Multivariable Generalized Predictive Scheme for Gas Turbine Control in Combined Cycle Power Plant

Transcription

1 Multivariable Generalized Predictive Scheme for Gas urbine Control in Combined Cycle Power Plant L.X.Niu and X.J.Liu Deartment of Automation North China Electric Power University Beiing, China, 006 Abstract he maor dynamics of the gas turbine in combined cycle ower lant(ccpp) include nonlinearities behavior, time delays, and uncertainties. raditional control strategy could not offer satisfactory result. Using the linearization modeling technique, this aer deals with the velocity and ower control by multivariable generalized redictive control method. Comarisons of generalized redictive control with conventional PID aroaches were made under different load condition. Simulation results show the effectiveness of the roosed method. Keywords combined cycle ower lant, gas turbine, generalized redictive control I. INRODUCION During the ast several years, the ever-growing demand for electric ower has given rise to increasing interest in combined cycle ower generation lants(ccpg) because of their high efficiencies and relatively low investment costs. In CCPG, the gas turbine is the comlex system with highly nonlinearity, uncertainty and couling effect. hough well-known control strategies, usually PID controllers, have been develoed for these lants, it is imortant to develo more advanced control strategies to reduce the oerational costs further. MPC[] is essentially an otimal control technique. Several roosals for redictive control of ower lant have been made in the literature. he alication of a decentralized redictive control scheme was roosed in [] based on a state sace imlementation of GPC for a combined-cycle ower lant, in which a two-level decentralized Kalman filter was used to locally estimate the states of each of the subrocess. In another related work [3], a comarison of control erformance obtained with a linear state sace model-based GPC and dynamic erformance redictive controller alied in a gas turbine ower lant simulation was resented. A nonlinear long-range redictive controller based on neural networks is develoed in [4] to control the main steam temerature and ressure, and the reheated steam temerature at several oerating levels. Plant non-linearity was accounted for without resorting to on-line arameter-estimation as in self-tuning control. A nonlinear generalized redictive controller based on neuro-fuzzy network is roosed in [5], which is alied to control the suerheated steam temerature of a 00MW ower lant. his aer rooses a multivariable generalized redictive control of a CCPG. Linearization is incororated to coe with the lant nonlinearity. Also, constraints on the amlitude and the slew rate of the maniulated variables are included. Power and velocity control of gas turbine in CCPG is resented to illustrate the imlementation and the erformance of the roosed method. he results suggest an imrovement over conventional controller. II. PLAN DESCRIPION Combined cycle is a ower lant system in which two tyes of turbines, namely a gas turbine and a steam turbine, are used to generate electricity. Moreover the turbines are combined in one cycle, so that the energy in the form of a heat flow or a gas flow is transferred from one of the turbines to another. he most common tye of combined cycle is where the exhaust gases from the gas turbine are used to rovide the heat necessary to roduce steam in a steam generator. he steam is then sulied to the steam turbine. Fig. shows the configuration of the gas turbine. Figure. he configuration of the gas turbine. a -environmental temerature ; Pa -environmental ressure P -comressor inlet ressure ; P -comressor outlet ressure yb -comressor ressure ratio ; Gt -turbine exhaust gas flux In gas turbine control, the obect is to maintain the active ower N e, velocity n and exhaust gas temerature 4 within the ermitted range, for economic and safety reasons. he maniulated variables are fuel flow G f and comressor inlet guide vanes( α IGV). hus, the gas turbine is a non-linear system with a strong interrelationshi amongst the variables. For examle, when the exhaust gas temerature needs to be increased, IGV closes its oening rate, resulting in the higher fuel/air ratio. his can result in a higher exhaust gas temerature and a lower turbine velocity /08 /$ IEEE CIS 008

