Control Of Heat Recovery Steam Generator

JADAVPUR UNIVERSITY, KOLKATA – 700032, INDIA, JANUARY 12 – 14, 2007

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Fuzzy Logic Control of a Heat Recovery Steam Generator A.Gangadhara Rao, M.S.R.Murthy

Abstract-- Increasing complexities of modern industrial processes and requirement of fast and accurate responses necessitated the invention of various control techniques. The designed control system should provide simple and practical solution in order to fulfill the performance requirements. Over the past few decades many concepts and techniques of intelligent control were developed. Fuzzy logic (FL) is one such technique, in which knowledge based design rules can easily be implemented to control a complex system. In this paper a fuzzy logic controller(FLC) has been developed using the pressure deviation and change in pressure deviation of a heat recovery steam generator(HRSG). The designed FLC is used as a pressure controller to regulate the exhaust gas input to the HRSG as per the steam demand . The feasibility and effectiveness of designed FLC is studied by simulation and the results are compared with the conventional proportional integral(PI) controller system. Index Terms—Heat recovery steam generator, Fuzzy logic, Pressure controller, Simulation study. I.

process. Recovery of heat exhausted from industrial process and combustion can improve thermal efficiency also. HRSG is the equipment used to recover the heat from exhaust gases and to generate steam. A simplified model of boiler for system dynamic performance studies was presented in 1991[7]. Constructionally HRSG has many differences with a conventional boiler. It has no means to adjust heat transfer distribution i.e, no burner tilt, no excess air control, no flue gas re-circulation etc. In this paper a simplified HRSG model[8] is considered and it is controlled by the designed FLC. Effectiveness of the FLC is investigated by simulation and the results are compared with a conventional PI controller. II.HEAT RECOVERY SYSTEM Fig.1 shows the schematic diagram of a typical heat recovery steam. It consists of a drum, evaporator, super heater(SH), steam turbine(ST) and electrical generator(G). It has both the gas turbine(GT) exhaust and supplementary fuel as inputs.

INTRODUCTION

A control system design should be simple and should give the desired performance requirement. One of the requirement of a control system is the flexibility, should be able to adapt to a new system with little modifications. FL is one such technique, which can be designed and implemented easily. It can also be modified easily. FLC can closely imitate the human control process. FL technology enables the use of engineering experience and experimental results in designing the knowledge base. This eliminates use of rigorous mathematical modeling to derive a control solution. The concept of fuzzy sets and fuzzy logic was initiated in the year 1965[1]. The first implementation of FL in control systems was accomplished in 1974[2]. Since then FL has been implemented to control many industrial processes, such as robot control[3], jet engine fuel control[4], traffic junction signals control[5] and furnace temperature control[6] etc. In this paper a FLC is developed to control a HRSG. In these days of escalating fuel costs, power shortages many of the industries are opting for co-generation. The need for energy recovery from low and medium sources has gained importance. Waste heat recovery is of prime importance to the efficient use of energy in the industrial

Fig.1 Schematic diagram of a HRSG The heat energy available in the GT exhaust or supplementary fuel is used to generate steam in the evaporator. The generated steam reaches the top position of the drum, from there it goes to the SH, and gets further heated and converted in to saturated steam. This steam is used to drive a ST, which is coupled to a electrical generator.

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INTERNATIONAL CONFERENCE ON EMERGING TRENDS IN ELECTRICAL ENGINEERING

III.SYSTEM MODEL Fig.2 shows the transfer function block diagram of heat recovery system used in this paper. There are various blocks representing the transfer function of the associated equipment. The input and output variables of each block are linked as shown in the fig. Description of parameters is provided in the appendix in table.1.

Fig.2 Block diagram of a heat recovery system The input to the model i.e, GT exhaust is represented by the block Blspm and it is fed to the steam generation equipment. The out put of steam generation equipment is represented by xme. This steam reaches the top portion of drum and then goes to the SH, where it will be further heated and converted in to saturated steam xp. In the actual functioning , a HRSG may be subjected to many disturbances. To control the steam generation a pressure controller is included in the system. The pressure controller actuates based on the difference between the SH steam pressure xp and the pressure controller set point pr. In a conventional control system , a PI controller is used as a pressure controller. In this paper a fuzzy logic controller(FLC) is used as a pressure controller and its performance is compared with a PI controller.

recovery system with FLC. As shown in the fig, inputs to the FLC are error e(k) and change in error ce(k).

e(k) = yref - y(k) ce(k) = y(k) - y(k-1)

Traditional control design methods use mathematical models of system and its inputs to design controllers to analyse their effectiveness. FLC uses fuzzy sets and fuzzy inference to derive control laws in which no precise model of the plant exists and most of the priori information is available only in qualitative form. The basic idea of FLC is to make use of expert knowledge and experience to build a rule base with linguistic rules. Proper control actions are then derived from this rule base. In this paper FLC is used as a pressure controller to control the HRSG. Fig.3 shows the diagram of a heat

