Transient Modeling of Single-Pressure Combined Cycle Power Plant Exposed to Load Reduction

Transcription

1 International Journal of Modelg and Optimization, Vol. 2, No. 1, February 2012 Transient Modelg of Sgle-Pressure Combed Cycle Poer Plant Exposed to Load Reduction Keyvan Daneshvar, Ali Behbahani-nia, Yasam Khazraii, and Azam Ghaedi Abstract Gas/steam combed-cycle is a ell-knon technology for poer generation due to its numerous advantages cludg high efficiency and lo environmental emission. The purpose of this paper as vestigation of thermodynamic parameters' behavior of sgle-pressure system due to load reduction of gas turbe. In this study, dynamic simulation is performed to analyze the transient behavior of a combed-cycle poer plant. This simulation as done usg mass and energy conservation equations for each component as a control volume. Governg equations set as solved by forard fite difference method and the results ere illustrated by some figures. For validation of this transient modelg, the bottomg cycle parameters values at the end of transient operation ere compared ith the numerical put of the ell-knon commercial softare Thermo flo steady state mode that acceptable adaption have been seen. Index Terms Combed-cycle poer plant, dynamic modelg, transient behavior, heat recovery steam generator (HRSG) I. INTRODUCTION As the electricity consumption has risen quickly over the past fe decades, the number of thermal poer plants has creased orldide. A heat recovery steam generator (HRSG) produces steam by usg the heat from exhaust gas of the gas turbe and feeds it to steam turbe. This combation produces electricity more efficiently than either the gas turbe or steam turbe alone hich causes a very good ratio of transformed electrical poer per CO 2 emission. The combed cycle poer plants are characterized as the 21 st century poer generation by their high efficiency and possibility to operate on different load conditions by reason of variation consumer load [1]. They are particularly suitable for managg peak and cyclic loads, i.e., daily start/stop operations, sce their response characteristics are better than those of other conventional poer plants such as fossil fuel and nuclear poer plants [2]. An creasgly important utilization for the combedcycle poer plants is the compensation of varyg electricity feed- from reneable energy source like d poer. A combation beteen d poer and other energy sources such as combed cycles ith improved load flexibility should be used order to mitigate the economic effects of d variability [1]. Manuscript received December 20, 2011; revised February 23, K. Daneshvar is ith Shahrood Branch, Islamic Azad University, Shahrood, Iran ( keivandaneshvar@gmail.com). A. Behbahani-nia is ith Khaje Nasir University of Technology, Tehran, Iran ( alibehbahania@kntu.ac.ir). Y. Khazraii and A. Ghaedi are ith Bandar Lengeh Branch, Islamic Azad University, Bandar Lengeh, Iran ( yasamkhazraii@yahoo.com; azam_ghaedi@yahoo.com). A poer plant is basically operated on its design conditions. Hoever, it also operates on the so called off-design conditions due to the variation a poer load, process requirement or operatg mode. Therefore, the transient behavior of the system should be ell-knon for the safe operation and reliable control [3]. So these parameters may be used for estimatg thermal and mechanical stresses hich are important HRSG design and operation [4]. Until no various authors studied field of combed cycle poer plants that some of them vestigate simulation and dynamic behavior of these poer plants: Ahlualia and his coorker [5] discusses the dynamic modelg of a gas-fired 60M combed cycle poer plant; Kim TS [2] simulates the transient behavior of a dual-pressure bottomg system for a combed cycle poer plant. Kim JH [6] describes models for transient analysis of heavy duty 150M gas turbes. Also Sh JY performs a dynamic simulation to analyze the transient behavior of a combed-cycle poer