Application of Dynamic Matrix Control To a Boiler-Turbine System

Transcription

1 Application of Dynamic Matrix Control To a Boiler-Turbine System Woo-oon Kim, Un-Chul Moon, Seung-Chul Lee and Kwang.. Lee, Fellow, IEEE Abstract--This paper presents an application of Dynamic Matrix Control (DMC) to a drum-type boiler-turbine system of a fossil power plant. Two possible inds of step response models are investigated in designing the DMC, one is developed with the linearization of theoretical model and the other is developed with the process step-test data. Then, the control performances of each model-based DMC are simulated and evaluated. It is observed that the simulation results with the step-response model based on the test data show satisfactory results, while the linearized model is not suitable for the control of boiler-turbine system. Index Terms--Power generation control, boiler-turbine control, process control, dynamic response, predictive control, dynamic matrix control. A I. INTRODUCTION boiler-turbine system supplies high pressure steam to rotate the turbine in thermal electric power generation. The purpose of the boiler-turbine system control is to meet the load demand of electric power while maintaining the pressure and water level in the drum within tolerance. This boiler-turbine system is usually modeled with a Multi-Input Multi-Output (MIMO) nonlinear system []. The severe nonlinearity and wide operation range of the boiler-turbine plant have resulted in many challenges of power system control engineers. Hogg and Ei-Rabaie presented an application of adaptive control, that is, selftuning eneralized Predictive Control (PC) to a boiler system []. Cori and Maffezzoni applied a Linear Quadratic aussian (LQ) controller [], Pellegrinetti and Bentsman designed an H Controller for boilers [4], Ben-Abdennour and Lee applied the Linear Quadratic aussian with Loop transfer Recovery (LQ/LTR) method [5]. Recently, Tan and others approximated the H to PI controller [6]. Many inds of artificial intelligence techniques have also been applied [7]- []. Model Predictive Control (MPC) refers to a class of control algorithms that compute a sequence of control inputs based on an explicit prediction of outputs within some future horizon. The computed control inputs are typically W.. Kim, U. C. Moon, S. C. Lee are with the School of Electrical and Electronics Engineering, ChungAng University, HuSu-dong DongJa-u, Seoul, Korea, ( ucmoon@cau.ac.r). K.. Lee is with the Department of Electrical Engineering, The Pennsylvania State University, University Par, PA 68, USA ( wanglee@psu.edu). implemented in a receding horizon fashion, meaning only the inputs for the current time are implemented and the whole calculation is repeated at the next sampling time. Therefore, MPC has the advantage that can consider the constraints of input and output variables []. One of the most well-nown MPC algorithms for the process control is Dynamic Matrix Control (DMC), which assumes a step-response model as the underlying system. Because DMC needs a lot of numerical calculation at every sampling time, it is a suitable technique for the systems which have slow dynamics. DMC has been successfully applied to numerous industrial processes, and many commercial software was developed; DMC+, SMC, RMPCT, HIECON, PFC, OPC, etc. []. In the power systems area, Rovna and Corlis presented simulation results of DMC to a supercritical boiler []. Nowadays, the MPC based on the state-space model is developed, however, it is hard to find industrial applications of the state-space MPC. In this paper, we present an application of DMC to a drumtype boiler-turbine system of a fossil power plant. In designing the DMC, one of the most important step is the development of step-response model to describe the system dynamics. In this paper, two possible inds of methods are considered for the development of the step-response model. First one is when the exact nonlinear theoretical model is given, the step-response model can be found by the linearization of the nonlinear model. The other situation is when the step-response model is identified from the process test data. A DMC is designed for each model, and the differences in control performances are evaluated and discussed. II. BOILER-TURBINE SSTEM MODEL A. Nonlinear Boiler-Turbine System Model The model of Bell and Åström [] is assumed as a real plant among various nonlinear models for the boiler-turbine system. That is a 6 MW oil fired drum-type boiler-turbinegenerator model for overall wide-range simulations. It is a third order MIMO nonlinear state equation as follows []: 9 / 8.8u x +.9u. 5u x& () 9 / 8 x & [(.7u.6) x x]/ () Authorized licensed use limited to: Baylor University. Downloaded on January 6, at :6 from IEEE Xplore. Restrictions apply.

