Analysis of the dynamic characteristics of a combined-cycle power plant

Energy 27 (2002) 1085 1098 www.elsevier.com/locate/energy Analysis of the dynamic characteristics of a combined-cycle power plant J.Y. Shin a,, Y.J. Jeon b, D.J. Maeng b, J.S. Kim b, S.T. Ro c a Department of Mechanical Engineering, Dongeui University, 614-714 Busan, South Korea b Hyundai Institute of Construction Technology, Hyundai Engineering & Construction Company Limited, 449-710 Yongin, South Korea c School of Mechanical Engineering, Seoul National University, 151-742 Seoul, South Korea Received 1 September 2001 Abstract Gas/steam combined cycle has already become a well-known and substantial technology for power generation due to its numerous advantages including high efficiency and low environmental emission. Many studies have been carried out for better performance and safe and reliable operation of combined-cycle power plants. A power plant is basically operated on its design conditions. However, it also operates on the so called off-design conditions due to the variation in a power load, process requirements, or operating mode. Therefore, the transient behavior of the system should be well-known for the safe operation and reliable control. In this study, dynamic simulation is performed to analyze the transient behavior of a combined-cycle power plant. Each component of the power plant system is mathematically modeled and then integrated into the unsteady form of conservation equations. Transient behavior was simulated when rapid changes and periodic oscillations of the gas turbine load are imposed. Time delay characteristic caused by the thermal and fluid damping is analyzed and overall time-response of the combined power plant system is shown. 2002 Elsevier Science Ltd. All rights reserved. 1. Introduction The outstanding features of combined-cycle power plants becomes more attractive with its increasing usage in power market. The features include its high efficiency in utilizing energy resources, low environmental emissions, short duration of construction, low initial investment Corresponding author. Tel.: +82-51-890-1650; fax: +82-51-890-2232. E-mail address: jyshin@dongeui.ac.kr (J.Y. Shin). 0360-5442/02/$ - see front matter. 2002 Elsevier Science Ltd. All rights reserved. PII: S0360-5442(02)00087-7

1086 J.Y. Shin et al. / Energy 27 (2002) 1085 1098 Nomenclature A area (m 2 ) A p amplitude of periodic oscillation e internal energy (kj) H enthalpy (kj/kg) h convective heat transfer coefficient K p proportional constant in PID control K d differential constant in PID control L drum level (m) ṁ mass flow rate (kg/s) p pressure (N/m 2 ) Q rate of heat flow (kw) t time (s) T temperature ( C, K) v specific volume (m 3 /kg) V volume (m 2 ) Ẇ rate of work or power (kw) x quality Greek letters a heat transfer coefficient (kw/ m 2 K) r density (kg/m 3 ) t time period of gas turbine load oscillation Superscripts control volume Subscripts 1, 2 stage inlet, outlet d value at design condition dr drum ec economizer exh exhaust condition ev evaporator

J.Y. Shin et al. / Energy 27 (2002) 1085 1098 1087 fw g gt in l M out sh st v w feedwater gas side gas turbine inlet liquid phase tube metal side outlet superheater steam turbine vapor phase water/steam side cost, low operation and maintenance cost, and flexibility of fuel selection, etc. Thus, combinedcycle power plants are quite competitive in the power market. It is presumed that a power plant is basically operated on the design condition and many researches have been focused on the design point analysis to date. However, most power plants operate on the so called off-design condition, which is caused by the variation of working condition. Extensive studies have been conducted to construct the mathematical model and simulate the plant operation as shown in Refs. [1 4]. However, most of them focus on the start-up and shutdown behavior of the combined-cycle power plant. Few works provide the operational plan during load ramping or oscillation, etc. Therefore, a reasonable estimation of the operational characteristics of the whole system during any transient process (shut-down and start-up, load ramping, load oscillation, equipment failure, etc.) is essential to safe operation and reliable control. In this study, each major component of combined-cycle power plant, gas turbine, heat recovery steam generator, steam turbine, and condenser, is mathematically modeled and then integrated to simulate its transient behavior. Some works introduce empirical coefficients only applicable to a specific power plant. Some systems cannot be simulated even with commercial software due to the diversity in the plant configurations. However, in this study, we did not consider the empirical constants only applicable to this system and could reflect any change of the steam cycle (e.g. HRSG) on the program directly. This paper includes a brief description of the model and the method of analysis. The results show three transient simulation cases concerned, which are respectively induced by the rapid decrease, rapid increase, and periodic oscillation in gas turbine load. 2. System description Combined-cycle power plant is composed of gas turbines, heat recovery steam generators (HRSGs) and steam turbines. The gas turbine exhaust gas flows through a HRSG in which thermal energy of the exhaust gas is used for steam production. The HRSG supplies high-pressure (HP) and low-pressure (LP) steam to the steam turbine and the deaerator, respectively. Combined-cycle