2 III. OBAINING HE LOAD DEPENDEN LINEAR MODEL Since the gas turbine is quite nonlinear, local linear models under different load condition is used to design the controller. he models, after linearization, could be exressed as: Under rated load condition[6]: 0.0s s N e 5.7s s s s α = n 0.3s.97s () G 5.7s s s s Under 60% load condition: 0.09 s s N e 9.9s +.38 s s +.38s α = n 0.44 s.64s () G 9.9s +.38s s +.38s Under 30% load condition: 0.03 s s N e.3 s +.98 s s +.98s α = n 0.5s 3.95s (3) G.3 s +.98 s s +.98s Fig. and Fig.3 show the modelling results. From Fig., while there is a ste change in fuel flow G f and α IGV, the turbine velocity fluctuates around the stable value within 0.068% range. Notice that the reaching time increases with load condition leaving far from the rated oint. (-a ) rated load condition (-b) 60% load condition (-d ) rated load condition (-e) 60% load condition (3-a ) rated load condition (3-b) 60% load condition (3-d ) rated load condition (3-e) 60% load condition (3-c) 30% load condition (3-f) 30% load condition Figure 3. he active ower resonse for a -0% ste change in α (a,b and c) and for a -0% ste change in G f (d, e and f) under different load condition From Fig.3, with a ste decrease in fuel flow G f, the turbine ower decreases and finally reaches a lower value. Similarly, with a ste decrease in α, the turbine ower increases and finally reach a higher value. his is because when IGV reduces its oening rate, the inlet air decreases, resulting the higher fuel/air ratio. his can give a higher exhaust gas temerature and thus a higher turbine outut ower. o verify the effectiveness of the model, we can calculate the ratio Ne Gf for different load condition. his is.5 for rated load condition,.505 for 60% load condition and.504 for 30% load condition. From the real-time data, while the turbine is in full velocity with vacant load, Gˆ f = Gf Gf 0 = 0.337, thus the defined ower/fuel ratio from the rated load to full velocity with vacant load condition is : Ne Ne / Ne0 (0% 00%) /00% β = = = =.508 G G / G (33.7% 00%) /00% f f f 0 (-c)30% load condition (-f)30% load condition Figure. he velocity resonse for a -0% change in α (a, b and c) and for a -0% ste change in G f (d, e and f)under diffferent load condition In this way, the calculated ratio N e G f under different load condition is quite near to that of β, demonstrating the effectiveness of the model. IV. DERIVAION OF MULIVARIABLE GPC A CARIMA model for a MIMO rocess can be exressed as[7]:

3 e() t A( z ) Y( t) = B( z ) U( t) + (4) na = n n na A( z ) I A z A z A z ; nb = nb B( z ) B B z B z B z ; he oerator is defined as = z.he variables Yt (), Ut ( ) and et ( ) are the n outut vector, the m inut vector and the n noise vector at time t. he noise vector is suosed to be a white noise with zero mean. Consider the following Diohantine equation: I n n ( z ) ( z ) z ( z = E A + F ) na ( z ) = F,0 + F, z + F, z + + F, naz F ( z ) = E,0 + E, z + E, z + + E, z E he rediction equation can now be written as: yˆ( t + t ) = G ( z ) u ( t + ) + f = + f G ( z ) u( t ) F ( z ) y ( t) he redictions can be exressed in condensed form as: Y ˆ ( t + t ) = G U ( t + ) + F (5) Yˆ ( t + t) = [ yˆ( t+ ), yˆ( t + ),, yˆ( t + N) ] U( t+ t) = [ u( t), u( t+ ),, u( t+ M) ] Consider the following finite horizon quadratic criterion: { N ˆ = i= min( J) = E R () Y( t+ ) t W( t+ ) + Qi () U( t+ i) } (6) If there is no constraints, the otimum can be exressed as: N3RGN3 Q GN 3R W N U = ( G + ) ( f ) (7) where R = diag( R,, R), Q = diag( Q,, Q),W is future setoint or reference sequence for the outut vector. R and Q are ositive definite weighting matrices. Because of the receding control strategy, only U is needed at instant t. hus only the first m rows of ( GN3RGN3 + Q) GN3R, say K, have to be comuted. his can be done beforehand for the non-adative case. he control law can then be exressed as U = K( W f ). In the resence of constrains, the above analytical resolution is no longer available. he Quadratic Programming algorithm available in MALAB SIMULINK oolbox will be used for otimization. V. APPLICAION Under the rated load condition, the discretized model for a samling time of 0.03 minutes is: 0.356z z+.46 N e z +.007z z +.007z α = n z z G z +.007z z +.007z A left matrix fraction descrition can be obtained by z making matrix A ( ) equal to a diagonal matrix with diagonal elements equal to the least common multile of the denominators of the corresonding row of the transfer function, resulting in: A( z ) 0 ( z ) = B( z ) B( z ) A B ( z ) 0 A( z ) = B( z ) B( z ) 3 4 A ( z ) = +.0 z +.5 z z z 3 4 A ( z ) = +.0 z +.5 z z z 3 4 B ( z ) = z z z z 3 4 B ( z ) =.7 z z +.73 z z 3 B ( z ) = z z z 3 4 B ( z ) = z 0.00 z z For a rediction horizon N=3, a control horizon M= and a control weight λ = 0.08, matrix G N3 is: Under rated load condition G N 3 = Under 60% load condition G N 3 = Under 30% load condition G N 3 = he evolution of the active ower the gas turbine velocity obtained when the GPC is alied can be seen in Fig.4. Simulation was then made under conventional roortional integral (PI) controller, which is exressed as: Ki Ki α K+ K+ s s w = G K K w s s f K i i + K+ Ne n

