I need to determine the Peak Envelope Power for the VSAT station. Given that the modulation is not AM, would it be correct to assume that the PEP will be the same as transmitter power?
There are modulations that would not be called "AM" which still modulate amplitude. For example, BPSK reverses phase at a zero amplitude point. BPSK could also be considered a digital amplitude modulation where the amplitude varies between 1 and -1.
Thus, you must be careful to specify what you mean by "not AM". If you mean to exclude all modulations that modulate power at all, then peak and average power could be considered the same in practice. MSK is an example that would qualify.
This would only apply to the extent that the transmitted waveform has an RMS average equivalent to a sine wave. For example consider that a square wave has a higher RMS average, and thus a higher power, than a sine wave of equal amplitude. In practice the difference will be small or nonexistent for most modulations.
For all intents and purposes they are the same, yes.
Here is a good quote from W8JI that explains it.
"Average power is same as equivalent work power or heating power of each cycle averaged over a significant time compared to the time when power level changes. With an unchanging (during the measurement period) power level, such as a steady unmodulated carrier applied to a constant resistance load, average power and peak envelope power are the same. If we close and hold-closed a manual telegraph key on a good stable CW transmitter, we will see the average power displayed on a power meter. It will not be the "RMS power". It is also the peak envelope power, because it is the maximum stable heating power level over some period of time that we hold the key."
This is from his website on AM, here: Amplitude Modulation
For VSAT (Very Small Aperture Terminal), I can't find anything that specifically identifies the modulation used other than to say that it uses TDMA (Time Division Multiple Access). But my experience with this type of equipment suggests that it is probably a constant envelope type of waveform while transmitting. (Such as QPSK). This is because the amplifiers used for these systems are typically non-linear and are designed to run at one power output level.
So PEP would be equivalent to Average Power for a steady transmission.
But your average power calculation might need to take into account the duty factor, since it is a TDMA signal. If that's important to you, you should say so in your question. If you do that, we can readdress your question.