A MODEL OF COGENERATION PLANTS BASED ON SMALL-SIZE GAS TURBINES THE MODEL

Transcription

1 A MODEL OF COGENERAION PLANS BASED ON SMALL-SIZE GAS URBINES S. Banetta, M. Iolito*, D. Poli, A. Possenti University o Pisa, Italy. * University o Palermo, Italy A dynamic mathematical model o a generic cogeneration lant ith microturbine is described and the corresonding regulating system is realized. he chie aim o this model is the evaluation o the services such a system is able to rovide to an interconnected electric netork, both in normal oeration and in case o ide erturbations, or to an islanded grid ater the searation rom the main netork. MICROURBINES FOR DIFFUSED COGENERAION he electricity market liberalization is sulying ne imulses to the cometition beteen generation systems. Small disersed generation in arallel to the main grid can reresent a very interesting solution that reduces oer los and losses on the lines and contributes to the local voltage regulation. On the other hand, these small lants have a cometitive eiciency esecially hen associated ith thermal energy roduction (cogeneration. his is the case, or examle, o densely-oulated areas here electricity reuest is locally associated ith heat demand, both or inter heating and or summer conditioning, also considering that heat roduction must necessary be local. In articular, the choice o microturbines or disersed cogeneration is justiied by lo installation and maintenance costs, recent imrovements in electric eiciency (u to 30%, high lexibility as regards the oer sharing beteen thermal side and electrical one; that essentially means a ayback time reduced to 3-4 years both in case o industrial and aggregated tertiary load. he articiation to the reuency regulation in case o large erturbation occurred on the main grid, as ell as the ability to oerate in a searated netork and eventually to restart the main grid in case o its black out, could be very imortant ancillary services. In order to analyze the real ossibilities o roviding these services, or hich the dynamic oint o vie and the running lexibility are undamental, a hysical model has been develoed ith Simulink, in order to deine the general eatures o these systems, identiying their main limitations and erormances. HE PROCESS he lant resents a gas microturbine and a high reuency synchronous machine, connected to the electric grid by a rectiier-inverter system. At the exit o the turbine, a byass modulation valve allos the sharing o gas beteen an air-gas recuerator (to increase the electric oer and a boiler, hich eeds a thermal user. HE MODEL he described model is non-linear, because o the adiabatic comression-exansion la or erect gases into the turbine and the comressor, and evaluates the steady state and dynamic behavior o each comonent, ithout geometric details, simly resecting general hysical las. he realization eculiarities are transerred to the values o the heat exchange coeicients and to the luid-dynamic resistances; the generality o this aroach allos the use o this model also ith lants having very dierent hysical eatures and sizes and in very irregular oerating situations or a model, like an out-o-service or a start u. RESULS OF SIMULAIONS he steady state simulations carried out ith the model sho that the current technology makes this kind o lants suitable or disersed cogeneration hen the electric/thermal oer ratio is in the -5 range. he dynamic simulations demonstrate the very romt resonse o the mechanical oer rovided at the shat, obtained by modulating the uel lo, so ste variations o the reuired electric oer are alloed ithout unaccetable erturbations to the main oerating variables. CONCLUSIONS he described model allos the valuation o the solutions oered by co-generation systems ith microturbines, in order to identiy hich roblems can aect this kind o lants and design the regulating and rotection system. he simulations carried out ith this model sho that the roblem concerning the suly o heat to the local users can be temorarily searated rom the uick and large electric oer variations reuired to suort the main grid in case o imortant erturbations, or the local islanded grid in case o large out-o-services ith searation rom the main netork; thanks to the current technology, these oer demands can be met ithout exceeding the limitations osed by the constructor as regards to the rotation seed and the gas temeratures. hese considerations, together ith the uick start o turbines and the romt oer and voltage modulation alloed by inverters, make systems ith microturbine very useul to contribute to the dierent needs o an electric grid.

