0. PRIME MOVERS AND GOVERNING SYSTEMS
Copyright © P. Kundur This material should not be used without the author's consent

1. Prime Movers and Governing Systems
Outline
Hydraulic Turbines and Governing Systems
hydraulic turbine transfer function
special characteristics of hydraulic turbines
nonlinear hydraulic turbine model
governors for hydraulic turbines
tuning of speed governors
Steam Turbines and Governing Systems
steam turbine configurations
steam turbine models
steam turbine controls
Gas Turbines and Governing Systems
simple-cycle configuration
combined-cycle configuration

2. Hydraulic Turbines and Governing Systems
The performance of a hydraulic turbine is influenced by the characteristics of the water column feeding the turbine:
water inertia
water compressibility
pipe wall elasticity in the penstock
The effect of water inertia is to cause changes in turbine flow to lag behind changes in turbine gate opening
The effect of elasticity is to cause traveling waves of pressure and flow in the pipe - a phenomenon referred to as water hammer
typically, the speed of propagation of such waves is about 1200 meters/sec
traveling wave model required only if penstock is very long

3. 1. Hydraulic Turbine Transfer Function
The representation of the hydraulic turbine and water column in stability studies usually assumes that (a) the penstock is inelastic, (b) the water is incompressible, and (c) hydraulic resistance is negligible
The turbine and penstock characteristics are determined by three basic equations relating to:
velocity of water in the penstock
turbine mechanical power
acceleration of water column
Figure 9.2: Schematic of a hydroelectric plant

4. The velocity of the water in the penstock is given by where
The velocity of the water in the penstock is given by where U = water velocity G = gate position H = hydraulic head at gate Ku = a constant of proportionality The turbine mechanical power is proportional to the product of pressure and flow; hence, The acceleration of water column due to a change in head at the turbine, characterized by Newton's second law of motion, may be expressed as where L = length of conduit A = pipe area ρ = mass density ag = acceleration due to gravity ρLA = mass of water in the conduit ρagH = incremental change in pressure at turbine gate

5. For small displacements (prefix ) about an initial operating point (subscript "0") we can shows that where
Tw is referred to as the water starting time. It represents the time required for a head H0 to accelerate the water in the penstock from standstill to the velocity U0. It should be noted that Tw varies with load. Typically, Tw at full load lies between 0.5 s and 4.0 s.
Equation 9.11 represents the "classical" transfer function of the turbine-penstock system. It shows how the turbine power output changes in response to a change in gate opening for an ideal lossless turbine.
(9.11)

6. Special Characteristics of Hydraulic Turbines
The transfer function given by Equation represents a "non-minimum phase" system Systems with poles or zeros in the right half of s-plane are referred to as non-minimum phase systems; they do not have the minimum amount of phase shift for a given magnitude plot. Such systems cannot be uniquely identified by a knowledge of magnitude versus frequency plot alone.
The special characteristic of the transfer function may be illustrated by considering the response to a step change in gate position. The time response is given by:
Figure 9.3 shows a plot of the response of an ideal turbine model with Tw = 4.0 s

7. Figure 9.3: Change in turbine mechanical power following a unit step increase in gate position

8. Immediately following a unit increase in gate position, the mechanical power actually decreases by 2.0 per unit. It then increases exponentially with a time constant of Tw/2 to a steady state value of 1.0 per unit above the initial steady state value
The initial power surge is opposite to that of the direction of change in gate position. This is because, when the gate is suddenly opened, the flow does not change immediately due to water inertia; however, the pressure across the turbine is reduced causing the power to reduce.
With a response determined by Tw, the water accelerates until the flow reaches the new steady value which establishes the new steady power output

9. Governors for Hydraulic Turbines
The speed/load control function involves feeding back speed error to control the gate position. In order to ensure satisfactory and stable parallel operation of multiple units, the speed governor is provided with a droop characteristic.
Typically, the steady state droop is set at about 5%, such that a speed deviation of 5% causes 100% change in gate position or power output; this corresponds to a gain of 20.
For a hydro turbine, however, such a governor with a simple steady state droop characteristic would be unsatisfactory
Requirement for a Transient Droop
Hydro turbines have a peculiar response due to water inertia: a change in gate position produces an initial turbine power change which is opposite to that sought.
For stable control performance, a large transient (temporary) droop with a long resetting time is therefore required. This is accomplished by the provision of a rate feedback or transient gain reduction compensation as shown in Figure 9.8

10. The rate feedback retards or limits the gate movement until the water flow and power output have time to catch up
The result is a governor which exhibits a high droop (low gain) for fast speed deviations, and the normal low droop (high gain) in the steady state
Figure 9.8: Governor with transient droop compensation

