Synchronous Generators Prime Movers

This article was downloaded by: 10.3.98.104 On: 23 Sep 2021 Access details: subscription number Publisher: CRC Press Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: 5 Howick Place, London SW1P 1WG, UK

Synchronous Generators

Ion Boldea

Prime Movers

Publication details https://www.routledgehandbooks.com/doi/10.1201/b19310-4 Ion Boldea Published online on: 05 Oct 2015

How to cite :- Ion Boldea. 05 Oct 2015, Prime Movers from: Synchronous Generators CRC Press Accessed on: 23 Sep 2021 https://www.routledgehandbooks.com/doi/10.1201/b19310-4

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by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor Figure 3.2). (Figure curves frequency/power generator toelectric according speed, the properly regulates that system) protection and control speed a governor fact, speed (in so-called a with 3.1) (Figure provided [1–3]. moveris necessarily The prime in Table shown is However,one 3.1. tocontrol. asimplified topology from turbines. by wind energy mechanical into converted is energy kinetic load. electric under generator electric the torque of “braking” the against as it rotates shaft turbine work at the mechanical produces and direction, and momentum changes turbine, of ahydraulic runner the hits that energy kinetic into engines. combustion or internal diesel, turbines, gas in air, itself. mover fuel. nuclear and oil, gas, coal, movers are prime in used commonly fuels The fossil engines.” or “turbines called also are energy.They mechanical into or fluid of afuel energy primary convert that machines mechanical movers are Prime movers. prime by produced is energy energy.Mechanical electrical into energy mechanical convert generators Electric 3.1 is allowed with power increased to rated value. torated power increased with allowed is of 2%–3% droop aspeed parallel, in generators with AC In power systems, not constant. is speed erence The ref speed. control and valves control or close toopen servomotor on the acts then controller speed shaft. turbine the power at mechanical the controlling thus turbine, (or the fuel in fluid)flow the ulate

as any departure from it would provide the conditions (through motion equation) to return toit. equation) toreturn motion (through conditions the provide it would from departure any as stable statically is 3.2 in powerFigure turbine and power generator between intersection A point of The Note that the turbine is provided with a servomotor that activates one or a few control valves that reg that one valves or afew control activates that aservomotor with provided is turbine the Note that atransmission or through generator directly, electric an drives mover or turbine aprime general, In construction, in variations many so dueto difficult is moversvery of prime A complete classification Wind turbines. hydraulic tidal special work in mechanical into converted Wave similarly is energy converted may be upper-level reservoir an from of water energy potential the hand, other the On with combination in or oil thegas butis it turbines, fuel or nuclear coal for fluid working the is Steam prime the in energy mechanical into converted and fluid by a working taken then is energy Thermal produced. is energy thermal thus and acombustor in burned is fuel fossil the Essentially, The speed droop is required for two reasons as follows: two reasons for is required droop speed The The speed. reference the with compared and precisely rather measured is shaft turbine at speed The 2. 1. &

With afe With When p When provided. to be shutto be off. Francis Introduction Group, ower increases too much, the speed decreases accordingly signaling that the turbine has has turbine the that signaling accordingly decreases speed much, the too ower increases w generators of different powers in parallel, fair (proportional) power load sharing is powersharing load (proportional) fair parallel, in powers of different w generators LLC Prime Movers 3 71 - - © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor 72 FIGURE 3.2 FIGURE 3.1 FIGURE .Gso i Gas (oil) + Gas or oil 2. or Coal 1. .Wind energy 4. Water 3. TABLE 3.1 Prime source energy & nuclear fuel energy Francis Fuel

Turbines control Basi Group, The refe The valve Fuel c prime mover generator system. generator mover c prime Steam Air Water Working

Speed (p.u.) air 0.95 LLC thermal turbines rence speed (frequency)/power curve. (frequency)/power speed rence Fluid 0.8 0.9 1.0 conversion/for Intermediate energy From watts Up to 1500 Up to 10 Up to 1000 Power Range of MW/unit to hundreds MW/unit MW/unit MW/unit Turbine Speed governor Servomotor Power (p.u.) controller lcrcpwrssesSemtrie High speed Large and distributed Steam turbines power systems Electric Distributed power Large and distributed 0.5 A power sources autonomous and off-highway vehicles), trains and highway and applications (vessels, automotive power systems, power sources systems, autonomous power sources systems, autonomous power electric Main Applications sensor Speed Transmi- ssion Generator power Generator reference curve Wind or wave Medium- and Hydraulic turbines Prime moverp Speed/power • • • turbines •

1 Stirlin engines combustion Inter engDiesel Gas turbin nal nal Type Synchronous Generators Synchronous g engines Frequency f generator power (P Electric ines es ower e ) 1 With rotary Speed downSpeed to Autonomous Power grid motion reciprocating but linear also 10 rpm 10 >75 rpm low speed Observation 3~ load © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor Prime Movers Prime mode dynamic their and governors speed main The for transients. models and performance steady-state ciple, of prin terms in movers prime with somedetail in deal us let clarified, have been mover requirements power done be through then would generators electric between power. Powerreference for smaller sharing ( ranges (and larger control) in variation for speed allow would power system, the and them between power electronics full or of AC generators, nous with generators of doubly fed synchro use the hand, other the On power tonot-so-fast control. leads It also etc. tia, iner tolarge governor—due speed on the strains strong implies which small, very is droop speed the in the HP stages than in the lower power the stages. in than stages HP the in lower is blades of the length the Consequently, increases. volume the thus and decreases stages turbine the along power, The pressure are produced. mechanical thus, Torqueand, rotor blades. shaft on the turbine force on the atangential exerting thus direction and momentum it where changes turbine steam the of blades the rotating into guided 3.3). (LP) toalower is (Figure pressure the fluid Then expands it as accelerated (MSVs) it where is (GVs)—the blades valves stop governor valves the and stationary emergency main the enter—through to is let boiler the in (IP), (LP).pressure lowsteam pressure HP The steam turbines. flow axial so-called the in energy into mechanical converted then is steam the in energy potential The aboiler. in steam temperature, (HP), pressure high toproducehigh burned are fuels or nuclear oil, Coal, 3.2 FIGURE 3.3 FIGURE With synchronous generators operating in a rather constant voltage and frequency power system, power system, frequency and voltage constant arather in operating generators synchronous With The steam turbines contain stationary and rotating blades grouped into stages—HP, intermediate intointermediate stages—HP, grouped blades and rotating stationary contain turbines steam The &

ls are also included for each main type of prime movers investigated here. movers investigated of prime type main for each included also are ls Francis Steam Turbines Steam elec tronics in a much faster and more controlled manner. Once these general aspects of prime of prime aspects general these Once manner. more controlled and amuch faster in tronics

Group, Sing Governor Bo le-reheat tandem-compound steam turbine. steam tandem-compound le-reheat iler LLC sensor Sp eed Reference sp w MS r V Reheater GV w HP * r (P eed * ) vs . power RS IV IP V MSV IV RS GV —intercept valve Crossover V— —governor valve —main emergenc rehe ± 20% and more). That is, smaller speed speed more). and 20% smaller is, That at emergenc LP y stopvalv y stopvalve To generator shaft e 73 - - - © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor 74 improved, up to 45% for modern coal-burn steam turbines. steam coal-burn up to45% forimproved, modern is efficiency overall the thus and increased is enthalpy its reheated; is steam the stages Between dem. separate shaft (Figure 3.4). (Figure shaft separate diff boiler. the in parameters its and admission mix fuel–air the tocontrol but also IV GV and the tooperate servomotor (oil) electrohydraulic or an ahydraulic contains governor system power. and The speed the toregulate governor system by the controlled are IV GV and the while open control. safe work done. is more where mechanical stage LP the through and pipes crossover the to is headed steam the expansion, For final work. todo mechanical it expands again where turbine the of stage IP the to (IV) valve intercept and (RSV) valve stop emergency the reheat through flows steam reheater, From enthalpy. the the its toincrease exchanger heat the in reheated and boiler tothe back guided is steam the Subsequently, expansion. partial a experiences where its stage HP the through flows tur FIGURE 3.4 FIGURE The two, three, or more stages (HP, IP, and LP) are all, in general, on same shaft, working in tan in working shaft, same on (HP,in general, or morestages IP,three, all, two, LP)andare The Nonreheat steam turbines are built below 100 MW, while single-reheat and double-reheat steam double-reheat steam and below single-reheat 100 MW, built while are turbines steam Nonreheat Turbines with one shaft are called tandem-compound while those with two shafts (eventually at (eventually twoshafts with those while tandem-compound called are one shaft Turbines with conditions. emergency under turbine the safely and stop quickly to used are RSV and MSV The fully is MSV generator synchronization—the synchronous starting—toward turbine steam During and fast to provide stage, IP the in IV the and stage, HP the in the GV both controls The governor stages. LP IP, HP, the the the in 30% in in 30% and 40% as divided is turbine power ofTypically, the the and HP,MSV 3.3: steam HP in Figure through the IP,GV, stages LP.and three passing are After There 3.3. inFigure is shown turbine steam shaft) tandem (same single-reheat The bines are common above 100 above MW, common general. are in bines erent speeds) are called cross-compound. In essence, the LP stage of the turbine is attributed to a attributed is turbine of the stage LP the essence, In cross-compound. called erent are speeds) & Francis

Group, Sin gle-reheat cross-compound (3600/1800 rpm) steam turbine. rpm) steam (3600/1800 cross-compound gle-reheat LLC Governor Boiler sensor Sp eed ω ω MS r r 2 1 V Reheater ω GV sensor 2 * r1,2 Sp HP (P eed 1, 2 ) RS IV IP V generator 1, 3600 rpm LP Shaft to Shaft generator 2, 1800 rpm Shaft to Shaft Synchronous Generators Synchronous - © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor often “linearized” through the control system. control the through “linearized” often are control, better for and, nonlinear arepartly 3.6).characteristics (Figure valve The type or butterfly turbine. of the tripping for emergency only used MSV, are 1,2,3 while RSV flow. steam HP the by reheated also is erosion.The and exhaust HP losses moisture steam to reduce 3.5). (Figure stages LP three and HP (50)one contain power systems.They Hz (1500) runrpm1800 at 60 for and configurations (single-shaft) tandem-compound general have in units used. Nuclear areoften more configurations shorter.are shaft) (single Tandem-compound shafts Also

the weight of the steam in the vessel (kg). vessel the in steam of the weight the for the single-stage steam turbine. steam single-stage for the 3.7)(boiler, reheater) (Figure [1–3], model vessel steam the simple power expression the derive first and is why wehere This present involved. rather is turbine steam completeof a The model multiple-stage 3.3 Prime Movers Prime FIGURE 3.5 FIGURE In general, the governor (control) valves are of the plug-diffuser type, while the IV may be either plug either maybe IV the while type, plug-diffuser of the governor (control) are the valves general, In stages LP 1,2,3 and HP the in admission steam the control to IV 1,2,3 and GV upon The acts governor stages, 1,2,3) LP (LP the (MSR)reheater before entering the moisture through passes exhaust HP The flexibility. brings more it though difficult rather is shafts powers of two and speeds the Controlling The mass continuity equation in the vessel is written as follows: written is the vessel in equation continuity mass The is the volume (m volume the V is &

Francis Steam Turbine Modeling Turbine Steam

Group, Typi sensor Sp Governor cal nuclear steam turbine. steam nuclear cal eed ω ω Boiler LLC r * r 3 (P ), ), * MS GV is the steam mass flow rate (kg/s), rateflow mass steam the Q is ) HP V MS R1 dW dt RS IV LP 1 V1 == 1L V d dt r MS QQ R2 inpu RS IV to - 2 V2 P2 is the density of steam (kg/m of steam density the ρ is utpu t

