Basics - Generators have been the backbone of the electrical grid for as long as the grid has been around. Other than solar energy, all dominant forms of power productions rely on the use of generators powered by turbines (hydro, nuclear, coal, gas, oil, wind). The turbine converts some form of energy into mechanical energy and the generator converts that mechanical energy into electrical energy.
The concept remains the same regardless of the original power source: a rotor (the part that moves) is rotated against a stator (the part that doesn't move). The interaction between the magnetic fields of the stator and rotor induces a voltage by Faraday's Law. The stator and rotor can consist of permanent magnets or windings. If coil windings are used for both the rotor and stator, then a separate source is required to excite them (at least initially).
Notice that the definition of the rotor and stator doesn't actually tell you which part of the generator the windings are attached to. You might think that the stator would always be the output source, but brushes and other mechanisms can be used to solve the issue of moving wires. The armature is the winding that has the load connected to it (and gets a voltage induced into it). The field is the winding that produces a magnetic field.
From a practical perspective, generators are required to be rated for a variety of key parameters, including:
Impedances
Output voltage
Output current
Output power (real or apparent)
Power factor capabilities
Frequency
Number of Phases
Operating temperature limits and characteristics
All of this information is used to design power systems fed from generators.
Generator Modeling - How do generators really run though? Does it behave like a voltage source? A current source? Or something else?
Figure 1: What does a generator do?
The answer is that generators behave as we control them! Generators are usually controlled in one of a few main ways. In each case, the set point for real power is considered to be constant (i.e. we are always trying to produce a certain amount of real power as required by the load). Two of the most common ways are explained here:
Voltage Control: In this mode, generators are designed to keep their voltage magnitude constant while allowing their reactive power to vary. The generator will absorb VARs when the grid voltage is higher than the generator terminal voltage. The generator will deliver VARs when the grid voltage is lower than the generator terminal voltage. In a typical synchronous generator, we can control the voltage by altering the field strength through a system known as "excitation". A stronger magnetic field will create a larger induced voltage in the stator.
Q Control: In this mode, generators are designed to keep their reactive power constant. Instead of allowing Q to vary, the generator lets the voltage vary. In effect, this is the opposite of voltage control. We still hold the real power constant, but we are trading off voltage for VARs.
Figure 2: Generator Control Schemes in a Nutshell
By this point it may already be clear, but we can't simultaneously control voltage, reactive power, and real power. If we try to fix all of those points, it's like having a system of equations with 3 equations and 2 unknowns. We've over-constrained the problem. In real world language, it means that we can only set P, Q, and V if we are designing for one super-specific case. Any deviation in the grid at all, any change in loads, etc., and the whole thing falls apart. If you tried to design the generator to do all of these things then the control system simply wouldn't work.
Which one gets used and when? Ultimately, generators that are connected to the grid get their mode of operation determined by the grid operator. The grid's impedance and the local network needs (as seen by the local utility or whoever the grid operator is) will be the deciding factors.
However the generator is operated, the generator needs to be run safely. For example, if a generator is run in Q control mode and the P and Q are so large that they lead to a voltage below the minimum operating voltage, then the setpoints have to be changed. Otherwise, you risk damaging the generator or worse.
Generator Output Conductors - For small generators, like those governed by the NEC, the requirement for output conductor sizing is that they be capable of continuously carrying 115% of the generator output current unless the generator has appropriate overload protection (in which case only 100% loading is required). Easy enough, and for many residential applications, the conductors will still end up being sized to 125% for consistency with other branch circuits and feeders.
Big generators are a bit more complicated. Often, generators don't have typical insulated cable coming out of them. Generators may produce so much current that using insulated wire and cable isn't cost effective. Instead, systems like isolated-phase bus duct (IPBD) and non-segregated phase bus duct (NSBD) are used. These are bus bars that, as their names suggest, are either isolated or not. They're a specialty kind of system made by specialty manufacturers and governed by IEEE standard for metal-enclosed bus (C37.23). Bus ducts are ordered with specific ampere ratings based on ambient temperatures. Testing is required of these assemblies and engineers don't size them like typical wire and cable. In any case, the output conductors from a generator need to be able to safely carry the expected output current at the expected worst-case temperature, irradiance, etc.
Example - Solve for the current magnitude I in the single-phase circuit below. Also, solve for the reactive power Q produced by the generator.
The generator is operating in voltage-control mode, meaning that the output voltage of the generator will be held constant with a magnitude V. The output power is also held constant with a value P.
First, solve for the current using Ohm's Law:
I = V / (R + jX)
The magnitude of this expression is:
I = V / √(R^2 + X^2)
With the current magnitude known, we can solve for the reactive power Q.
By conservation of complex power, the reactive power drawn by the load must be equal to that produced by the generator.
The load draws a reactive power given by:
Q = X I^2
Which is necessarily the same as the generator.
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