2 A MODEL OF COGENERAION PLANS BASED ON SMALL-SIZE GAS URBINES S. Banetta, M. Iolito*, D. Poli, A. Possenti University o Pisa, Italy. * University o Palermo, Italy ABSRAC In the olloing a dynamic mathematical model o a generic cogeneration lant ith microturbine is described and the corresonding regulating system is realized. he chie aim o this model is the evaluation o the services such a system is able to rovide to an interconnected electric netork, both in normal oeration and in case o ide erturbations, or to an islanded grid in conseuence o the searation rom the main netork. he design o the regulating system takes into account the maximum accetable oer variations, in observance o the limitations the constructor has imosed to the rocess variables and resecting the reuirements o the local thermal loads; the result is a uick and robust regulation, even in case o internal ailures. INRODUCION he electricity market liberalization is sulying ne imulses to the cometition beteen generation systems. In this context small disersed generation in arallel to the main grid can reresent a very interesting solution that reduces oer los and losses on the lines and contributes to the local voltage regulation. On the other hand, these small lants have a cometitive eiciency esecially hen associated ith thermal energy roduction (cogeneration. his is the case, or examle, o densely-oulated areas here electricity reuest is locally associated ith heat demand, both or inter heating and or summer conditioning, also considering that heat roduction must necessary be local. In articular, the choice o microturbines or disersed cogeneration is justiied by lo installation and maintenance costs, recent imrovements in electric eiciency (u to 30%, high lexibility as regards the oer sharing beteen thermal side and electrical one; that essentially means a ayback time reduced to 3-4 years both in case o industrial and aggregated tertiary load. he emloy o clusters o turbines could reresent another interesting develoment, since in case o islanded oeration the use o a single turbine is oten not accetable. Besides the above mentioned advantages rovided by disersed generation to the system management in case o arallel oeration, the articiation to the reuency regulation in case o large erturbation occurred on the main grid, as ell as the ability to oerate in a searated netork and eventually to restart the main grid in case o its black out, could be very imortant ancillary services. In order to analyze the real ossibilities o roviding these services, or hich the dynamic oint o vie and the running lexibility are undamental, the olloing model has been develoed, not in order to simulate the behavior o a articular lant, but to deine the general eatures o these systems, identiying their main limitations and erormances. HE PROCESS he scheme o the lant is shon in Fig.1. Control Signals Fuel Air B urbo Alternator M Exhaust gas Recuerator Byass-Flo Modulation Valve SM high reuency R Cogeneration Microturbine B: Burner M: Mixer SM: Permanent-magnet Synchr. Machine R: Rectiier I: orced-commutated inverter Electric Poer Conditioner I hermal Load From other microturbines or boilers (Electricity Distributor Electric Load From other microturbines Figure 1 Scheme o the analyzed rocess Such a system, ith a 45 kwe microturbine, is going to be installed at the University o Pisa by the Deartment o Electrical Systems and Automation and the Deartment o Aerosace Engineering, in order to artially meet the electric and thermal load o the Faculty o Engineering; this lant ill be emloyed also or the identiication tests o the model and or the erormance veriies. HE MODEL A dee model, based on energy and mass balances and on general oerating rinciles o comressors and gas turbines, has been develoed ith Simulink; the obtained results are thereore ualitatively valid also or lants ith very dierent characteristics and sizes. In acts hysical models, even though to the detriment o the recision o the results, have a larger validity than the behavioral ones ( shados models, hich are more emloyed by the constructors and derive rom the exerimental oututs obtained as anser to tyical inuts. he model is non-linear, because o the adiabatic

3 comression-exansion la or erect gases into the turbine and the comressor, and evaluates the steady state and dynamic behavior o each comonent, ithout geometric details, simly resecting general hysical las. he realization eculiarities are transerred to the values o the heat exchange coeicients and to the luiddynamic resistances; the generality o this aroach allos the use o this model also ith lants having very dierent hysical eatures and sizes and in very irregular oerating situations or a model, like an out-oservice or a start u. o dierent versions o the model are available: the irst emloys the exact deendences o the thermodynamic arameters (the seciic heats and the exchange coeicients rom temeratures and los, hose variability comes into lay in the case o large erturbations, like start rams, big oer changes or eighty oenings o the gas byass valve. he second version eects drastic simliications, assuming those arameters to be constant; the conseuent mathematical model, reorted as aendix, is very simliied and, although its validity is limited to the small variations, it turn out very useul to understand the hysical henomena, to analyze the steady state stability o the regulated system and or the on-line comensation o noises. Inuts As shon in Fig., the model resents the olloing inuts: the reuested (and rovided electric oer the uel lo the osition o the byass valve in the recuerator the temerature and the lo o ater at boiler entrance the temerature o external air. Reuested