Regulation of a three-phase alternator by the EMF (synchronous impedance) method
Regulation of a three-phase alternator by the synchronous impedance (EMF) method: open-circuit and short-circuit tests, calculations, why the method is pessimistic, and viva questions with answers.
Aim
To determine the voltage regulation of a three-phase alternator at a given load power factor by the EMF (synchronous impedance) method, using open-circuit and short-circuit test data.
Apparatus required
| Apparatus | Specification | Qty |
|---|---|---|
| Three-phase alternator with DC motor prime mover | 3 kVA, 415 V, 4.2 A, 1500 rpm | 1 set |
| DC field regulator (rheostat) | For the alternator field | 1 |
| Motor field regulator (rheostat) | For the prime mover | 1 |
| Voltmeter (MI) | 0–600 V | 1 |
| Ammeter (MI) | 0–10 A | 1 |
| Ammeter (MC) | 0–2 A, for field current | 1 |
| TPST switch / shorting link | For the short-circuit test | 1 |
| Tachometer | Digital or contact type | 1 |
Theory
An alternator's terminal voltage falls under load for three reasons: the resistance of the armature winding, its leakage reactance, and the armature reaction — the effect the load current's own magnetic field has on the main field. The synchronous impedance method rolls the last two into one fictitious reactance X_s and treats the machine as a constant emf E₀ behind an impedance R_a + jX_s.
Two tests provide the numbers. The open-circuit test, run at rated speed with the armature open, gives the generated emf against field current — the OCC. The short-circuit test, at the same speed with the armature shorted, gives the armature current against field current — a straight line, because the machine is heavily demagnetised and never approaches saturation.
The synchronous impedance is read off both curves at the same field current: Z_s = E_oc / I_sc, both per phase. The field current chosen is normally the one that drives rated current on short circuit. Subtracting the separately measured armature resistance gives X_s = √(Z_s² − R_a²).
E₀ then follows from the phasor sum, and regulation is (E₀ − V)/V. The catch is that Z_s was taken from a short-circuit condition where the machine is unsaturated, but the OC voltage used is from the saturated region. The method therefore over-estimates the impedance drop, and its answer for regulation is always higher than reality — which is why it is called the pessimistic method.
The MMF method makes the opposite assumption and comes out optimistic. The ZPF (Potier) method separates leakage reactance from armature reaction properly and is the accurate one of the three.
Circuit connections
Check every point below against your board before switching on. There is no diagram here on purpose — a wrong diagram is worse than none, and this is the list a demonstrator actually walks through with you.
- The alternator is coupled to a DC shunt motor acting as the prime mover; the motor is started through its starter with the field regulator at minimum resistance.
- Alternator field supplied from the DC source through the field rheostat and a moving-coil ammeter, so field current can be set and read.
- For the OC test: a voltmeter across two of the three armature line terminals, with the TPST switch open.
- For the SC test: the ammeter in one line with the TPST switch closed, shorting all three lines together.
- Armature resistance is measured separately, with the machine at rest, by applying a small DC voltage across two lines and reading the current.
Procedure
- 1Start the prime mover and bring the alternator to its rated speed. Hold that speed for every reading in both tests — generated emf is directly proportional to speed.
- 2OC test: with the armature open, raise the field current in equal steps from zero and record the open-circuit line voltage at each step, up to about 125 % of rated voltage. Increase the field current in one direction only.
- 3Bring the field current back to zero and close the short-circuit switch.
- 4SC test: raise the field current until the armature current reaches its rated value, and record the field current and armature current. Do not exceed rated armature current.
- 5Reduce the field current to zero, open the switch and stop the machine.
- 6Measure the DC resistance between two lines with the machine at standstill. For a star winding, half that value is the per-phase DC resistance; multiply it by about 1.3–1.6 to get the effective AC value.
- 7From the two curves at the chosen field current, compute Z_s, X_s, E₀ and the regulation at the required power factor.
Work out your readings
Type in the numbers off the meters. This fills the tabular column, works the calculation through step by step, plots the characteristic — and tells you when a reading cannot physically be right, which is the part a manual can't do. Everything stays on this device, and it works with the network off.
Nameplate and machine data
DC value × 1.3–1.6 for skin effect
0 to 1
Fill in the machine data to see the results, the worked calculation and the curve.
Precautions
- Hold the speed at its rated value throughout. A 5 % speed error puts a 5 % error straight into every OC voltage.
- Raise the field current monotonically during the OC test. Reducing it part-way traces the other branch of the hysteresis loop and puts a kink in the curve.
- Never exceed rated armature current during the short-circuit test.
- The field rheostat must be at maximum resistance (minimum field current) before the SC switch is closed.
- Measure armature resistance with the machine stationary and the field de-energised.
Sources of error
Every record asks for these, and every record gets the same three lines copied from the one before. These are the errors this particular experiment actually has.
- The unsaturated synchronous impedance is used with saturated OC data — the built-in error that makes the method pessimistic.
- Effective AC resistance is larger than the measured DC value because of skin effect; the 1.3–1.6 multiplier is an estimate, not a measurement.
- Speed drift on the prime mover between the OC and SC runs.
- For a star-connected machine, forgetting to halve the line-to-line DC resistance gives an R_a twice what it should be.
Viva questions with answers
Why is the EMF method called pessimistic?
Because the synchronous impedance is calculated from short-circuit conditions, where the flux is small and the magnetic circuit unsaturated, so Z_s comes out larger than the value that actually applies at rated voltage. A larger impedance means a larger calculated drop, so the regulation predicted is always higher than the machine really has.
Why is the short-circuit characteristic a straight line?
On short circuit the terminal voltage is zero, so the net flux only has to drive current through the small leakage impedance. The machine works far below saturation, and in the linear region armature current is directly proportional to field current.
Why must the OC and SC readings be taken at the same field current?
Z_s is the ratio of a voltage to a current that the same excitation produces. Taking them at different field currents compares two different magnetic states of the machine, and the ratio means nothing.
What is armature reaction, and how does it depend on power factor?
It is the effect of the armature current's own MMF on the main field. At zero power factor lagging it is purely demagnetising; at zero power factor leading it is purely magnetising; at unity power factor it is cross-magnetising, distorting the field without changing its total strength.
Can voltage regulation be negative? When?
Yes, on a leading power factor load. The armature reaction then magnetises the field, so the terminal voltage on load is higher than the no-load emf and the regulation comes out negative.
Name the three methods of finding alternator regulation and rank them.
EMF (synchronous impedance) — pessimistic; MMF (ampere-turn) — optimistic; ZPF or Potier triangle — the most accurate, because it separates the leakage reactance drop from the armature reaction instead of lumping them together.
Why is effective armature resistance larger than the DC value?
Skin effect. Alternating current concentrates towards the surface of the conductor, so the effective cross-section is smaller than the physical one. The usual allowance is a factor of about 1.3 to 1.6.
What decides the frequency of the generated voltage?
f = PN/120, where P is the number of poles and N the speed in rpm. For 50 Hz, a 4-pole alternator must be driven at exactly 1500 rpm.