Synchronization of Power and Torque Coefficient

Synchronizing Power-ka Definiciya

Synchronizing power, da yake ake nufi da P_syn, ana bayyana cewa shi ne farkon karamin abubuwa na synchronism P saboda hanyoyin load angle δ. Wannan ya zama stiffness of coupling, stability factor, ko rigidity factor, wanda ya gina abubuwan da take sa mai karfi a kan synchronism idan an haɗa ita da infinite busbars.

Principle of Synchronism Maintenance

Idan akwai generator mai synchronism tare da abubuwan Pa a kan load angle δ0. Hanyoyi mai tsayawa wadanda ke haɗa rotor (misali, ƙarin δ da dδ) ke gudanar da pointin da ake yi wa curve na constant-power, ɗaya ta ƙara load zuwa Pa+δP. Saboda input power mechanical bai ɗaukar ba, abin da aka ƙara ta ci rotor, wanda ya kammala synchronism.

Amma, idan hanyoyi ke ƙoƙarin rotor (kadan δ), load ta ƙara zuwaa Pa−δP. Input power constant bai ƙoƙarin rotor, wanda ya kammala synchronism.

Synchronizing Power Coefficient: A Measure of Corrective Efficiency

Gaskiya na wannan yanayi mai tsayawan system shine rate da power transfer yake ɗauki saboda hanyoyin load angle. Wannan ana gina da synchronizing power coefficient, wanda ake nufin cewa yana nuna hanyoyin da power yake ɗauki don kammala equilibrium ba a ƙarin hanyoyi.

• Key Characteristics:

• Tied to the machine’s dynamic response to angular deviations.

• Determines the system’s resilience against transient instability.

• Higher Psyn values signify stiffer coupling and faster synchronism recovery.

Wannan principle ya gina muhimmanci na synchronizing power a kan maintaining grid stability, wanda ke ɗaukan synchronous machines su dace don ƙoƙarin hanyoyi da suke kammala steady-state operation.

Power output per phase of the cylindrical rotor generator synchronizing torque coefficient

In many synchronous machines Xs >> R. Therefore, for a cylindrical rotor machine, neglecting saturation and stator resistance equation (3) and (5) become

Unit of Synchronizing Power Coefficient Psyn

The synchronizing power coefficient is expressed in watts per electrical radian.

If P is the total number of pair of poles of the machine.

Synchronising Power Coefficient per mechanical radian is given by the equation shown below:

Synchronising Power Coefficient per mechanical degree is given as:

Synchronising Torque Coefficient

The synchronising torque coefficient is defined as the torque generated at synchronous speed, where synchronising torque specifically corresponds to the torque yielding synchronising power at this speed. Denoted by τ_sy, the coefficient is expressed by the equation:

Where,

• m is the number of phases of the machine

• ω_s = 2 π n_s

• n_s is the synchronous speed in revolution per second

Significance of Synchronous Power Coefficient

The synchronous power coefficient Psyn quantifies the stiffness of the magnetic coupling between a synchronous machine's rotor and stator. A higher Psyn signifies a stiffer coupling, but excessive rigidity can expose the machine to mechanical shocks from abrupt load or supply variations—potentially damaging the rotor or windings.

The above two equations (17) and (18) indicate that Psyn is inversely proportional to synchronous reactance. A machine with larger air gaps exhibits relatively lower reactance, making it stiffer than one with smaller air gaps. Since Psyn is directly proportional to Ef, an overexcited machine demonstrates greater stiffness than an underexcited one.

The restoring capability is maximized when δ = 0 (i.e., at no load), while it diminishes to zero when δ = ±90^∘. At this point, the machine reaches an unstable equilibrium and the steady-state stability limit. Thus, operating a machine at this stability limit is infeasible due to its zero resistance to small disturbances—unless equipped with a specialized fast-acting excitation system.