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor

where vessel: 76 Let us assume that the flow rate out of the vessel Q the vessel rate flowout of the that assume us Let Steam tables provide ( provide tables Steam FIGURE 3.7 FIGURE 3.6 FIGURE (a) As the temperature in the vessel may be considered constant: considered may be vessel the in temperature the As Finally, from Equations 3.1 through 3.3: 3.1 through Equations from Finally, P P is the pressure (kPa) pressure the is 0 & and Q and Valve flow rate 0.5 Francis 1 0

are the rated pressure and flow rate out of the vessel rate flowout of and pressure rated the are Group, The st Stea m valve characteristics: (a) plug-diffuser valve and (b) butterfly-type valve. (b)and butterfly-type valve (a) plug-diffuser characteristics: m valve eam vessel. LLC ∂ρ V alve ex / ∂ P 0.5 ) functions. ) Q cursion input QQ inpu to -= Q d dt 1 rr output utpu = ¶ V ¶ tV = P output (b Q P T × 0 dP ) dt 0 Valve flow rate is proportional to the internal pressure in the the in pressure internal tothe proportional is 0.5 P dQ 1

dt output

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor follows:

The first-order model of the steam vessel has been obtained. The shaft T torque The been obtained. has vessel steam the of first-ordermodel The constant T time larger equivalent An larger. is delay time response its of steam, amount a large holds reheater the As approximation. afirst in neglected may be time delay their thus and conditions,

There bines is proportional to the flow rate: flow tothe proportional is bines

Prime Movers Prime T T constant time by a characterized is delay time This chest. steam and piping inlet of the time charging the delay to due time a exhibits in GV opening flowchange toa of steam response the Consequently, (reference) control. (speed) (power)/frequency load conditions. delays/time constants. of time asuccession identifying turbine, the through journey steam the follow We will (Figure 3.8). turbine steam tandem-compound of asingle-reheat, complete model rather Now the consider CH V is the time constant of the steam vessel. With d With vessel. steam of the constant time the is The steam flow in the IP and LP stages may be changed with the increase of pressure in thereheater. in of pressure increase the with changed be may stages LP and IP the in flow steam The power) 70% of overspeed power handle during (they rapid control forof mechanical used are IV The The crossover piping also introduces a delay that may be characterized by another time constant T constant time another by characterized maybe that delay a introduces also piping crossover The The GV has a steam chest where substantial amounts of steam are stored, also in the inlet piping. piping. inlet the in also stored, are steam of amounts wheresubstantial chest steam a has The GV required the tofor provide turbine the through flow steam the The governor modulate valves (control) emergency in only intervene they because 3.8 in Figure RSV are shown not and MVS(stop) The valves in the order of 0.2–0.3 s. the in & fore, the power P fore, the The reheater steam volume of a steam turbine is characterized by characterized is turbine steam of a volume steam reheater The 3.1 Example

Francis Q We just use Equations 3.4 and 3.5 and, therefore Equation 3.6: Equation therefore 3.4 3.5 and, and Equations We use just Calculate the time constant T constant time the Calculate 0 RM = 100 m V=100 =200 kg/s, of 5–10 s is characteristic to this delay. tothis of 5–10 characteristic sis Group, LLC m is T 3 , P R =× 0 = 4000 kPa, ∂ρ kPa, =4000 Q R P of the reheater and its transfer function. transfer its and reheater of the 0 0 PT V mm =× ¶ ¶ Q QT T P r Q Qs output V inpu TK output =´ inpu mm =× W tV 4000 200 t =× Q mm P = / / 0 = dt 0 ∂ =× 1 V = 0.004 P = 18

KQ +× → +× 100 1 Q 1 ¶ ¶ the Laplace form of Equation 3.4 is written as as 3.4 written of Equation form is Laplace s the P r

´= s 2

0 p

.. 004 n m

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor We may integrate these aspects of steam turbine model into a structural diagram as in Figure 3.9. Figure in as diagram astructural into model turbine of steam aspects We these may integrate power that: such 78 smaller. FIGURE 3.9 FIGURE 3.8 FIGURE po Typically, as already stated: F stated: already Typically, as In a nuclear–fuel steam turbine, the IP stage is missing ( missing is stage IP the turbine, steam anuclear–fuel In We should also consider that the HP, the that IP, consider produce F We stages also LP should As T As Valve & sition Francis CH is largest, reheat turbines tend to be slower than nonreheat turbines. nonreheat slower tobe tend than turbines reheat largest, is

GV Group, Str Sin uctural diagram of single-reheat tandem-compound steam turbine. steam tandem-compound of single-reheat diagram uctural gle-reheat tandem-compound steam turbine. steam tandem-compound gle-reheat (CV) LLC GV pressure From boiler stea Main m che Inlet and 1+sT stea st dela HP 1 =F HP m CH y IP Steam chest =0.3, F flow HP po + F IV sition IV HP +F – LP IP = 0.4, T 0.4, = Reheater dela IP Crossover piping +F 1+sT 1 LP Intercep CH RH =1 To condenser F valve 0.2–0.3 s, T s, ≈0.2–0.3 IP

y =0, F pressure LP t HP HP LP , Shaft togenerator =0.7) T and F flow IP IP , RH Crossover F F 1+sT HP LP = 5–9 s, T s, =5–9 dela Synchronous Generators Synchronous F fractions of total turbine turbine of total fractions 1 IP y CO RH and T and F LP CO + = 0.4–0.6 s. 0.4–0.6 = CH + + are notably notably are turbin torque Tm (3. e 9) © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor intricate transient phenomena. transient intricate various model better to maybe required valve, the across (fast) difference for the pressure counting prov GV to of the control the through 3.2)(frequency/power)control (Figure achieved speed/load is The the following: as such functions of a multitude performs turbine of a system The governor 3.4

Prime Movers Prime shown in Figure 3.10 for T Figure in shown toGV opening. response straightforward a has turbine steam the that shows Equation 3.10clearly in function transfer The for paralleling generators with adequate load sharing. load adequate with generators for paralleling nozzle sections distributed around the periphery of the HP stage. HP of the periphery the around distributed sections nozzle below 120%. speed the tolimit fail controls overspeed and normal occurs. condition rejection aload case in turbine of the tripping turbine. the flow to steam integrity. turbine the order topreserve in of 120%, mum FIGURE 3.10 FIGURE Enhanced steam turbine models involving various details, such as IV more rigorous representation representation more rigorous IV as such details, various involving models turbine steam Enhanced After neglecting T neglecting After A typical response in torque (in PU)—or in power—to 1 s ramp of 0.1 (p.u.) change in GV opening is is of 0.1 power—to(p.u.) 1sramp torque GV opening in (in in in PU)—or response change A typical Following a reduction in electrical load, the governor system has to limit the overspeed toamaxi overspeed the tolimit has governor system the load, electrical in areduction Following A steam turbine is provided with four or more governor (control) valves that admit steam through through steam admit or more four governor (control) that with valves provided is turbine A steam case in solution 3.5) 3.3RSV; and and aprotection is MSV Figures tripping (through emergency The to prevent overspeed speed rated of 110%–115% about to set is control the overspeed of objective The the control to rapidly (GV groups IV) and valving separate have two turbines steam Reheat-type • • • •

& ide linearly decreasing speed with load, with a small speed droop of 3%–5%. This function allows allows function of This 3%–5%. droop speed asmall with load, with speed decreasing ide linearly

Start Over Over ( Speed Francis Speed Governors for Turbines Steam -up and shutdown -up and speed trip: through MSV and RSV and MSV through trip: speed IV through mainly control: speed

frequency)/load (power) control: mainly through GV through (power)frequency)/load mainly control: Group, Stea m turbine response to 0.1 (p.u.) 1 s ramp change of GV opening. of GV 0.1 to (p.u.) change 1sramp response m turbine LLC CO ∆T (p.u.) ∆V (p.u.)

0.9 m GV and considering GV as linear, the simplified transfer function maybeobtained: function transfer simplified the linear, GV as considering and 1 CH = 8 s, F =8s, HP 1 opening (p.u.) D = 0.3, and T =0.3, and D V T GV Valve m » () 234 11 + () 1 TsT sT CH Time (s) + CH =T sF Torque (p.u.)orpower HP () CO T + = 0. = RH RH

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor the start-up, all the GVs are fully open and stop valves control the steam admission. steam the control valves stop and open GVs the fully are all start-up, the the electronic speed controller. speed electronic the and response. more robust faster and more flexibility bring they lower power stages, [2]. IV the control 80 Pilot valve (a) hydraulic ones [4]. ones hydraulic used for the scope (Figure 3.12). (Figure scope for the used valve. steam the activates finally that servomotor electric an and controls electronic 3.11). (Figure servomotor loaded governor)spring- andspeed a the by valve (activated a pilot contains relay speed The valves. steam the in governor contains, [4]. IV the controls and Amechanical–hydraulic operates governor system gene Figure 3.13). (Figure obtained nor is FIGURE 3.12 FIGURE 3.11 FIGURE supply Governor systems for steam turbines evolved continuously, from mechanical–hydraulic toelectro mechanical–hydraulic continuously, from evolved turbines for steam systems Governor During load. partial at efficiency better toprovide GVs the sequentially open operation, are normal In We should notice the two stages in actuation: the electrohydraulic converter plus the servomotor and and servomotor plus the converter electrohydraulic the actuation: in stages two We the notice should 3.14. in Figure shown is system governor electrohyraulic of a generic structure The compensation. relay unbalance power and load detection acceleration with provided in general, are, They the in control electronics but by using functions; similar perform governor systems Electrohydraulic In some embodiments, the main governor systems activate and control the GV while an an GV while the control and activate governor systems main the embodiments, some In Combining the two stages—the speed relay and the hydraulic servomotor—the basic turbine gover turbine basic servomotor—the hydraulic the relay and speed stages—the two the Combining are servomotors Hydraulic is needed. amplification of energy level additional an turbines, large In by replaced relay are speed governor and speed the governor systems, turbine electrohydraulic In For a speed droop of power, 4% at droop rated For K aspeed Oil & ral, a centrifugal speed governor (controller) whose effect is amplified through a speed relay to open open relay to speed a through amplified governoris (controller) speed effect whose acentrifugal ral, Francis

Oil drain Group, Spee Hydr output Speed relay d relay: (a) configuration and (b) transfer function. (b)transfer and (a)d relay: configuration aulic servomotor structural diagram. structural servomotor aulic LLC speed governor Mechanical – T 1 SM Servomotor L s2 limiter Rate Steam valve SR = 25 (Figure 3.13). A similar structure may be used to used may be structure 3.13). (Figure =25 Asimilar 0 Mechanical L spring s1 Position limiter S 1 (b) 1.0 Synchronous Generators Synchronous Valve stroke T SR 1+sT 0.1–0.3s = K SR SR auxi liary liary - - © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor monly used seems to be the open regenerative cycle type (Figure 3.15). (Figure type cycle regenerative open the tobe seems used monly operationand com most the[1], topology turbine but gas in variations many are There fluid. working the as used is Air work. mechanical into converted is energy thermal whose gas, burn turbines Gas 3.5 controllers [5,6]. here. controllers scope our beyond However, fall they turbine-generator steam or total controllers speed of electronic recent variety toawide led etc.) has Prime Movers Prime FIGURE 3.15 FIGURE 3.14 FIGURE 3.13 FIGURE Speed reference ω * r ω The development of modern nonlinear control (adaptive, sliding mode, fuzzy, neural networks, H networks, neural fuzzy, mode, sliding control (adaptive, nonlinear development The of modern – r &