electric oer Fuel lo Byass valve osition Water lo Cold ater temerature External air temerature Read this (double click to me Cogeneration Plant Model Pt urbine oer Exhausted gas lo i em.at turbine exit m em.at mixer exit Rc Boiler eiciency h Hot ater temerature ex Gas temerature at boiler exit Ren otal eiciency Rotation seed ci Comressed air temerature cu Heated air temerature P hermal oer u Gas temerature at recuerator exit g Gas temerature at turbine entrance Pc Comressor oer Figure Initial age o the Simulink model Among these inuts, only the olloing can be maniulated: the uel lo (methane or oil, by means o a regulation servo-valve; the byass valve, that shares the available heat beteen the to loads: the mechanical one at the rotor o the comressor-turbine-alternator unit, and the thermal one o the boiler or the ater heating. he other inuts are so considered like noises; the most imortant, as or amlitude and seed o action, are the reuested electric oer and the ater lo to be heated. Oututs he model resents a lot o measurable oututs, some o an electromechanical nature (or examle the seed o the rotor and the sulied electric energy, others o thermal kind (the air and gas los, the comression ratio and the temeratures o gas. It s orth mentioning that the temerature o the gas delivered by the combustion chamber, both or its high value and the lack o sace or the measurement, can t be hysically taken, but the model can on line estimate it. Its value reresents the main constraint restricting the outut oers, considering his eects on the lietime o blades. he controlled variables, or hich a set-oint is imosed, are the olloing: the rotation seed o the shat, rom hich a lot o system erormances deend (irst o all the air-gas lo and the mentioned gas temerature. hanks to the converter, the rotation seed is not constrained to the electric reuency, so it can vary as one likes; in articular, it can be maintained as close as ossible to the value corresonding to the maximum system eiciency (hich in its turn deends on the reuired electric oer, on condition that the combusted gas temerature does not exceed the limit imosed by the constructor; the temerature o the ater rovided to the boiler, that must vary as little as ossible in comarison ith the reuired value, to avoid big noises to the thermal users. he other oututs are on-line available to veriy the values o variables on hich constructive, security or running constraints are ixed. Steady state erormances he model allos the simulation o the lant in a large range o steady state conditions (or examle varying the thermal/electric oer ratio by means o the byass valve laced in the recuerator, or the reuested electric oer, in order to analyze the values o the main internal variables (like the temeratures along the airgas ath and deduce oerational criteria hich allo the resect o the technical limits. Dynamic erormances he model simulates the dynamic behavior o the system, due to: the store o mechanic energy in the comressorturbine-alternator unit: because o its lo inertia, the rotation seed is very sensitive to imbalances beteen

4 the driving torue rovided by the turbine and the resistant torue o comressor and alternator 1 ; the store o air into the volume o the recuerator, air side; the store o heat into the metals o recuerator; the store o heat into the metals and the ater contained in the boiler. Moreover the time reuired or the uel combustion (ractions o a second is considered; this time is very shorter than the other thermal time constants, but it s signiicant to analyze the resonse o the lant in case o large and ast variations o the reuired electric oer in islanded oeration. For this urose, tests ith rotation seed regulated by means o the uel lo are generally useul. he model use concentrated arameters, so it s adeuate to describe the system behavior only at lo reuencies (corresonding to time constants o some seconds and more, useul to investigate the regulation systems and the main mechanical and thermal henomena. he model is on the contrary inadeuate to analyze ast henomena like high reuency electric transients; thanks to the very uick resonse o the inverter, the electric art has been alays assumed in steady state, i.e. the rovided oer coincides ith the reuested one, ithout taking into account the corresonding dynamic. HE REGULAING SYSEM he rocess resents variable arameters and a strong interaction among its comonents; the regulating system is multivariable, ith to inuts and to oututs; or its design the rincile o non-interaction could be used, so to avoid that reuests o thermal oer inluence the mechanical one and then the shat seed and vice versa. he to regulating systems have nevertheless very dierent reuirements. he regulation o the ater temerature has e constraints, thanks to the thermal caacity o the boiler and to the big store reresented by the distribution lants o hot ater and heating, in comarison ith the accetable luctuations o the hot ater temerature; or examle, in case o urbane users this temerature can amly vary, u to a temorary interrution o its suly in extreme cases during critical contingencies, on condition that his average value kees right on a long term basis. On the contrary, the regulation o the rotor seed has very stricter constraints. 