Equipment and Governor FR
Frequency Responses
Written by: Berardino (Dino) Porretta, September 2016.
1.0 Introduction
Adequate Frequency and Inertial Responses are of fundamental importance to the reliable operation of our interconnections. At the time of this writing there are concerns that these responses are declining and that they may become insufficient for acceptable reliability. One of the reason mentioned often in the literature as being responsible for this decline, is the increased penetration of Solar, Wind and, to some extent, Combined Cycle generation. A much less mentioned reason, and perhaps even as important, is the emerging new types of loads and new ways of supplying these loads such as the use of Variable Speed Drives to supply motor loads. As a result, much work is being done to develop ways to monitor the decline of these responses and to remedy the trend by finding ways to inject these responses into the power system using special controls.
The motivation for this page is to provide a more complete treatment of this very important subject. It is hoped that this discussion will help to gain a better insight into why these responses are declining and what needs to be done to reverse this trend. This page focusses on Frequency Response. The Inertial Response is discussed in the Inertial Response page.
2.0 What is Frequency Response?
Frequency Response (FR) is the MW change in the Generation-Load balance due to frequency changes alone affected automatically by the system itself. FR can be beneficial to interconnection reliability or not. To be beneficial, FR must act to oppose the interconnection frequency change. FR derives from the intrinsic frequency characteristics of power system equipment and from the Governors of the individual generators. The fundamental differences between these two components of FR are as follows:
1. The FR from the intrinsic frequency characteristics of power system equipment becomes available without delay immediately after the start of the frequency change. This component of the FR can always be counted on. In current literature, this component is referred to as Equipment FR. In the "good old days" this component was referred to as system Self Regulation. Herein this component of FR will be referred to as Self Regulation (SR).
2. The FR from the response of Governors (GFR) becomes available with a time delay of about 2 to 5 seconds after the start of the disturbance and it is not fully deployed until two to thre seconds later. This delay is due to governors dead bands, time constants, and velocity limits imposed on valves or gates to prevent equipment damage. The magnitude of this component depends on Droop settings and on generator loading practices. For this reason the extent to which GFR can be counted on cannot be predicted.
It is important to realize that GFR combined with SR cannot restore frequency to 60 Hz because power from these sources becomes available only if the frequency is different from 60 Hz. So FR reduces the frequency deviation but cannot eliminate it. Frequency recovery is completed by AGC (Automatic Generation Control) control and manual operator actions; both of these remedial actions increase generation by raising the generator loading set points. It is also noteworthy that those same factors that slow down frequency decay, namely Inertia and FR, will also act in a similar way to oppose frequency recovery.
The capability of the system to recover is established within the first 5 seconds or so after the start of the disturbance. During this time SR plays a very important role as GFR has not yet materialized in significant amounts until about 5 seconds after the disturbance. For this reason, the first part of this discussion, Section 2.1, focusses on SR alone. The GFR, which is fundamental to the first phase of frequency recovery, is discussed later in Section 2.2.
2.1 Self Regulation (SR)
To develop a convenient model to illustrate SR, the system equipment is separated into two groups: power generation equipment and power consuming equipment. Henceforth these two groups will be referred simply by Generation and Load.
The Generation aggregates the SR from all individual generators. The SR characteristics of the Generation are determined by the SR characteristics of each individual generator. It is important to keep in mind that not all generators have necessarily beneficial SR. As beneficial SR from Generation is very important to the reliability of the system, it is important to ensure that all generators are designed to have beneficial SR.
The Load aggregates the SR of all individual power consuming devices such as motors, computers, battery chargers, heaters, and so on. The SR charactecteristics of the Load are determined by the SR characteristices of each of these power consuming devices. As beneficial SR from Load is also very important to the reliabilty of the system, it is important to ensure that, in the aggregate, Load has sufficient beneficial SR. This might need regulations to require loads supply technologies to provide sufficient beneficial SR.
