Voltage & reactive-power control
The key idea
You can hold a bus voltage in one of two ways. You inject reactive power at the bus, so less reactive power travels down the line. Or you change the ratio of the transformer that feeds the bus. Every voltage control device does one of these two things. Every device also has a limit.
The idea
Power that reaches a load must cross an impedance, and both parts of the flow cost voltage. Active power P pushes against the resistance R. Reactive power pushes against the reactance X. Reactive power does no net work, but motors, cables and transformers need it to build their magnetic fields. Above low voltage, X is typically five to ten times R, so the reactive flow decides the voltage at the far end. For this reason, voltage control and reactive power are one subject.
The same relationship shows you how to correct a bus voltage that is too low. Make the reactive power at the bus itself, and the line no longer carries that reactive power. The voltage drop then falls, and the bus voltage rises. You can also leave the reactive flow alone and raise the source voltage instead. To do that, you move the turns ratio of a transformer. Four levers do this work in practice.
Nothing. The bus voltage settles at the value that the voltage drop leaves. This case is the baseline for comparison. On a feeder with a light load, it is often the correct choice.
A generator's AVR. The automatic voltage regulator (AVR) measures the terminal voltage. It adjusts the excitation of the machine continuously, and it produces exactly the reactive power that the target needs. The control is smooth, fast and precise, and it is the reason a bus is a PV bus in a power flow. But the machine has a reactive capability limit, Qmax. When the target needs more reactive power than that limit, the AVR stops holding the voltage. The reactive output stays at the limit, and the bus becomes a PQ bus for the rest of the solution.
A switched capacitor bank. A capacitor bank produces reactive power with no moving parts and no fuel, and you switch its fixed steps in and out. The bank has two disadvantages. Its output is discrete, so the bus voltage lands near the target rather than on it. Its output also falls with the square of the voltage across the bank. A bank rated 0.15 pu at nominal voltage makes about 0.13 pu at 0.93 pu. The bank is therefore weakest when the bus needs it most.
A tap changer. A tap changer moves the turns ratio of a transformer in small steps, typically ±1.25% each. The change shifts the source voltage that the downstream network sees. A tap changer makes no reactive power of its own. The reactive demand of the load still travels down the line and through the transformer. The tap changer therefore moves the problem upstream, and it does not remove the problem. This works when the upstream network is strong, and it fails when the upstream network is weak.
Try it
Pick a lever and load the feed. Then watch the gauge. Some levers hold the bus inside the band, and some levers stop holding it. Find the point where each lever stops working.
Bus voltage
1.000 pu
Reactive power injected
0.48 pu
Lever state
holding 1.00 pu
The regulator adjusts its reactive output continuously, so the bus sits exactly on target. This behavior is the definition of a PV bus.
This teaching model uses a 1.00 pu source behind R = 0.02 and X = 0.10 pu that feeds one bus. It calculates V ≈ E′ − (R·P + X·Q)/E′. Here E′ is the source voltage after the tap, and Q is the load demand minus the reactive power injected locally. The load reactive demand is fixed at 0.4·P, which is a power factor of about 0.93. The linearization is accurate near 1 pu, which is the range that voltage control works in. A real power flow solves the full equations instead.
Why it matters
- A voltage target is a reactive-power budget. Every PV bus in a study claims that a machine can produce the reactive power that the target needs. If the machine does not have that capability, the study describes a network that does not exist.
- The Q limit is a common source of error in voltage studies. A generator that reaches Qmax converts to a PQ bus, and the voltage profile you designed against disappears. Phasor reports every conversion for this reason. The conversion is a result of the study, not a minor detail.
- A capacitor bank is weakest when you need it most. The V² dependence means that the bank produces the least reactive power during the deep voltage drop that you installed it to correct. Each step you add also makes the next step more effective. This behavior is the mechanism behind voltage collapse on feeders with many capacitor banks.
- A tap changer and reactive power are not interchangeable. A tap changer corrects the bus voltage downstream, but it draws more reactive power through the transformer. On a weak upstream network, that extra flow lowers the voltage on the upstream side. The tap changer then moves again, and it never reaches a stable position.
The math, if you want itOptional — the page reads completely without it
Take a short feed of R + jX from a source at E′ to a load bus. The bus carries P and a net reactive demand Q. The voltage at the bus is then approximately:
voltage at the load bus
V ≈ E′ − R · P + X · QE′
Q here is the net flow. It is the demand of the load minus the reactive power that you inject at the bus. Inject more than the load needs, and Q goes negative, which raises V above E′. The widget uses R = 0.02 and X = 0.10 pu. Each 0.1 pu of Q therefore costs five times the voltage that 0.1 pu of P costs. That ratio is the practical meaning of X ≫ R.
Rearrange the equation for Q to get the dispatch of the AVR. The result is the reactive power that a machine must produce to hold the bus at Vset.
AVR dispatch
Qgen = Qload − E′ (E′ − Vset) − R · PX
If that value exceeds Qmax, the machine produces Qmax instead. The first equation then gives a new value for V. A capacitor bank has no such choice. The voltage across the bank sets its output:
capacitor bank output
Qcap = n · Qstep · V²
That relationship is circular. The voltage depends on the output of the bank, and the output depends on the voltage. The widget starts at V = 1 and repeats the calculation until the two values agree. Five rounds are more than enough at this size. A tap changer uses a simpler method, and it scales the source:
tap changer
E′ = E · (1 + t)
Here t is the tap position, and each step is ±1.25%. The equation contains no Q term. A tap changer redistributes the reactive flow, and it does not create reactive power.
All of this is a linearization. It drops the angle between the two ends, and it assumes that E′ is close to 1 pu. The result is accurate within a few percent of nominal voltage, which is the range that voltage control works in. Outside that range the error grows. A real study does not linearize. It solves the full power-balance equations at every bus and repeats until the equations close, which is the method that Newton–Raphson uses.
See it in Phasor
In Phasor, the voltage target and the reactive limits belong to the generator element. A capacitor bank is a shunt element with a step size, and a transformer carries its own tap range. Run a power flow. The results show which machines reach their limits and which buses convert from PV to PQ. The results also show the voltage profile after those conversions.