Multi-variable state closed-loop control for a steam generator of a thermal power plant

Abstract

A device for closed-loop control of a plurality of state variables of a steam generator of a thermal power plant is provided. In order to achieve stable and exact closed-loop control of the plurality of state variables, a multi-variable control/controller controls the plurality of state variables and uses a linear quadratic controller for this multi-variable control/controller.

Claims

1. A method for closed-loop control of a plurality of state variables in a steam generator of a thermal power plant, comprising: providing a spatially discretized steam generator model of the steam generator of the thermal power plant, wherein the steam generator has at least one evaporator and a superheater, wherein the steam generator has a plurality of discretized volume elements with a constant volume, and wherein the spatially discretized steam generator model has at least one of energy and mass balance set by way of the plurality of discretized volume elements; simultaneously controlling the plurality of state variables using a multi-variable state controller, the multi-variable state controller being a linear quadratic controller, wherein the multi-variable state controller uses the spatially discretized steam generator model.

2. The method as claimed in claim 1, wherein the plurality of state variables simultaneously controlled by the multi-variable state controller are a temperature, a pressure and/or an enthalpy of a steam generator medium of the steam generator, at least a fresh steam pressure, an evaporator output enthalpy and superheater output temperatures of the steam generator.

3. The method as claimed in claim 1, wherein manipulated variables of the multi-variable state controller are selected from the group consisting of: mass flows of the steam generator, a fuel mass flow, a feedwater mass flow, and an injection mass flow in a superheater or injection mass flows in superheaters.

4. The method as claimed in claim 1, wherein manipulated variables of the multi-variable state controller are subject to statistical feedforward control.

5. The method as claimed in claim 1, wherein an overall observer is used during multi-variable state control, with the use of which state variables and/or disturbance variables are estimated at the steam generator.

6. The method as claimed in claim 5, wherein at least one of a Kalman filter and an extended Kalman filter is used in the overall observer.

7. The method as claimed in claim 6, wherein at least one of the Kalman filter and the extended Kalman filter is designed for linear quadratic state feedback.

8. The method as claimed in claim 1, wherein the spatially discretized steam generator model is used in an overall observer.

9. The method as claimed in claim 1, wherein reference values are predetermined centrally during the multi-variable state control, which reference values are used for feedforward control and for state control during the multi-variable state control.

10. A device for closed-loop control of a plurality of state variables in a steam generator of a thermal power plant, wherein the multi-variable state controller as claimed in claim 1 controls the plurality of state variables.

Description

BRIEF DESCRIPTION

(1) Some of the embodiments will be described in detail, with reference to the following figures, wherein like designations denote like members, wherein:

(2) FIG. 1 shows a schematic diagram of an embodiment of a steam generator (also steam generator model) in a power plant unit/thermal power plant comprising one evaporator and three superheaters (also controlled system);

(3) FIG. 2 shows a scheme of an embodiment of a multi-variable state control;

(4) FIG. 3 shows an overall closed-loop control structure of an embodiment of a multi-variable state control/controller with static feedforward control and multi-variable state control, and with an overall system observer (state/disturbance variable observer);

(5) FIG. 4 shows a schematic diagram of an embodiment of a steam generator model;

(6) FIG. 5 shows a schematic diagram of an embodiment of an extended Kalman filter as an overall system observer;

(7) FIG. 6 shows a list of variables of an embodiment of a multi-variable state control/controller;

(8) FIG. 7 shows an embodiment of an extended steam generator model with coal burning;

(9) FIG. 8 shows an embodiment of a temperature controller/superheater output temperature controller with measured and observed (dashed) variables (control engineering process model);

(10) FIG. 9 shows an embodiment of an evaporator output enthalpy controller with measured and observed (dashed) variables (control engineering process model); and

(11) FIG. 10 shows an embodiment of a fresh steam pressure controller with measured and observed (dashed) variables (control engineering process model).

DETAILED DESCRIPTION

(12) FIG. 1 shows a schematic illustration of a section of a thermal power plant 2, in this case a coal power plant unit, comprising a steam generator 1 (FIG. 1 is also model illustration of the steam generator 1).