plant thoroughly [3]. Additionally Sanaye prepared a developed thermal model for predictg the orkg conditions of HRSG elements durg transient startup procedure [4]. Also Alobaid vestigates start up process of a combed cycle poer plant by usg both static and dynamic simulation [1]. In this study sgle-pressure combed cycle poer plant has been designed, mathematically modeled and its transient behavior vestigated. This modelg is useful to analyze the transient behavior of a combed cycle poer plant durg load reduction of gas turbe of system. Knog the transient performance helps to estimate mechanical and thermal stresses hich are important poer plant design and operation. Transient analysis of gas turbe has been done [6] and its data is utilized this paper. Geometric and thermodynamic of bottomg cycle of studied poer plant has been performed by the ell-knon commercial softare [7]. Each component of the poer plant system is mathematically modeled and then tegrated to the unsteady form of conservation equations, and then the governg equations have been solved by Forard Fite Difference method; Computational program of this method ritten by mathematical softare EES [8]. II. SYSTEM DESCRIPTION Generally, combed cycle poer plant is composed of gas turbes, heat recovery steam generators (HRSGs), and steam turbes. The gas turbe exhaust gas flos through a HRSG hich thermal energy of the exhaust gas is used for steam production. The HRSG supplies high-pressure (HP) and lo-pressure (LP) steam turbe and the deaerator, respectively. Combed cycle poer plant may have various configurations accordg to the number of HRSG pressure 64

2 International Journal of Modelg and Optimization, Vol. 2, No. 1, February 2012 levels, deaerator type, steam turbe type and so on [3]. A schematic diagram of the system of this study is shon Fig.1. Designed cycle cludes one 150 M GE 7F enge, sgle-pressure type HRSG and an tegral self-heatg deareator ith a condensg steam turbe. Feed ater supplied from the condenser by the boiler feed pump is heated LP preheater (LTE) before it enters the LP drum (LPB). Saturated ater the LP drum is recirculated through the LP evaporator. Steam produced the LP drum is supplied to the tegral self-heatg deaerator. Water is also dran from LP drum to the HP drum (HPB1) through the HP economizers (HPE1 & HPE3). Steam is produced the HP drum and superheated through the HP super heater (HPS3) for electrical poer generation. The system design variables are also shon Fig.1. Also TABLE I contas design data of cycle. III. COMPONENT MODELS A. Gas turbe Transient behavior of a combed cycle poer plant may be caused by star-up, shut don or load reduction. In this study, gas turbe of the cycle is imposed to load reduction, so the system shos its transient behavior affected by this load change from full load state to 80%. For modelg of gas turbe, the necessary data extracted from [6] and variation of gas turbe parameters can be seen Fig.2, Fig.3 and Fig.4. B. Heat Recovery Steam Generator (HRSG) HRSG is an important component of combed cycle poer plant; Because it sufferg thermal and mechanical stresses that can be important for design and control of hole system. The flue gas reduction rate ( Q g ) after passg an HRSG component is expressed as follos: Q g = m ( h h 2 )(1 K g g1 g loss here m g dicates the flue gas mass flo rate and (h g1 -h g2 ) is the gas enthalpy reduction. It as assumed that a part of the gas energy as lost through HRSG casg (ab 2% as the typical value for K loss ). Also gas energy reduction rate is equal to heat transfer beteen gas and HRSG element ~ ~ Q = U A T T ) (2) g o o ( g m here U o represents the gas side heat transfer coefficient (cludg convection and radiation effects) and A o is the er heat transfer surface area. Also T ~ m and T ~ g describe average metal and gas temperature respectively. Q g is absorbed by the tube all ( Q m,(4)), fs ( Q f,(5)), as ell as steam super heaters, ater economizers and