2 x& 4u (.u.9) ]/ 85 () [ x y x y x y.5(.7x + a cs + qe / ) (4) (5) (6).6 / 8 u x A ( u ) x ( u) / 8 (4) where, cs (.58ρ f )(.8 p 5.6) ρ (.94.4p) α (7) q e f (.854u.47) p u u (8).9 B.8x.7 x. x 85 9 /8 9 / (5) The three state variables x, x and x are drum steam pressure (P in g/cm ), electric power (E in MW) and steamwater fluid density in the drum (ρ f in g/m ), respectively. The three outputs y, y and y are drum steam pressure (x ), electric power (x ) and drum water level deviation (L in m), respectively. The y, drum water level L, is calculated using two algebraic calculations α cs and q e which are the steam quality (mass ratio) and the evaporation rate (g/sec), respectively. The three inputs u, u and u are normalized positions of valve actuators that control the mass flow rates of fuel, steam to the turbine, and feed water to the drum, respectively. Positions of valve actuators are constrained to [,], and their rates of change per second are limited to:.7 du dt.7 (9) C D (5 a x.5 cs x.474 q ) x e ( a x.4 ) cs (6) (7) The, X and U are the differences from the respective operating points. With the assumption that the system is in a steady state with (5, 85, ), X (5, 85, 4.759), U (.447,.7787,.546), the constant matrix A, B, C and D are as follows:. du dt. ().5 du dt.5 () A (8) B. Step-Response Model with Linearization In most cases of designing boiler-turbine control systems, it is assumed that the exact theoretical model is given, therefore, the linearization of the nonlinear theoretical model is used to design the linear controller []-[6]. With this assumption, the step response model for DMC can be developed with familiar linearization technique. In using the nonlinear model, ()-(8) is linearized using Taylor series expansion at the operating point, (y, y, y ), X (x, x, x ), U ( u, u, u ). The result of linearization is as follows: X & ( t) AX ( t) + BU ( t) () ( t) CX ( t) + DU ( t) () where, B (9) C () D () Then, a simple algebraic operation gives transfer functions as follows: ( s) [ C( si A) B + D] U ( s) () Authorized licensed use limited to: Baylor University. Downloaded on January 6, at :6 from IEEE Xplore. Restrictions apply.

3 U ( s) () The transfer functions ij are as follows:.9s +.9 s +.s +.9 (4).746s.746 s +.s +.9 (5).5s.5 s +.s +.9 (6) 7.88* s +.44 s +.s +.9 (7) 5.9s +. s +.s +.9 (8) -.77 s +.s +.9 (9) -6.5s +.78s +.544s.6* () s +.s +.9s In the figure, horizontal axes are time (second), and vertical axes represent the outputs, y, y and y. The three columns of plots are the responses corresponding to the respective step inputs, u, u and u. C. Step-Response Model with Process Test In the case when the reliable theoretical model is not available, the step-response model is obtained from experimental data. The usual process test signal is the step signal or a Pseudo Random Binary Signal [][4]. In this paper, the step response model is developed with a step input. With the same operating point of the linearized model, (5, 85, ), X (5, 85, 4.759), U (.447,.7787,.546), the three step inputs, u, u and u, are applied independently, and then the corresponding output responses are stored. With a simple normalization, the stepresponse model of the plant can be developed. Fig. shows the developed step response model of a plant. y y u u u -7.54s +.566s.576s + 7.8* () s +.s +.9s -6.4 s +.59s +.698s +.87* () s +.s +.9s y u u u Fig.. Step-response model by the process test data. y y y Fig.. Step-response model by linearization. With (4)-(), the step-response model is given in Fig.. In the DMC design, nine step responses of Fig. or Fig. are discretized with a sampling time. The discretized step response coefficients are stored as a matrix form, dynamic matrix, to describe the dynamics of nonlinear boiler-turbine system. By comparing Fig. and Fig, we can find out the difference of the two step-response models. Though the outputs y and y of both models are very similar, the output y shows some differences. The models and show some difference in slopes and, the response from the amount of governor steam to the drum water level, shows a significant difference. The response of the linearized model is increasing in Fig., while that of the test data is decreasing in Fig.. From physical point of view, the water level is decreased as the steam in the drum is released. Therefore, the linearized model has modeling error in describing the dynamic of. Authorized licensed use limited to: Baylor University. Downloaded on January 6, at :6 from IEEE Xplore. Restrictions apply.