1088 J.Y. Shin et al. / Energy 27 (2002) 1085 1098 power plant may have various configurations according to the number of HRSG pressure levels, deaerator type, steam turbine type and so on. A schematic of the combined-cycle power plant of this study is shown in Fig. 1. Simulated model includes a single-pressure type HRSG and an integral self-heating deaerator with a condensing steam turbine. Feedwater supplied from the condenser by the boiler feed pump is heated in the LP preheater before it enters the LP drum. Saturated water in the LP drum is recirculated through the LP evaporator. Steam produced in the LP drum is supplied to the integral self-heating deaerator. Water is also drawn from the LP drum to the HP drum through the HP economizer. Steam is produced in the HP drum and superheated through the HP superheater for electrical power generation. The system variables of the mathematical modeling are also shown in Fig. 1. 3. Component models 3.1. Gas turbine In the gas turbine model, the rotor-inertia and fluid thermal inertia are considered and fluid thermal inertia of the inlet- and outlet-duct system are also included. The compressor and turbine are analyzed stage-by-stage. In addition, the effect of the cooling air into the turbine system is taken account of. The load-control is achieved by the modulation of the fuel mass flow. The Fig. 1. Schematic view of a combined-cycle power plant with its system variables.

J.Y. Shin et al. / Energy 27 (2002) 1085 1098 1089 detailed description of the gas turbine transient model and the verification of the results can be found in the previous works of the co-work group of this research project [5 7]. 3.2. Heat recovery steam generator (HRSG) For each component of the HRSG, the conservation of mass and energy conservation can be written as following equations through the lumped heat capacitance method [8]. Since a pressure drop in each component is not considered, the momentum conservation equation is not required. V dr ṁ dt in ṁ out (1) d(me) H dt in H out Q Ẇ s (2) Above equations may be directly applied, respectively, to the gas side, steam side and tube side of a heat exchanger. The heat absorbed by the working fluid through the tube wall can be written as follows, Q g a g A g (T M T g) (3) Q w a w A w (T M T w) (4) Thermodynamic properties of steam and water are calculated using the program package of PROPATH Group [9]. The heat transfer coefficients of the water and steam are determined using the well-known correlation equations [10,11]. To decide the heat transfer coefficient related with fin, ESCOA [12] relation is adopted. Eqs. (1) and (2) are applied to the drum parts as follows; dm dr ṁ dt ec,out ṁ sh,in ṁ ev,out ṁ ev,in (5) d(me) dr ṁ dt ec,out h ec,out ṁ sh,in h sh,in ṁ ev,out h ev,out ṁ ev,in h ev,in (6) It is assumed that the drums are thermally insulated from their surrounding, and that the water and steam inside the drums are saturated in quasi-steady state. 3.3. Steam turbine Because the response time of a steam turbine is known to be shorter than that of a HRSG, quasi-steady assumption could be applied to the steam turbine model. The steam turbine in this study is a 3600-rpm-condensing turbine with one-row governing stage. Quasi-equilibrium state at each time step in a fluid dynamic, thermodynamic, and mechanical status is assumed. A sectionby-section analysis was applied rather than a complicate stage-by-stage analysis. Thus, Eqs. (1) and (2) are applied to each section of a steam turbine. The rotor inertia is neglected and the isentropic efficiencies for each section (HP, LP) are given from Spencer et al. [13]. The flow function [14] is introduced, which is the modification of the earlier Stodola s Ellipse

