Q7Economic Operation of Power System

(A) Parallel Operation of Generators

Parallel operation refers to connecting two or more synchronous generators to the same electrical bus/network so that they simultaneously supply a common load, a standard and essential practice in virtually all power systems (from small isolated microgrids to large interconnected national grids), providing improved reliability (loss of any single generator does not cause total loss of supply), improved economy (allowing the most efficient available combination of units to be brought online to match varying total demand, as discussed in the corresponding economic dispatch and unit-loading answers elsewhere in this paper), and the ability to scale total generation capacity by adding further units as system demand grows.

Conditions for synchronization (paralleling): before a new generator can be safely connected in parallel with an already-energized bus or grid, several conditions must be satisfied to avoid damaging transient currents and mechanical stress at the moment of connection: the incoming generator's terminal voltage magnitude must match the bus voltage magnitude; its frequency must match the bus frequency; its phase sequence (rotation order of the three phases) must match the bus phase sequence; and its instantaneous phase angle must match the bus's phase angle at the moment of closing the connecting breaker (verified using synchronizing lamps, a synchroscope instrument, or modern automatic synchronizing relay equipment) - only when all these conditions are simultaneously satisfied should the connecting circuit breaker be closed, safely paralleling the new generator onto the bus without any damaging inrush current or mechanical shock.

Load sharing after synchronization: once successfully synchronized and connected, the newly-paralleled generator's actual share of the total system load is controlled independently for active and reactive power - active power output is increased by increasing the prime mover's mechanical input (opening the steam/water/fuel valve further, as governed by the unit's speed governor and its droop setting, discussed in the corresponding parallel-operation-load-sharing answer elsewhere in this paper), while reactive power output is increased by increasing the generator's field excitation current (raising its internal generated EMF relative to the bus voltage, causing it to supply more lagging reactive power) - these two control actions (governor/prime-mover setting for active power, and excitation/AVR setting for reactive power) are largely independent of one another for a generator operating in parallel with a strong system, allowing an operator to adjust each separately to achieve the desired load-sharing outcome among all the parallel-connected units.

(B) Infinite Bus Bars, and Active/Reactive Power Control for Synchronizing

An infinite bus bar is an idealized theoretical concept representing a bus (or an entire external power system) whose voltage magnitude and frequency remain constant and unaffected by any amount of power drawn from or supplied to it by a single connected generator - in practice, this idealization is a good approximation for a generator connected to a very large, strong interconnected grid, where that single generator's own capacity is negligible compared to the total capacity of the entire interconnected system, meaning its individual actions have essentially no measurable effect on the overall system voltage or frequency.

Active power control relative to an infinite bus: when a generator is connected to an infinite bus, its active power output is controlled entirely by adjusting its prime-mover mechanical input (via the governor/speed-changer setting), since the bus frequency itself is fixed (by definition of the infinite-bus idealization) regardless of this generator's own action - increasing mechanical input causes the generator's rotor to advance to a larger power angle relative to the fixed infinite-bus voltage phasor (rather than causing any change in system frequency, as it would in an isolated, non-infinite-bus system), delivering correspondingly more active power to the bus according to the standard power-angle relationship P=(EV/X)sin(delta).

Reactive power control relative to an infinite bus: similarly, the generator's reactive power output is controlled entirely by adjusting its field excitation current (via the automatic voltage regulator, AVR), since the bus voltage magnitude itself is fixed (by the infinite-bus idealization) - increasing excitation increases the generator's internal EMF magnitude relative to the fixed bus voltage magnitude, causing it to supply more lagging reactive power to the bus, while decreasing excitation (under-exciting) causes it to instead absorb reactive power from the bus.

Application to synchronizing: during the actual synchronizing process itself (bringing a new generator up to match the bus conditions before closing the connecting breaker), the incoming generator's speed/frequency is adjusted (via its prime mover) to closely match the bus frequency, and its excitation is adjusted (via its AVR/field rheostat) to closely match the bus voltage magnitude, with phase-angle coincidence verified via synchronizing lamps or synchroscope before finally closing the breaker - once connected, if the bus is a genuine infinite bus (or a close practical approximation), these same active-power (governor-based) and reactive-power (excitation-based) control mechanisms continue to independently determine the generator's ongoing active and reactive power contribution to the interconnected system, exactly as described above.

The necessity for parallel operation of generators in a modern power system arises directly from the fact that electrical demand varies continuously and substantially over the course of a day and across seasons, while any individual generator has a fixed maximum capacity and, for good efficiency and mechanical-life reasons, also a practical minimum stable loading below which it should not be operated - by connecting multiple generators to a common bus, the system operator gains the flexibility to bring additional units online as demand rises and to take units offline (or reduce their loading) as demand falls, thereby always operating the online generating fleet within its efficient and safe range regardless of the instantaneous system demand, a flexibility that a single, very large generator sized to meet peak demand alone could not offer during the many hours when actual demand is well below that peak.

Beyond load-following flexibility, parallel operation dramatically improves system reliability: with multiple generators sharing the load, the sudden loss of any single unit (due to a fault, protective trip, or scheduled maintenance) results only in the loss of that unit's contribution to total generation, which the remaining online units (and any available spinning reserve) can typically absorb without total system collapse, whereas a single-generator system would suffer complete loss of supply upon that one unit's failure. This redundancy is the foundation of modern power system reliability planning, formalized through criteria such as N-1 contingency analysis (ensuring the system can withstand the loss of any single major component, including a generator, without cascading failure) that are only meaningful in a system with multiple parallel sources.

The successful synchronization of a generator to an already-energized bus (or to another generator) requires four conditions to be simultaneously satisfied: the incoming generator's terminal voltage magnitude must match the bus voltage magnitude; its frequency must closely match the bus frequency; its phase sequence (for three-phase machines) must match that of the bus; and its instantaneous phase angle must align with the bus phase angle at the moment of breaker closure. Modern synchronizing equipment (synchroscopes, or increasingly automatic synchronizing relays) continuously monitors these quantities and permits breaker closure only within a narrow tolerance band for each, since closing the breaker with a significant mismatch in any of these quantities can produce a large transient inrush current and correspondingly severe mechanical torque shock on the generator shaft, potentially causing serious damage to the machine and its prime mover coupling.

Once synchronized, active and reactive power sharing among the parallel generators is governed by fundamentally different physical mechanisms: active power output is primarily controlled by adjusting the mechanical input (governor setting, i.e., the steam or water flow to the prime mover), which effectively shifts the generator's speed-versus-power droop characteristic and thereby its share of the total active power demand, while reactive power output is primarily controlled by adjusting the field (rotor) excitation current, which alters the internal EMF magnitude and thereby the machine's contribution to (or absorption of) reactive power without significantly affecting its active power output, allowing active and reactive load sharing to be adjusted largely independently of one another through these two separate control actions.