Multi-model Predictive Control of Ultra-supercritical Coal-fired Power Unit☆

Guoliang Wang*,Weiw u YanShihe Chen,Xi Zhang,*,Huihe ShaoAutomation Department of Shanghai Jiao Tong University,Shanghai0040,China

2Guangdong Electric Power Research Institute,Meihua Rd.,Guangzhou 510600,China

Multi-model Predictive Control of Ultra-supercritical Coal-fired Power Unit☆

Guoliang Wang1,*,Weiw u Yan1,Shihe Chen2,Xi Zhang2,*,Huihe Shao11Automation Department of Shanghai Jiao Tong University,Shanghai200240,China

2Guangdong Electric Power Research Institute,Meihua Rd.,Guangzhou 510600,China

A R T I c L E IN F o

Article history:

Received 7 January 2014

Received in revised form 17 February 2014 Accepted 3March 2014

Available on line 20 June 2014

The control of ultra-supercritical(USC)power unit is a difficult issue for its characteristic of the nonlinearity,large dead time and coup ling of the unit.In this paper,model predictive control(MPC)based on multi-model and double layered optimization is introduced for coordinated control of USC unit.The linear programming(LP)combined with quadratic programming(QP)is used in steady optimization for computation of the ideal value of dynamic optimization.Three inputs(i.e.valve opening,coal flow and feed water flow)are employed to control three outputs(i.e.load,main steam temperature and main steam pressure).The step response models for the dynamic matrix control(DMC)are constructed using the three inputs and the three outputs.Piece wise models are built at selected operation points.Double-layered multi-model predictive controller is implemented in simulation with satisfactory performance.

?2014 Chemical Industry and Engineering Society of China,and Chemical Industry Press.All rights reserved.

1.Introduction

Compared to traditional coal-fired power generation,USC coal-fired power generation units are promising for its higher efficiency and less harmful emission[1].However,USC units are characterized by the strong coup ling characteristic between boiler and turbine,strong nonlinear and dead time characteristic.Without the steam drum buffer, USC boiler dynamic characteristics are affected greatly by terminal dynamic at boiler outlet header.USC units have a complex characteristic for strong nonlinearity under the different output power conditions. Along with the load changes,the dynamic characteristic parameters of units change dramatically.After fuel water ratio changes,steam temperature has a long delay response.Due to the above control difficulty,the parameters of the control system bas ed on PID have a large fluctuation in the process of load changing.

Generally,power units run in four modes:base mode,boiler following mode,turbine following mode,and coordinated control mode.In the first mode,the boiler master and turbine master are both in manual mode.For the 2nd and 3rd modes,the boiler master and turbine master are both in auto mode,respectively[1].Coordinated control is the main control mode of thermal power unit control now[2].Many effective control strategies for power unit coordinated control were proposed in literatures[3].As model predictive control(MPC)can naturally deal with the coup ling and dead time problems,it also began to be applied to the power plant control.Actually,MPC has been applied successfully in chemical industry and many other fields[4].Dynamic matrix control (DMC)method,which is an initial algorithm of MPC,is suitable for the multiple input and output system of traditional power unit[5].Non linear MPC was also utilized in coordinated control of fossil power units [6].Application of DMC method to the super-critical power units was discussed on theoretical and practical aspects[7].The DMC was also applied to the superheater and reheater temperature control problem, which built a 4-input by 4-output model and presented the simulation results to show the effectiveness ofDMC method in power industry[8].

In above literatures,step response was applied to establish dynamic response matrix.Bu t for coal-fired USC power unit,there is a strong nonlinearity in constant load and changing load because the parameters of the units vary largely in different operation points.MPC based on multiple models were proposed to deal with nonlinearity.The basic thought of multi-model MPC was introduced in Ref.[9].Multi-model DMC has been applied to a multi-tank process[10].The application result shows that multi-model DMC is more reliable to keep the controlled variable sat set points over the range of nonlinear operation.There is an intelligent model used in MPC for coordinated control of USC unit[11]. The linearized state space model was used in MPC for coordinated control of USC unit[12].The predictive outputs of multiple models are weighted in a fuzzy manner according to the operation points and the optimization uses the DMC algorithm for main steam temperature control[13].The different linear MPC controllers based on state space predictive model are set up for a Two Tank Conical Interacting System [14]but the constraints are not taken in to account,especially the MV, which is important in practice.The steady-state economic objectivesare em bedded in to dynamic objectives as a penalty function[15].Bu t the equality constraints of steady-state optimization are not considered in the literature.So,the in formation of steady gain of the controlled plant is missing in this manner as mentioned in Ref.[15].A double layered optimization structure,i.e.multivariable constrained predictive control(MCPC),is proposed for the coordinated control of a USC unit in[16].The focus of the paper is on the optimization structure but not on the nonlinearity of USC unit.Considering the nonlinearity of the USC unit,a multi-model MPC based on DMC method with a double-layered algorithm is proposed for USC unit coordinated control in this paper.

