Q7Power System Instrumentation

(a) Active and Reactive Power in Different Plants

Active (real) power represents the actual, useful component of electrical power that performs real work or is converted into heat, light, or mechanical output at the load — it is the power component in phase with the voltage waveform, given by P=VI*cos(phi), where phi is the phase angle between voltage and current. Active power generation at any type of power plant (thermal, hydro, nuclear, or renewable) fundamentally depends on the availability and control of the prime mover's mechanical input power (steam flow and turbine governor position in a thermal plant, water flow and gate/wicket-gate position in a hydro plant, wind speed and blade pitch in a wind plant), with the generator's active power output following its prime mover's mechanical power input (subject to generator and mechanical losses), and is the power component actually billed to and consumed by end-use consumers.

Reactive power represents the power component associated with the cyclic storage and release of energy in the magnetic fields of inductive equipment (transformers, motors, transmission line inductance) and the electric fields of capacitive equipment (cable/line capacitance, capacitor banks), given by Q=VI*sin(phi), and does not perform any net useful work over a complete cycle, but is nonetheless essential for establishing the magnetic fields required for the operation of transformers and induction motors, and for maintaining acceptable voltage levels throughout the transmission and distribution network.

Reactive power supply across different plant types: in thermal and hydro power plants, synchronous generators can supply (or, when operated at a leading power factor, absorb) reactive power by appropriately adjusting their field excitation current via the automatic voltage regulator (AVR) discussed in an earlier answer, over-exciting the field to supply additional lagging reactive power to the system, or under-exciting to absorb reactive power — however, a generator's reactive power capability is constrained by its capability curve (armature current limit, field current limit, and stability/under-excitation limit), meaning generators cannot supply unlimited reactive power without exceeding safe thermal or stability limits. Beyond generator-based reactive support, dedicated reactive power compensation equipment is also deployed throughout the network: synchronous condensers (essentially synchronous machines run purely as reactive power sources/sinks with no mechanical prime mover or load, controlled via field excitation exactly like a generator's reactive capability, but dedicated purely to reactive support); shunt capacitor banks (providing fixed or switched leading reactive power injection, commonly installed at substations and along distribution feeders to improve voltage profile and power factor); shunt reactors (absorbing reactive power, commonly installed on lightly-loaded long EHV transmission lines to counteract their capacitive charging effect, the Ferranti effect); and modern FACTS devices such as the STATCOM discussed elsewhere in this paper, providing fast, continuously-variable reactive power compensation using power-electronic converters rather than rotating machinery or switched passive components. The specific mix and control strategy for reactive power support at any given plant or substation depends on the plant type, its role in the network (base-load, peaking, or purely reactive-support), and the specific voltage-regulation requirements of the surrounding transmission/distribution network.

Relevance of Power Factor Correction

Since the total apparent power (S=VI) drawn from a supply comprises both the active power P and the reactive power Q, according to S^2=P^2+Q^2, a load operating at a poor (low) power factor draws a larger total current, and hence a larger apparent power, than is strictly necessary to deliver its required active power alone, for a given supply voltage. This has direct practical consequences throughout the power system: generators, transformers, and transmission/distribution lines must all be sized (and their conductors rated) for the larger apparent current associated with a poor power factor rather than for the smaller current that would suffice at unity power factor, increasing I-squared-R copper losses in generation and transmission equipment for the same delivered active power, and reducing the active power capacity available from a given piece of equipment before its current rating is reached. Electricity utilities and industrial consumers therefore commonly install power factor correction equipment — typically shunt capacitor banks connected at or near the load — specifically to supply the lagging reactive power demanded by inductive loads (such as induction motors, which form the bulk of typical industrial load) locally, reducing the reactive current that must otherwise be drawn from the supply network and transmitted over the lines feeding that load. Many electricity tariffs in Indian industrial practice explicitly penalize consumers whose average power factor falls below a specified threshold (commonly 0.85 or 0.9 lagging), directly incentivizing power factor correction, and this is precisely why accurate reactive power (and power factor) measurement, as discussed in this answer, is essential both for correct tariff billing and for planning appropriately-sized power factor correction equipment at industrial and utility installations.