(13) The steam generator 1 consists of an evaporator (VD, 7) and a superheater (UH, 4, 5, 6), in this case a three-stage superheater (referred to for the sake of simplicity as first, second and third superheater (UH1 4, UH2 5, UH3 6) below), comprising two injections (in the second and third superheater, Einsp1/injection 1 14, Einsp2/injection 2 15).

(14) Feedwater (SPW) flows into the evaporator 7 and is evaporated there under the take-up of heat Q. The inflowing feedwater mass flow rate (m(P).sub.SPW) can be set by means of a control valve (not depicted here).

(15) Furthermore, the (onward flowing) steam (D) is superheated to fresh steam (FD)by the further take-up of heat Qin the three superheaters 4, 5, 6 of the steam generator 1 and flows out of the superheaters 4, 5, 6/the third superheater 6 or out of the steam generator 1 (m(p).sub.FD).

(16) The take-up or transmission of heat or the level thereof in the evaporator VD 7 or in the superheaters 4, 5, 6 is adjustable by way of the fuel mass flow rate (m(P).sub.b).

(17) Subsequently, after emerging from the superheaters 4, 5, 6, the third superheater 6 or the steam generator 1, the fresh steam (FD) is fed to the steam turbine (not depicted here).

(18) By means of two injection coolers 15, 16, water is injected into the steamin the second and third superheater 5, 6and thus cools said steam. The amount of water injected in the respective (second or third) superheater 5, 6 (injection rate/rates of mass flow, m(P).sub.Einsp1 or 2) is set by a corresponding control valve (not depicted here).

(19) In the following text, the steam (downstream of the evaporator 7 and) upstream of the superheaters 4, 5, 6/the first superheater 4 is referred to as steam (D) and the steam downstream of the superheaters 4, 5, 6/the third superheater 6 is referred to as fresh steam (FD) for the purposes of a better distinction only (upstream of the evaporator 7, the medium is feedwater (SPW)), wherein the fact that the invention in the embodiment described below is naturally also applicable to steam which may possibly not be referred to as fresh steam is highlighted.

(20) Temperature sensors (not depicted here) and pressure sensors (not depicted here) measure the temperatures T.sub.SPW, T.sub.VD and pressures p.sub.SPW, p.sub.VD of the feedwater and of the steam upstream and downstream of the evaporator 7. A temperature sensor (not depicted here) and a pressure sensor (not depicted here) measure the fresh steam temperature T.sub.FD and the fresh steam pressure p.sub.FD of the steam downstream of the superheaters 4, 5, 6. A sensor (not depicted here) measures the feedwater mass flow rate m(P).sub.SPW.

(21) Enthalpy values h can be calculated from the temperature value and the pressure value with the aid of the water/steam table such that this sensor system can also indirectly measure the feedwater enthalpy or evaporator input enthalpy h.sub.SPW and the fresh steam enthalpy or superheater output enthalpy h.sub.FD.

(22) A steam generator model, the installation-technical (model) structure of which is elucidated in FIG. 1, is based inter alia on a spatial discretization of the steam generator 1 (made of the evaporator 7 and the three superheaters 4, 5, 6) into elements with a constant volume (denoted below by VE for volume elements).

(23) The evaporator 7 can comprise a preheater (not depicted here). However, this is irrelevant to embodiments of the invention and, in the following, the term evaporator is also understood to mean a system consisting of an evaporator with a preheater.

(24) Unit Closed Loop Control

(25) The unit closed loop control in the coal power plant unit is brought about by means of a multi-variable state control 3, which comprises the control loops: fresh steam pressure, evaporator output enthalpy and superheater output temperatures (via the injections) (cf. FIGS. 8 to 10).

(26) FIG. 2 shows a principle of this multi-variable state controller 3 with the controlled and manipulated variables thereof.