Francis Gas Turbines Gas Electronic speed controller

Air inlet ∆ω Group, Gener Basi Open re Open 1 c turbine governor. c turbine ic electrohydraulic governing system. governing ic electrohydraulic LLC Compressor K generative cycle gas turbine. gas cycle generative SR (C) pressure Exhaust Steam reference feedback Load Steam – referenc flow Loa d 1+sT Sp e re Electrohydraulic Heat exchanger 1 eed la y converter SR – T (governor valve) 1 SM valve Pilot L Combustion Fuel input S2 chamber (CH) 0 turbine Feedback L Gas (T) S1 Servomotor 1 s Po 1.0 sition limiter flow GV generator Shaft to flow GV Valve positio 81 ∞ n - , © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor make the gas turbines a way of the future in this power range. this in future of away the turbines gas the make at 50(60) mode operation Hz, standalone or in power grid, distributed the generator and the between turbines. gas cycle of combined merits main all are (gas) handling fuel easy the combustion chamber (CH). chamber combustion the 82 tem shaft. on same section turbine asteam power through toproducemore mechanical used is turn, in which, 3.16.in Figure shown is turbine cyclegas combined more. The generic 55% slightly or even [1]. performance in ments (slight) improve for further used are recooling and regeneration with or intercooling reheating and intercooling as compressor such cycles is35%.turbine More complicated gas a of efficiency typical The exchanger. the heat in compressor from air the heats gas exhaust The turbine. gas of the blades moving the to energy transfers and whereexpands it turbine the into directed then is product combustion The tion and in distributed power systems in the megawatt or even tenth and hundreds of kilowatt per unit. per of kilowatt hundreds and tenth or even megawatt the in power systems distributed in and tion FIGURE 3.16 FIGURE Their construction at very high speeds (tens of krpm) up to 10 MW range, with full power electronics power electronics full with range, krpm)MW up to 10 of speeds (tens high at very construction Their The fuel enters the CH through the GV where it is mixed with the hot-compressed air from air the hot-compressed with mixed whereis the GV it through CH the enters fuel The and (T) itself turbine (C) by compressor the driven air of 3.14 an consists in Figure turbine gas The Already in the tens of megawatts, combined cycle gas turbines are becoming popular for cogenera popular becoming are turbines gas cycle combined of megawatts, tens the in Already delivered. be may for homeindustries (office) steam some or process Additionally, heating HRB the burning, fuel additional and 500°C above turbine gas the exiting exhaust gas the With steam, to produce (HRB) boiler therecovery heat through directed is turbine thegas from heat exhaust The of efficiency an deliver to haveprovenbeen recently turbines gas steam-cycle and combined-gas The Besides efficiency, the short construction time, low capital cost, SO low cost, capital time, low construction the short efficiency, Besides perature may rise further the temperature of the HP steam and thus increase efficiency more. efficiency increase thus and steam HP of the temperature the further may rise perature & Francis

Group, Air inlet Com bined cycle unishaft gas turbine. gas unishaft cycle bined LLC C CH Fuel in GV1 turbine Heat recovery Gas (T) boiler HRB Exhaust GV2 turbine Steam (T) 2 emission, little staffing, and staffing, little emission, Synchronous Generators Synchronous com pressor. - - © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor The frequency of power stroke f power of stroke frequency The Prime Movers Prime

The cylinders are arranged symmetrically on the crankshaft such that the firing of theN of firing the that such crankshaft the on symmetrically arranged are cylinders The electric power delivered to the local power grid or to the connected loads, in standalone applications. standalone in loads, connected or tothe power grid local tothe power delivered electric the of the quality to important is very admission mix fuel–air control andof governor.dynamics The toafew megawatts. of kilowatts tenth from a few varies unit power The per generators. electric movers for their prime as combustion) engines (or of diesel internal use make generators wind with tandem in systems or for power leveling vehicles, hybrid or parallel or series locomotives or on vessels, of emergency case in intervention for quich ready kV at 12 (or feeders it), power sets around standby distribution with power systems, electric Distributed 3.6 shaft revolution T revolution shaft of one period the with one is of them, [7] engine engines diesel and combustion internal four-cycle In 3.6.1 For an engine with N with engine For an

uniformly spaced in angle terms. angle in spaced uniformly

energy recovery device with about 2% power about recovery. with device recovery energy gas. exhaust [9]. inertia and dynamics by its toperturbations response dynamic the notably thegenerator voltageoutput in flicker [8].as reflect 3.20. stroke); Figure power engine (I), compression (C), intake (E) is: 3.17b). powersequence (see (P), Figure exhaust and two-revolution the 3.17a, while inFigure illustrated are engine diesel cylinder 12 for a angles firing The As for steam or gas turbines, the speed of diesel-engine generator set is controlled through a speed a speed through controlled is generator set of diesel-engine speed the turbines, or gas for As steam Consequently, the angular separation ( separation angular the Consequently, The compressor provides compressed air to the engine cylinders. The turbocharger works as an as works turbocharger The cylinders. theengine to air compressed compressor provides The theengine on runs that turbine by a driven is that compressor air an essentially is turbocharger The 3.21) influences which (Figure aturbocharger with general, in provided, are engines diesel Large that would the torque in severe pulsations produce would cylinders the in one or a of few misfire Any of (period over 720° peaks 12 with pulsations, have much smaller torque will the cylinders, 12 With positive. cycleis powerit during while compression The torqueis negative 3.19. inFigure as angle shaft with varies cylinder torque of one shaft The resultant state. steady at simultaneously firing 12 out of cylinders are 3 There 3.18. in Figure shown is timing 12-cylinder The &

Francis

Diesel Engines Diesel Engine Operation Engine Diesel Group, REV LLC =1/ c cylinders, the number of cylinders that fire per each revolution, N revolution, each per fire that of cylinders number the cylinders, n ( -shaft speed in rev/s), the period of one engine power stroke T in rev/s),power stroke speed of oneengine period the n-shaft PS is θ c ) between successive firings in a four-cycle engine is engine in a four-cycle firings successive ) between TT q N f PS c PS F = = = = 720 2 N T N 1 2 PS RE c c ° V

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor 84 FIGURE 3.19 FIGURE 3.18 FIGURE 3.17 FIGURE & (a) 5 6 Francis

–0.25 Group, 1 0.25 0.75 The 12-cylinder four-cycle diesel engine: (a) configuration and sequence. and (b) (a)configuration engine: diesel four-cycle 12-cylinder The The 12-cylinder engine timing. engine 12-cylinder The p.u. Torque/angle for one cylinder. 2 0.5 3 0 1 4 5 6 10 –50° –100° 10 LLC 4 1 7 7 8 10 9 11 12 (c ompression) Negative torque 2 3 ab 8 9 c (b ) 0 IC First revolution (power) Po torque sitive 50° 100° 720° Synchronous Generators Synchronous Second revolution PE © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor Figure 3.22. in Figure shown is control and turbocharger with engine diesel of a diagram structure The general 3.6.2 Prime Movers Prime FIGURE 3.21 FIGURE 3.20 FIGURE The most important components are as follows: are components important The most • • • •

& flow flow act The The ine The lash. back aging-produced an and temperature, on oil cont fle The The act The Francis

Diesel Engine Modeling Engine Diesel ain atransmission). ain Ф

. This actuator is represented by a gain K gain by a is represented actuator . This

xible coupling that mechanically connects the diesel engine to the alternator (it might also (it also might alternator to the engine diesel the connects mechanically that coupling xible uator (governor) fuel controller that converts the actuator’s driver into an equivalent fuel- equivalent an into driver actuator’s the converts that (governor)uator controller fuel uator (governor) driver that appears as a simple gain K gain asimple as appears that (governor)uator driver rtias of engine J of engine rtias Group, Dies p.u. T p.u. Torque el engine with turbocharger. with engine el 0.4 0.8 0.9 1.0 1.1 orque versus shaft angle in a 12-cylinder ICE (internal combustion angle). combustion ICE (internal 12-cylinder in a angle shaft orque versus LLC Interco E , turbocharger J , turbocharger Airb 2°20 6°40 6°720° 560° 480° 360° 240° 120° oler ox Compresso Engine T Exhaus and electric generator (alternator) J electric and r Shaft angle t 2 and a time constant (delay) constant τ a time and Tu Clutch rbine 3 . Ge train To ar generator 2 G which is dependent dependent is which . 85 © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor 86

enough torque will be available for the electric load, and the generator may pull out of synchronism. generator may pull the and load, electric for the available be torque will enough not situation second the in while be apparent will exhaust smoky case, first the In mix. fuel the in air too or less much be either will there result, Asa inertia. erf flow fuel–air of effects nonlinear due tothe tooscillations may lead 3.22 that Figure in pictured system the in totransients leads change load Any FIGURE 3.22 FIGURE sp Ref. The turbocharger acts upon the engine in the following ways: the following in theengine upon acts turbocharger The eed • • • • • •

& – where The diesel engine is represented by the steady-state gain K gain steady-state the by is represented engine diesel The The dea The exhaust. tolow smoky torque and leading occurs, combustion incomplete increases, fuel/air ratio the when because reduced, is erf essence In 3.22. Figure in shown also is eer with of erf variation Atypical value. stoichiometric by its ized d erf The cylinders produce torque at engine shaft: producetorque at engine cylinders all until time to producetorque, and time burning fuel cylinder, the in fuel injects output actually saturated for large Ф for large saturated by including the turbocharger inertia. turbocharger the by including at low speeds, thus changes inertia system the speeds; at all air abletosupply enough tobe speeds, tur The flow rate. air the by influenced is engine the in erf ultimate and speed turbine the thus and turbine, It com available. It dra Francis Dr ws energy from the exhaust to run its turbine; the more fuel in engine the more exhaust is is more exhaust the engine in more fuel the turbine; its torun exhaust the from energy ws n Control

presses air at a rate that is a nonlinear function of speed; the compressor is driven by the by the driven is compressor the of speed; function anonlinear is that at arate air presses oo bocharger runs freely at high speed, but it is coupled through a clutch to the engine at low engine tothe aclutch but coupled through it is speed, at high freely runs bocharger Group, E d time of the diesel engine comprises three delays: the time elapsed until the actuator actuator the until elapsed time the delays: three comprises engine diesel of the d time is the engine speed engine the is Dies p epends on engine equivalence ratio (eer) which in turn is the ratio of fuel/air normal of fuel/air ratio the is (eer) ratio turn in which equivalence on engine epends Identi el engine with turbocharger and controller. and turbocharger with engine el LLC fica K 3 tion , multiplied by the equivalence ratio factor (erf) and by a time constant τ constant by atime and (erf) factor ratio equivalence by the , multiplied i Ba ckla 0.7 1 erf sh . 1.2 0.5 (g Ac t overnor) 1 +st 1 ee tu »+ K r 2 ator A 2 n Φ B EE + K n C 1 2 e –

Tu st 1 rbine disturbance Load 1 and for Фand low fuel–flow , constant erf torque Net T Equivalence ratiocompensation – – T Compressor torque T T – Synchronous Generators Synchronous C E sJ (flexible) (flexible) Coupling 1 T sJ sJ 1 1 G E n T – (3.15 n G 1 n . E - ) © 2016