4 4 III. DMC FOR BOILER-TURBINE SSTEM The design of DMC in this paper follows the standard approach []. For a Single Input Single Output (SISO) system, the prediction equation is in the following form: d S U + + () where, + represents a prediction of future output trajectory, [y +,, y +p ], at t, and p is the prediction horizon. is the unforced output trajectory [y + +,, y +p ], which means the open-loop prediction given that the input u remains constant at the previous value u -. is input adjustments vector, [ u,, u +m- ], and m is the control horizon. S is the dynamic matrix containing the step d response coefficients, and + is an estimate of unmeasured disturbance on the future output. To compute the inputs, the following on-line optimization is performed at every sampling time: u + + U Λ Γ U min E (4) where, E + + R + [e +,, e +p ], and R + [r +,, r +p ] is a vector containing the desired trajectory of future output, and x represents the weighted Euclidean Λ norm, x T Ax. To the above, additional constraints of the following are added: min + (5) max U U (6) min U max each e and u are weighted for three output and input as follows: T e e e e e (8) Λ e e u u u u u (9) Γ u T u where, e i is defined as -step error between i-th output and i- th reference setpoint. In (8), the weight of e is while the other weights are ones, because the nominal value of y and y are about times than that of y. The control actions are equally weighted as ones. d + is taen as a constant bias of difference between the actual measurement and the open loop model output. Output constraint (5) is not considered in this study and input constraints (9) () are implemented as a form of (6), and three inputs are constrained in [, ] in (7). Fig. shows the system configuration. The DMC controller is applied to the nonlinear bolier-turbine system, and the control algorithm optimizes the control performance (4) at every sampling step with the developed step-response model. For comparison purpose, the same DMC controller is applied with both step-response models independently. DMC Step Responses U where min U U max (7) U is a vector [u,,u +m- ]. R On-Line Optimization with Input Constraints U Nonlinear Boiler- Turbine System The resulting problem is a Quadratic Programming (QP) problem with the inequality constraints (5) - (7). Once the optimal inputs are computed, the first input u is implemented and the rest is discarded. The procedure is repeated at the next sampling time. In this study, the boiler-turbine system is a Multi-Input Multi-Output (MIMO) system which has three inputs and three outputs. Therefore, all the elements in vectors in () - (7), y in, u in U, e in E and r in R, etc., are also vectors, each with three elements. And, a dynamic matrix S of () contains nine step responses of Fig. or Fig.. The sampling time is determined as 5 [sec]. The prediction horizon p is 6 [sec] and control horizon m is also 6 [sec], and R + is fixed with three constant setpoint values. In (4), Fig.. DMC-based system configuration. IV. SIMULATION RESULTS The control system and process model were simulated with Matlab in a personal computer environment. With the assumption that the system is in a steady state with (, 5, ), X (, 5, 449.5), U(.7,.64,.6) initially, the setpoints of outputs are implemented as (,, ) for both DMCs. This case describes that the setpoints of pressure and electric load are increased to and, respectively, while the drum water level is ept to zero. Authorized licensed use limited to: Baylor University. Downloaded on January 6, at :6 from IEEE Xplore. Restrictions apply.