2.1.1 Self Regulation (SR) of Generators
The SR of the Generation derives from the Torque and Power speed characteristics of the turbines or motors that provide the turning power for synchronous generators. These speed characteristics are shown in Figure 1 below. At frequency fe the turbine would produce maximum power with maximum efficiency. It is noted that turbine operating points to the right of Pe are such that the power output of the turbine increases for frequency perturbations in the r direction and decreases for frequency perturbations in the t direction. The opposite happens for operating points to the left of Pe. This means that operating points to the right of Pe have beneficial SR while those to the left of Pe do not. Therefore, for stable operation, turbines need to be designed so that their 60 Hz operating point is as far to the right of Pe as other considerations, such as cost and vibrations, permit. These characteristics are present only in generators driven by turbines and motors. Wind and solar generators, by virtue of how they are coupled to the system, do not provide SR. Studies made in 2005 (Gillian R. Lalor, Phd thesis, School of Electrical, Electronic and Mechanical Engineering, University College, Dublin, September 2005) showed that Combined Cycle gas units, as operated at the time, did not provide beneficial SR. New studies should be done in this area to ensure that the design and operation of combined cycle plants has been modified to ensure beneficial SR. If this issue is not addressed, the current plan to retire coal plants and replace them with combined cycle, wind, and solar plants will result in a system with severily diminished SR from generators.
2.1.2 Self Regulation (SR) of Load
There is not much information in the literature about the power consumed by the various loads as frequency changes. In the "Handbook of Power Quality" edited by Angelo Baggini, there is a good discussion of this subject. As the SR from the load is very important to the capability of the system to recover following a disturbance it would be highly desirable to have a study in place that continually evaluates the SR of different load types especially the emerging once. Motors loads have long been the highest contributors to the beneficial SR of the load. However, due to the increasing use of variable speed drives to supply motor loads, this component of load SR is declining.
For the purpose of this qualitative discussion, the consensus that, in the aggregate, Load increases as frequency increases and vice versa will be used. Figure 2 below shows such Load vs Frequency characteristic.
2.1.3 Combining the Turbine and Load Power Frequency Curves
Figure 3 below shows the Generator power output frequency curve combined with the Load power frequency curve.
On our interconnections underfrequency protection is set to be deployed for frequencies in the range of 59.5 Hz to 58.5 Hz. So, the operating situations to be analyzed are within the frequency range of plus or minus 1.5 Hz from 60 Hz. In this range the Generation and Load frequency response curves can be considered linear. This simplification is used in Figure 4 below. As it will be demonstrated in the discussion herein, this diagram is a very useful tool to visualize and quantify the impact of Self Regulation.
With reference to Figure 3, the generators have to produce synchronous speed power, namely 60 Hz power. The designer of the turbines that drive the synchronous generators has to ensure that to produce 60 Hz power the turbine speed is such that: (1) It is sufficiently away from a critical speed; (2) It results in a power speed curve for the synchronous generator which intersects the Load line at an equilibrium point that is sufficiently stable and sufficiently away from an unstable equilibrium point; (3) It is as close as possible, within constrains (1) and (2), to the speed that results in maximum efficiency and power. These considerations lead to a design that results in the 60Hz operating point to be in the orange shaded area. This is so because operating points too close to Pe or to the left of it are unstable.
Figure 4 above illustrates a system in which the generation is in equilibrium with the system load at point P. The diagram shows that P is a stable operating point because any frequency perturbation in the “q” direction will result in a generation deficit causing the frequency to decelerate back towatds P, and any frequency perturbation in the “r” directions results in a generation surplus causing the frequency to accelerate back towards P. For example, if the frequency were perturbed to 59.9 Hz, the frequency response would results in the positive imbalance A which accelerates the system back to P . If the frequency were perturbed to 60.1 Hz, the frequency response woud be negative A which decelerates the system back to P.
If this diagram had been drawn for a balancing area (BA) within an interconnection, the diagram shows that the BA generation is in equilibrium with the BA load at 60 Hz. If generation loss elsewhere in the interconnection causes the frequency to decay to 59.9 Hz, then A MW would flow out of the BA. If load loss elsewhere in the interconnection causes the frequency to increase to 60.1 Hz , then A MW would flow into the BA.
2.1.4 Beneficial and Non-Beneficial SR
As mentioned above, a system or a system component can have beneficial or non-beneficial SR. An SR is beneficial if it opposes the change in frequency. By experimenting graphically with the slopes of the Generation and Load on the diagram in Figure 4 above, the following conclusions are arrived at:
1. A generator has beneficial FR if its power output versus frequency line has a negative slope.2. A load has beneficial FR if its power consumption versus frequency line has a positive slope.3. A system has beneficial FR if the slope of its Generation line is less than the slope of its Load line.