1 he rotation seed is the variable interacting ith nearly all the others in the system, because it establishes the lo o comressed air, hich in its turn inluences the turbine gas inlet temerature, thence the temeratures at recuerator and boiler. For examle, an increase in uel lo imlies initially the groth o temeratures and thereore o the oer delivered by the turbine; but the conseuent rise o the rotation seed increases the air and gas lo, so that the outut temeratures o the combustion chamber and o the turbine go don to a loer value than the initial one. hereore a reuency searation beteen the to regulation systems is ossible: a uick control is carried out on the rotation seed by means o the uel lo, hile a sloer control system (o an integral nature controls the temerature o the hot ater by acting on the byass valve. o avoid excessive values o the gas temerature at the combustion chamber exit, in the big gas turbines the air lo is artialized by means o IGV valves; likeise, in the case o microturbines the same result is obtained by varying the set oint o rotation seed and the osition o the byass valve. hen the regulating scheme assumes the tyical cascade rameork: to external loos or the limitation o the mentioned gas temerature, lus an internal one that acts on the uel lo or the seed regulation. When the limit temerature is exceeded, the irst external loo modiies ith a dynamic unction the otimal value o the seed set oint (rogrammed or the maximum eiciency, hile the second loo transitorily acts on the osition o the byass valve (hose steady state value is controlled by the regulator o the hot ater temerature. Because o the slo action o these regulations, a ast limiting device, that romtly acts on the uel lo in case o a dangerous exceeding o the above mentioned limit temerature, is installed. his scheme assures a sae behavior against ailures or unexected restrictions o the uel suly, using the stores o the system u to the limit alloed by the erormance o the machinery. o avoid that large variations o the reuired electric oer can generate excessive seed variations o the shat or unaccetable unbalances o electrical vs thermal oer demand, a load demand rogrammer is also suerimosed, ith oen chain restrictions to the admitted range o variations. SIMULAIONS AND RESULS he steady state simulations carried out ith the model conirm that the current technology makes this kind o lants suitable or disersed cogeneration hen the electric/thermal oer ratio, hose modulation is alloed by the byass valve, is in the -5 range, as already declared by the microturbines constructors (1. hese values seem to be comatible (4 ith the reuirements o our main categories o users: industrial loads ith discontinuous running; industrial loads ith continuous running; tertiary inter loads; tertiary summer loads (assuming the use o chiller systems or the air conditioning. As examle o the dynamic simulations the model allos, in Fig. 3 the resonses to a +10% ste variation o the reuested electric oer (rom 45 to 50 kw are shon. his simulation demonstrates the very romt resonse o the mechanical oer rovided at the shat, obtained by modulating the uel lo, so ste variations o the reuired electric oer are alloed ithout unaccetable erturbations to the main oerating variables.

5 Fuel lo (kg/s x ime (sec Fig 3a Resonse o uel lo to a +10% ste o the reuested electric oer Rotation seed (krm ime (sec Fig 3b Resonse o rotation seed to a +10% ste o the reuested electric oer urbine and comressor oer (kcal/s ime (sec Fig 3c Resonse o turbine oer (Pt and comressor oer (Pc to a +10% ste o the reuested el. oer emeratures ( C ime (sec Pt Pc ggas temerature in turbine igas temerature at turbine exit mgas temerature at mixer exit Fig 3d Resonse o gas temeratures to a +10% ste o the reuested electric oer In this examle, a 10% variation o the electric oer, ith the corresonding modiications o uel lo (ithout overiring and rotation seed set oint, entails a luctuation o the gas temerature at turbine exit (the most restricting oint ithin 5%. CONCLUSIONS In another aer (5, the useulness o emloying also diused microgeneration to suly the ancillary services, hich the electric system needs to oerate according to uality and security reuirements, is discussed; some o these services involve imortant variations o the rovided active oer, e.g. rimary reuency regulation ith erturbed or islanded interconnected grid, caability to load rejection and black start. he described model allos the valuation o the solutions oered by co-generation systems ith microturbines, in order to identiy hich roblems can aect this kind o lants and design the regulating and rotection system. he simulations carried out ith this model sho that the roblem concerning the suly o heat to the local users can be temorarily searated rom the uick and large electric oer variations reuired to suort the main grid in case o imortant erturbations, or the local islanded grid in case o large out-o-services ith searation rom the main netork; thanks to the current technology, these oer demands can be met ithout exceeding the limitations osed by the constructor as regards to the rotation seed and the gas temeratures. hese considerations, together ith the uick start o turbines and the romt oer and voltage modulation alloed by inverters, make systems ith microturbine very useul to contribute to the dierent needs o an electric grid. Reerences 1. Boman Poer Systems Ltd, echnical documentation or cogeneration microturbines, Ocean Quan, Belvidere Road, Southamton SO14 5QY UK.. S. Barsali, M. Ceraolo, R. Giglioli, P. Pelacchi: Microturbines or disersed generation, CIRED 1999 Nice, June S. Barsali, M. Ceraolo, R. Giglioli, P. Pelacchi: Distributed Cogeneration: ne ossibilities and challenges EPEM, Nales, Cari 1-18 May S. Barsali, G. Celli, M. Ceraolo, R. Giglioli, P. Pelacchi, F.Pilo, Distribution grids containing diuse generation, CIRED 001, Amsterdam, June S.L.Dixon, Fluid mechanics, thermodinamics o turbomachinery, Pergamon Press, London A.De Marco, M.J.Whitmarsh-Everiss, he steady state and dynamic modelling o oen cycle and combined cycle gas turbine lants, CIGRE Meeting, Sydney 1993.

