# Paralleling two synchronous AC generators – phasor diagram with AVRs

This article Paralleling two synchronous AC generators presented phasor diagrams for two synchronous generators in parallel, and Paralleling two synchronous AC generators – simple AVR discussion discussed a simple automatic voltage regulator system that can be used to share two identical machines.

To recap, the first configuration presented follows.

Above is a phasor diagram of two machines of the type discussed in parallel. This is just after ACB closure, and they are not well adjusted in this case to allow visibility of the various phasors.

The phase reference is the bus voltage v3, and one can note that i3 lags v3 by 26°, a consequence of the specified load PF=0.9.

Note that i1 is not exactly in phase with i2 which indicates less than perfect sharing of reactive current / power. This leads to the same angle between i1*zs1 and i2*zs2.

Most power (92%) is carried by the outgoing machine (#1) which is a little high as an initial condition on ACB close.

The scenario discussed assumed manual adjustment of the excitation to achieve the EMF v1 and v2.

Let’s take exactly the load sharing scenario presented above, and add to the phasor diagram the two control inputs to an AVR. Let’s assume quadrature droop factor is 0.04pu.

Above is a zoomed in view of the phasors.

The orange phasors are the additional ones relating to the quad droop AVR.

v1q and v2q are the quadrature droop sense voltages, they are derived from a current sample rotated 90°. So, whilst phase of i1 is -27° and phase of i2 is -13° (see first diagram), the phases of v1q and v2q are 63° and 77° respectively as seen above.

Taking machine #2 initially, v2q is the quadrature current feedback voltage, the other control input is the bus voltage v3. These two are summed to produce v2p, and |v2p| is the Process Value (PV) in the AVR control loop which is also the Set Value (SV) in the stable loop. Note that the AVR will adjust the excitation to maintain PV=SV, and EMF v2 will be as shown.

The same thing happens for machine #1, though more of its phasors are outside the graph window.

The key voltages and currents are as follows:

• v1: 3.132e+02+1.324e+02j, v2: 2.397e+02+1.223e+01j, v3: 2.361e+02-2.842e-14j
• |v1|: 3.40000e+02, |v2|: 2.40000e+02, |v3|: 2.36144e+02
• i1: 6.765e+01-3.433e+01j, i2: 6.148e+00-1.407e+00j, i3: 7.379e+01-3.574e+01j
• i1: 7.58608e+01∠-26.91°, i2: 6.30714e+00∠-12.89°, i3: 8.33333e+01∠-25.84°
• s1: 1.59743e+04+8.10767e+03j, s2: 1.45187e+03+3.32218e+02j, s3: 1.77108e+04+8.57772e+03j
• pa1: 22.922°, pa2: 2.922°,ta1: 139.831°, ta2: 105.810°
• v1p: 2.401e+02+7.793e+00j, v2p: 2.363e+02+7.083e-01j, v3: 2.361e+02-2.842e-14j
• |v1p|: 2.40225e+02, |v2p|: 2.36307e+02, |v3|: 2.36144e+02

So, the two control inputs to AVR #1 sum to v1p, and |v1p|=240.2 controls the excitation of machine #1. Likewise, the two control inputs to AVR #2 sum to v2p, and |v2p|=236.3 controls the excitation of machine #2. In practice, the speed SV of machine #2 would be increased to transfer real load (real component of load current) from machine #1, and the speed SV of machine #1 reduced. Concurrently, the voltage SV of both AVRs would be adjusted to adjust the sharing of reactive load current.

In this configuration, whether load sharing or a single machine, voltage droop with changing load current remains quite small, much better than the case of manually controlled excitation.

A follow on from this is that quite small difference in the voltage SV will result in relatively large reactive circulating current.

There are more sophisticated controls available, the AVRs described here operate semi-independently in that there is not control signal connected between them, the bus voltage and the droop characteristic control the sharing of reactive current.