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An approximate formula for thermal efficiency η efficiency for thermal formula approximate An = 2, x=10,η ρ=2, For K=1.4, ε=3, and control. and for transients performance engine diesel the detail in simulate required. are etc.) structure, variable (adaptive, Prime Movers Prime time to dwell a little on the thermodynamic engines cycles to pave the way to Stirling engines. toStirling way topave the cycles engines thermodynamic on the alittle todwell time chapter, this is but it now in briefly described been already have all They engines. diesel and engines, spark-ignited turbines, gas turbines, steam engines: of thermal family of the part are engines Stirling 3.7 3.23). (Figure cylinders tothe boiler the from directed is steam the Subsequently, machine. combustion continuous is a invented by James Watt, engine, steam The 3.7.1 where FIGURE 3.23 FIGURE (a) 3 1 xp ρ =V A higher-order model may be adopted both for the actuator [11,12] and for the engine [13] [11,12]engine for tobetter the and actuator for the both adopted may be model A higher-order controllers and nonlinear are notadequate speed engine of that controllers PI indicates situation This The typical four steps of the steam engine (Figure as follows: 3.23)are (Figure engine steam the of steps four typical The ε 4 3 2 =V 1 & =

→ temperature. at constant compressed is steam the then and volume constant → → → the cylinder through the open valve at constant volume; then, it expands at constant temperature. at constant it expands then, volume; at constant valve open the through cylinder the Francis Stirling Engines Stirling Summary of Thermodynamic BasicCycles ofThermodynamic Summary 11 ¢ 3 2 /

/ p V V D D D D 1 Isen 3 Isot 2 The iso 2 The 1 Iso 1 is the pressure ratio pressure the is 1 1 ' ' is the compression ratio compression the is =V

Group, choric heat regeneration (3–3 regeneration heat choric tropic compression takes place after the valve is closed and the gas is mechanically compressed. is mechanically thegas and closed is valve the after place compression takes tropic ropic expansion: once the valve is closed the expansion goes on till the maximum volume (3). volume maximum the on till goes expansion the closed is valve once the ropic expansion: The ste The 3 / V choric compression (1–1choric 4 is the partial compression ratio partial the is LLC am engine “cycle”: (a) the four steps and (b) diagram. PV “cycle”: and (a) steps engine four am the 4 2 h th =31%. th D D D D th ' ' =- ′ 1 ) followed by isothermal expansion (1 expansion by) followed isothermal ′ ) and isothermal compression (3 isothermal ) and er K rr - K 1 th is [13]: is th () - xK 1 () K -+ 11 (b P -+ ) 11 () () - ln 1 ln V 1 1'

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The four steps are as follows: are steps The four have low efficiency at low loads ( at loads lowhave low efficiency have low vibrations, tostart, easy are they machines; thermal other than more compact are turbines Gas

Similarly, with T with Similarly, power. mechanical to produce shaft turbine the turns expansion gas The 88

With ideal, complete, heat recirculation, heat complete, ideal, With effici FIGURE 3.24 FIGURE (a) P Figure 3.25. in Figure cycle the work on spark-ignited The (Otto)engines The four steps include the following: include steps The four 3.24).cycle (Figure work on a Brayton turbines gas The air. precompressed with combination in combusted continuously also is fuel engine turbine gas The 4 4 2 2 3 3 1 1 &

ency ency → → → → → → → → Francis

23 1—Iso 4—Ise 3—Is 2—Ise 1 Isob Ise 4 3 Isob Ise 2 η th is th

Group, ntropic compression ntropic ntropic expansion (work generation) expansion ntropic ochoric input of thermal energy inputof thermal ochoric Bray aric thermal energy loss energy thermal aric aric input of thermal energy inputof thermal aric choric heat loss heat choric ntropic compression ntropic ntropic expansion (kinetic energy output) energy (kinetic expansion ntropic 1 / T ton cycle for gas turbines: (a) PV diagram and (b) diagram. TS and (a) diagram PV turbines: for gas cycle ton 4 LLC =T 14 2 / T 3 for the isentropic steps and the injection ratio ρ=T ratio injection the and steps isentropic for the small), and tend to have poor behavior during transients. during behavior to have tend poor and ρ small), Isentropic processes h h th th »- »- V 1 1 r 1 (b) r 1 T T

2 4 Temp.

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor for isentropic processes. η efficiency thermal The Prime Movers Prime

where FIGURE 3.26 FIGURE 3.25 FIGURE (a) P The diesel engine cycle is shown in Figure 3.26. in Figure shown is cycle engine diesel The η and K=1.5 coefficient (say compression ratio ε=9) adiabatic the ahigh and With & Francis 2 3

Group, Spar The die The k ignition engines: (a) PV diagram and (b) diagram. TS and (a) diagram PV engines: k ignition LLC P sel engine cycle. engine sel th is th V 23 2 T T h 4 3 th 1 4 == T T =- 2 1 1 V è ç æ V e V V K 3 1 - 4 3 1 ø ÷ ö (b T ; K ) - 1 e = = e V V K 1 2 1 - 1

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor (2 of →3): fuel injection the working fluid to the regenerator, which cools at T thecools regenerator, to which fluid working the from transferred Heat is compression space. tothe expansion the from regenerator the volume) through fluid constant (at working the totransfer simultaneously moving pistons both (4–1) with step occurs, transfer a again, Then, source. external an from added is heat because constant stays temperature the but increases, the volume and decreases The pressure point. dead at inner idle stays compression piston regenerator, the moves away but from the still piston expansion the 3–4, step expansion 2 to3. the In much lower: is engines cycle Stirling of efficiency one. Practical ideal the from depart cycles Stirling-type Practical is. cycle Carnot the as temperatures minimum and maximum the dependent on is heavily Therefore, it 90 The Stirling engine (born in 1816) is a piston engine with continuous heat supply ( heat continuous with in 1816) engine is a piston (born engine Stirling The 3.7.2 kept at the high temperature T temperature high at the kept between. in aregenerator and pistons opposed two at various speeds. various at worst). the air and best hydrogenthe (with helium ture ture of it) is in the cold compression cold space. of it) the in is increases, in contrast to spark-ignited engines for same ε for same engines tospark-ignited contrast in ρincreases, load when decreases Efficiency

sion to expansion space, and is heated from T from heated is and space, sion to expansion from compres regenerator porous the through transferred consequently is fluid The working stant. con stays the volume Thus, it. moves away piston from expansion the regenerator, the while toward surroundings. tothe cylinder space pression thermal efficiency. thermal ( ratios pression During the downward movement of the piston, an isobaric state change takes place by controlled by controlled place takes change state isobaric an movement piston, of downward the the During The ideal thermal efficiency η efficiency thermal The ideal The regenerator is made in the form of strips of metal. One of the two volumes is the expansion space space expansion the is two volumes the One of of metal. strips theof form in made is The regenerator steps). It contains isothermal two its (with cycle toCarnot similar is cycle Stirling respect, some In [14] for three working fluids [14] 3.28 fluids inFigure working are shown for three density versus HP/liter efficiencies total Typical or hydrogen, air, as such fuels working various use can and source heat any may use engines Stirling - com the from extracted is heat because compression (1–2), constant kept is During temperature the During the transfer step (2–3), both pistons move simultaneously; the compression piston moves compression piston the (2–3), step move pistons simultaneously; transfer both the During & T

min Francis Stirling Cycle Engine Stirling . Thermal axial conduction is considered negligible. Let us suppose that the working fluid (all (all fluid the working that suppose us Let negligible. considered is conduction axial . Thermal hh Group, ht th th th ε < ) than for spark-ignited engine are characteristic for diesel engines to obtain higher higher toobtain engines for diesel characteristic are engine for spark-ignited ) than i LLC K ( K th < 0.5, in general). <0.5, in max th is th , while the other volume is the compression space kept at low kept tempera compression space the is volume other the , while h th r =- == h 1 V V min i th 2 3 =- toT e K 1 11 T T - 1 2 3 min max T T × ; K ma mi in the compression space. the in . An increase in pressure takes place also from from also place takes pressure in increase . An n x r r

K - - 1 1

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor a stable steady-state operation point. There are many variants for rotary-motion Stirling engines [14].engines Stirling for rotary-motion variants many are There point. operation steady-state a stable 3.29b. Figure in appear parameter, Vas voltage and speed, generator, with electric power of apotential performance. for better air ( production or for homeelectricity for generators spacecraft forcompanies) linear STC and Sunpower (by developed recently were rather engines Stirling linear-motion Free-piston 3.7.3 Prime Movers Prime FIGURE 3.27 FIGURE (b P The intersection at A of Stirling engine and electric generator power/speed curves looks clearly like like clearly looks power/speed generator curves andelectric engine at A of Stirling intersection The the While 3.29a. Figure in shown pare pressure with engines of Stirling power/speedTypical curves for replacement agood may be Methane decreases. power go density up, the speed power and the As The dynamic equations of the Stirling engine (Figure 3.30)are (Figure engine the Stirling of equations dynamic The ) &

Francis 2 Free-Piston Linear-Motion Stirling Engine Modeling 3

Group, The Stirling engine: (a) mechanical representation and (b) and (c) the thermal cycle. (b)and and thermal (c) the representation (a)mechanical engine: Stirling The LLC Hot volume( (a) Piston p K , T Fr To E om heater co oler exp ( He by regenerator) ansion) Close ater MX 1 4 ddd dd cy ·· cl += e V DX Regenerato · (c) T AP dp () Cold volume(c r Cooler - 2 P

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor for the piston, where piston, for the 92 and: displacer normal the For FIGURE 3.29 FIGURE 3.28 FIGURE (a) P X P D N/m in pressure gas working the P is D A d d d & d p is the gas spring pressure in N/m in pressure spring gas the is is the displacer position (m) position displacer the is is the displacer rod area in m in area rod displacer the is is the piston damping constant (N/ms) constant damping piston the is is the displacer damping constant in N/ms in constant damping displacer the is Francis

Group, Powe Effici η (%) total 50 60 10 20 30 40 ency/power density of Stirling engines. of Stirling density ency/power r/speed curves: (a) the Stirling engine and (b) the electric generator. electric (b) the and engine (a) Stirling the r/speed curves: LLC Sp 125 eed MX P (pressure) p 250 Air ·· p 400 rpm ++ 2 DX 20 Power density(HP/L) 500 p 2 · 2 p 500 FK 750 el mp ++ Me 40 thane XA (b pd 750 ) Pel () He 1000 - 1000 A 60 ¶ ¶ x P Gas pressur T 225 HP/cylinder T d min max X =25°C d =700°C = 1500 0 Sp H Synchronous Generators Synchronous

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tion modes. generator opera electric or power-grid-connected stand-alone in proven been stable has a combination range such kilowatt the in thatleast at sayhere to It suffices generators. electric reciprocating to linear dedicated 20 Chapter in discussed be PM generator will a linear driving when Its stability variables. as FIGURE 3.30 FIGURE M F M is the cylinder area (m area cylinder the A is X Equations 3.23 and 3.24 may be linearized as follows: as linearized 3.24 may be and 3.23 Equations The free-piston Stirling-engine model in Equation 3.25 is a fourth-order system, with with system, is a fourth-order Equation 3.25 in model Stirling-engine free-piston The 3.31. in Figure shown is Equation 3.25 of correspondent circuit electric The generator current the Iis where The merits and demerits of Stirling engines are as follows: are engines of Stirling anddemerits The merits • • • elm

p & p d is the power piston position (m) power position piston the is is the power piston mass (kg) power mass piston the is is the displacer mass (kg) mass displacer the is is the electromagnetic force (of linear electric generator) (N) electric force (of linear electromagnetic the is T High t High q Very Inde Francis min =40°C pendence of heat source: fossil fuels, solar energy solar fuels, fossil of source: heat pendence

uiet heoretical efficiency; not so large in practice yet, but still 35%–40% for T 35%–40% still but yet, practice in large so not efficiency; heoretical Group, Linea B space ounce r Stirling engine with free-piston displacer mover. displacer free-piston with engine r Stirling LLC Regenerato KA Cooler 2 pd ) He =- () ater KA dd MX r =- p A ·· X p p MX P ¶ ++ 0 ¶ X ¶ ¶ ddd dd P DX X P p ·· d p dd ; T += -

