How does the driving torque affect the power system?

India has one of largest electrical networks in the world. Different types of sources and load are feeding and consuming power from this massive mesh called the NATIONAL GRID. All the sources are connected in parallel. Parallel operation of the generators improves the reliability of the power system by allowing the isolation of few generators for maintenance or under fault condition without any loss of load.

Maximum percentage of power generation is done by Coal based and hydro-based power plants which use synchronous generators as the generating unit. Wouldn't it be interesting to understand how these power plants control the flow of power and maintain such a large network where there is so much variation of load time to time. Let’s become adept over it.

To begin with lets analyze two synchronous generators working in parallel and observe how various circuit parameters are affected. There are two ways how the generating unit control the power flow to the grid:

•  Adjusting the Driving Torque
• Adjusting the Excitation Voltage

In this post we shall discuss just the affect of change of driving torque on various parameters.

NO LOAD OPERATION:

Let us consider two alternators connected in parallel and are unloaded. With respect to external circuit, both the emfs of generators are in phase and with respect to the local circuit they are in phase opposition.

   

Driving torque can be varied by controlling the gate openings of the hydro turbines or by throttle openings of steam turbine. In this article, we have considered cylindrical rotor generator but the results are equally relevant to salient pole generator too.          

If we increase the driving torque of generator 1, then speed increases and generator 1 emf (E_f1)  gets ahead of generator 2 emf (E_f2) there by a resultant emf (E_c) appears. Due to this resultant emf, E_c a circulating current I_c (fig i) flows which lags E_c by almost 90^.  (as the value of resistance is too small compared to the reactance of the machine). This current flows out of gen 1 nearly in phase with it’s emf E_f1 and enters gen 2 in near phase opposition with E_f2. Thus Gen 1 produces power (=E_f1I_c) as a generator and supplies it to Gen 2  which acts as a motor. This would thus retard the faster machine and accelerates the slower one, finally leading to auto equalization of speed.
  

It is necessary that the machines impedance shouldn’t be purely resistive. If they are purely resistive, then the circulating current would be in phase with E_c      (fig ii) and thereby both will act as generator. There would be no tendency of auto equalization of speed. It implies that there would be frequency mismatch leading to power surges and harmonics.

ON LOAD:

The load current I_L = I_a1 + I_a2 (can be seen in the circuit beside).  Increasing the driving torque would result a change in the amount of load shared, the currents I_a1 and I_a2 and respective power factors. Howsoever, the load current I_L remains constant. First, we’ll see how load sharing varies.
On load operation depends upon the speed-load characteristics of the alternator. Generally these characteristics are not linear. Hence a governor mechanism is used to make them linear as in the figure beside.

If we increase the driving torque of Gen1, speed increases and the speed-load curve shifts upwards indicating the increase in speed. Obviously decreasing the driving torque would shift the characteristics downwards. 

Consider the two generators are supplying to a load P_L (=P₁+P₂ initially). Now if we increase the driving torque of gen1. It’s speed-load characteristics shift upwards. In order to maintain the frequency (as the load is constant) the driving torque of gen2 should be decreased. Thus the dotted lines in the figure indicate the speed load characteristics of both the generators and the line2 indicates the frequency of the constant load. Thus the load shared by gen1 increases to P₁’ and the load of gen 2 decreases to P₂’ but to the end the sums of loads shared by both the generators would be constant and equal to the total load P_L.
Now let us see how the currents and power factors of each generator is effected.

At first assume that E_f1= E_f2 and therefore Ia₁=Ia₂ and the load shared will be equal.

Now increase the driving torque of gen 1 which increases the speed and frequency and thereby increasing the power angle δ to δ1 and the power increases to P₁’.

                                     

 The driving torque of gen2 is now decreases in order to supply to the load at constant frequency. E_f2 decreases and power angle also decreases to δ2 and the power decreases to P₂’.

More over, this change in the emfs will lead to a resultant emf E_c. Hence,  a circulating current flows which lags E_c almost 90^.. This current adds up to I_a1 and hence current through gen 1 increases (indicating that the load shared by this gen has increased). The power factor angle decreases thereby improving the power factor. The current I_c reduces the current from gen 2 and there by indicating that the load shared by this gen is reduced. The power factor angle increases and thereby decreasing the power factor.

Thus we can conclude that, by increasing the driving torque on load increases the load shared, current and also improves the power factor.