1090 J.Y. Shin et al. / Energy 27 (2002) 1085 1098 Law considering the variation of the inlet condition. From this equation we could obtain section outlet pressure if we know the inlet mass flow rate, temperature, and pressure through the transient process of a steam turbine. p ṁ st,in K st,in v st,in 1.0 p 2 st,out p st,in 3.4. Condenser and miscellaneous devices Volume of a condenser is normally quite small and its response during transient process is very fast compared to that of HRSG. Thus, the assumption that the condenser is in 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 [15]. Heat exchanger area was determined based on that coefficient and the off-design performance was estimated. We also assume that the steam/water mixture introduced in the condenser is condensed to a 0 quality level. In addition, it is assumed that cooling water flow rate is constant at design value. Deaerator and pump are considered to have high enough quick response time compared to the characteristic response time of the total system and no pressure drop in steam/water piping is considered. (7) 4. Numerical method The system variables shown in Fig. 1 are solved simultaneously. The continuity and energy equations, Eqs. (1) and (2) for both gas and water apply to a control volume and the energy equation to a wall (Eq. (1)). For n control volume, 5n governing equations for a system were setup. Temperature and mass flow for both gas and water at each control surface, tube wall temperature for each control volume, and pressure at each drum are the unknown variables with total number of variables (5n 6). Boundary conditions such as mass flow, temperature at the gas inlet, constant size for two drum, mass flow rate of two feedwater pump are given for each control volume. Modified multi-variable Newton Raphson method is applied to solve a set of non-linear governing equations at each time step. A fully implicit method is adopted to provide numerical stability. Feedwater pumps control the water level of the drums of a HRSG. LP boiler feed pump that supplies water from the condenser keeps the LP drum level constant. In the same way, HP feed pump that connects the LP drum and HP economizer keeps the HP drum level constant. The modified PID control algorithm adjusts the flow through each pump based on water level in each drum. ṁ new fw where, E L L d. ṁ old fw K p E K d de dt (8)

J.Y. Shin et al. / Energy 27 (2002) 1085 1098 1091 5. Result Three cases are considered to illustrate the dynamic performance. These include rapid load reduction, rapid enhancement, and periodic oscillation of the gas turbine, which starts from 100% load. Table 1 shows a summary of design specifications of the combined-cycle plant system. Simulated gas turbine (V64.3: a model of the current study) performance is compared with experimental data in the previous work [5]. For the validation of the combined-cycle performance, the steam cycle performance is compared with the results of the well-known commercial software gtpro and gtmaster [16]. Even though the software doesn t give transient performance, gtmaster provides the off-design performance, which should be identically same as the converged performance after the transient process (e.g. from 100 to 90% gas turbine load). Off-design performance could be estimated from full-transient method of this study and also from off-design performance prediction program such as gtmaster. Table 2 shows that the current simulation program is in a good agreement with the commercial software comparing the off-design performance. 5.1. Rapid decreases in gas turbine load Rapid reduction of the gas turbine load from 100 to 90% was simulated. Figs. 2 and 3 give the transient response of key system parameters. Fig. 2 shows the variation of exhaust-gas flow rate and exhaust-gas temperature of the gas turbine. The variation of gas turbine power with respect to time is also included. Because the gas turbine load is controlled mainly by the fuel Table 1 Summary of design specifications Gas turbine Siemens KWU 64.3 Power output 61 MW Efficiency 34.6% Exhaust mass flow 684.2 ton/h Exhaust gas temperature 535 C HRSG Single pressure type Pinch temp difference 15 C Approach temp. difference 9 C Stack temp. 164 C Deaerator pressure 2.0 bar Feed water temp. 36 C LTE exit temp. 100 C Steam turbine Two pressure condensing with One-row governing stage Power output 26 MW HP inlet pressure 42.2 bar HP inlet temperature 506 C LP inlet pressure 7.34 bar LP inlet temperature 286 C Working flow rate at throttle 85.2 ton/h Vacuum pressure 0.0588 bar

1092 J.Y. Shin et al. / Energy 27 (2002) 1085 1098 Table 2 Comparisons of the steam cycle performance (off-design condition of 90% gas turbine load) Present work (transient scheme) gtmaster (Steady scheme) ST throttle flow, ton/h 77.1 77.2 ST throttle temp, C 484 481 ST throttle pressure, bar 37.8 38.1 Vacuum pressure, bar 0.0531 0.0530 Deaerator pressure, bar 2.46 2.37 Stack temp, C 166.6 166.1 1st Feed water temp. C 34.0 34.2 Fig. 2. Gas turbine working condition with rapid decrease in gas turbine load. supply not by inlet guide vane, the exhaust-gas flow rate of gas turbine is controlled to be almost unchanged. As gas turbine power output reaches 90% of the design condition, exhaust-gas temperature drops significantly within a few seconds. Gas turbine power output also approaches to a setting value with minor undershooting. It shows that gas turbine system stabilizes within 4 s. Fig. 3(a) presents the variation of steam flow rate and temperature at HRSG exit. Due to the reduction of the gas turbine exhaust-gas temperature, mass flow rate and temperature of the steam are decreased until approximately 200 s, which is significantly longer than the response time of the gas turbine. HP superheated steam temperature also shows minor undershooting performance. Fig. 3(b) shows the variation of steam turbine output and exhaust pressure. Steam turbine power output decreases sharply within a few minutes. It shows little undershooting effect and a longer response time as compared to those of the gas turbine transient performance. It is noted that the undershooting effect in the temperature of HP superheated steam does not affect the steam turbine performance in this case. Fig. 3(c) illustrates the variation of HP and LP steam drum pressure. As shown in the figure,

