Voltage & reactive-power control
The key idea
There are only two ways to hold a bus voltage: make the reactive power at the bus itself, so the line no longer has to carry it, or change the ratio of the transformer that feeds the bus. Every voltage-control device does one of these two things, and every one of them has a limit.
The idea
Power reaching a load must cross an impedance, and both parts of the flow cost voltage: active power P pushes against the resistance R, and reactive power pushes against the reactance X. Reactive power does no net work, but motors, cables and transformers cannot run without it: they need it to build their magnetic fields. And because X is typically five to ten times R above low voltage, it is the reactive flow that decides the voltage at the far end. That is why voltage control and reactive power are one subject.
The same relationship tells you how to fix a bus that sits too low. Make the reactive power at the bus itself and the line no longer carries it: the drop shrinks, and the voltage rises. Or leave the reactive flow alone and raise the source voltage instead, by moving the turns ratio of a transformer. In practice, four levers do this work.
Nothing. The bus settles wherever the voltage drop leaves it. This is the baseline the other levers are measured against, and on a lightly loaded feeder it is often the right choice.
A generator's AVR. The automatic voltage regulator measures the terminal voltage and adjusts the machine's excitation continuously, producing exactly the reactive power the target needs. The control is smooth, fast and precise: it is the reason a bus is a PV bus in a power flow. But the machine has a reactive capability limit, Qmax. Ask for more than that and the AVR simply stops holding: the reactive output sits at the limit, and the bus becomes a PQ bus for the rest of the solution.
A switched capacitor bank. A capacitor bank makes reactive power with no moving parts and no fuel; you switch its fixed steps in and out. It has two weaknesses. Its output is discrete, so the voltage lands near the target rather than on it. And its output falls with the square of the voltage across it: a bank rated 0.15 pu at nominal makes only about 0.13 pu at 0.93 pu. The bank is weakest at exactly the moment 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, shifting the source voltage the downstream network sees. But it makes no reactive power of its own: the load's reactive demand still travels down the line and through the transformer. A tap changer moves the problem upstream; it does not remove it. That works when the upstream network is strong, and fails when it is weak.
Try it
Pick a lever and load the feed. Some levers hold the bus inside the band; some stop holding it. Find the point where each one gives up.
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 is a claim that some machine can produce the reactive power the target needs. If the machine cannot, 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 quietly disappears. That is why Phasor reports every conversion: it is a result of the study, not a footnote.
- A capacitor bank is weakest when you need it most. The V² dependence means the bank produces the least reactive power during the deep sag it was installed to correct, and each step you add makes the next step more effective. This is the mechanism behind voltage collapse on feeders stacked with capacitor banks.
- A tap changer and reactive power are not interchangeable. A tap changer corrects the downstream voltage but draws more reactive power through the transformer. On a weak upstream network that extra flow drags the upstream voltage down, the tap changer moves again — and it never finds 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 carrying P and a net reactive demand Q. The bus voltage is then approximately:
voltage at the load bus
V ≈ E′ − R · P + X · QE′
Q here is the net flow: the load's demand minus whatever you inject at the bus. Inject more than the load needs and Q goes negative, lifting V above E′. The widget uses R = 0.02 and X = 0.10 pu, so each 0.1 pu of Q costs five times the voltage that 0.1 pu of P does. That ratio is the practical meaning of X ≫ R.
Rearrange for Q and you have the AVR's dispatch, the reactive power 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, and the first equation gives whatever voltage results. A capacitor bank has no such choice; the voltage across it sets its output:
capacitor bank output
Qcap = n · Qstep · V²
Notice the circularity: the voltage depends on the bank's output, and the output depends on the voltage. The widget starts at V = 1 and repeats the calculation until the two agree. Five rounds are plenty at this size. A tap changer is simpler still; it just scales the source:
tap changer
E′ = E · (1 + t)
where t is the tap position, in steps of ±1.25%. There is no Q in that equation — a tap changer redistributes the reactive flow, it does not create any.
All of this is a linearization: it drops the angle between the two ends and assumes E′ stays near 1 pu. It is accurate within a few percent of nominal, which is the range voltage control operates 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 they close, which is exactly what Newton–Raphson does.
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 and the results show which machines hit their limits, which buses converted from PV to PQ, and the voltage profile that remains after those conversions.