(27) In this multi-variable state controller (MIMO) 3, the state or controlled variables: fresh steam pressure p.sub.FD, evaporator output enthalpy h.sub.VD and superheater output temperatures T.sub.UH1/2/3 are controlled simultaneously, wherein a clear assignment from the manipulated variables: fuel mass flow rate m(P).sub.b, superheater injection mass flow rates m(P).sub.i,UX2/UX3 and feedwater mass flow rate m(P).sub.SPW to the controlled variables: fresh steam pressure, evaporator output enthalpy and superheater output temperatures is dispensed with.

(28) All manipulated and controlled variables are linked (in the multi-variable state controller 3) to one another (by the respective control error), as a result of which physical couplings between individual closed-loop controls (SISO, fresh steam pressure control, evaporator output enthalpy control and superheater output temperature control) are accounted for.

(29) As is also elucidated by FIG. 2, the multi-variable state controller 3 is a linear quadratic controller or linear quadratic regulator (LQR). That is to say, the feedback matrix of the multi-variable state controller is established in such a way that it has the control quality of a linear quadratic controller.

(30) Such a linear quadratic controller or linear quadratic regulator (LQR) is a (state) controller, the parameters of which can be determined in such a way that a quality criterion for the control quality is optimized.

(31) Here, the quality criterion for linear quadratic closed-loop control also considers the relationship of the variables: the manipulated variable u and the controlled variable y. Here, priorities can be determined by the Q.sub.y and R matrices. The quality value J is determined according to:
J(x.sub.0,u(t))=.sub.0.sup.(y(t)Q.sub.yy(t)+u(t)Ru(t))dt.

(32) The static optimization problem in this respect, which is solved by the linear quadratic closed-loop control, is as follows (with K as controller matrix and x.sub.0 as initial state):

(33) $\underset{u\left(t\right)}{\min }J\left(x_0,u\left(t\right)\right)=\underset{u\left(t\right)=-Kx\left(t\right)}{\min }J\left(x_0,u\left(t\right)\right)=\underset{K}{\min }J\left(x_0,-\mathrm{Kx}\left(t\right)\right).$

(34) In order to calculate the controller matrix, the feedback matrix of the LQR is converted into a set of scalar equations, into so-called matrix Riccati equations, in the multi-variable state control 3 and solved.

(35) These matrix Riccati equations emerge from ideal linear quadratic control problems on a continuous time interval that is unbounded on one side if these problems are tackled, as is the case here, using a feedback approach, i.e. with (state) feedback.

(36) FIG. 3 shows the overall closed-loop control structure of the multi-variable state control/controller 3 with its components: steam generator/steam generator model 9, overall system observer (state/disturbance variable observer) 10, central reference value default 11 and (the actual) multi-variable state controller (in this case abbreviated to only state controller 12).

(37) In the following text, the following nomenclature also denotes used variables:

(38) Measured variables are denoted by the nomenclature measured, reference values are denoted by the nomenclature reference, open-loop controlled variables are denoted by the nomenclature open-loop control, closed-loop controlled variables are denoted by the nomenclature closed-loop control and observer variables are denoted by the nomenclature obs. Fuel is represented by b, SPW denotes feedwater, FD denotes fresh steam, p represents pressure, h represents enthalpy, m represents mass, Q represents heat and T represents temperature. Flows are denoted by (P).

(39) FIG. 6 also lists used variables for the overall closed-loop control structure of the multi-variable state control/controller 3.

(40) Steam Generator Model 9 (FIG. 1, FIG. 4)

(41) The steam generator model 9, the installation-technical (model) structure of which is elucidated by FIG. 1, is based on a spatial discretization of the steam generator 1 (made of the evaporator 7 and the three superheaters 4, 5, 6) into elements with a constant volume (denoted below by VE for volume elements) and a concentrated pressure storage DSP.

(42) FIG. 4 elucidates this VE/DSP setup of the steam generator model 9. Input variables and state variables in the steam generator model 9 or in the volume elements VE and the pressure storage DSP are denoted by opposing slashes (input variables (\), state variables (/)).

(43) A VE with the index k consists of an energy storage, described by the enthalpy h.sub.a,k. Moreover, it is defined by the mass m.sub.a,k and the volume V.sub.a,k thereof.

(44) For the sake of simplicity, flows in the state variables/input variables are denoted by (P) or by the dot thereover.