2.Ultra-supercritical Un it System

Coal-fired USC unit generally is com posed of boiler and turbine.The boiler includes economizer,water wall,seperator,superheater and reheater.The turbine includes high pressure turbine(HP),inter mediate pressure turbine(IP),low pressure turbine(LP)and generator.In USC unit,water and steam only flow once through economizer,seperator and superheater.Water is turned into vapor entirely under dry condition.Drum,in which steam is separated from water,is not necessary in the USC boiler.

The schematic diagram of a USC coal-fired power generation units is shown in Fig.1.The coal burned in furnace heats all sections of the boiler.The feed water is warm ed up by an economizer in the process cycle firstly.Then hot water is converted to steam in water wall.After passing through the separator,the steam is superheated by superheaters.The valve controls the quantity of superheated steam to the HP turbine. The extraction steam from HP turbine goes to the rehaeater inlet.The reheated steam from the reheater outlet is used to d rive the IP/LP turbine.The extraction steam from IP/LP turbine goes in to the feed water pump and feed water storage tank for the next cycle[17].Without the buffering of steam d rum,the valve influences the characteristics of turbine and terminal resistance of the boiler heavily.This leads to strong non-linearity and parameter coup ling of the USC unit,which can be seen as a complicated system with multiple-input and multiple-output (MIMO)system.The design of the control system,especially the coordinated control,is of more challenge for the USC unit compared to the traditional power units.This paper will focus on the design of the three input by three-output coordinated control system based on the MPC of the USC unit.

3.Double-layered Multi-Model MPC for Coordinated USC Unit Control

MPC arises from chemical process control[18,19].Based on the thoughts of predictive model,on line optimization and feedback correction,MPC has been successfully applied to many industry fields with satisfied results.In this paper,MPC structure used in the coordinated control of USC unit is based on DMC,taking the algorithm of QP (quadratic programming)as following:

where Wkis the reference of the controlled variables(CVs),Ykis the measurement of the CVs,Q and R are the weight matrices of CV and delta m an ipu lated variables(MVs),respectively,Cduand Cyare the constrain t matrix coefficients,bduand byare the constraints of ΔUkand Yk.The solution of Eq.(1)is an M×m vector of MVs,where Mis the control horizon and m is the number of CVs.Only the first of every MV vector is implemented and the rest is discarded.This is typical in MPC algorithm.The procedure is repeated at next sample time.

For coordinated control of USC unit,the purpose of the control strategy is to keep the key parameters within the safe zone and to follow the load demand as quick as possible.When USC unit runs under different conditions,its steady and dynamic characteristic varies greatly.The dynamic optimization of MPC can only track the local optimal targets in time.Steady optimization can reach the global optimal targets in certain operation point.This paper introduces a double-layered MPC with steady optimization and dynamic optimization.

Double-layered MPC comprises of upper layer as steady optimization and lower layer as dynamic optimization.The steady optimization layer of MPC is the supervisor of dynamic optimization layer.The solution of steady optimization will be used as setpoint in dynamic optimization layer.The upper layer gives the control target of the USC unit and the lower layer pushes the USC unit to the optimal target gradually.The LP(linear programming)is used as steady optimization in Ref.[16]. When the economic target is more than linear,economic objective can be expressed as the QP manner.Thus,the steady optimization usesthe combined LP and QP for the IRV computation in this paper.The objective function is as fo llow s:

Fig.1.Schematic diagram of USC unit.

where MV is the optimization variables,MV0and CV0are the economic ideal value of MVs and CVs,PMVand PCVare the weighted matrices of economic optimization,v and ware the coefficients of MV and CV,α and β are the coefficients of linear programming for adjustment,h and g are the equality constraints and inequality constraints and neand ninare the number of equality and inequality constraints.