11. Mechanical Hydraulic Governor
On older units, the governing function is realized using mechanical and hydraulic components
Speed sensing, permanent droop feedback, and computing functions are achieved through mechanical components; functions involving higher power are achieved through hydraulic components
A dashpot is used to provide transient droop compensation. A bypass arrangement is usually provided to disable the dashpot if so desired.
Water is not a very compressible fluid; if the gate is closed too rapidly the resulting pressure could burst the penstock
Consequently, the gate movement is rate limited
Often, the rate of gate movement is limited even further in the buffer region near full closure to provide cushioning

12. Figure 9.9: Schematic of a mechanical-hydraulic governor for a hydro turbine

13. Figure 9.10: Model of governors for hydraulic turbines
Parameters
Sample data Tp =
Pilot valve and servomotor time constant
0.05 s Ks
Servo gain
5.0 TG
Main servo time
0.2 s Rp
Permanent droop
0.04 RT
Temporary droop
0.4 TR
Reset time
5.0 s
Constraints
Maximum gate position limit = 1.0
Minimum gate position limit = 0
Rmax open
Maximum gate opening rate
0.16 p.u./s
Rmax close
Maximum gate closing rate
Rmax buff
Maximum gate closing rate in buffered region
0.04 p.u./s
gbuff
Buffered region in p.u. of servomotor stroke
0.08 p.u.
Figure 9.10: Model of governors for hydraulic turbines

14. Electro-Hydraulic Governor
Modern speed governors for hydraulic turbines use electric-hydraulic systems. Functionally, their operation is very similar to those of mechanical-hydraulic governors
Speed sensing, permanent droop, temporary droop, and other measuring and computing functions are performed electrically
Electric components provide greater flexibility and improved performance with regard to dead-bands and time lags
Dynamic characteristics of electric governors are usually adjusted to be essentially similar to those of mechanical-hydraulic governors

15. Tuning of Speed Governing Systems
There are two important considerations in the selection of governor settings:
Stable operation during system islanding conditions or isolated operation; and
Acceptable speed of response for loading and unloading under normal synchronous operation
For stable operation under islanding conditions, the optimum choice of the temporary droop RT and reset time TR are as follows:
For loading and unloading during normal interconnected system operation, the above settings result in too slow a response. For satisfactory loading rates, the reset time TR should be less than 1.0 s, preferably close to 0.5 s.
The dashpot bypass arrangement can be used to meet the above conflicting requirements

16. 2. Steam Turbines and Governing Systems
A steam turbine converts stored energy of high pressure and high temperature steam into rotating energy
the heat source may be a nuclear reactor or a fossil fired boiler
Steam turbines with a variety of configurations have been built depending on unit size and steam conditions
normally consist of two or more turbine sections or cylinders coupled in series
A turbine with multiple sections may be
tandem-compound: sections are all on one shaft with a single generator, or
cross-compound: sections are on two shafts, each with a generator; operated as a single unit
Fossil-fuelled units can be of tandem-compound or cross-compound design
may be of reheat or non-reheat type

17. Figure 9.16: Common configurations of tandem-compound steam turbine of fossil-fueled units

18. Figure 9.17: Examples of cross-compound steam turbine configurations

19. Nuclear units usually have tandem-compound turbines
moisture separator reheater (MSR) reduces moisture content, thereby reducing moisture losses and erosion rates
Large steam turbines for fossil-fuelled or nuclear units are equipped with four sets of valves
main inlet stop valves (MSV)
main inlet control (governor) valves (CV)
reheater stop valves (RSV)
reheater intercept valves (IV)
The stop valves (MSV and RSV) are primarily emergency trip valves.
The CVs modulate steam flow during normal operation.
The CVs as well as the IVs limit overspeed.
Figure 9.18: An example of nuclear unit turbine configuration

20. Steam Turbine Model
For illustration, let us consider a fossil-fuelled single reheat tandem-compound turbine, a type in common use
Figure 9.21(a) identifies the turbine elements that need to be considered
Figure 9.21(b) shows the block diagram representation
The CVs modulate the steam flow for load/frequency control
the response of steam flow to CV opening exhibits a time constant TCH due to charging time of the steam chest and inlet piping
TCH is of the order of 0.2 to 0.3 s
The IVs are used only for rapid control of turbine power in the event of an overspeed
control about 70% of total power
the steam flow in the IP and LP sections can change only with the build-up of pressure in the reheater volume
the reheater time constant TRH is in the range 5 to 10 s
the steam flow in LP sections experiences a time constant TCO associated with the crossover piping; this is of the order of 0.5 s

