle θ 31.7 ° Phase angle between voltage and current

Interpretation

For a 90 kW motor at 400V with power factor 0.85 and efficiency 97%, the motor will draw approximately 157.00 A of line current. The apparent power is 109.00 kVA, with a reactive component of 57.50 kVAr. The phase angle is 31.70°.

Three-Phase Voltage and Current Phasors - Motor Operation

Three-Phase Voltage and Current Phasors - Motor Operation VA IA VB IB VC IC φ = 31.7° Phase-to-Phase Voltage: 400.0 V Line Current: 157.0 A PF: 0.850 lagging Solid lines: Voltage | Dashed lines: Current Phases separated by 120° (three-phase system)

The phasor diagram shows the three-phase voltage and current phasors with the phase angle (φ) between them. Each phase (A, B, C) is separated by 120°. Solid lines represent voltage phasors, while dashed lines represent current phasors lagging behind voltage due to motor inductance.

Figure 1: Three-phase phasor diagram showing voltage and current relationships for motor operation

Motor Power Triangle (Three-Phase AC)

Motor Power Triangle (Three-Phase AC) P = 92.78 kW Q = 57.50 kVAr S = 109.00 kVA θ = 31.7° Active Power (P): Real electrical power drawn from supply Reactive Power (Q): Magnetic field power (inductive) Apparent Power (S): Total power supplied (vector sum) Power Factor = P / S = 0.851 (cos θ) Relationship: S² = P² + Q² (Pythagorean theorem)

The power triangle illustrates the relationship between active power (P), reactive power (Q), and apparent power (S) for the three-phase motor. Active power does useful mechanical work, reactive power maintains the motor magnetic field, and apparent power is the vector sum of both.

Figure 2: Power triangle showing P, Q, and S relationships for three-phase motor

Approval:

This calculation has been reviewed and approved by:
Created By
Engineer Name
Date: ..........................
Checked
By: .............................
Date: ..........................
Approved
By: .............................
Date: ..........................
Client Approved
By: .............................
Date: ..........................

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