The solution of linear programming in Eq.(2)is the ideal resting value(IRV)of MV.The ideal resting value of MV will be used in the dynamic optimization of double-layered MPC.The IRV of MV is a soft constraint.The dynamic optimization of double-layered MPC is shown below:

where MVIRVis the IRV,i.e.ideal resting value,of MV,Q and R are the weight matrix of CV and ΔMV,respectively,V the weight matrix for IRV and Cuthe constraints matrix coefficients.

For dealing with the strong nonlinearity at different operation points,piece wise models are set up at chosen operation points of the USC unit.The output power is selected as the multi-model switching sign in this paper.When the USC unit enters the interval of new condition for a period of time(e.g.1 m in),the predictive model in proposed algorithm will switch.This switching policy prevents the predictive model to switch frequently between the adjacent conditions in order to avoid the instability of the system.Because of the constraints of ΔMV,the switch of models in the algorithm will not cause the fluctuation of CVs.The switched models lead to the different steady values of the MVs,but the ΔMVs still obey the constraints.

4.Simulation Results and Discussion

4.1.Nonlinear model of1000MW USC unit

The nonlinear model of 1000 MW USC unit in literature[20]is built in Mat lab system.The relation of temperature,enthalpy and pressure can be obtained by X Steam too l[21],which perm its the direct calculation within Matlab of the water-steam properties through the implementation of the IAPWS-97 laws.The model of the USC unit is simplified under several assumptions[20].The Dw(superheater outlet steam flow rate),ut(valve opening)and rB(the coal flow)are taken as inputs and Ne(load),pst(the pressure of superheater outlet)and hst(the outlet enthalpy of superheater) as outputs of the USC unit.The model is described as state space model as follows[13]:

In the above formula,hm(kJ·kg?1)is the outlet enthalpy of the separator,pm(MPa)is the outlet pressure of the separator,Dec(kg·s?1)is the economizer inlet feed water flow rate,Dw(kg·s?1)is the superheater outlet steam flow rate,rB(kg·s?1)is the coal flow,uB(kg·s?1)is the coal flow setpoint,Dsw(kg·s?1)is the desuperheater spray flows at all levels,Dst(kg·s?1)is the steam flow rate of turbine inlet,ut(%)is the valve opening for steam turbine,Ne(MW)is the load of the unit,pst(MPa)is the outlet pressure of the superheater,hst(kJ·kg?1)is the outlet enthalpy of superheater and Tst(°C)is the temperature of superheater outlet.k0,k1,k2,l,c0,c1,c2,d1and d2are the coefficients of the USC unit and can be estimated by the practical data from real unit.

4.2.Multi-model of USC unit system

In the simulation of coordinated control based proposed method, the feed coal flow,feed water flow and the valve opening are chosen as the three MVs,respectively.And the load,main steam temperature and main steam pressure are chosen as three CVs,respectively.The parameters of 1000MW USC unit are chosen as:l=1.33,k0=19212, k1=133175,k2=0.000560,c0=180,c1=1060000,c2=59830, d1=500,d2=3000,andτ=17.The parameters are identified from the operation data of a 1000 MW USC unit in[12].

The operation range of the USC unit from 1000 MV to 500 MW is separated into five intervals.Six operation points with load of 1000 MV,900 MV,800 MV,700 MV,600 MV and 500 MW,are selected to build models,respectively.The valve opening is chosen as constant 78.04%and the main steam temperature is set at599.9°C.Parameters of the USC unit at six operation points are shown in Table 1.

Table 1Parameters at six operation points

At each operation point,a step increment of 10%is added on a MV meanwhile other MVs keep constant.The responses of the CVs are recorded to identify step response model.The step response models corresponding to other MVs can be obtained by repeating the same procedure.When the proposed algorithm is put in to practice,the model testing procedure will be taken at the steady state of USC unit and the step increment is as small as possible in order to get the characteristic of the inputs and outputs without huge disturbance on the unit. The three input and output step response models of the USC unit are shown in Fig.2.