J.Y. Shin et al. / Energy 27 (2002) 1085 1098 1093 Fig. 3. Transient behavior of steam cycle induced by rapid decrease in gas turbine load. (a) HRSG steam flow rate and temperature; (b) Steam turbine output and exhaust pressure; (c) HRSG drum pressure; (d) HRSG drum level. HP drum pressure stabilizes relatively in the shorter period than LP drum pressure. The amount of heat recovered in the HP section decreases according to the reduction of the gas turbine exhaustgas temperature. As a result, HP steam production rate diminishes, which results in the drop of HP drum pressure. This could be verified by the flow function describing the relation between steam flow rate and pressure as shown in (7). In order to keep the LP drum level constant, the LP steam production rate decreases with the reduction of HP steam flow rate. Finally, the LP drum pressure and temperature are increased. Fig. 3(d) represents the variation of HP and LP drum level. One of the most important parameters of power plant operation is the variation of the drum levels. The control system should keep the drum level as close as possible to the preset value. In this study the feedwater flow rate is adjusted through the modified PID control algorithm being independent on the steam flow leaving the drum. As shown in the figure, the drum levels undergo oscillation and reach the steady state value within a short time by damping down the external disturbance.

1094 J.Y. Shin et al. / Energy 27 (2002) 1085 1098 Fig. 4. Gas turbine working condition with rapid increase in gas turbine load. 5.2. Rapid increase in gas turbine load Gas turbine load increase from 100 to 110% was assumed as shown in Fig. 4. Further description is not illustrated in this section, because the variation of system parameters could be estimated from the results of the load reduction case before. For example, as presented in Fig. 5(a), the characteristic time of stabilization shows similar Fig. 5. Transient behavior of HRSG steam cycle induced by rapid increase in gas turbine load. (a) drum pressure; (b) steam and exhaust gas temperature.

J.Y. Shin et al. / Energy 27 (2002) 1085 1098 1095 tendency. The HP pressure goes up as the gas turbine exhaust-gas temperature increases. This is mainly due to the augmentation of the energy absorbed at the HP section. Vice versa, the LP pressure goes down because less energy is provided at the LP section. The variation of HP steam temperature (T w,1 ) and exhaust-gas temperature at HRSG exit (T g,6 ) are also shown in Fig. 5(b). The characteristic time for the stabilization of these parameters is very close to that of the variation of HP and LP drum pressure. From these results, two main time scales were identified. One is the time scale related to the HP section (200 s; e.g. HP pressure and T w,1 ) and the other to the LP section of HRSG (2000 s; e.g. LP pressure and T g,6 ). 5.3. Periodic oscillation in gas turbine load Fig. 6 illustrates the periodic oscillation in gas turbine load. The gas turbine load is varying within ±10% and the oscillation frequency is given to 1/20 and 1/200 Hz, respectively. The gas turbine exhaust-gas flow rate is also controlled constant. The variation of steam turbine output was accompanied by the periodic oscillation in gas turbine load, as shown in Fig. 7. As conjectured by the previous results, steam cycle shows a relatively slower response time than that of the gas turbine because of the thermal and fluid-inertial damping effect. The amplitude of periodic variation of steam turbine output is smaller than that of periodic disturbance of gas turbine output. This reflects damping effect of the steam cycle. In the previous example, as presented in Fig. 3(b), steam turbine output decreases about 10% after stabilization with the rapid decrease in gas turbine load. However, when the 1/20 Hz periodic oscillation is imposed on the gas turbine output, the effect on the steam turbine output is extremely small as illustrated in Fig. 7. This might be due to the fact that 20 s is very short time considering the characteristic time scale of the HRSG (200 and 2000 s). On the contrary, with the 1/200 Hz Fig. 6. Gas turbine working condition with periodic oscillation in gas turbine load.