(45) The input variables are the external heat supply Q(P).sub.k by the flue gas, the mass flows m(P).sub.i,k flowing in from the outside and m(P).sub.o,k flowing out to the outside and the specific enthalpy h.sub.i,k of the mass flow m(P).sub.i,k.

(46) Enthalpy values can be calculated with the aid of the water/steam table from the temperature value and the pressure value.

(47) In order to represent the piping, and hence the delay in the heat transfer from the flue gas to the steam, an iron mass is assigned to each VE. The iron masses are denoted by the temperature T.sub.E,k and the mass m.sub.E,k thereof.

(48) However, these are not further state variables of the steam generator model 9, but they can be included in the calculation as auxiliary variables.

(49) The heat flow which acts from the iron masses onto the steam is denoted by Q(P).sub.E,k. Therefore, the enthalpy of each VE is additionally dependent on Q(P).sub.E,k.

(50) The pressure p is modeled by the concentrated pressure storage DSP. The VEs are coupled to one another by way of the mass flows m(P).sub.VE,k and the enthalpies h.sub.a,k: thus, in the case of n VEs, there are n+1 states (pressure and enthalpies) and n1 mass flows between individual VEs.

(51) First of all, the model equations of the steam generator model 9, set up by the mass and energy balances which are set up for the volume elements VEs, are specified below; these subsequently being converted into a matrix representation.

(52) Model Equations

(53) From the mass balance of a volume element VE with the mass m.sub.a,k:

(54) $\frac{m_{a,k}}{t}={m\left(P\right)}_{\mathrm{VE},k-1}-{m\left(P\right)}_{\mathrm{VE},k}+{m\left(P\right)}_{i,k}-{m\left(P\right)}_{o,k}$
and of the energy balance for a volume element VE:

(55) $\frac{d{h}_{a,k}}{dt}=\frac{1}{m_{a,k}+a_k}\left(h_{a,k-1}{m\left(P\right)}_{\mathrm{VE},k-1}-h_{a,k}{m\left(P\right)}_{\mathrm{VE},k}+h_{i,k}{m\left(P\right)}_{i,k}-h_{a,k}{m\left(P\right)}_{o,k}-h_{a,k}\frac{d{m}_{a,k}}{dt}+{Q\left(P\right)}_k\right),$
the following emerges for the state equation for each volume element VE:

(56) $\frac{dp}{dt}={\left(\frac{m_{a,k-1}}{p}\right)}^{-1}.Math.\left(-{m\left(P\right)}_{\mathrm{VE},k-1}+{m\left(P\right)}_{i,k-1}-{m\left(P\right)}_{o,k-1}-\frac{m_{a,k-1}}{h_{a,k-1}}\frac{d{h}_{a,k-1}}{dt}\right)$$\frac{dp}{dt}={\left(\frac{m_{a,k}}{p}\right)}^{-1}.Math.\left(-{m\left(P\right)}_{\mathrm{VE},k-1}-{m\left(P\right)}_{\mathrm{VE},k}+{m\left(P\right)}_{i,k}-{m\left(P\right)}_{o,k}-\frac{m_{a,k}}{h_{a,k}}\frac{d{h}_{a,k}}{dt}\right)$$\frac{dp}{dt}={\left(\frac{m_{a,k+1}}{p}\right)}^{-1}.Math.\left({m\left(P\right)}_{\mathrm{VE},k}+{m\left(P\right)}_{i,k+1}-{m\left(P\right)}_{o,k+1}-\frac{m_{a,k+1}}{h_{a,k+1}}\frac{d{h}_{a,k+1}}{dt}\right),$
wherein the unknown variables in the mass and energy balance are the mass flows between the VEs: m(P).sub.VE,k-1 and m(P).sub.VE,k, which can be determined by way of the pressure dependence of the masses stored in the VE with the aid of the water/steam table.

(57) What emerges from this in the case of three volume elements is three equations for three unknowns, specifically the two mass flows between the VEs and the time derivative of the pressure.

(58) Hence, all variables are determined uniquely.

