PW-C4 · Transmission and per-unit

Voltage regulation: hold the voltage by steering reactive power

When the load changes, the I·Z drop makes the receiving-end voltage swing: it sags under heavy load and rises under light load. Yet the voltage must stay within the prescribed range, so drag the handle that fills in reactive power with a capacitor to shrink the drop, and learn how a sagging voltage is brought back into the range.

Grow the capacitor, bring the voltage into the band

Under heavy load the receiving-end voltage has sagged below the lower limit (red). Dragging the handle grows the capacitor's reactive power Q_C, so the lagging reactive power flowing in the line shrinks, the X drop gets smaller, and the voltage marker rises into the green band (0.95 to 1.05). Grow it too much and it overshoots the band into overvoltage.

Drag the handle left and right to change the amount of capacitance. At first there is no capacitor and V_r = 0.88; with Q_C between 0.175 and 0.425 it is inside the band, and where Q_C equals the load's reactive power Q_L = 0.3 it is exactly 1.000.

Receiving voltage (allowed band 0.95 to 1.05)

V_r ≈ 0.880 pu

Under-voltage · below band

Q_C ≈ 0.00   Q_L = 0.30

Voltage swings with the load

The receiving-end voltage is lower than the sending end by the I·Z drop the load current makes across the line impedance. So under heavy load at midday the voltage falls sharply, and under light load at night the drop is small and the voltage stays nearly the same, or on long lines the charging current can even push it above the sending end (the Ferranti effect). Equipment works properly only near its set voltage, so the voltage must be kept within the prescribed range however the load changes.

Reactive plant pushes the voltage

In the drop e ≈ I(R cosφ + X sinφ), X is large on high-voltage lines, so the X sinφ term, that is, the reactive current, governs the drop. Fitting a capacitor next to the load to fill in the lagging reactive power reduces the reactive current flowing in the line, shrinks the drop and raises the receiving-end voltage. Conversely, when overvoltage appears at light load, a shunt reactor absorbs reactive power and pulls the voltage down; equipment that supplies or absorbs reactive power to push the voltage like this is called reactive compensation equipment.

ObserveVR(%) = (V_nl − V_fl) / V_fl × 100

Voltage regulation is the difference between no-load and full-load voltage divided by the full-load voltage.

Choosee ≈ I(R cosφ + X ?)

On high-voltage lines the drop is governed by the X sinφ term.

Fill inQ_C ↑ → V_r ?

Filling in reactive power with a capacitor raises the voltage.

On your ownOvervoltage → with a reactor, V_r ?

Overvoltage at light load is brought down with a reactor.

Tap changing · directly by ratio

Another handle is the transformer tap. Changing the winding tap adjusts the turns ratio and raises or lowers the load-side voltage directly, so at times of heavy load the turns ratio is lowered to raise the voltage, and at light load the reverse. On-load tap changers (OLTC), which change taps during operation without interrupting the current, are widely used. By running reactive compensation and tap changing together, the receiving-end voltage is held within the prescribed range even as the load swings all day.

Back to the first screen

Growing the capacitor brought the receiving-end voltage marker, sagging in red, up into the green band, and growing it further made it overshoot into overvoltage, because the capacitor filled in the line's lagging reactive power and shrank the X sinφ drop. Voltage regulation means supplying or absorbing reactive power like this and, when needed, even changing the turns ratio with transformer taps, so that however the load swings the voltage stays tied within the narrow strip of the prescribed range.

Voltage regulation: as the load changes, the I·Z drop makes the receiving-end voltage sag (heavy load) or rise (light load · Ferranti). Voltage regulation VR = (V_no-load − V_full-load)/V_full-load. Because the X sinφ term governs the drop, reactive compensation (capacitor = supplies reactive → voltage ↑, reactor = absorbs reactive → voltage ↓) and transformer tap changing (turns-ratio adjustment) hold the voltage within the prescribed range (such as ±5%) as the load swings.

The next step

That was the transmission side, sending electricity far. The next unit (PW-C5) covers the distribution systems that divide it out to customers: connections such as single-phase 2-wire, three-phase 3-wire and three-phase 4-wire, and layouts from radial lines that branch one way to rings and meshed networks with several paths; how a distribution network is laid out by weighing reliability against cost closes section C.