· p c p

a 1 DX P

¶ T ¶ Td

X hr P FK =- el · mp ;

() V AA

c V

a c -- p KX = dp XX ¶ ¶ ¶ X pT ¶ P X P d - Hot space d A a a ;; d pp X X FK d d el Cold space me

= Displacer rod Piston Cylinder (pressure (area (area Gas spring Alternato I Displace

A) A d ) P d r ) r max = 800°C and and =800°C XXX dd ,, ·· (3.2 (3.2 pp , X 93 6) 5) -

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor 94 cal transmissions but have active control. Hydrodynamic transmissions fall beyond our scope here. scope our beyond fall transmissions Hydrodynamic control. but have active transmissions cal the role of mechani play They frame. asingle in machines hydraulic mounted or more conveniently of two made transmissions also hydrodynamic are There pumps. turbine hydraulic called also are pump. They as or turbine as a either may that operate machines reversible hydraulic also are There motors. is that movers, prime only general, in are, turbines Hydraulic particularities. however, separately, many treated due to their be will turbines energy. Wind kinetic water the replaces energy kinetic air wind but the similar, are turbines (tide energy). gravitational are respectively, and, nature, in circuit water of the results are They (wave) renewable. are or energy tidal sea energy water River shaft. turbine work at the mechanical into of rivers energy water the convert turbines Hydraulic 3.8 Thermal EngineThermal A general comparison of thermal engines is summarized in Table in 3.2. summarized is engines of thermal comparison A general islegnsDiscontinuous Rather Moderate engines Diesel Discontinuous Spark-ignited engines Stirling engines Gas turbines Steam turbines TABLE 3.2 3.31 FIGURE Figure 3.32). (Figure water of Wind energy kinetic the ingeneral, water: is fluid and working agent energy The used. has man movers that prime oldest one of the are turbines Hydraulic • • • • • •

Not ea For hi Mate Cond i High gases of noxious emissions Reduced Francis Hydraulic Turbines

Parameter rials have to be heat resistant heat have tobe rials uction and storage of heat are difficult to combine in the regenerator the in combine to difficult of are heat storage and uction Therma gh efficiency, a heat exchanger is needed for the cooler the for needed is exchanger heat efficiency, a gh

nitial costs nitial sy tostabilize sy Group, M Free- d l Engines piston Stirling engine dynamics model. dynamics engine Stirling piston LLC Continuous Continuous Continuous Combustion Combustion D 1/K d Type Efficiency Quietness Emissions FuelType Emissions Quietness Efficiency Type d –+ Good High in at full Good Poor lower far so theory, at low load lowloads, α P X P Bad Very Good Not so bad good good Larger Still large Independent Very low Independent Reduced Low 1/K –+ p α T X One type Rather Rather One type One type Multifuel +– d Synchronous Generators Synchronous K D e I p Fast NA Slow Easy Slow Starting fast M p Good Very good Good Poor Response Dynamic Dynamic - © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor Axial ailailReaction Radial–axial Tangential Prime Movers Prime are of geometrical and functional type: functional and of geometrical are variables [16]. main The characteristics and variables to is related turbines in hydraulic terminology The 3.8.1 Turbine as follows in general, are, turbine of a hydraulic characteristics main The in both potential and kinetic form to the runner. tothe form kinetic and potential both in runner. the hits that of water energy kinetic into turned is energy potential where nozzles the in occurs drop pressure all and pressure at atmospheric is run the inventor (Table 3.3). turbines, impulse In tothe or related rotor axis, tothe or transverse bent rotor axially zone: the in particles water the of direction tomain related is classification A more m. detailed below 300 for heads turbines tion TABLE 3.3 3.32 FIGURE Hydraulic turbines are of two main types: impulse turbines for heads above 300–400 m and reac mand 300–400 above for heads turbines impulse types: main of two are turbines Hydraulic In reaction turbines, the pressure in the turbine is above the atmospheric one; water supplies energy energy supplies one;water atmospheric the above is turbine the in pressure the turbines, reaction In • • • • • • • • • •

& Rotor s Speci Turb elasticity module E(N/m module elasticity Turb Gene Rotor d Liqu Turb Turb Effici Francis

Basics of Hydraulic Turbines ofHydraulic Basics

id (rotor properties): density ρ(kg/m id (rotor density properties): ine input flow rate: Q(m rate: inputflow ine ine gross head: H head: gross ine ine shaft power: P shaft ine torque: T shaft ine ency ral sizes of the turbine of the sizes ral fic energy Y energy fic Hydrau

H peed Ω peed Group, ecin(rple)<0Kpa K,Srfl S,Bl B Bented axial the into plane Kaplan (K),Strafflo (S),Bulb (B) <50 (propeller) Reaction Impulse iameter D iameter turbine ydraulic Hydr lic Turbines opower plant schematics. plant opower Type T LLC (rad/s) T r =gH (m) 3~ T T (m) T T (kW, MW) , W(kW, (N m) (N (J/kg) 2 ) G Head (m) enerato 5 Francis (F) <50 30Pelton (P) >300 3 /s) r h T == P Wi P 3 ), cinematic viscosity ν(m viscosity ), cinematic T h cke r T t gate gH Tr Inventor ×W T Q

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In general, n general, In 96

T = 10 rate Q= flow = 0.8–0.96, the The maximum efficiency [16] depends on the specific speed n specific efficiency the on depends [16] maximum The 3.33. inFigure given are of efficiency load [16] with variations Typical In general the rotor diameter rotor diameter the general In The specific speed is a good indicator for of the best type of turbine for a specific hydraulic site. site. hydraulic specific for turbine a of type best the for of indicator good isa speed specific The In general, G general, In • • • • •

& where where where where G where Specific weight G weight Specific n speed Specific where Δh where Cavi The specific speed corresponds to a turbine that for a head of 1 m produces 1 HP 1 that head of1m for a produces (0.736turbine kW) toa corresponds speed specific The Reac ch the Francis = 0 for Pelton turbines ( γ =0for Pelton turbines H p is the flow rate in m rate flow the Q is rpm in rotor speed the n is P rpm in rotor speed the n is It is good forIt good σ is H 1 T , p T T tation coefficient σ coefficient tation tion rate γ rate tion in kW in axial and axial turbines (Francis, Kaplan turbines) Kaplan (Francis, turbines axial and axial in m in m in

aracteristic speed n speed aracteristic 2 Sopt Group, are the water pressure right before and after turbine rotor turbine after before and right pressure water the are T is the turbine mass ×g mass turbine the is sp i = 2–64 for Pelton turbines, n for Pelton turbines, =2–64 is the net positive suction head suction positive net the is 70–150 N/kW. ≈70–150 LLC s t sp to be small, σ small, tobe : T : 3 /s c : D –3 r p –10 = 0.2–12.0 m, the head head = 0.2–12.0 the m, 1 =p t = 0.01–0.1. It increases with n =0.01–0.1. with It increases 3 , in N. , in m nn 2 < 1 for radial 0<γ1for radial and (impulse) turbine reaction )—zero s 3 /s, n≈50–1000 rotor speed rpm. = G n sp c g = s = s = 50–500 for Francis turbines and n and turbines for Francis =50–500 = P T nQ H G T P H pp = T r T × T 34 12 T 0 54 / gH D ,N H / - . 736 h ,r T T i /k pm

, rp H

s m T and on the type of the turbine— of the type on the and = 2–2000 m, the efficiency at full load is load full at efficiency = 2–2000 the m,

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor division in multiple turbines rotors or injectors and the turbine head. turbine the and rotors or injectors turbines multiple in division Prime Movers Prime (Figure 3.35a). (Figure governor (servomotor). turbine by the shaft. at torque turbine produced is mechanical thus and runner turbine the around placed buckets the bowl-shaped hit jets water high-speed The nozzles. of fixed a set 3.35a–c. Figure in shown are turbines Kaplan and for Pelton, topologies Francis, Basic operation. speed able for variable thesuit one more thus is It turbine. Francis the is load part at efficiency. Theworst show better turbines risk. cavitation of higher Kaplan turbines. The specific speed n speed specific The Kaplan turbines. FIGURE 3.34 FIGURE 3.33 FIGURE The tendency is to increase n increase is to tendency The In the event of sudden load reduction, the water jet is deflected from the buckets by a jet deflector deflector by ajet the buckets from deflected is jet water the reduction, eventload of sudden the In actuated is needle The the nozzle. centerthe of in placed by a needle controlled is the jet of area The by jets water high-velocity into converted is water HP the (Pelton) impulse turbine, head, high the In load Pelton part At load. rated at high be to tends turbines all hydraulic of efficiency the expected, As & Francis

Group, Typ Max ηTmax efficiency ηT 0.95 ical efficiency/load for Pelton, Kaplan, and Francis turbines. Francis and Kaplan, forPelton, efficiency/load ical 0.75 0.25 0.9 imum efficiency versus specific speed. specific versus efficiency imum 0.5 1 LLC 1 100 Pe Pelton lton S in order to reduce turbine size, by increasing rotor speed, at the costs costs at the rotor speed, by increasing size, order turbine toreduce in Kaplan 300 0.25 s could be changed by changing the rotor speed n, the total power total the n, rotor speed the by changing changed be could Francis F n rancis s , rpmspecificspeed Deriaz 0 700 500 . .5101.2 1.0 0.75 0.5

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor (a) servomotor placed within the main turbine shaft. turbine main the within placed servomotor rotor blades are tightened to a crown and the lower toaband. ends the and toacrown tightened are rotor blades reservoir. water tail the to tube, draft the through then, and runner turbine onto gates the movable wicket the through then at lower speeds. run and of water volumes 98 with the square root of head. root net square the with and opening the gate with varies water of flow volume thevelocity and of head flow rate),(volume while product tothe proportional power is turbine the inelastic, is penstock the incompressible, is water that assumes model a lossless Such used. is turbine the hydraulic of model classical asimplified, a power grid, to generator connected electrical coupled to an [17], turbine the studies with stability system in Usually, 3.8.2 FIGURE 3.35 FIGURE At even lower head, in Kaplan hydraulic turbines, the rotor blades are adjustable through an oil oil an through adjustable are rotor blades the turbines, hydraulic Kaplan in lowerAt even head, the of ends the upper turbines, In Francis axis. turbine the to parallel axis their have gates wicket The passes chamber, spiral a through penstock, or passage intake the from turbine the enters water The 3.35b) (Figure high lower head, use turbines hydraulic or Francis (radial–axial) reaction contrast, In & Francis

First-Order Ideal Model for Hydraulic Turbines Model for Hydraulic Ideal First-Order Tu runner rbine

Group, Hydraulic turbine topology: (a) Pelton type, (b) Francis type, and (c) type. and Kaplan type, (b) Francis (a) Pelton type, topology: turbine Hydraulic B owl-shap Je bucke t defl Need Spiral LLC (c) ro Nozzle wa om ts ec te blades ed le Rotor to r r Surg tank e Wa generato Shaf Ru te r nner t to r Se Wi (b rvomotor ga ) cket te re Wa se rv te oir r Draft Synchronous Generators Synchronous tu be Tu Runner rbine blades © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor and finally and

