02 3 prime-movers


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02 3 prime-movers

  1. 1. 1539pk PRIME MOVERS AND GOVERNINGPRIME MOVERS AND GOVERNING SYSTEMSSYSTEMS Copyright © P. Kundur This material should not be used without the author's consent
  2. 2. 1539pk PM - 2 Prime Movers and Governing SystemsPrime Movers and Governing Systems 1. 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 2. Steam Turbines and Governing Systems  steam turbine configurations  steam turbine models  steam turbine controls 3. Gas Turbines and Governing Systems  simple-cycle configuration  combined-cycle configuration Outline
  3. 3. 1539pk PM - 3 Hydraulic Turbines and GoverningHydraulic Turbines and Governing SystemsSystems  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
  4. 4. 1539pk PM - 4  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 1. Hydraulic Turbine Transfer Function1. Hydraulic Turbine Transfer Function Figure 9.2: Schematic of a hydroelectric plant
  5. 5. 1539pk PM - 5 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 HGKU u= HUKP pm = ( ) ( ) HaA dt Ud LA g ∆ρ−= ∆ ρ
  6. 6. 1539pk PM - 6  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. ST 2 1 1 ST1 G P w wm + − = ∆ ∆ 0g 0 w Ha LU T = (9.11)
  7. 7. 1539pk PM - 7 Special Characteristics of Hydraulic Turbines  The transfer function given by Equation 9.11 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 ( ) Ge31tP t T 2 m w ∆         −=∆      −
  8. 8. 1539pk PM - 8 Figure 9.3: Change in turbine mechanical power following a unit step increase in gate position
  9. 9. 1539pk PM - 9  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
  10. 10. 1539pk PM - 10 Governors for Hydraulic TurbinesGovernors 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
  11. 11. 1539pk PM - 11  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
  12. 12. 1539pk PM - 12 Mechanical Hydraulic GovernorMechanical 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
  13. 13. 1539pk PM - 13 Figure 9.9: Schematic of a mechanical-hydraulic governor for a hydro turbine
  14. 14. 1539pk PM - 14 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 0.16 p.u./s 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
  15. 15. 1539pk PM - 15 Electro-Hydraulic GovernorElectro-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
  16. 16. 1539pk PM - 16 Tuning of Speed Governing SystemsTuning 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 ( )[ ] M w wT T T 15.00.1T3.2R −−= ( )[ ] wwR T5.00.1T0.5T −−=
  17. 17. 1539pk PM - 17 2. Steam Turbines and Governing2. Steam Turbines and Governing SystemsSystems  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
  18. 18. 1539pk PM - 18 Figure 9.16: Common configurations of tandem-compound steam turbine of fossil-fueled units
  19. 19. 1539pk PM - 19 Figure 9.17: Examples of cross-compound steam turbine configurations
  20. 20. 1539pk PM - 20  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
  21. 21. 1539pk PM - 21 Steam Turbine ModelSteam 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
  22. 22. 1539pk PM - 22 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
  23. 23. 1539pk PM - 23 Simplified Transfer Function of a SteamSimplified Transfer Function of a Steam TurbineTurbine 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 ( )( ) ( )( )RHCH RHHP RHCH HP CH HP CV m sT1sT1 TsF1 sT1sT1 F1 sT1 F ΔV ΔP ++ + = ++ − + + =
  24. 24. 1539pk PM - 24 Turbine ResponseTurbine Response The response of a tandem-compound turbine to a ramp down of the CV opening is shown in Figure 9.22.  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
  25. 25. 1539pk PM - 25 Steam Turbine ControlsSteam 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%
  26. 26. 1539pk PM - 26  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.
  27. 27. 1539pk PM - 27 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
  28. 28. 1539pk PM - 28  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
  29. 29. 1539pk PM - 29 Figure 9.31: MHC turbine governing system with auxiliary governor
  30. 30. 1539pk PM - 30  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. 9.33 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.
  31. 31. 1539pk PM - 31 Fig. 9.33 EHC governing system with PLU relay and IV trigger
  32. 32. 1539pk PM - 32 3. Gas Turbines3. 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: 38.02.25 report published in April 2003 addresses modeling issues