---
title: "d and q axis concept and need of dq0"
subject: "Electric Machines II"
chapter: 1
key: "semester_5/electric_machines_ii:d-q-axis-dq0-need"
source: https://www.bctengineer.com/q/semester_5/electric_machines_ii/d-q-axis-dq0-need
site: BCT Engineering
---

# d and q axis concept and need of dq0

Electric Machines II · Chapter 1: Three Phase Synchronous Generator

- Asked in: 2083 Baisakh (new course), 3 marks
- Video: [The Clarke and Park transformations (Episode 8)](https://www.youtube.com/watch?v=mbJOxqxLkLE) — Jantzen Lee
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/electric_machines_ii/d-q-axis-dq0-need
- Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machines_ii/chapter-1

## Question

Illustrate the concept of d axis and q axis in synchronous machine. Why dq0 plane in synchronous machine is needed?

## Short answer

The d-axis aligns with the rotor field pole center (low reluctance, high Xd); the q-axis is 90° ahead, between poles (high reluctance, lower Xq). The dq0 transformation converts time-varying stator inductances to constant values, simplifies analysis, and makes AC quantities DC in steady state, aiding control and stability studies.

## Answer

#### d-axis and q-axis
In a synchronous machine two axes are fixed on the **rotor** and rotate with it:

- **Direct axis (d-axis)**: along the centre line of the rotor field poles (the axis of the field mmf). The air gap is smallest here, so reluctance is low and reactance $X_d$ is high.
- **Quadrature axis (q-axis)**: 90° electrical ahead of the d-axis, i.e. midway between the poles. The air gap is large in a salient-pole machine, so $X_q < X_d$.

```text
             q-axis
               ^
               |
     S ---- [ rotor ] ---- N  ---> d-axis
               |        (field axis)
```

The armature current and mmf are resolved into $I_d$ along the d-axis and $I_q$ along the q-axis (Blondel's two-reaction theory), each acting on its own reactance.

#### Need for the dq0 frame
1. In the phase (abc) frame, the self and mutual inductances of the stator windings vary with rotor position $\theta$ (especially in salient-pole machines), giving differential equations with **time-varying coefficients**.
2. **Park's (dq0) transformation** refers stator quantities to the rotor axes; the inductances become **constant** ($L_d$, $L_q$, $L_0$).
3. In steady state, sinusoidal ac quantities become **dc quantities**, which makes analysis, simulation and control (e.g. vector control, AVR, stability studies) much simpler.
4. The zero-sequence component (0) handles unbalanced conditions; it is zero for balanced operation.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Where are the d-axis and q-axis located?
   A. Both fixed on the stator
   B. d along the pole centre line, q 90 electrical degrees away between poles, both on the rotor
   C. d between poles, q along the poles
   D. Both along phase a
   Answer: B. The d-axis is along the field pole axis; the q-axis lies 90 electrical degrees ahead, midway between poles, rotating with the rotor. (Key point: Definition of axes)

2. Why is Xq < Xd in a salient-pole machine?
   A. The q-axis gap is large, so reluctance is high
   B. The q-axis has more turns
   C. The q-axis gap is small
   D. Xq includes field resistance
   Answer: A. Between poles the air gap is large, so reluctance is high and reactance lower than along the d-axis. (Key point: Reactance relation)

3. Why is the dq0 frame needed?
   A. To increase the rated power
   B. Inductances become constant and steady-state ac becomes dc
   C. To remove the rotor
   D. To change frequency
   Answer: B. In abc the inductances vary with rotor position; Park's transformation makes them constant and simplifies analysis and control. (Key point: Need for dq0)

## Related in Electric Machines II

- [Construction of synchronous machine and rotor types](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asynchronous-machine-construction-rotors) — Electric Machines II, chapter 1, asked 2×
- [Synchronous reactance and regulation from test data](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aregulation-1500kva-2300v-test) — Electric Machines II, chapter 1
- [Power angle characteristics of salient pole machine](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asalient-power-angle-derivation) — Electric Machines II, chapter 2

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