(59) What follows from the model equations is that the steam generator model 9 is scalable as desired. This means that the steam generator model 9 can be configured for differently designed steam generators (number and size of the superheaters, number of injections, multi-stranded plants).

(60) Matrix Representation

(61) Converting the mass balance into matrix representation yields:

(62) $\begin{array}{c}\frac{dm}{dt}=F_{+}{m\left(P\right)}_m-F_{-}{m\left(P\right)}_m+F_i{m\left(P\right)}_i-F_0{m\left(P\right)}_0\\ ={\mathrm{Fm}\left(P\right)}_m+F_i{m\left(P\right)}_i-F_0{m\left(P\right)}_0.\end{array}$

(63) Converting the energy balance into matrix representation yields:

(64) $\frac{d\left(\mathrm{Hm}\right)}{dt}=H\frac{dm}{dt}+M\frac{dh}{dt}={\mathrm{FH}}_m{m\left(P\right)}_m+F_i{H}_i{m\left(P\right)}_i-F_0{H}_0{m\left(P\right)}_0+Q\left(P\right)-\frac{dh}{dt}.$

(65) From this, the matrix equation of the model can be specified as:

(66) $\frac{dx}{dt}=D_i{m\left(P\right)}_i-D_0{m\left(P\right)}_0+D_{Q}Q\left(P\right)$$D_i=\left[-C_p{B}_{\mathrm{pm}}^{-1}{B}_i;A_i-A_m{C}_m{B}_{\mathrm{pm}}^{-1}{B}_i\right]$$D_0=\left[-C_p{B}_{\mathrm{pm}}^{-1}{B}_0;A_0-A_m{C}_m{B}_{\mathrm{pm}}^{-1}{B}_0\right]$$D_Q=\left[-C_p{B}_{\mathrm{pm}}^{-1}{B}_Q;A_Q-A_m{C}_m{B}_{\mathrm{pm}}^{-1}{B}_Q\right]$

(67) The matrices D.sub.i, D.sub.o and D.sub.Q depend on the enthalpies and the pressure, i.e. the states, but neither on the in-flowing and out-flowing mass flows nor on the heat flows. If the variables are combined in a vector, the following emerges for the nonlinear steam generator model 9:

(68) $\frac{dx}{dt}=G_{\mathrm{nl}}\left(x\right)u,G_{\mathrm{nl}}\left(x\right)=.Math.D_i,-D_0,D_Q.Math.,u=\left({m\left(P\right)}_i,{m\left(P\right)}_0,Q\left(P\right)\right),$

(69) For the (overall) observer design, the steam generator model 9 must be linearized 17 about the current work point x.sub.o, u.sub.o. The linearized equations are:

(70) 0${{{\frac{dx}{dt}=A_{\mathrm{de}}x+B_{\mathrm{de}}u,A_{\mathrm{de}}=\frac{d\left(G_{\mathrm{nl}}\left(x\right)u\right)}{dx}.Math.}_{x_0,u_0}=\frac{d\mathrm{Gnl}\left(x\right)}{dx}.Math.}_{x_0}.Math.u_0{B}_{\mathrm{de}}=\frac{d\left(G_{\mathrm{nl}}\left(x\right)u\right)}{du}.Math.}_{x_0,u_0}=G_{\mathrm{nl}}\left(x_0\right)$
Overall System Observer (FIG. 5) 10

(71) FIG. 5 elucidates the extended Kalman filter (EKF) 13 used as state and disturbance variable observer 10 (overall system observer; also abbreviated as observer 10 only).

(72) The (conventional) Kalman filter is a state and disturbance variable observer. The object thereof is to observe or estimate, with the aid of measured data, the state variables and disturbance variables of the system by means of an underlying model.

(73) The conventional Kalman filter assumes a linear system.

(74) However, since the model of the steam generator is nonlinear, an extended Kalman filter 13 is used in the present case.

(75) FIG. 5 shows the setup of the conventional linear Kalman filter using full lines; dashed signal paths and blocks symbolize the extension to nonlinear models.