Different types of the line represent the different models.From 1000 MW to 500 MW,the types of the lines are dash dot,dashed, so lid,dotted with dot,dotted and dotted with square,respectively. The lines of same color in Fig.2 rep resent one three input by three output model at a specific operation point.For example,the nine blue lines represent the three input by three output model at 1000MW operation point.The models also show the characteristic of the USC unit.From Fig.2,it can be seen that valve affects the dynamic and static characteristic of load lightly at different operation points.Dynamic characteristic of main steam temperature is also influenced lightly by valve opening but its steady gain increases largely with the load decreasing.Coal has the same dynamic and steady influence on load and pressure at different operation points,respectively.Steady gain of main temperature to coal is of large deviation at different operation points.Feed water has a large influence on dynamic characteristic of load at different operation points but has a small influence on steady gain of feed water to load. Both of the steady gain of temperature and pressure to feed water decrease with increasing load.

4.3.Simulation results and discussion

The algorithm parameters in simulation are set as follows.The prediction horizon is 600 s and the control horizon is 200 s.The numbers of MVs and CVs are both three.The weight matrix is chosen as Q=diag[1000 200 80],R=diag[1 1 1],V=diag[1 1 1]and the coefficients in steady optimization are constant,which are chosen as one in this paper.The constraints are chosen as:

The control modes of load and main steam temperature are set as setpoint control.The load follow s the load demand.The main steam temperature is set600°C.The control mode of the main steam pressure is set as zone control mode.Switching points of piece wise models are chosen at:950MW,850 MW,750 MW,650 MW and 550 MW.When the USC unit crosses the switching point and does not switch back for 1 m in,the predictive models witches to the new model.

The simulation results are shown as in Figs.3 and 4.Figs.3 and 4 show the simulation results of MVs and CVs when the load demand (AGC)is changing from 1000 MW to 900 MW and 620 MW,and then back to 800 MW and 1000 MW.

Fig.2.Step response models at different operation points.

Fig.3.CV responses in the following load.

The top graph in Fig.3 is the response curve of load following the load demand.The red line is the response curve of the load.The blue line is the curve of the load demand.It can be found that the load can follow the load demand with an extremes mall error when the load is changing largely.The middle graph in Fig.3 shows the response curve of main steam temperature.The main steam temperature can keep around the set point600°C closely.Bu t the steam temperature still fluctuates.The main steam valve influences the parameters of the steam, even when the unit operates at steady state.The main steam temperature can only beheld around the steady value temperature at coordinated control of unit.The accurate value of main steam temperature can be controlled at supreheater section.The maximum error is smaller than 1.5°C.The bottom graph in Fig.3 shows the main steam pressure response curve.The control mode of main steam pressure is set as the zone control.Because the operation point of valve is set as constant, the simulation is similar to the sliding pressure control in traditional control of power unit.Fig.4 shows the MV responses corresponding CVs in Fig.3.The valve varies around the initial operation point,i.e. 78.04%.During the whole process,the coal water ratio constant is kept almost a constant and main steam temperature is maintained stable.

As for the set point control mode of output power and temperature, there are three MVs and two CVs with set point control mode.There is freedom left for the MVs.Thus,the valve opening varies around its steady state value 78.04%as its IRV value.

The proposed algorithm is compared with the other methods in the simulation.Fig.5 shows the comparison among the MMCPC,MCPC and conventional coordinated control method mentioned by Ref.[22]under the given AGC command.The proposed method can follow the AGC timely and no huge overshot compared with other algorithm.

5.Conclusions

In this paper,double-layered multi-model predictive control is developed for coordinated control of USC unit.The USC unit response is represented by three input and three output step responses at differ ent operation points where valve opening,coal flow and feed water flow are inputs and load,main steam temperature and main steam pressure are outputs.The double-layered optimization is performed to determine the optimal operation value of feed water flow and coal flow sothat the load will follow the load demand quickly.The main steam temperature is also kept stable at set point.Simulation results show that the proposed method can implement coordinated control of USC unit with satisfactory performance.

Fig.4.MV responses in the following load.

Fig.5.Comparison among different methods.

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☆Supported by the National Natural Science Foundation of China(60974119).

*Corresponding authors.

E-mailaddresses:g lgw ang@gm ail.com(G.Wang),zhangx.sjtu@163.com(X.Zhang).

Ultra-supercritical power unit

Coordinated control

Multi-model constrained predictive control