6 Comressor Inuts: exit ressure P sc [bar] rotation seed ω [krm] external air temerature a [ C] external air ressure P a [bar] Oututs: comressed air lo c [kg/s] comressed air temerature ci [ C] mechanical oer P c [kcal/s] here: c a 0 Φ 0 1 r c ρ n Φ ϖ ( r P / P Aendix: he mathematical model Mixer Inuts: Oututs: m exit gas lo t [kg/s] reduced gas lo r [kg/s] recuerator exit gas temerature u [ C] turbine exit gas temerature i [ C] mixed gas temerature m [ C] u t + i ( t Φ (characteristic lo number (* urbine c sc a (comression ratio Inuts: combusted gas temerature g [ C] gas lo [kg/s] (1 1/ γ ci a { 1+ ζ [ rc 1] }, here: Oututs: ressure at turbine entrance P sc [bar] γ c / c v, ζ ζ ( exit gas lo t [kg/s] 0 rc (eiciency -1 (* exit gas temerature i [ C] mechanical oer P t [kcal/s] Pc c ( ci a δρ dpsc V t δpsc Combustor Inuts: comressed air lo c [kg/s] Psc t Kt, 1 Pa uel lo cb [kg/s] 1 + i g heated air temerature cu [ C] g ζ Psc Oututs: gas lo [kg/s] combusted gas temerature g [ C] Pt t ( g i a + cb, c u + cb cb + cb ci g Boiler c Inuts: ater lo [kg/s] entry ater temerature [ C] Recuerator exit gas lo t [kg/s] Inuts: mixed gas temerature m [ C] Oututs: gas byass valve oening K by (.u. exit gas lo t [kg/s] comressed air temerature ci [ C] turbine exit gas temerature i [ C] reduced gas lo r [kg/s] heated air temerature cu [ C] exit gas temerature u [ C] average metal temerature m [ C] gas to metal heat lo Q [kcal/s] metal to air heat lo Q c [kcal/s] r t ( 1 Kby, dm Q Qc M m m i + u Q ( i u S m Γ m ( m Qc c c ( cu ci ci + cu Scm Γcm ( m Oututs: t exhausted gas temerature ex [ C] heated ater temerature h [ C] thermal oer P [kcal/s] t ( u ex r 1 1/ γ, c 1 γ c dm Q + ( h ( M + M m m Q c c Q m + ex S Γ ( m, m + h Comressor-turbine shat Inuts: mechanical oer o turbine P t [kcal/s] mechanical oer o comressor P c [kcal/s] reuested electric oer P e [kw] Oututs: rotation seed ω [krm] ( Pt Pc Pe dϖ Ca J, C a C 0 + C1 ϖ A ϖ ϖ v Parameters ρ a cold air density n 0 comressor dimension Φ 0 comressor base lo number ζ 0 1/comressor base eiciency c, c v air seciic heats ci uel inerior caloriic oer c cb uel seciic heat c, c v gas seciic heats V recuerator volume, air side δρ/δ deendence o gas density rom ressure ( cost K t turbine euivalent admittance (Stodola coe. η 0 turbine base eiciency S m, S am exchange suraces o recuerator (gas and air side Γ m, Γ am exchange coe. o recuerator M r, c r mass and seciic heat o metal in recuerator S boiler exchange surace (gas side Γ boiler exchange coe. M m, c m mass and seciic heat o metal in boiler M, c mass and seciic heat o ater in boiler C 0, C 1 riction actor at shat A kw/(kcal/s J inertia o comressor-turbine-alternator unit (* 1(r c and (r c ill be deined by means o exerimental tests; at resent their value has been assumed 1.