Linearizing this equation and normalizing it to rated quantities ( quantities it torated normalizing and equation this Linearizing where Subs Prime Movers Prime equation: motion by its described is turbine the at in head change due to accelerates that column water The

After

The tur The

According to the above assumptions the water velocity in the penstock Uis penstock the in velocity water the assumptions above tothe According

where There are three fundamental equations to consider: to equations fundamental three are There is the net head at the gate at the head net the H is opening gate the G is is the acceleration of gravity acceleration the gis pipe area, the A is length conduit the L is density mass the ρ is 2. 3. 1. & tituting Δ normalization ( normalization

Turb Wate Acce Francis bine mechanical power P mechanical bine ine shaft (mechanical) power equation (mechanical) shaft ine leration of water volume equation volume water of leration r velocity Uequation penstock the in r velocity Group, H / H 0 or Δ or LLC P m 0 U =K / U 0 p from Equation 3.34 into Equation 3.36 yields Equation into 3.34 Equation from H 0 U m writes 0 ) and linearization, Equation 3.35 becomes Equation linearization, and ) r LA DD DD P P DD P DD U P 00 00 P dU m m P U UK 00 D 00 dt PK m =+ mp = = =+ =+ 15 32 = . 2 = H U H u H H -r U H GH H Ag HU - () D D U G D

D U G G G

0 0 G G D 0 0

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor The tra The

is the w the is

where

comp and conduit (penstock) elastic the of case the investigate is to answer 0.5 The rad/s. than higher is inertia. water is to due of 1p.u. This value state steady expected tothe exponentially increases After 3.39 becomes: Equation normalization By 100

The time response to such a gate step opening is opening step gate a such to response time The curve. amplitude/frequency its from amplitude its only investigating maycompleted be by not identification whose system phase minimum FIGURE 3.36 FIGURE plane. It anon- is splane. right the in zero a Equation 3.43has of function power/gate transfer The opening Replacing d Replacing Practice has shown that this first-order model hardly suffices when the perturbation frequency frequency perturbation the when suffices hardly model first-order this that shown has Practice For a step change in gate opening, the initial and final value theorems yield theorems value final and initial the opening, gate in change For astep & ressible water where the conduit of the wall stretches at the water wave front. water at the stretches wall of conduit the the where water ressible a unit step increase in gate opening the mechanical power goes first to −2 p.u. value and only then to and only first power−2 goes value p.u. mechanical the gate opening in increase step a unit Francis nsfer functions in Equations 3.42 and 3.43 are shown in Figure 3.36. Figure in 3.42 3.43 shown and are Equations in functions nsfer ater starting time. It depends on load, and it is in the order of 0.5–5 s for full load. order of 0.5–5 sfor the full in it is and on load, It depends time. starting ater

Group, / The line The dt with the Laplace operator, from Equations 3.34 and 3.40 and 3.34 one obtains: operator, Equations from Laplace the with LLC ar ideal model of hydraulic turbines in p.u. in turbines of hydraulic model ideal ar ∆G G 0 1 + D D- P P P 2 1 P 0 0 1 m m T D W () () P ¥ P 0 ·s 0 D D D D m T UU PP GG GG W = = () mW te / // // li s s li dt / ® d ® T m = m 0 0 0 0 ¥ W ¥ () D U s 13 = = ∆U s U = 11 U s - 11 s 00 0 12 12 11 11 LU 1 gH + + = + + - () () - Ts Ts - () Ts 2 () 0 0 1 - tT W W / / D / Ts

H Ts 2 2 W (1 –T H w × w Ts Ts D w G w

0 W = =

·s) - 10 . 2

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor where where circuited at forebay. at circuited short- end and turbine at the circuited open is that line transmission electric an as modeled may be

where a Prime Movers Prime the order of fractions of a second, larger for larger penstocks (Pelton turbines). penstocks for larger larger of asecond, order of fractions the turbine: hydraulic of the model linear deviation small more general aslightly with We start 3.8.3 ing Δ ing

where

22 T factor friction the F is Finally, the incremental head and volume flow rate h flow volume and head incremental the Finally, conduit the in wave equation the compressible, as water and elastic considered Now, is conduit the if m opening gate the z is speed turbine the n is head net the h is q As expected, the coefficients a coefficients the expected, As If we now introduce Equations 3.42 and 3.43 into Equation 3.48, then the power Δ the 3.48, 3.42 3.43 then Equation and into Equations we nowIf introduce are around 1200 m/s for steel conduits and around 1400 m/s for rock tunnels. T m/s 1400 tunnels. for rock around and m/s conduits for steel 1200 around of αare values Typical pipe material for the Young’s the E is of elasticity modulus compression of water modulus bulk the K is diameter conduit the D is ofwall conduit thickness the f is of gravity acceleration the g is density water the ρ is 0 and, with constant a constant with ≈0and, is the volume flow volume the is e & is the elastic time constant of the conduit of the constant time elastic the is t is the shaft torque, all in values p.u. all torque, shaft the is z Francis

( s Second- and Higher-Order Models of Hydraulic Turbines ofHydraulic Models Higher-Order and Second- ) in p.u. transfer function can be obtained as follows: as obtained be can function p.u. transfer ) in Group, LLC ij coefficients, the first-order model is reclaimed. is first-ordermodel the coefficients, Gs () 11 , = T a e 12 D == D , Pm hs qs a z conduit_length () () 13 wave_velocit ma , () qa a s t ar =× 21 =+ =+ , =+ = - a T 11 13 12 11 12 23 22 21 12 T 22 1 hana g w hana + e , - è ç æ a ta () () TT K 23 TT 1 n We We vary with load, etc. To a first approximation a To etc. approximation load, afirst with vary y hT / / : () : ( a Ef s + L + D )/ e ; q ta ta ø ÷ ö sF ( s n z

a + z n ) transfer function of the turbine is [2]: is turbine of the function ) transfer hT

hT () () e

e a g ×+ ×+ sF sF

P m ( s ) to gate open ) togate (3.47) (3.5 (3. (3. (3.5 101 12 48) 49) e

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor that occurs at ω=π occurs that Figure 3.37 shows comparative results for G results 3.37 shows comparative Figure 3.47, Equation from following: the Alternatively, we obtain 102 ( response frequency The that is for very low frequencies: for is very that where

range of interest [19,20]. of interest range FIGURE 3.37 FIGURE The second-order transfer function performs quite well to and slightly beyond the first maximum maximum first the beyond slightly and to well quite performs function transfer second-order The Such models can be obtained with advanced curve fitting methods applied toG applied methods fitting curve advanced with obtained be can models Such required. is approximation ahigher-order frequency this beyond well however,It that is, clear With With Now, we may approximate the hyperbolic function with truncated Taylor [18]: series truncated with function Now, hyperbolic the we may approximate in some hydraulic plants calls for a higher-order model. for a higher-order calls 3.39) plants (Figure hydraulic some in tank surge of a The presence & q Francis p F =q is the friction the is

p Group,

Arg G(s) |G| h tan provided order model first 3.52 the 3.51 into and degenerate =0, Equations 1 2 High /2 er-order hydraulic turbine frequency response. frequency turbine hydraulic er-order LLC T e = 6.28 rad/s in our case (Figures 3.37 and 3.38). 3.37 and (Figures case our rad/sin =6.28 Gs s =j ¢ () ω G(s) Figure 3.36. Figure in shown F=0is 3.51 with ) of Equation = D D Pm z ta Gs () s 2T 2 n π () hT Gs = e () 1 ( 10 () = s e ++ ), G ), 1 × () () s Ts = -- Ts ./ eW 52 qT 1 e 12 = ( × qT × s pW + ) and G ) and 1 pW 12 log ω () 2 -× +× Ts 2 () G - Ts W () + () 2 T W () 22 π (s) T Ts Ts Ts e / WW e Th e 2 × ee ( ×+ × T ×+ s s ) for T e ta /

n ta 2 2 n ()

hhT Ts e = 0.25 s and T sand =0.25 () 2T ×+ 3π e e ×+ sF F G(s) Synchronous Generators Synchronous

w 2π T 2 =1s. ( G e s G ) for the frequency frequency ) for the 2 G 1 (s) (s) 1 log ω (s) T es

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor and surge tank can be approximated toF approximated be can tank surge and

where Prime Movers Prime where

FIGURE 3.39 FIGURE 3.38 FIGURE h U T h The wave (transmission) line equations apply now both for tunnel and penstock. Finally, the tunnel tunnel the Finally, penstock. and tunnel for apply nowboth equations line wave The (transmission) T q T Now for the penstock, the wave equation yields (in p.u.) yields wave equation the Now penstock, for the q h T T Z c t r S ep ec p p S Wp WC & p is the turbine head turbine the is is the the surge tank friction coefficient friction tank surge the the is is the riser head riser the is is the surge tank head tank surge the is is thefriction coefficient in the penstock the in coefficient thefriction is is the hydraulic impedance of the penstock ( penstock of the impedance hydraulic the is is the surge tank riser time ( time riser tank surge the is is the upper penstock water speed water penstock upper the is is the elastic time constant of the tunnel of the constant time elastic the is is the penstock elastic time elastic penstock the is Francis is the penstock water starting time starting water penstock the is is the water starting time in the tunnel the in time starting water the is H turbine ydraulic

Group, Hydraulic plant with surge tank. surge with plant Hydraulic The second-order model of hydraulic turbines (with zero friction). zero (with turbines of hydraulic model second-order The 3~ LLC differential opening Ga G te ∆Z enerato hh tr =× UU T Fs 1 S pt r ≈600–900 s) () se =× ct s hT s = 2 2 T () T co 1 1 ( e e ta 2 s +× ep 2 ) [2]: ) s –2 + n hT sT sT sZ hT () sT qs Z () W cW sc -- ep W c +× ×+ +2 cec ec +2 qs Z = s × p pt T sT Uh =T T T + WWC ec =× 2 Z C h an TT Wp t Penst p WC Surg ssi / tank differentia T () n ∆P s Ts ep S Power hT oc ep ) e = m () k × (s) - ep U h × S s p l h qU r pt

Rise ω≤1.5 G h fo ood s

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor included (Figure 3.40) (Figure obtained. included is effects tank surge and penstock with turbine hydraulic of the model complete nonlinear 3.58,the and F The overall water velocity U water velocity The overall 104 gate-servomotor. or electrohydraulic. mechanohydraulic are They turbines. gas and for steam used tothose similar are governors turbine hydraulic principle, In 3.8.4 Fortunately, only in long-term dynamic studies it is mandatory. it is studies long-term dynamic in only Fortunately, [21]. bands frequency preferred for system linear higher-order even and fourth-, third-, toa fitted may be tests response frequency test Alternatively, parameters. given with model theoretical the to applied fittings curve various through p.u. values. in ferential

load water speed at turbine, ω at turbine, speed water load The power differential is written as follows: written is differential power The

may be also adequate, especially in plants with long penstocks. with plants in especially adequate, also may be suffices. model second-order the but in general, considered be should effect hammer on, the Further not necessary. is sideration FIGURE 3.40 FIGURE ( s Notice that g that Notice 3.57 to Equations gate opening and head at turbine speed the ties 3.33 we that nowIf Equation add Figure 3.41. Figure in shown is control speed with system performance good classical of arather example An power alarger and servomotor valve apilot stages: have two they power levels, for large general, In For governor timing studies, as the surge tank natural period ( period natural tank surge the as studies, For governor timing used. tobe it of is when as arises question the involved, rather is complete model nonlinear the As model or more)high-order linear toa (three 3.40maybe reduced in Figure model The nonlinear Also Also For small signal stability studies linearization of the turbine penstock model (second-order model model) penstock turbine of the linearization studies stability signal For small considered. be should effect hammer the again, studies, stability transient In ) represents now the hydraulic turbine with wave (hammer) and surge tank effects considered. effects tank surge and wave (hammer) with turbine hydraulic now the ) represents & Francis

h Hydraulic Turbine Governors Turbine Hydraulic ∆G G 0 0 is the normalized turbine head, U head, turbine normalized the is

g Group, fL Nonl fL – g 1 and g and NL inear model of hydraulic turbine with hammer and surge tank effects. tank surge and hammer with turbine of hydraulic model inear LLC