Accordingly, Figure 4 above illustrates a system with beneficial FR, while Figure 5 below illustrates a system that has non-beneficial FR. It is noteworthy that a system that has non-beneficial FR does not have stable operating points. In such a system the frequency would have continually to be forced back to 60 Hz as the system would be continually try to move away from 60 Hz. Such a system would be very difficult, if not impossible, to operate.
This simple analysis points to a solution to the current deterioration of SR, namely, ensure that all generators and loads exibit Power vs Frequency characteristic lines similar to those shown in Figure 4.
2.1.5 Can a Power System Be Operated if It Does Not Possess Self Regulation?
Figure 2 below illustrates an interconnection in which the Load and the Generation MW vs Frequency lines are flat. That is, neither the Generation nor the Load is responsive to frequency changes. In such case, Tthe operators would have a very hard time to keep the Generation line matched to the Load line and, whether it is matched or not, the interconnection would not able to pick a frequency value to settle at.
It is evident from above diagram that this system cannot be operated. The system has a potentially infinite equilibria points, but "it does not know" how to pick one to settle at.
What about if the interconnection were to have Generation and Load that exibit the MW vs Frequency relationship illustrated in Figure 7 below. In this case, the slope of the Load vs Frequency line is zero , that is the load line is flat, and the slope of the Generation vs Frequency line is positive, that is, the generation increases as the frequency increases. That is, the Generation has no beneficial Self Regulation.
In above case, the Interconnection has an equilibrium point at P but it is not stable. In fact: (a) A frequency perturbation in the “t” direction causes the interconnection to develop a generation surplus and, therefore, the frequency will keep increasing in the “t” direction; (b) A frequency perturbation in the “r” direction causes the interconnection to develop a generation deficit and, therefore, the frequency will keep decreasing in the “r” direction. This situation is similar to that illustrated in Figure 5 above. This type of graphic anaysis will show that, in general, to have beneficial Self Regulation, namely stable equilibrium points, the slope of the Generation line has to be less than the slope of the Load line as shown in Figure 1 above. The farther apart the two slopes are, the more stable the equilibrium points are, and the higher the frequency response megawatts are.
The above discussion leads to the conclusion that a power system that does not have beneficial Self Regulation is extremely difficult, if not impossible, to operate reliably.
2.1.7 Impact of Self Regulation Following Generation Loss.
Suppose that while the interconnection is operating in balance at point P as illustrated in Figure 4 above, there is a disturbance that causes the loss of ΔP MW of generation. Immediately after, the generation line can be visualized as moving vertically ΔP MW down. This is illustrated in Figure 8 below, where the generation remaining after the loss is shown as a red line.
To better visualize the impact of Self Regulation, assume that there is no governor response nor any other external remedial action. With this assumption, as soon as the generation loss occurs, an accelerating power Pa starts acting on the rotating masses to slow them down and the frequency starts to decay towards point C in Figure 8 above. Immediately after the disturbance Pa is equal to ΔP. As the frequency decays, Pa is decreased by the action of Self Regulation D. From Figure 8, at any frequency f the accelerating power Pa is given by:
Where:Pa = ΔP - Δf D (1)
ΔP = Amount of generation loss in MWΔf = Frequency deviation from predisturbance frequency in HzD = System Self Regulation in MW/Hz
Accordingly, as Pa decreases the rate of frequency decay decreases and at point C the frequency decay is arrested and the accelerating power Pa becomes zero. At this point, the system Self Regulation D has compensated for the ΔP loss of generation. The maximum frequency deviation can be computed from equation (1) at point C as at this point Pa can be set to zero and Δf can be solved for. This results in the following equation :
Δf = ΔP/D (2)
This illustrates how Self Regulation arrests the frequency decay. The frequency at C is the lowest frequency that the interconnection would attain in the absence of any external remedial actions. As discussed below in Section 2.2, governor response will results in a higher resting final frequency, and as discuseed in the page "Inertial Response", the system Inertia although has no impact on the value of the frequency at which the frequency decay is arrested, it prolongs the time needed to get there. This highlights the importance of Inertia in stabilizing the system and in buying time for the automatic controllers, such as governors and load shedding relay, to operate before the frequency gets too low.
2.2.1 Frequency Response from Governors