Reactive Power Capability Curve (P-Q Diagram) of a Generator

A synchronous generator's ability to supply active and reactive power simultaneously is not unlimited in every combination, but is bounded by a capability curve (also called the P-Q diagram), typically plotted with active power P on the horizontal axis and reactive power Q on the vertical axis, showing the full range of operating points the machine can sustain continuously without exceeding its design limits. This capability curve is bounded by several distinct physical constraints acting over different regions of the diagram: the armature (stator) current limit, a constant-MVA arc centered at the origin, beyond which the stator winding would carry more current than its thermal rating allows, regardless of the particular P-Q split; the field (rotor) current limit, an arc-shaped boundary in the over-excited (lagging power factor, positive Q) region, beyond which the rotor field winding would carry more current than its own thermal rating permits; and the stability/under-excitation limit, a boundary in the under-excited (leading power factor, negative Q) region, set by the practical stability margin against loss of synchronism as field excitation is reduced, since operating too far into the under-excited region reduces the internal EMF and the resulting synchronizing torque available to hold the machine in step with the system. The capability curve is an essential reference for power plant operators and system dispatchers, since it directly defines, for any given active power output the generator is scheduled to produce, the maximum lagging and leading reactive power the machine can additionally be called upon to supply or absorb in support of system voltage regulation, without risking thermal overload of the stator or rotor windings or a loss-of-synchronism instability.

(b) Working Principle of Single Phase Induction Type Energy Meter

The single-phase induction-type energy meter (the traditional electromechanical watt-hour meter) measures cumulative electrical energy consumption by continuously integrating instantaneous power over time, using the rotation of an aluminium disc as the measuring mechanism.

Construction: the meter has two electromagnets — a series (current) coil, wound with a few turns of heavy-gauge wire and connected in series with the load circuit (so it carries the full load current and produces a flux proportional to load current), and a shunt (pressure/voltage) coil, wound with many turns of fine wire and connected across the supply voltage (so it produces a flux proportional to supply voltage, appropriately phase-shifted, typically by 90 degrees relative to the applied voltage, using a shading coil or similar phase-adjustment arrangement, to ensure the meter's torque is correctly proportional to true power rather than apparent power). A thin aluminium disc is mounted so that it passes through the air gaps of both electromagnets, free to rotate about a vertical spindle.

Working principle: the alternating fluxes produced by the current coil and the pressure coil both induce eddy currents in the aluminium disc as it passes through their respective air gaps, and the interaction between each coil's flux and the eddy currents induced by the other coil's flux produces a net driving torque on the disc (by the same fundamental induction-motor-like principle underlying any AC induction machine), with this driving torque proportional to the product of the current-coil flux, the pressure-coil flux, and the sine of the phase angle between them — since the pressure-coil flux is deliberately phase-shifted by approximately 90 degrees relative to the supply voltage (compensating for the coil's own inherent inductive phase lag), the resulting net torque works out to be directly proportional to the true (active) power being consumed by the load, VI*cos(phi), rather than merely the apparent power VI.

Braking and speed-torque balance: a permanent braking magnet is positioned so that the rotating aluminium disc also passes through its field, inducing further eddy currents in the disc that, by Lenz's law, oppose the disc's motion, producing a retarding (braking) torque proportional to the disc's instantaneous rotational speed. Since the driving torque (proportional to instantaneous active power) causes the disc to accelerate until the resulting braking torque (proportional to speed) exactly balances it, the disc settles into rotating at a steady-state speed directly proportional to the instantaneous active power being consumed at that moment — and since the disc's cumulative total number of revolutions over any given time period is the time-integral of its rotational speed, and speed is proportional to instantaneous power, the total number of disc revolutions over time is directly proportional to the total energy (power integrated over time) consumed during that period. This cumulative revolution count is registered via a geared mechanical counter (or, in modern meters, an optical/electronic pulse counter) connected to the disc's spindle, providing the meter's final displayed reading of total accumulated energy consumption, typically in kilowatt-hours.