4 K and K i are otimized by a genetic algorithm. While K =, K = 0., K = 3, K =.5, K = 0.5, K i = 0.0, K i =.58, K i =., the outut resonse is also shown in Fig.4. i (4-e) Gas turbine velocity resonse under 60% load condition (4-a) Active ower resonse under rated load condition (4-f) Gas turbine velocity resonse under 30% load condition Figure 4. Comaring results between PID(dotted line) and GPC(solid line) (4-b) Active ower resonse under 60% load condition (4-c) Active ower resonse under 30% load condition From Fig.4, under conventional PID controller, while the model is far away from normal oerating condition, the overshoot become quite large, meantime the settling time is notably lengthened. Obviously, conventional PID control strategy can t offer satisfactory results under diverse oerating conditions. Under GPC, while the model is far away from normal oerating condition, the overshoot become a little bit larger, meantime the settling time is slightly lengthened. Obviously, GPC strategy has referable control effect under diverse oerating conditions. In gas turbine control system, the fuel flow change rate should be lower than the real device accelerate rate to avoid damage. he increasing rate of IGV should be lower than that of the servo valve. In order to show the influence of constraints on the slew rate and the amlitude of the maniulated variable, consider the following realistic constraints: 0. 0 Ut ( + i) 0. 0 (8) Ut ( + i) (9) i=,, M (4-d) Gas turbine velocity resonse under rated load condition

5 (5-a) Active ower resonse under rated load condition (5-e) Gas turbine velocity resonse under 60% load condition (5-b) Active ower resonse under 60% load condition (5-f) Gas turbine velocity resonse under 30% load condition Figure 5. Comaring results with constraint handling (5-c) Active ower resonse under 60% load condition (6-a) Control efforts of G f under rated load condition (5-d) Gas turbine velocity resonse under rated load condition (6-b) Control efforts of G f under 60% load condition

6 he obtained results are shown in Fig.5. he control efforts are shown in Fig.6. he constraint otimal controller is comared with constraint limiting controller. he control signal for the constrained otimal controller seems to be better in anticiating the effect of the actuator limits. When u exceeds the constraints, a new set of control signals is obtained, anticiating the control is going to exceed the limits. In contrast, the constraints limited controller reaches a nature saturation condition, offering a much lower erformance. (6-c) Control efforts of G f under 30% load condition (6-d) Control efforts of IGV under rated load condition V. CONCLUSION he modelling and control of a gas turbine in combined cycle ower lant is resented in this aer. Multivariable generalized redictive scheme has been constituted for gas turbine control, after using the local linearization method. Comarison with the traditional PID controller is also made on the simulated ower lant. he roosed method therefore rovides a useful alternative for controlling this class of nonlinear gas turbine generation, which shows strong couling effect and nonlinearity. ACKNOWLEDGMEN his work was suorted by Program for New Century Excellent alents in University under Grant NCE , Natural Science Foundation of Beiing under Grant REFERENCES (6-e) Control efforts of IGV under 60% load condition [] J. A. Rossiter, Model-Based Predictive Control, A Practical Aroach. CRC Press LLC., 003. [] M.R. Katebi, and M.A. Johnson, Predictive control design for largescale systems, Automatica, vol.33, no.3,.4-45, 997. [3] A.W. Ordys, and P. Kock, Constrained redictive control for multivariable systems with alication to ower systems, International Journal of Robust Nonlinear Control, vol. 9, , 999. [4] G. Prasad, E. Swidenbank and B.W. Hogg, A neural net model-based multivariable long-range redictive control strategy alied thermal ower lant control, IEEE rans. Energy Conversion, vol. 3, no.,. 76-8, June 998. [5] X.J. Liu, and CW. Chan, Neuro-fuzzy generalized redictive control of boiler steam temerature, IEEE rans. Energy Conversion, vol., no.4, , Setember, 006. [6] L..Pan, Y. Yang, and Z. Lin, Research on Integrated Modeling Method of Heavy-Duty Single-Shaft Gas urbine-generators, Journal of Power Engineering, vol., no. 5, ,.00. (In Chinese) [7] D.W. Clarke, C. Mohtadi and P.S. uffs, Generalized redictive control, Parts and, Automatica, vol. 3, no., , 987 (6-f) Control efforts of IGV under 30% load condition Figure 6. Comaring results with constraint handling