Section II: Automatic Generation Control
Automatic Generation Control
Electric power is generated by converting mechanical energy into electrical energy. The rotor mass, which contains turbine and generator units, stores kinetic energy due to its rotation. This stored kinetic energy accounts for sudden increase in the load. Let us denote the mechanical torque input by Tm and the output electrical torque by Te . Neglecting the rotational losses, a generator unit is said to be operating in the steady state at a constant speed when the difference between these two elements of torque is zero. In this case we say that the accelerating torque
 | (5.20) |
is zero.
When the electric power demand increases suddenly, the electric torque increases. However, without any feedback mechanism to alter the mechanical torque, Tm remains constant. Therefore the accelerating torque given by (5.20) becomes negative causing a deceleration of the rotor mass. As the rotor decelerates, kinetic energy is released to supply the increase in the load. Also note that during this time, the system frequency, which is proportional to the rotor speed, also decreases. We can thus infer that any deviation in the frequency for its nominal value of 50 or 60 Hz is indicative of the imbalance between Tm and Te. The frequency drops when Tm < Te and rises when Tm > Te .
The steady state power-frequency relation is shown in Fig. 5.3. In this figure the slope of the ΔPref line is negative and is given by
 | (5.21) |
where R is called the regulating constant . From this figure we can write the steady state power frequency relation as
Fig. 5.3 A typical steady-state power-frequency curve.
 | (5.22) |
Suppose an interconnected power system contains N turbine-generator units. Then the steady-state power-frequency relation is given by the summation of (5.22) for each of these units as
 | (5.23) |
In the above equation, ΔPm is the total change in turbine-generator mechanical power and ΔPref is the total change in the reference power settings in the power system. Also note that since all the generators are supposed to work in synchronism, the change is frequency of each of the units is the same and is denoted by Δf. Then the frequency response characteristics is defined as
 | (5.24) |
We can therefore modify (5.23) as
 | (5.2 |
Example 5.5
Consider an interconnected 50-Hz power system that contains four turbine-generator units rated 750 MW, 500 MW, 220 MW and 110 MW. The regulating constant of each unit is 0.05 per unit based on its own rating. Each unit is operating on 75% of its own rating when the load is suddenly dropped by 250 MW. We shall choose a common base of 500 MW and calculate the rise in frequency and drop in the mechanical power output of each unit.
The first step in the process is to convert the regulating constant, which is given in per unit in the base of each generator, to a common base. This is given as
 | (5.26) |
We can therefore write
|
Therefore
 per unit |
We can therefore calculate the total change in the frequency from (5.25) while assuming ΔPref = 0, i.e., for no change in the reference setting. Since the per unit change in load - 250/500 = - 0.5 with the negative sign accounting for load reduction, the change in frequency is given by
 |
Then the change in the mechanical power of each unit is calculated from (5.22) as
|
It is to be noted that once ΔPm2 is calculated to be - 79.11 MW, we can also calculate the changes in the mechanical power of the other turbine-generators units as
|
This implies that each turbine-generator unit shares the load change in accordance with its own rating.
Load Frequency Control
Modern day power systems are divided into various areas. For example in India , there are five regional grids, e.g., Eastern Region, Western Region etc. Each of these areas is generally interconnected to its neighboring areas. The transmission lines that connect an area to its neighboring area are called tie-lines . Power sharing between two areas occurs through these tie-lines. Load frequency control, as the name signifies, regulates the power flow between different areas while holding the frequency constant.
As we have in Example 5.5 that the system frequency rises when the load decreases if ΔPref is kept at zero. Similarly the frequency may drop if the load increases. However it is desirable to maintain the frequency constant such that Δf=0 . The power flow through different tie-lines are scheduled - for example, area- i may export a pre-specified amount of power to area- j while importing another pre-specified amount of power from area- k . However it is expected that to fulfill this obligation, area- i absorbs its own load change, i.e., increase generation to supply extra load in the area or decrease generation when the load demand in the area has reduced. While doing this area- i must however maintain its obligation to areas j and k as far as importing and exporting power is concerned. A conceptual diagram of the interconnected areas is shown in Fig. 5.4.
Fig. 5.4 Interconnected areas in a power system.
We can therefore state that the load frequency control (LFC) has the following two objectives:
- Hold the frequency constant ( Δf = 0) against any load change. Each area must contribute to absorb any load change such that frequency does not deviate.
- Each area must maintain the tie-line power flow to its pre-specified value.
The first step in the LFC is to form the area control error (ACE) that is defined as
 | (5.27) |
where Ptie and Psch are tie-line power and scheduled power through tie-line respectively and the constant Bf is called the frequency bias constant .
The change in the reference of the power setting ΔPref, i , of the area- i is then obtained by the feedback of the ACE through an integral controller of the form
 | (5.28) |
where Ki is the integral gain. The ACE is negative if the net power flow out of an area is low or if the frequency has dropped or both. In this case the generation must be increased. This can be achieved by increasing ΔPref, i . This negative sign accounts for this inverse relation between ΔPref, i and ACE. The tie-line power flow and frequency of each area are monitored in its control center. Once the ACE is computed and ΔPref, i is obtained from (5.28), commands are given to various turbine-generator controls to adjust their reference power settings.
Example 5.6
Consider a two-area power system in which area-1 generates a total of 2500 MW, while area-2 generates 2000 MW. Area-1 supplies 200 MW to area-2 through the inter-tie lines connected between the two areas. The bias constant of area-1 ( β1 ) is 875 MW/Hz and that of area-2 ( β2 ) is 700 MW/Hz. With the two areas operating in the steady state, the load of area-2 suddenly increases by 100 MW. It is desirable that area-2 absorbs its own load change while not allowing the frequency to drift.
The area control errors of the two areas are given by
 and  |
Since the net change in the power flow through tie-lines connecting these two areas must be zero, we have
 |
Also as the transients die out, the drift in the frequency of both these areas is assumed to be constant, i.e.,
 |
If the load frequency controller (5.28) is able to set the power reference of area-2 properly, the ACE of the two areas will be zero, i.e., ACE1 = ACE2 = 0. Then we have
 |
This will imply that Δf will be equal to zero while maintaining ΔPtie1 =ΔPtie2 = 0. This signifies that area-2 picks up the additional load in the steady state.
Coordination Between LFC And Economic Dispatch
Both the load frequency control and the economic dispatch issue commands to change the power setting of each turbine-governor unit. At a first glance it may seem that these two commands can be conflicting. This however is not true. A typical automatic generation control strategy is shown in Fig. 5.5 in which both the objective are coordinated. First we compute the area control error. A share of this ACE, proportional to αi , is allocated to each of the turbine-generator unit of an area. Also the share of unit- i , γi X Σ( PDK - Pk ), for the deviation of total generation from actual generation is computed. Also the error between the economic power setting and actual power setting of unit- i is computed. All these signals are then combined and passed through a proportional gain Ki to obtain the turbine-governor control signal.
Fig. 5.5 Automatic generation control of unit-i.
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