NL Ac opening are the full-load and no-load actual gate openings in p.u. in openings gate actual no-load and full-load the are tu al gat % p to head at turbine h at turbine tohead Fs r is the shaft speed, P speed, shaft the is e () == x U h h t t t – - PU h + mt () 0 0 1 qF is the normalized water speed at turbine, U at turbine, speed water normalized the is = + pp + Fs t F(s) ratio is [2] is ratio 1 () h 1 t m () sZ is the shaft power, and m shaft the is in ´× + +× ta U p.u. t n hT U ta

() 0 n ep hT () sZ T ep U s ) is of the order of minutes, its con its order of minutes, of the ) is / NL s p x

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor (5.0 s),(5.0 Prime Movers Prime

maximum gate opening rate ≈ rate opening gate maximum stant (0.05stant s), T FIGURE 3.41 FIGURE A few remarks on model in Figure 3.41 are in order: 3.41 in are Figure in on model A few remarks of magnitudes. afeeling [2] data for getting sample only are given parenthesis in Numbers • • • • • • •

& reference sp related to water starting time constant T constant time starting towater related Acco where generator set T generator set For is The pre Stabl b Dead required. is motion slower even Wate response. more controllable and faster toprovide tend servomotors The pil requirements that determine the governor the settings. determine that requirements main the are variations load under robustness and quickness response acceptable and system) Francis R P is the permanent droop (0.04), droop R and permanent the is Turbine ω S (kg m J (kg 0 0 is the rated apparent power (VA) of the electrical generator power (VA) apparent rated the is electrical of the e operation during system islanding (stand-alone operation mode of the turbine—generator turbine—generator of the mode operation (stand-alone islanding system during e operation is the rated angular speed (rad/s) speed angular rated the is rding to Reference 2, toReference rding r is not very compressible, and thus the gate motion has to be gradual; near the full closure closure full the near gradual; to be has motion gate the thus and compressible, not very r is landing operation, the choice of temporary droop R droop of choice temporary the operation, landing – ω

ot valve servomotor (lower power stage of governor) may be mechanical or electric; electric electric or electric; of governor) (lower power stage servomotor mechanical may be ot valve and effects are considered in Figure 3.41, but their identification is not an easy task. easy an is not identification their 3.41, butin Figure considered are effects and r Group, GV sence of transient compensation droop is mandatory for stable operation. for stable mandatory is droop compensation of transient sence Typi Turbine is the main (gate) servomotor time constant (0.2 s), constant time (gate) servomotor main the is eed 2 sp shaft ) is the turbine/generator inertia turbine/generator the ) is eed cal (classical) governor for hydraulic turbines. T turbines. for hydraulic governor (classical) cal LLC M . Also the gain K gain the . Also 0.15 p.u./s, R 0.15 De adband TH R RT TT H M T TW RW 1+sT V R = =- == =- should be high. be should max max sT P 2 ë é ë é J 2 T R ser 01 05 10 01 10 50 23 w is the transient droop (0.4). droop transient the is S close Pilot valve .. .. R 1+sT 0 0 2 ; vomotor () wi is the maximum closing rate ≈ rate closing maximum the is s W 1 () () th and mechanical (inertia) time constant of the turbine/ of the constant time (inertia) mechanical and R PV max cl max - - Pe Tr os rmanent dr e ansient dr K . . V Min gat 5 û ù R T PV û ù max open max K W T T is the pilot valve with servomotor time con time servomotor with valve pilot the is T V W oo M and reset time T time reset and oo is the servo (total) gain (5), gain (total) servo the is p e

p 0 1/s Ma 1 0.15 p.u./s, T 0.15 x gat ser e vomotor 1+sT Ga R te is essential; they are are they essential; is 1 GV R is the reset time time reset the is openin R Valve max max ΔG G open 0 g (3. is the the is 105 59) - © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor 106 gen (constant) speed synchronous with plants Pump-storage near. seems deployment “industrial” their day. of the hours over the of loads variations of fast presence the in power systems electric improvement in vehicle stability and asafety It also is hours. consumption hydropower plants. storage pump- in especially pumps, as time work part that turbines fact in are machines hydraulic Reversible 3.8.5 think. [23,24]. ripe seems generator system whole turbine of the control on line digital hensive for compre time the generator excitation, electric the only serve usually that stabilizers power system (Figure 3.42). perspective anew into [22] control governor system methods the puts optimization powerful various and of networks) neural or artificial fuzzy-logic, structure, variable (adaptive, controllers motion ear nonlin high-performance of availability The involved. more becomes thus system The governing FIGURE 3.42 FIGURE As up to 400 MW/unit pump storage hydraulic turbine pumps have been already in operation [25], operation in already have been pumps turbine hydraulic MW/unit storage pump up to400 As energy electric off-peak during storage or for energy for irrigation either required may be Pumping Still, problems with safety could delay their aggressive deployment; not for a long time, though, we though, not for along time, deployment; aggressive their delay could safety problems with Still, on especially and movers prime thermal on tried havebeen controllers advanced such most Though • erators (motors) are a well-established technology. (motors)erators a well-established are

& co to has governor system the used, 3.41) (Figure also gates are wickets where turbines hydraulic In Francis

Reversible Machines Hydraulic ntrol their motion also, based on an optimization criterion. optimization on an based also, motion their ntrol

Group, Coo Guide vane St rdinated turbine governor–generator–exciter control system. control governor–generator–exciter turbine rdinated runner ate f LLC sign Reaction turbine a eed als ba ck U Blade runner govern φ or Control system Interface G Ex enerato ci te Y r r Z Synchronous Generators Synchronous Ca ba paci tter Infinite to y bus r - - © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor machine is started by the electric machine as motor to prepare for pumping. This transition takes time. takes transition This for motor pumping. toprepare as machine electric by the started is machine power plants. for tidal-wave adequate may be reversible. is of motion direction the when for turbining, performance the check then and for pumping machine the design to feasible also is it pumps; turbine existing in variations topological many are There

Prime Movers Prime

FIGURE 3.44 FIGURE 3.43 FIGURE The passing from turbine to pump mode implies the emptying of the turbine chamber before the before chamber turbine the of theemptying implies mode to pump turbine from passing The 3.43 inFigure pump turbine axial flow, of fluid the directions both in turbining and pumping With A classification of turbine-pumps is in order: is turbine-pumps of A classification b. a. c. &

By di By By d By By topBy Francis • • • • • •

Bid Uni Wit s With Axi Rad irection of motion of irection rection of fluid flow/operation of fluid mode rection ology

Group, irectional/operation mode (Figure 3.44) (Figure mode irectional/operation al (Annapolis) (Figure 3.44) (Figure (Annapolis) al directional/operation mode (Figure 3.43) (Figure mode directional/operation hout speed reversal for pumping for reversal speed hout ial–axial (Russel Dam) (Figure 3.43) (Figure Dam) (Russel ial–axial Rad Axi peed reversal for pumping (Figures 3.43 3.44) and (Figures for pumping reversal peed al turbine pump. turbine al ial–axial turbine/pump with reversible speed. reversible with turbine/pump ial–axial Wi LLC ga cke te t Q T U T U΄ Q P turbine ω T U U ΄ T P ω Q p pump Q ΄ T Spiral pipe 107 © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor ratio for speed would be ω be would for speed ratio typical A pumping. flow the volume in andlower larger is the head effect In one for turbining. the than much shorter. is mode topumping turbining from toswitch time the though turbining, generator rotor windings, through power electronics. through generator rotor windings, the power in control instantaneous through practiced is speed adjustable as used, is governor system 3.46). [25] (Figure general. in heads, 3.45. Figure in shown are turbine/pumps a radial–axial [16] for flowcharacteristics head/volume Typical side. machine electric on the control power electronics 108 FIGURE 3.46 FIGURE 3.45 FIGURE (a) In order to preserve high efficiency in pumping the speed in the pumping regime has to be larger larger be has to regime pumping the in speed the pumping in efficiency high order topreserve In and pumping for both rotation unidirectional tosecure required are topologies More complicated MW output by control gate wicket Only for pumping. typical are speeds higher and speed, with Power increases openings gate wicket for head various static outputpower versus the portray characteristics Similar higher and at turbining than speed higher is moreefficient at that pumping fact the illustrate They 300 200 & Francis 1 5 7 9 420 390 370 350

Group, T Typ Tur max rp m bine/pump system power/static head curves at various speeds: (a) turbining and (b) pumping. and (a) turbining speeds: atvarious curves head power/static system bine/pump ical characteristics pumping of radial–axial turbine +pumps. turbine of radial–axial pumping characteristics ical 0.9 0.8 y-wi 0.6 LLC He 0.7 cket ga Q turbining ad (m) y 0.5 = p

0.7 ≈ (1.12–1.18) ω te op 85 80 ening 90 1300 n 1100 85 900rp = h (P 335 rp 340 rp 350 rp 80 T U) . Evidently such a condition implies adjustable speed and thus thus and speed adjustable implies acondition such . Evidently n 1200rp = 0.4 m m m m 1.0 m 1300 (b ) 1500

Electric power input 1400 200 300 400 Q pumping(P MW 4 370 340 60 0.7 1.0 0.9 0.8 U) He 330 70 ad (m) Synchronous Generators Synchronous 0.7 0 430 400 80 85 340 0.6 P P max Efficienc 1 350 360 y (% 370 ) 390 rp 380 m © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor power (turbining) and for pumping [25]. for pumping and power (turbining) example, 3.49). overload (Figure inadmissible or mechanical toavoid governor control structural turbine Prime Movers Prime speed ( speed vibrations. structural toincreased subjected towers of moreexpensive the price At extraction. energy higher and flow tomore lead uniform diameter year. per wind from energy largest the of extracting sense Figure 3.48a. turbulent. considered maybe flows air wind general, In irregularities. terrain local variable. highly are speed and direction whose producewind earth of the surface the along gradients pressure Air 3.9 the quality of power delivered to the electrical power system. electrical tothe of power delivered quality the to improve used to be are storage on energy based solutions electric and occurs turbining and pumping between operation Discontinuing turbine/pump. generator/motor by the by the power delivered driven day. asingle in of motion direction other the in and of motion one direction in topumping ing FIGURE 3.47 FIGURE In tidal-wave turbine/pumps, to produce electricity, a special kind of transit takes place from turbin from place takes of transit kind aspecial toproduceelectricity, turbine/pumps, tidal-wave In electric forgenerating specific rather are schemes control machine andelectric governor turbine The For a given site, the wind is characterized by the so-called speed deviation (in p.u. year). per For deviation speed so-called by the characterized is wind the site, For agiven With constant energy conversion ratio, the turbine power increases approximately with cubic wind wind cubic with approximately power increases turbine the conversion ratio, energy constant With height/turbine higher with Designs more uniform. becomes and height with increases speed Wind the in turbine, wind the of directioning the optimum to as it leads information important an is This in as shown maybe directions cardinal the along speed wind of variation location, aspecific In of size and ground, the above height on location, dependent are wind of the strength and Uniformity These large changes in head are expected to produce large electric power oscillations in the electric electric the in power oscillations electric large to produce expected are in head changes large These 3.47). (Figure sign and reverses from 0% to 100% changes head static The &

