Page 84 - Handbook of Electrical Engineering

64 HANDBOOK OF ELECTRICAL ENGINEERING

3.3 PHASOR DIAGRAM OF VOLTAGES AND CURRENTS

The following points apply to the drawing of phasor diagrams of generators and motors:-

• The terminal voltage V is the reference phasor and is drawn horizontally.
• The emf E lies along the pole axis of the rotor.
• The current in the stator can be resolved into two components, its direct component along the
‘direct or d-axis’ and its quadrature component along the ‘quadrature or q-axis’.

The emf E leads the voltage V in an anti-clockwise direction when the machine is a generator.
Each reactance and resistance in the machine has a volt drop associated with it due to the
stator current flowing through it. Consider a generator. The following currents and voltages can be
shown in a phasor diagram for both the steady and the dynamic states.

• E the emf produced by the field current I f .
• V the terminal voltage.
the component of V along the d-axis.
• V d
the component of V along the q-axis.
• V q
• I the stator current.
the component of I along the d-axis.
• I d
the component of I along the q-axis.
• I q
the volt drop due to the armature or stator current.
• IR a
• I d R a the component of IR a along the d-axis.
the component of IR a along the q-axis.
• I q R a
• I d X d the volt drop due to the d-axis synchronous reactance.
• I d X the volt drop due to the d-axis transient reactance.
d
• I d X the volt drop due to the d-axis sub-transient reactance.
d
• I q X q the volt drop due to the q-axis synchronous reactance.
• I q X q the volt drop due to the q-axis transient reactance (normally taken as I q X q ).
• I q X the volt drop due to the q-axis sub-transient reactance.
q
• E the emf behind the transient impedance.
• E the emf behind the sub-transient impedance.

Explanations of the two-axis, or d-q, theory are given in Reference 1, Chapter 17 and in more
detail in References 2 and 3.

Figure 3.1 has been drawn for a 15 MW generator operating at full-load and a power factor
of 0.8 lagging.
The following per-unit data were used:-

E = 2.098
V = 1.0, V d = 0.423, V q = 0.906

I = 1.0, I d = 0.882, I q = 0.472