21. Figure 9.21: Single reheat tandem-compound steam turbine model
Parameters
TCH =
time constant of main inlet volumes and steam chest
TRH
time constant of reheater
TCO
time constant of crossover piping and LP inlet volumes Pm
total turbine power in per unit of maximum turbine power
Pmc
total turbine mechanical power in per unit of common MVA base
PMAX
maximum turbine power in MW
FHP,FIP,FLP
fraction of total turbine power generated by HP, IP, LP sections, respectively
MVAbase
common MVA base
Figure 9.21: Single reheat tandem-compound steam turbine model

22. Simplified Transfer Function of a Steam Turbine
A simplified transfer function of the turbine relating perturbed values of the turbine power and CV position may be written as follows: It is assumed that TCO is negligible in comparison with TRH, and that the CV characteristic is linear

23. Turbine Response
The response of a tandem-compound turbine to a ramp down of the CV opening is shown in Figure
has no peculiarity such as that exhibited by a hydraulic turbine due to water inertia
governing requirements more straightforward
Figure 9.22: Steam turbine response to a 1-second ramp change in CV opening TRH=7.0 s, FHP=0.3; TCH and TCO negligible

24. Steam Turbine Controls
Functions:
The governing systems have three basic functions:
normal speed/load control
overspeed control
overspeed trip
In addition, the turbine controls include a number of other functions such as start-up/shut-down controls and auxiliary pressure control
The speed/load control is a fundamental requirement
achieved through control of CVs
the speed control function provides the governor with a 4 to 5% speed drop
the load control function achieved by adjusting speed/load reference
The overspeed control and protection is peculiar to steam turbines
of critical importance for safe operation
speed should be limited to well below the design maximum speed of 120%

25. The overspeed control is the first line of defense
involves fast control of CVs and IVs
limits overspeed following load rejection to 0.5 to 1.0% below overspeed trip level
returns the turbine to a steady-state condition with turbine ready for reloading
The overspeed or emergency trip is a backup protection
designed to be independent of the overspeed control
fast closes the main and reheat stop valves, and trips the boiler
The characteristics of steam valves are highly nonlinear
compensation is often used to linearize steam flow response to the control signal
compensation may be achieved by a forward loop series compensation, a minor loop feedback, or a major loop feedback.

26. Governing Systems
Systems used for the above control functions have evolved over the years:
older units used mechanical-hydraulic control
electro-hydraulic control was introduced in the 1960s
most governors supplied today are electro-hydraulic or digital electro-hydraulic

27. Figure 9.25: Functional block diagram of MHC turbine governing system
The functional block diagram of a mechanical- hydraulic control (MHC) system is shown in Figure 9.25
the speed governor is a mechanical transducer which transformers speed into position output
the speed relay is a spring loaded servomotor which amplifies the speed governor signal
the hydraulic servomotor provides additional amplification to the energy level necessary to move the steam valves
Figure 9.31 shows the block diagram of an MHC speed governing system, including the overspeed control (auxiliary governor) applicable to a specific make
Figure 9.25: Functional block diagram of MHC turbine governing system

28. Figure 9.31: MHC turbine governing system with auxiliary governor

29. The electro-hydraulic control (EHC) systems use electronic circuits in place of mechanical components associated with the MHC in the low-power portions
offer more flexibility and adaptability
Fig shows an example of EHC governing system. It has two special features for limiting overspeed: IV trigger and power load unbalance (PLU) relay.
the IV trigger is armed when the load (measured by reheat pressure) is greater than 0.1 p.u. It is designed to fast close IVs when the speed exceeds set value.
the PLU relay is designed to fast close CVs and IVs under load rejection conditions. It trips when the difference between turbine power and generator load exceeds a preset value (0.4 p.u.) and the load decreases faster than a preset rate.

30. Fig. 9.33 EHC governing system with PLU relay and IV trigger

31. 3. Gas Turbines The heat source is a hydrocarbon-based fuel
in either gaseous or liquid state
fuel is burned directly in the working fluid
like any internal combustion engine, requires external source for startup
The power produced by the gas turbine is used to drive an alternator to produce electrical power at frequencies compatible with local grids
Exhaust heat is often used to generate steam, which can be used for a process, as in the case of cogeneration
simple-cycle configuration
Alternatively, steam produced using exhaust heat can be used in a steam turbine to generate additional electrical power
combined-cycle configuration
Many variations in configurations and controls
no standard models
CIGRE TF: report published in April 2003 addresses modeling issues