the mixture of steam and ater evaporator tubes ( Q,(7)) as is shon the follog equation[4]: Q g Q m + Q f + Q ) (1) = (3) The rate of energy absorbed by the metal of HRSG heatg element ( Q ) is expressed as m e i M c T T Q m m( m m) m = (4) Also the rate of energy absorbed by fs ( Q f ) is e i M c T Tf Q f f ( f ) f = (5) here M and c (4) and (5) represent mass and specific heat, respectively; Also T m and T f are metal and f temperature respectively. Equation (6) predicts an average value for the f temperature as follos: T f = T +.3 ( T T ) (6) 0 g here T g and T are the gas and steam/ater temperatures, respectively. The absorbed energy by steam or ater ( Q ) can be estimated by the follog equation: Q = ( Q Q ) + Q Q (7) accum here Q and Q are the rate of energy flog and of an HRSG heatg element as explaed belo[4] = (8) Q m, h, Q m. h, = (9) here ṁ denotes the mass flo rate of steam or ater hile h, and h, refer to the enthalpy of let and let flos respectively. Q accum is the energy accumulation side a heatg element hich is produced by the change temperature and mass of steam/ater ith time and is computed by belo equation: e e i i e e i i M u M stust M tut M tut Q ( st st ) ( ) accum = + (10) here u stands for ternal energy and Δ t represents the time step. Superscripts e and i refer to the end and the begng of a time step [4]. Durg the transient operation of an HRSG, due to slo energy variation durg a time terval a heatg element hich is a control volume, SSSF process (de cv /=0) as applied for the gas flo, as ell as the ater or steam flo economizers and super heaters. Hoever, due to large mass of ater/steam mixture evaporator and drum, and the high rate of energy variation due to boilg, USUF process as considered the mass and energy analysis. Subsequently Q accum (10) as set equal to zero for sgle phase flo (cludg gas/ater/steam flos). Hoever, for analyzg to-phase flo evaporators and drums, the numerical bd 65

3 International Journal of Modelg and Optimization, Vol. 2, No. 1, February 2012 value of Q accum as computed from (10) [4]. Fig. 1. Schematic vie of designed combed cycle poer plant ith its system variables Q bd describes the amount of energy loss drum due to blo don to keep the ater side the drum chemically balanced. The blo don mass flo rate as considered to be ab 1% of ater mass flo rate ( m bd ) enterg the drum and as evaluated by follog equation:. Q bd = mbd ht, bd. (11) here h t, bd denotes the enthalpy of saturated ater the drum. To estimate the heat transfer rate beteen tube alls and steam/ater, (12) can be used: ~ ~ Q = U A T T ) (12) i i ( m here Ui is the overall heat transfer coefficient computed based on the ner heat transfer surface area (A i ) and T ~ is average steam/ater temperature. The mass conservation relation side the drum and evaporator is: d( M t + M st ) = m t, m (13) m st, is the mass flo rate of the steam flog of the drum and is computed by (16). de t m ( ) t,, t+ = m t, t + K pe( t) + Kd (14) e( t) = Wl( t) Wl d (15) K st p m = (16) T K p and K d are related to HP and LP drum ater level control system. The numerical values of these parameters ere equal to 180kgm -1 s -1 and 9200kgm -1, respsectively. Wl d is computed from drum centerle and expressed mm. In (16), T and P are the saturation temperature and pressure the drum and m st, is the steam mass flo rate of drum at the steady-state operation. K st as estimated and for HP drum (HPB1) and LP drum (LPB), respectively; calculated from design results of system done by [7]. C. Steam Turbe Because the response time of a steam turbe is knon to be shorter than that of a HRSG, quasi-steady assumption could be applied to the steam turbe model [3]. While steam turbe is treated as a control volume, the follog mass and energy equations are applied: here M t and M st are the ater and steam mass evaporator, respectively. dicates the ater mass flo rate m t, enterg the evaporator and is estimated by (14) and (15) and And ρ d st V = m m (17) 66