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The inputs e(k) and ce(k) are multiplied by the scaling or weightage factors Ke and Kce before feeding to the FLC. The output of the FLC is also multiplied by a factor Ku. These scaling factors are used to tune the controller to get the desired response. In this paper the values of Ke, Kce and Ku are taken as 0.02, 0.0001 and 17 respectively. As shown in the fig.3 FLC contains a fuzzifier, inference engine, rule base and de-fuzzifier and it has two inputs and one output. FUZZIFICATION The fuzzification block converts real world variables in to fuzzy sets. In order to decide the number of fuzzy sets and their parameters, the universe of discourse(UD) is to be decided. The UD is the range over which the selected variable can vary. In this paper UD is taken as [-1,1] for both the inputs and output. After selecting the UD the no of membership functions and their shape and ranges are to be selected. The number of membership functions used in the fuzzification play a crucial role in the final performance of a FLC system and the choice of membership function has strong influence on the control effect. There are several types of membership functions used in FLC such as triangular function, gaussian function, bell function, trapezoidal function etc. After selecting the membership functions, their parameters are to be decided. As shown in the fig.4(a) for the input variable error there are seven membership functions known as,

II.FUZZY LOGIC CONTROLLER

Fig.3 Heat recovery system with FLC

…….. 1

(a) input variable ‘error’

(b)input variable ‘change of error’ and output Fig.4 Membership functions

JADAVPUR UNIVERSITY, KOLKATA – 700032, INDIA, JANUARY 12 – 14, 2007

NB NM NS Z PS PM PB

= = = = = = =

negative big negative medium negative small zero positive small positive medium positive big

Among these seven, the membership functions NB and PB are the trapezoidal functions and all other are the triangular functions. In order to decrease the steady state error, the range of Z set is made small and the peaks of NS and PS are made to be close to Z set. To have quick control on large errors, the shape of NB and PB are taken as trapezoidal form. To reduce programme execution time only seven membership functions are considered. The input variable change of error also has 7 member functions. But they are symmetrically arranged. As shown in the fig.4(b) all the membership functions are triangular, except NB and PB. These two functions are in trapezoidal form. The output variable is almost the same as input variable ce.

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A rule is generated using the control engineering knowledge. In this paper the heuristic method proposed by Mamdani[2] is used to build the rule base. ri : IF e is NB and ce is NB THEN u is NB

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where ri denotes the ith fuzzy rule, i =1,2,3……,n. In the above rule the first part i.e, upto the word THEN is known as a antecedent and the part after the word THEN is known as the consequent. Consequent is the control action to be taken based on the antecedent. INFERENCE ENGINE The basic function of inference engine is to compute the overall value of the fuzzy control output based on the individual contributions of each rule in the rule base. Each such individual contribution represents the value of the fuzzy control output as computed by single rule. In this paper the direct inference system is used. It determines directly the outputs from the knowledge base and on line data by min-max operation. It simply transfers the operators know-how in to the control system employing IFTHEN rules and membership functions.

RULE BASE DEFUZZIFICATION A control algorithm is coded using the fuzzy statements in the block containing the rule base, by taking in to account the control objectives and the system behavior. While differential equations are the language of conventional control, IF-THEN rules about how to control the system are the language of fuzzy control, since IFTHEN operator is the simplest and widely used interpretation. Fuzzy rules serve to describe the qualitative relationship between variables in linguistic terms. Instead of developing a mathematical model of the system, knowledge based system is implemented. The number of rules in the rule base depends on the number of linguistic variables. As shown in the fig.5, 49(7 x 7) rules are used to control the heat recovery system.

For real life applications we need a crisp output to control the systems. The process of converting a aggregated fuzzy set in to a crisp value is known as defuzzification. Defuzzification plays a great role in a FLC system. It is the process in which the fuzzy quantities defined over the output membership functions are mapped in to non fuzzy number. Many different methods exists to accomplish defuzzification. In this paper the center of gravity(COG) method is used. The control output ∆u is determined using the following expression.