5 5 Figs. 4 and 5 show the simulation results with two stepresponse models, Fig. and Fig., respectively. In the figures, the horizontal axis is time [sec], and the vertical axis is [g/cm ] for y, [MW] for y and [cm] for y, respectively. In Fig. 4, y and y show fluctuation, while y tracs the reference after 5 seconds. This shows that even if we have a good nonlinear theoretical model of boiler-turbine system, its linearized model is not suitable in the control of drum-type boiler-turbine system with DMC. In Fig. 5, three outputs are stabilized after seconds. This result shows that the drum-type boiler-turbine system is successfully controlled by DMC based on the step-response model obtained by the process test. Considering the two DMCs are the same except the stepresponse model, the poor performance stems from the poor quality of the linearized model. This can be interpreted that the process test model partially contains the nonlinearity of the plant while the nonlinearity is removed in the linearization procedure. V. CONCLUSION AND DISCUSSION This paper presents an application of Dynamic Matrix Control (DMC) to a boiler-turbine system of a fossil power plant. Two possible inds of step-response models are investigated in designing the DMC, one is developed with the linearization of theoretical model and the other is developed with the process step test data. The two step-response models show a clear difference in describing the response from the amount of governor steam to the drum water level,. The DMC simulation shows satisfactory results with the process test data model while the linearized model shows poor results. We have identified two results with this study. First, the drum-type boiler-turbine system can be effectively controlled by the DMC. Second, a careful validation of the step-response model is necessary in designing the DMC though we have a good quality of nonlinear model. These results can provide a good practical guidance in implementing the DMC to the drum-type boiler-turbine system. REFERENCES y y y [sec] Fig. 4. DMC with the linearized model. y y y [sec] Fig. 5. DMC with the process test data model. [] R. D. Bell and K. J. Åström. Dynamic models for boiler-turbinealternator units: Data logs and parameter estimation for a 6 MW unit, Report: TFRT-9, Lund Institute of Technology, Sweden [] B. W. Hogg and N. M. Ei-Rabaie, "Multivariable eneralized Predictive Control of a Boiler System", IEEE Transactions on Energy Conversion, Vol. 6, No., pp. 8-88, June 99. [] R. Cori and C. Maffezzoni, Practical Optimal Control of a drum boiler power plant, Automatica, Vol., pp. 6-7, 984. [4]. Pellegrinetti and J. Bentsman, H Controller design for boilers, Int. J. Robust Nonlinear Contr., Vol. 4, pp , 994. [5] A. Ben-Abdennour and K.. Lee, "A Decentralized Controller Design for a Power Plant Using Robust Local Controllers and Functional Mapping", IEEE Transactions on Energy Conversion, Vol., No., pp. 94-4, June 996. [6] W. Tan, H. J. Marquez and T. Chen, Multivariable Robust Controller Design for a Boiler System, IEEE Transactions on Control System Technology, Vol., No. 5, pp , Sep.. [7]. Prasad, E. Swidenban and B. W. Hogg, "A Neural Net Model-based Multivariable Long-range Predictive Control Strategy Applied in Thermal Power Plant Control", IEEE Transactions on Energy Conversion, Vol., No., pp. 76-8, March 99. [8] R. Dimeo and K.. Lee, "Boiler-Turbine Control System Design using a enetic Algorithm", IEEE Transactions on Energy Conversion, Vol., No. 4, pp , December 995. [9] F. A. Alturi and A. B. Abdennour, "Neuro-Fuzzy Control of a Steam Boiler-Turbine Unit", Proceedings of IEEE International Conference on Control Applications, pp , Hawai, U.S.A., 999. [] U.-C. Moon and K.. Lee, "A Boiler-Turbine System Control Using A Fuzzy Auto-Regressive Moving Average (FARMA) Model ", IEEE Transactions on Energy Conversion, Vol. 8 No., pp. 4-48, Mar. [] J. H. Lee, Model Predictive Control in the Process Industries: Review, Current Status and Future Outloo", Proceedings of the nd Asian Control Conference, Vol II, pp , Seoul. July -5, 997. [] C. R. Culter and B. L. Ramaer, "Dynamic Matrix Control - A Computer Control Algorithm.", Proceedings of Joint Automatic Control Conference, San Francisco, CA, 98. [] J. A. Rovna and R. Corlis, "Dynamic Matrix based Control of Fossile Power Plant", IEEE Transactions on Energy Conversion, Vol. 6, No., pp. -6, June 99. [4]. F. Franlin, J. D. Powell and A. Emami-Naeini, Feedbac Control of Dynamic System, Prentice-Hall,. Authorized licensed use limited to: Baylor University. Downloaded on January 6, at :6 from IEEE Xplore. Restrictions apply.

6 6 Woo-oon Kim was born in Seoul, Korea, on Nov., 978. He received the B.S. degree in Electrical Engineering in 4 from the Chung-Ang University in Seoul, Korea. He is currently pursuing the M.S. degree at the Chung-Ang University. His research interests include automatic control, optimizations and their applications to power systems and industrial processes. Un-Chul Moon received his B.S., M.S. and Ph.D. degrees from the Seoul National University, Korea, in 99, 99 and 996, respectively, all in the Electrical Engineering. From, he has been a professor in electrical engineering at the Woo-Seo University, Korea, and from at the Chung-Ang University, Korea. His current research interests are in the areas of power system analysis and automations. Seung-Chul Lee received his B.S. degree from the Seoul National University, Korea, in 969, and M.S. and Ph.D. degrees from the University of Florida in 98 and 985, respectively, all in the Electrical Engineering. From 969, he wored for industry in the area of power plant construction, test operation and design until 98. when he was a senior electrical engineer at the Hyundai Engineering Company. From 985, he has been the professor in the electrical engineering at the University of Tennessee Space Institute and the Chung-Ang University. His current research interests are in the areas of intelligent systems application to power systems, power system planning, and reliability analysis. Kwang. Lee (F ) received the B.S. degree in electrical engineering from Seoul National University, Seoul, Korea, in 964, the M.S. degree in electrical engineering from North Daota State University, Fargo, in 968, and the Ph.D. degree in system science from Michigan State University, East Lansing, in 97. Currently, he is Professor of Electrical Engineering at the Pennsylvania State University, University Par. He has been on the faculties of Michigan State, Oregon State, and University of Houston. His interests are power system control, operation and planning and intelligent system techniques, and their application to power system and power plant control. Dr. Lee is an Associate Editor of IEEE Transactions on Neural Networs and Editor of IEEE Transactions on Energy Conversion. Dr. Lee is a Fellow of the IEEE. Authorized licensed use limited to: Baylor University. Downloaded on January 6, at :6 from IEEE Xplore. Restrictions apply.