4 International Journal of Modelg and Optimization, Vol. 2, No. 1, February 2012 d(ρe ) st V = m h n m h W st (18) ρ is density and e is energy; Also V is volume and W st is shaft poer. m m st, and m st, are steam turbe let and let mass flo rate, respectively. The shaft poer is evaluated from a quasi-steady assumption (20). Also accordg to this assumption, (17) can be changed to (19). m st, = m W st = m ( h h ) (19) (20) determed based on that coefficient and the off-design performance as estimated [10]. We also assume that the steam/ater mixture troduced the condenser is condensed to a 0 quality level. In addition, it is assumed that coolg ater flo rate is constant at design value [3]. Deaerator and pump are considered to have high enough quick response time compared to the characteristics response time of the total system and no pressure drop steam/ater pipg is considered [3]. Sce the flo side the turbe is fast enough, the quasi-steady assumption is quite reasonable. The condition of the turbe let is determed usg the Stodola Ellipse La for the off-design characteristics of turbes [2]. The Stodola Ellipse La states: ( m T ( m T p ) p ), d = 1 ( p 1 ( p 2 p ) 2 p) d (21) T and p represent temperature and pressure of turbe. The condensg pressure is assumed to be constant [2]. Subscripts d,, and refer to design, let and let condition respectively. The flo function is troduced, hich is the modification of the earlier Stodola Ellipse La considerg the variation of the let condition. From this equation e could obta section let pressure if e kno the let mass flo rate, temperature, and pressure through the transient processs of a steam turbe [3]. m, = k p ν p 2 1 ( ) p ν represents specific volume, also subscript st refers to steam turbe. For steam turbe of present study, k is equal to D. Condenser and Miscellaneous Devices Fig. 2. Variation of gas turbe partial load ith time (22) Volume of a condenser is normally quite small and its response durg transient process is very fast compared to that of HRSG. Thus, the assumption that the condenser is a steady state at each time step can be applied. The overall heat transfer coefficient could be calculated from the HEI (Heat exchanger Institute) standard [9]. Heat exchange areaa as Fig. 3. Variation of gas turbe flue gas temperature ith time Fig. 4. Variation of gas turbe flue gas mass flo rate ith time IV. NUMERICAL METHOD The system variables shon Fig. 1 are solved simultaneously. The mentioned governg equations constructed a set of equations hich ere solved by forard fite difference method to get temperature of gas, tube all and ater/steam and also pressure of both drums at the end of each time terval. To simplify solvg the governg equations, the follog pots ere considered: 1) In each time terval, enthalpy and thermo-physic cal properties of gas and steam/ater ere computed based on the average temperature a time step. 2) There as no heat accumulation HRSG duct, economizers and super heaters (as a control volume) durg a time terval, therefore Q as set to accum zero (7) [4]. Numerical evaluation of terms (10) shoed that Q accum as negligible comparison ith Q and Q (7) durg a time step (SSSF process). Hoever, due to large masss of ater/steam mixture evaporator and drum and the highh rate of energy variation due to boilg, the numerical 67

5 International Journal of Modelg and Optimization, Vol. 2, No. 1, February 2012 values of heat accumulation computed from (10) ere comparable ith the correspondg numerical values of other terms (7) durg a time step (USUF process) [4]. V.. RESULTS AND DISCUSSIONS Governg equations set, imported to the mathematical softare [8] and have been solved simultaneously. As results of modelg, that seen as the conclusions of load reduction gas turbe, Fig.5, Fig.6, Fig..7, Fig.8, Fig.9 and Fig.10 can be considered. Fig. 7. Variation of condenser temperature ith time Fig. 5. Variation of steam turbe put poer ith time Fig. 8. Variations