Thread Subject: Calculation of Terminal Voltages of Synchronous Generator

Hello,

Currently i am working on a simulation involving Synchronous Machine PU Fundamental Block in Simulink. The problem that i am having is to compute the Terminal Voltage of the machine. Currently the way i am doing is to connect the V-I block at the terminals and measuring the phase to phase voltage or phase to ground voltage. But i want to compute the terminal voltage from the "m" output of the synchronous machine PU Fundamental block. As you will know all the values in the "m" output are calculated in Per units system and are mostly in dq0 reference frame. I have tried to use the following formulas to compute the terminal voltage from the data provided.

Method 1:

Vphase = Ea - jXs*Ia - Ra*Ia

where: Xs = Xad + Xl

Xad = (Eq + Ra*Iq + Xd*Id) / Ifd

Method 2:

Ed = Xq*Iq - Ra*Id

Eq = -Xd*Id + Xad*Ifd - Ra*Iq

Voltage at the terminals

VT = Sqrt(Ed*Ed + Eq*Eq)

where:

ABC Reference Frame Quantities:

Vphase = Terminal phase voltage in a wye connected generator in abc reference frame
Ea = Stator voltage in abc reference frame
Ra = Stator resistance
Ia = Stator current in abc reference frame
Xs = Synchronous reactance

DQ0 Reference Frame Quantities:

Xl = Leakage reactance
Xad = Magnatizing reactance in d-axis
Eq = Stator voltage in q-axis
Ed = Stator voltage in d-axis
Id = Stator current in d-axis
Iq = Stator current in q-axis
Ifd = Field current in d-axis

Using Machine Parameters as Base quantities.

Example: Pbase = 80KVA
Vbase(rms) = 480V

Ibase = sqrt(2/3) * (Pbase / Vbase)
Zbase = Vbase/Ibase

I have used both of these methods but the answer doesn't match the measurements from the V-I measurements block in fact the difference is quite large. Can someone please help me out to guide me in the correct direction with the right formula so that i can compute the Terminal Voltage directly from the parameters mentioned in the "m" output of the synchronous machine PU fundamental block.

Thanks in advance

Kind Regards

Hammad Khan

Hello,

if you connect the V-I measurement block straight after the machines terminals its voltage inputs are line to line voltages. The voltages in the machines m-output vector are line-to-earth voltages. So my guess is that the differences you came across is the factor sqrt(3) between these values (magnitude). In order to get the instantenous line-to-line terminal voltages its
Vab = Va-Vb
with Va, Vb from the machines vector m. For computation of the phasors (magnitude and angle) just do like in te example 'power_simplealt'. Please note that in the example line-to-earth voltages are used (so again there is the factor sqrt(3) between the voltage Va and the one you get if you'd use Vab).

If you need to use the 'Synchronous Machine Standard' model the m-output will include the vd and vq voltages. With these you have to use dq-to-abc blocks to compute the instantenous voltages. The magnitude is simply vt=sqrt(vd*vd+vq*vq) when using this model.

Hope that helps
Frank

G'day Frank,

Thanks for the reply. Sorry i think i explained myself in a confusing manner before. I hope this is correct, from V-I measurement block we can measure line-ground voltage and can also measure line-line voltage. We can just select the option in the V-I measurement block to measure line - ground or line - line.

The reason for me to use the Synchronous Machine PU fundamental block is because that the Governor and the excitation blocks require a PU input in dq0 frame from the synchronous machine and Synchronous Machine PU fundamental block provides me with that specific inputs for the governor and the exciter. In Matlab synchronous machine PU fundamental block "m-signal" output has stator voltages Vd, Vq. I want to calculate the instantaneous terminal voltages from the stator voltages or the data provided in the "m-signal" output.

Thanks again. Have a good day.

Kind Regards

Hammad Khan

G'day Frank,

Thanks for the reply. Sorry about the confusion, In simulink V-I measurement block, we can measure line-line or line-ground voltages. We just need to select the the option of either line-line or line-ground.

The reason i have to use simulink Synchronous Machine PU fundamental block is because the simulink governor and the exciter block requires PU inputs in dq0 frame and Simulink Synchronous Machine PU Fundamental block provides those outputs from the "m-signal" output. I want to calculate the the terminal voltages from the "m-signal" outputs like from stator voltages Vd, Vq or some other m'output. Thanks again.

Kind Regards

Hammad Khan