1096 J.Y. Shin et al. / Energy 27 (2002) 1085 1098 Fig. 7. Variation of the steam turbine load with periodic oscillation in gas turbine load. disturbance of gas turbine, the steam turbine output shows periodic variation with relatively large amplitude. Steam turbine power shows different response with respect to the period of gas turbine output disturbance. The amplitude of oscillation of the steam cycle is represented in Fig. 8, with the oscillation period of the gas turbine load. It is normalized by the amplitude of steam turbine variation with sufficiently long oscillation period. The amplitude of the steam cycle is dramatically reduced for higher frequency of sinusoidal disturbance. The variation of oscillatory amplitude in Fig. 8. Variation of the relative amplitude of steam cycle variation with the period of gas turbine output disturbance.

J.Y. Shin et al. / Energy 27 (2002) 1085 1098 1097 steam cycle shows sharp increasing trend near the characteristic time scale of HP steam cycle (200 s) and no further change after the characteristic time scale of LP steam cycle (2000 s). In this respect, it should be carefully reviewed when the gas turbine load oscillation occurs near the characteristic steam cycle frequency range. 6. Concluding remarks A model to predict the transient behavior of a combined-cycle power plant has been developed. The model is based on the transient form of conservation of mass and energy for each component. For illustration, the transients driven by step and sinusoidal variations in the gas turbine load have been included. It is shown that the thermal inertia of the steam cycle is larger than that of gas turbine cycle. The response of steam cycle has a time lag and shows a damping effect on the variation of the gas turbine load. Two different time scales characterized by HP and LP drum dominates the time response of steam cycle. The transient variation in drum level seems to be controlled well by a proper control scheme. When the periodic disturbance is imposed to the gas turbine and the time scale of the disturbance is quite less than the characteristic time scales of steam cycle, the effect of the disturbance on the steam cycle is negligibly small. In this respect, the characteristic frequency of the steam cycle has to be carefully reviewed for the safe operation of the power plant during gas turbine load oscillation. Acknowledgments The work was supported by Hyundai Engineering & Construction Co. Ltd., BK21 at Seoul National University and BK21 at Dong-Eui University. References [1] Ahluwalia KS, Domenichini R. Dynamic modeling of a combined cycle power plant. ASME J Eng Gas Turbines Power 1990;112:164 7. [2] Jolly S, Gurevich A, Pasha A. Combined cycle HRSGs: evaluation of start-up at bottled-up conditions. ASME paper 93-GT-408; 1993. [3] Dechamps PJ. Modeling the transient behavior of combined cycle plant. ASME paper 94-GT-238; 1994. [4] Akiyama T, Matsumoto H, Asakura K. Dynamic simulation and its applications to optimum operation support for advanced combined cycle plants. Energy Convers Mgmt 1997;38(15-17):1709 23. [5] Kim JH, Song TW, Kim TS, Ro ST. Model development and simulation of transient behavior of heavy duty gas turbines. ASME J Eng Gas Turbines Power 2001;123:589 94. [6] Kim JH, Kim TS, Ro ST. Analysis of the dynamic behavior of regenerative gas turbines. Proc Inst Mech Eng, Part A, J Power Energy 2001;215(A3):339 46. [7] Kim JH, Kim TS, Song TW, Ro ST. Dynamic simulation of full start-up procedure of heavy duty gas turbines. ASME paper 2001-GT-0017; 2001.

1098 J.Y. Shin et al. / Energy 27 (2002) 1085 1098 [8] Kim TS, Lee DK, Ro ST. Dynamic behavior analysis of a heat recovery steam generator during start-up. Int J Energy Res 2000;24:137 49. [9] PROPATH Group. propath: A program package for thermophysical properties, Version 10.2. Japan: Kyushu University, 1997. [10] Collier JH, Thome JR. Convective boiling and condensation., 3rd ed. Oxford University press, 1994. [11] Chen JC. Correlation for boiling heat transfer to saturated fluids in convective flow. I&EC Proc Des Dev 1966;5(3):322 9. [12] ESCOA Corp. ESCOA fin tube manual; 1979. [13] Spencer RC, Cotton KC, Canon CN. A method for predicting the performance of steam turbine-generators 16,500 kw and larger. J Eng Power 1963;85:249 301. [14] Enter Software Inc. Gate cycle user s guide 4.1. Appendix G: 9 10;2000. [15] Heat Exchange Institute. HEI standards for steam surface condensers., 8th ed Cleveland, OH: Heat Exchange Institute Inc., 1984. [16] Thermoflow Inc. gtpro & gtmaster Ver 7.1;1998.