ater level of HP drum (HPB1) In Fig. 5 variation of put poer of steam turbe ith time, can be seen. As shon this figure, load reduction gas turbe causes decrease steam turbe put poer. Fig.9. Variation of let steam temperature of super heater ith time Fig. 6. Variation of metal temperature of the preheater (LTE) ith time Metal temperature of elements HRSG varies as shon Fig.6 that is related to preheater (LTE), this temperature decreasg after a short crease t=150 sec. Condenser temperature also decreases ith time as shon Fig.7 but more sharply comparison ith earlier figure. Variation of ater level HP drum (HPB1) is shon Fig.8, lo oscillation this parameter obviously seen. As result of load reduction of system, temperature of superheated steam exitg super heater of HRSG reduces ith time that can be seen Fig. 9. Fally Fig. 10 shos variation of hot gas temperature exhaustg HRSG stack ith time, decrease this temperature can be seen as expected. Fig. 10. Variation of let flue gas of stack ith time Steady-state condition occurs hen there is no change gas turbe load and HRSG operatg parameters [4]. This situation occurs at the end of load reduction process studied system. To validate present transient modelg of combed cycle poer plant, the numerical put steady-state condition (at the end of transient process) for bottomg cycle as compared ith the results of ell-knon commercial softare [7]. That is a computer 68

6 International Journal of Modelg and Optimization, Vol. 2, No. 1, February 2012 program for designg, modelg, and analysis of steam, gas and combed cycle poer plants steady-state mode usg mass and energy conservation equations. Table П shos that there as a good agreement beteen to groups of results. An average difference of ab 1.35% as found. Gas turbe TABLE I: SUMMARY OF DESIGN DATA OF CYCLE GE7F Speed, rpm 3600 Electrical Poer, M 150 Cycle Efficiency, % 34.5 Outlet gas mass flo rate, kg/s Outlet gas temperature, K HRSG Stack temperature, K Deaerator pressure, kpa Feed ater temperature, K Outlet flo temperature of LTE, K Steam turbe Gross put poer, k Input pressure, kpa Input temperature, K Mass flo rate, kg/s Dual-pressure type Sgle-pressure, Condensg type, With reheat TABLE П: COMPARISON OF THE MODEL OUTPUT FOR BOTTOMING CYCLE WITH THE COMMERCIAL SOFTWARE RESULTS IN STEADY CONDITION Parameters Outlet hot gas temperature of super heater, K Outlet hot gas temperature of economizer, K Outlet flue gas of stack temperature, K Outlet steam temperature of super heater, K HP drum pressere, kpa LP drum pressure, kpa Modelg Results GT MASTER Difference (%) VI. SUMMARY AND CONCLUSION A mathematical model for transient analysis of a combed cycle poer plant as developed. Studied system as designed by the ell-knon commercial softare geometrically and thermodynamically. This study considered load reduction gas turbe as a dynamic behavior of cycle and its result have been shon some figures. The model put at the end of transient operation (durg hich there as no change parameter values and system as approximately steady-state mode of operation) as compared ith the numerical put of ell-knon commercial softare. The agreement beteen these to groups of data as good. REFERENCES [1] F. Alobaid, R. Postler, J. Strohle, B. Epple, and K. Hyun-Gee, Modelg and vestigation start-up procedures of a combed cycle poer plant, Applied Energy vol. 4, pp , [2] T. S. Kim, H. J. Park, and S. T. Ro, Characteristics of transient operation of a dual-pressure bottomg system for the combed cycle poer plant, Energy vol. 26, pp , [3] J. Y. Sh, Y. J. Jeon, D. J. Maeng, J. S. Kim, and S. T. Ro, Analysis of the dynamic characteristics of a combed-cycle poer plant, Energy vol. 27, pp , [4] S. Sanaye and M. Rezazadeh, Transient thermal modelg of heat recovery steam generators combed cycle poer plants, Int. J. Energy Res. vol. 31, pp , [5] K. S. Ahlualia and R. Domenichi, Dynamic Modelg of a Combed-Cycle Plant, ASME J Eng Gas Turbes Poer vol. 112, pp , [6] J. H. Kim, T. W. Song, T. S. Kim, and S. T. Ro, Model development and simulation of transient behavior of heavy duty gas turbes, ASME J Eng Gas Turbes Poer vol. 123, pp , [7] Thermoflo Inc.GTPRO & GTMASTER Ver , [8] Engeerg Equation Solver (EES), Commercial Version D, [9] Heat Exchange Institute, HEI standards for steam surface condensers, 8 th ed Cleveland, OH: Heat Exchange Institute Inc., [10] M. M. EL-Wakill, Poer plant Technology, 1st ed. McGra Hill, 1985, ch 6, pp Keyvan Daneshvar has been born shahrood, Iran He graduated ith BS mechanical engeerg from Shahrood University of Technology, Shahrood, Iran Then he graduated ith a Master of Science degree Mechanical Engeerg from Khaje Nasir university of Technology (KNTU), Tehran, Iran Keyvan as orkg at Semnan regional Electricity Co sce June, 2010 until July, He is orkg as a lecturer at Islamic Azad University, Shahrood branch, Semnan, Iran sce September, Experimental and numerical simulation on no x emission liquid fuel spray flames, Vahid Nejati, Yasam Khazraii, Keyvan Daneshvar and Shir Khazraii,Chia Laguna, Cagliari, Sardia, Italy, September 11-15, 2011; Numerical Modelg of No x Emission In Turbulant Spray Flames Usg Thermal And Fuel Models, Yasam Khazraii, Keyvan Daneshvar, Hosse Poorkhademnam, ICMET 2011, Dalian, Cha. August 26-27, Research Energy systems like Poer Plants (Reneable Energy and Combed cycles) and Numerical Solutions are his research terests. Ms. Daneshvar has received fund through his MSc fal project from MAPNA GROUP (2009). Ali Behbahani-nia has been born Tehran, Iran He graduated With Phd Mechanical Engeerg from Tehran University, Tehran, Iran He is orkg at Khaje Nasir University of Technology (KNTU), Tehran, Iran as a Faculty Member sce September A dual reciprocity be-based sequential fuction specification solution method for verse heat conduction problems, A. Behbahani-nia, F.Kosary, International Journal of Heat and Mass Transfer 47 (2004) pp ; Transient Heat Flux Function Estimation Utilizg The Variable Metric Method, F.Kosary, A. Behbahania, A. Pourshaghaghi, International Communications Heat and 69

7 International Journal of Modelg and Optimization, Vol. 2, No. 1, February 2012 mass transfer 33 research terest. (2006), pp Research Heat transfer is his 2011, Dalian, Cha. August 26-27, Research Practical Combustion Systems and Air Pollution is her terest. Yasam Khazraei has been born Shahrood, Iran She graduated ith BS Mechanical Engeerg from Shahrood University of Technology, Shahrood, Iran Then she graduated ith a Master of Science degree Energy Transmutation Mechanics from Islamic Azad University, Mashhad branch, Khorasan Razavi, Iran, Yasam as orkg as a lecturer at Islamic Azad University, Marvdasht Branch, Fars, Iran She is orkg at Islamic Azad University, Bandar Lengeh Branch, Hormozgan, Iran as a lecturerr sce January, Experimental and numerical simulation on no x emission liquid fuel spray flames, Vahid Nejati, Yasam Khazraii, Keyvan Daneshvar and Shir Khazraii,Chia Laguna, Cagliari, Sardia, Italy, September 11-15, 2011; Numerical Modelg of No x Emission In Turbulant Spray Flames Usg Thermal And Fuel Models, Yasam Khazraii, Keyvan Daneshvar, Hosse Poorkhademnam, ICMET Azam Ghaedi has been born Bandarabbas, Iran She graduated ith BS Computer Engeerg from Islamic Azad University, Maybod Branch, Yazd, Iran Then she graduated ith a Master of Science degree Mechatronic Engeerg from Islamic Azad University, Science and Research Branch, Tehran, Iran, Azam as orkg as a lecturer at Islamic Azad University, Bandarabbas Branch, Hormozgan, Iran She is orkg at Islamic Azad University, Bandar Lengeh Branch, as a Faculty Member sce September Hormozgan, Iran 3-Axes Satellite Attitude Control Based on Biased Angular Momentum, Azam Ghaedi, Mohammad 2008; The Effect Ali Nekoui, Poznan,Poland, September 1-3, of PD Controller on 3-Axes Orbital Satellite Attitude Control Steady State Mode Azam Ghaedi, APPEEC2012, Shanghai, Cha March