Σ(membership of i/p x o/p corresponding to

membership of i/p)

∆u =------------------------------------------------------------------

Σ(membership of i/p)

∑ µ ju j 49

∆u =

j =1 j = 49

∑ µj j =1

Fig.5 Rule base

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INTERNATIONAL CONFERENCE ON EMERGING TRENDS IN ELECTRICAL ENGINEERING

IV.SIMULATION AND RESULTS

(a)

(a)

(b) Fig .6 HRSG response for case-1

(b) Fig.7 HRSG response for case-2

In the practical application a HRSG may be subjected to various disturbances such as sudden changes in steam demand, variations in GT exhaust etc. During these disturbances the pressure controller has to control the system. In order to study the control action of the designed FLC, a heat recovery system is modeled as per fig.2 using MATLAB software. The response of the system with FLC is compared with the conventional PI controller. The following two cases are considered for the simulation study. Case 1. sudden increase in steam demand by 0.2 pu Case 2. sudden decrease in steam demand by 0.2 pu Fig shows the effect of sudden increase in steam demand on HRSG response. Initially steam demand was 1.0 pu, which is suddenly increased to 1.2 pu. When the steam demand suddenly increases, the steam pressure in the SH falls immediately, which actuates the pressure controller. The pressure controller immediately increases the exhaust input to the steam generation system to meet the steam demand. Fig 6(a) shows the variation of steam generation for case-1. There is a overshoot of 0.03 pu with the

conventional PI controller, where as there is no over shoot with the FLC. Fig 6(b) shows the controller’s output variation for case-1. In order to meet the increased steam demand the controllers output increases sharply in positive direction to increase the exhaust input to the steam generation system. But with a conventional PI controller, there is a overshoot of 0.13 pu. Fig 7 shows the effect of sudden decrease in steam demand on HRSG response. Initially steam demand was 1.0 pu, which is suddenly decreased to 0.8 pu. When the steam demand suddenly decreases, the steam pressure in the SH immediately raises, which actuates the pressure controller. The pressure controller immediately decreases the exhaust input to the steam generation system to meet the new steam demand. Fig 7(a) shows the variation of steam generation for case-2. There is a undershoot of 0.03 pu with the conventional PI controller, where as there is no undershoot with the FLC. Fig 7(b) shows the controllers output variation for case-2. In order to meet the decreased steam demand the controller’s output increases sharply in negative direction to decrease the exhaust to the steam generation system. But with a conventional PI controller, there is a undershoot of 0.13 pu.

JADAVPUR UNIVERSITY, KOLKATA – 700032, INDIA, JANUARY 12 – 14, 2007

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V.CONCLUSIONS In this paper a FLC is developed to act as a pressure controller for the HRSG. The response of the system with the developed FLC and a conventional PI controller is investigated. The conventional design requires a deep understanding of the system, exact mathematical models and precise numerical values, a basic feature of FLC is that a process can be controlled with out the knowledge of its underlying dynamics . The control strategy learned through experience can be expressed by a set of rules to describe the behavior of the controller using linguistic terms. Proper control action can be inferred from this rule base that emulates the role of human operator. Computer simulation has been conducted for PI, FLC based systems. The results shows that the FLC yields more improved control performance than the PI controller.

[7]F.P.De mello, “Boiler models for system dynamic performance studies”, IEEE trans. on power systems, vol.6, No.1, pp 66-74, 1991 [8] Dr.Ing. Gunter Klefenz, “Automatic control of steam power plants”, 3rd revised edision, Hartman & Brann AG, Minden.

A.Gangadhara Rao received B.Tech degree in Electrical and electronics from JNTUniversity college of engineering, Kakinada in 1992 and M.Tech degree in Electrical power systems from Regional engineering college, Warangal in 1995. Since 1995 he is working as a Lecturer with the Department of Technical Education, Government of Andhra Pradesh.

APPENDIX Table.1 Model Parameters

REFERENCES [1] L.A.Zadeh, “Fuzzy sets”, Inform.Control, Vol.8, pp 339 – 353, 1965 [2] E.H.Mamdani, “Application of fuzzy algorithms for control of simple dynamic plant”, Proc.IEE 121(12), pp 1585 – 1588, 1974 [3] I.S.Akkizidis, G.N.Roberts, P.Ridao, J.Batlle, “Design a fuzzy like PD controller for an under water robot”, Control engineering practice, pp 471 – 480, 2000 [4] A.Zilouchian, M.Juliano, T.Healy, J.Davis, “Design of fuzzy logic controller for a jet engine fuel system”, Control engineering practice, Vol.8, pp 873 – 883, 2000 [5] C.H.Chou, J.C.Teng, “A fuzzy controller for traffic junction signals”, Information sciences, Vol.43, pp 73 – 97, 2002 [6] Z.R.Radakovic, V.M.Milosevic, S.B.Radakovic, “Application of temperature fuzzy controller in a indirect resistance furnace”, Applied energy, Vol.73, pp 167-181, 2002

M.S.R.Murthy graduated in Electrical engineering in 1971, and obtained M.E degree in control systems in 1974 from Andhra University college of engineering, Visakhapatnam. He obtained his Ph.D degree from IIT-Bombay in 1985. Currently he is a Professor in Electrical and Electronics department, ICFAI Institute of science and technology, ICFAI University, Hyderabad.