Francis Wind Turbines Wind u 3 ) up to a design limit, u limit, ) up toadesign

Group, 10 12 Head 2 4 6 8 /time of the day in a tidal-wave turbine/pump. atidal-wave in day of the /time LLC (Flux) Turbine max 61 . Above u Above . max t ( ma t P x (Hours) rated 21 = Pump e ) the power of the turbine is kept constant by some constant kept is turbine power of the ) the - U 4

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor quency curve experiences a maximum, in general. The average speed U speed The average general. in amaximum, experiences curve quency The spe The 110 f: curve speed/frequency called is curve this slope of The Othe

FIGURE 3.49 FIGURE 3.48 FIGURE We (a) South st & r mean speed definitions are also used. also are definitions speed r mean Francis ed/duration is monotonous (as speed increases its time occurrence decreases), but the speed/fre but the decreases), occurrence time its monotonous is increases (ased/duration speed

Group, Wind tu Wind Wind sp Wind LLC Ti rbine power vs. wind speed. wind vs. power rbine eed vs. (a) location and (b) height. (a) and vs. eed location me Power P rated (c U ut in) min U Ea rated fU UU st () Nor av e P th = =- ≈ ò ¥ 0 Cu dt fU (b 3 () () dU ) Height (c t ma dU ut out) u max x

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor speed in such locations. such in speed variable at to capable operate be to has generator electric The range. speed over apertinent turbine wind time. in variations tohave tend smaller sea the from winds day, over the while month, of speed variations by large characterized are sites inland general,

Prime Movers Prime the maximum energy per unit speed range E range speed unit per energy maximum the forth. The best locations are situated either in the mountains or by the sea or by the ocean shore ocean the (oroffshore). or by sea the or by the mountains in either are situated locations best The forth. so and Portugal, Greece, Denmark, Holland, like countries in operated have been mills wind For centuries, 3.9.1

where FIGURE 3.50 FIGURE There are constant speed and variable speed wind turbines. wind speed variable and speed constant are There of the operation 3.50 implies Figure in as span speed large over arather of energy extraction Good In on location. heavily depend approximations, or their curves, these that mind in kept be It should 3.50. inFigure is apparent extraction for zone energy efficient speed adequate the addition, In The energy content of the wind E wind contentthe of energy The Wind turbines are characterized by the following: by the characterized are turbines Wind The time average speed falls below the frequency/speed maximum f maximum frequency/speed the below falls speed average time The • • • • •

& E

Rate Tip speed ratio: Tip speed Rotor s to Shaft Mech Francis Principles and Efficiency of Wind Turbines ofWind Efficiency and Principles ( u ) =u d wind speed U speed d wind anical power P(W) anical

peed n(rpm)peed or ω Group, rque m) (N 3 Samp f ( u ), the energy available at speed u at speed available energy ), the le time/speed frequency/speed ( frequency/speed le time/speed LLC E(U)(PU f (U)(P t/ max R U) 1 2 ) r (rad/s) l = Energy , during t , during w r× rr × U 0.5 () D disc during Be max 2r max f st ener (U) area = . (1 year) is then obtained from the integral: the from obtained (1 year) then is f ) and energy E/speed. energy ) and otor t . Figure 3.50 illustrates this line of thinking. line this 3.50 illustrates . Figure t/ ma gy U max ave x extractionzone wind blad = 1 ò ¥ 0 uf et speed 3 ip () ud E(U) speed u

max

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor Three or two blades are typical for rapid axial wind turbines. wind axial rapid for typical are two blades or Three two subtypes: drag type and lift type. The axial (horizontal axis) wind turbines are all of lift lift subtype. all of are turbines wind axis) (horizontal axial The type. lift and type drag subtypes: two (design conditions): P In general, C general, In turbines self-start at higher speed (above 5 m/s wind speed) but, for an optimum tip speed ratio λ ratio speed tip optimum for (abovebut, an speed) speed 5m/s wind at higher self-start turbines they have maximum power coefficient C power coefficient have maximum they > 1 for high-speed wind turbines. wind λ>1for high-speed and turbines λ<1for wind slow-speed ratio tipspeed The 112 their maximum power coefficient C power coefficient maximum their

around 1.5 U 1.5 around

A The axial wind turbines may be slow (Figure 3.51a) and rapid (Figure 3.51b). rapidand (Figure 3.51a)slowmaybe (Figure turbines wind axial The FIGURE 3.51 FIGURE (a) Rotor blad clas In general, the optimum tip speed ratio λ ratio speed tip optimum the general, In The rotor diameter D diameter The rotor Figure 3.52. in Figure shown are configurations turbine wind tangential ofSome the are of They configurations. a few in quite built havebeen turbines shaft—wind Tangential—vertical For each location, the average wind speed U speed wind average the location, For each The slow axial wind turbines have a good starting torque and the optimum tip speed ratio λ ratio tipspeed the optimum and torque starting have a good turbines wind axial slow The configurations. two the different for are quite number their and the rotor blades of shape The • • •

& U foundation Concrete sification of wind turbines is thus in order: thus is turbines wind of sification The pow The Tang Axia Francis wi nd l (with horizontal shaft) horizontal (with l ential (with vertical shaft) vertical (with ential e

ave p Group, is a single maximum function of function maximum a single is Axia er efficiency coefficient C coefficient efficiency er . l wind turbines: (a) (b) (propeller). rapid and (multiblade) slow turbines: l wind LLC rated ( r , λ λ , may be, to a first approximation, calculated from Equation Equation 3.65 fromrated for calculated approximation, toafirst , may be, opt opt , Z , C 1 Nacelle wi ) = (1, 8–24; 2, 6–12; 3, 3–6; 4, 2–4; 5, 2–3; 2–4; 4, >5, 3,) =(1, 3–6; 2) 8–24; 6–12; 2, popt and transmission , U p max Tower Ta R with the turbine speed from Equation 3.64. Equation from speed turbine the with ( p λ il th generator p : opt max C ) is moderate ( moderate ) is p opt 0.4. That is, a higher energy conversion ratio conversion ratio (efficiency). energy higher ≈0.4. a is, That = increases as the number of rotor blades Z of rotor blades number the as increases rp ave DU that strongly depends on the type of the turbine. turbine. of the type on the depends strongly λ that 8 is known. The design wind speed U speed wind design The known. is r P 23 × (b ) U C <> wi p nd max 1

0.3). In contrast, high speed axial wind wind axial speed high ≈ 0.3). contrast, In Nacelle Synchronous Generators Synchronous

ω 1 decreases: r R is in general general in is opt

Rotor ≈ 1, but opt (3.6 (3.6

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor differential takes place. takes differential 3.53). (Figure turbine the after and before profile wind turbines have a higher self-starting torque but a lower power efficiency coefficient C coefficient torque but alower power efficiency self-starting have ahigher turbines wind Prime Movers Prime FIGURE 3.53 FIGURE 3.52 FIGURE (a) The wind speed decreases immediately before and after the turbine disk plane while also a pressure a also pressure while plane disk turbine the after and before immediately decreases speed wind The andpressure speed wind ideal the portraying by calculated limit) be may (Betz limit efficiency The While drag subtype works at slow speeds ( at slow speeds works subtype drag While & Francis A 1

Group, (a) Drag type Bas Tan Wind ic wind turbine speed and pressure variation. pressure and speed turbine ic wind U gential—vertical axis—wind turbines: (a) drag subtype and (b) lift subtype. (b) lift and (a) subtype drag turbines: axis—wind gential—vertical 1 LLC λ opt (b) Lift type ω Wind 0.9–1.0 = r F U D A λ opt A u < 1) the lift subtype works at high speeds ( speeds high at works subtype <1) lift the ∞ ∞ Shielded paddle wheel Darrius types (b ) Wind U Pressure 1 Giromill λ opt Sp 0.2–0.6 = eed Drag-cup u p max λ opt . >1). Slow u 113 ∞ © 2016

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor tion velocity r velocity tion

The effici The

with Let us a us Let 114 dynamic properties are given as functions of local radius from the hub. the from radius of local functions as given are properties dynamic andaero mechanical, geometrical, whose sections of into a number divided is The blade (BEM) model. element the blade momentum through usually out carried is turbines wind of behavior steady-state The 3.9.2 If the s the If With

The maximum ideal efficiency is obtained for∂η obtained is efficiency ideal maximum The This ideal maximum efficiency is known as the Betz limit Betz [26]. the as known is efficiency maximum ideal This The pow The The wind power P wind The The continuity principle shows that shows principle continuity The The local attack angle αis angle attack The local The local relative velocity U velocity relative local The 3.54. Figure in shown is blade element of the airfoil cross-sectional the radius local At the The induced velocities induced velocities (− The & Equation 3.61, η Equation

Francis peed decreases along the direction of the wind speed, u speed, wind of the direction the along decreases peed Steady-State Model of Wind Turbines ModelofWind Steady-State ssume: ency limit, η limit, ency er extracted from the wind, P wind, the from extracted er Group, ω r (1 +a LLC wind ideal ′ ideal ) at the rotor plane. ) at the in front of the wind turbine is the product of mass flow to speed squared per 2: per squared flowspeed to of mass product the is turbine wind of front the in becomes: , is aU rel UU and a and ( r »= ) is obtained by superimposing the axial velocity U velocity axial the by superimposing obtained ) is h id ea 1 ′ -D PU r l wind ω U h == PU r ¥ i ) are produced by the vortex system of the machine. of the system vortex by the produced ) are turbine turbine P / =- 2 P =× turbine ;; wind ta è ç æ rr 1 n UU is =- uA f ¥¥ 11 11 α =ϕ r Y AU = 2 i / () ∂Ψ ra 12 ø ÷ ö A = 2 1 Ua w ë é 1 uA 11 è ç æ r −θ ×= =0at Ψ () -D ¥¥ UU () -- () 1 r 1 22 12 2 - () 1 22 UA +

¢ 2 1 r () Y UU AU

opt ¥ AU 1 22 1 2 Y >u ø ÷ ö =2/3 ( û ù - 1 3

= 1 3 ∞

¥ D and thus A thus and U U U

1 ¥ ∞

/ U 1 = 1/3) with η =1/3) with Synchronous Generators Synchronous 1

by Downloaded By: 10.3.98.104 At: 10:14 23 Sep 2021; For: 9781498723558, chapter3, 10.1201/b19310-4 Taylor

where θ θ is pitch blade The local Prime Movers Prime where

FIGURE 3.54 FIGURE The lift and drag forces F forces drag and lift The The lift F force lift The pitch angle global the β is angle twist blade local the τ is C section blade chord of the local the C is L & and C and Francis D are lift and drag coefficients, respectively, known for a given blade section [26,27] blade a given for known respectively, coefficients, drag and lift are

Group, Blad lift is rectangular toU rectangular is e element with pertinent speed and forces. and speed pertinent with e element LLC Φ rω U—Undistur U xy lift rel r Rotorplan – F –T and F and —L θ lift angential velo oc FU li rω F al velo ft α C drag T =× r Φ 1+ (1 be rel may be written as follows: as written may be 2 1 d winds , while the drag force F drag the , while rr city a΄) FU drag re city ofbladesection lL y =× U CC F peed N rel 1– U(1 2 1 =τ+β ×= (r) r ;. a) re F lD drag CC

× 1 225

drag kg/m is parallel toit. parallel is 3