(76) This extension consists in a linearization of the model 17, which is recalculated in each time step; i.e., the (nonlinear) model 21 is linearized 17 about the current state thereof. Expressed differently, the observer approach is based upon a nonlinear observer 21, which is linearized 17 about the work point at each time step and thus supplies the system matrices for the observer 10 and the closed-loop controller 3 and 12.

(77) The input variables of the EKF 13 are the measured input and output variables of the system. The state and disturbance variables output by the observer 10 are: firing (x.sub.firing), pressure (p), enthalpy (h)state variables; injections (m(P).sub.Einsp, fresh steam mass flow (m(P).sub.FD), heat flow (Q(P).sub.n)disturbance variables).

(78) As shown in FIG. 5, the observer model (A.sub.ds, B.sub.ds) 20 is formed from the linearized model 17 (A.sub.de, B.sub.de), the firing model 18 and the disturbance variable model 19.

(79) The observer gain L is calculated on the basis of this observer model 20.

(80) By means of this observer gain L, the observer errors e.sub.obs, i.e. deviations between measured data and model outputs, are applied to the nonlinear model 17.

(81) These applied correction terms Le.sub.obs consist, firstly, of corrections of the states of the nonlinear model and, secondly, of the estimated disturbance variables which act on the model.

(82) Deviations between the model and the real process are compensated for by this application.

(83) The design of a Kalman filter can be traced back to the design of an LQR by way of the concept of duality. This design is based on the solution of the matrix Riccati differential equation 22:

(84) $-\frac{d{P}_{\mathrm{obs}}}{dt}=A_{\mathrm{ds}}^{}{P}_{\mathrm{obs}}+P_{\mathrm{obs}}{A}_{\mathrm{ds}}-P_{\mathrm{obs}}{B}_{\mathrm{ds}}{R}_{\mathrm{obs}}^{-1}{B}_{\mathrm{ds}}^{}{P}_{\mathrm{obs}}+Q_{\mathrm{obs}},$
where L emerges from the solution p.sub.obs in accordance with:
L=(R.sub.obs.sup.B.sub.dsP.sub.obs).

(85) The described steam generator model 9 (cf. FIG. 1) is used in the observer 10.

(86) Since the heat flow Q(P) is only an internal variable and results from the fuel mass flow m(P).sub.b, the steam generator model 9 must be extended accordingly in this respect.

(87) FIG. 7 shows the steam generator model 9 extended in this respect.

(88) The coal combustion and heat release, i.e. the transfer behavior from the fuel mass flow m(P).sub.b to the heat flow Q(P), are described by a third order delay element 14 with the time constant T.sub.firing.

(89) The output of the actual PT3 element 14 is a scalar variable, but it is distributed amongst the individual VEs by way of a constant distribution matrix Q.sub.0.

(90) The firing model 18 or the differential equation of the PT3 element 14 is as follows:

(91) $\frac{d{x}_{\mathrm{firing}}}{dt}=\frac{1}{T_{\mathrm{firing}}}\left(\begin{array}{ccc}-1& 1& 0\\ 0& -1& 1\\ 0& 0& -1\end{array}\right).Math.x_{\mathrm{firing}}+\left(\begin{array}{c}0\\ 0\\ \underset{\_}{1}\\ T_{\mathrm{firing}}\end{array}\right).Math.{\stackrel{.}{m}}_b$$\stackrel{.}{Q}=Q_0\left(\begin{array}{ccc}1& 0& 0\end{array}\right).Math.x_{\mathrm{firing}},$
where the states of the PT3 element are denoted by x.sub.firing (firing) in this case.

(92) The state vector in the observer 10 is consequently extended by x.sub.firing and has the following setup:

(93) $x_{\mathrm{obs}}=\left(\begin{array}{c}{x}_{\mathrm{firing}}\\ p\\ h\end{array}\right),$
where:
x.sub.firing.sup.31
p.sup.11.
h.sup.n1

(94) In addition to the state observation, the EKF 13 serves as disturbance variable observer.

(95) Here, both actual disturbance variables, such as the variable heat flow transferred by the flue gas, and further variables not explicitly modeled count as disturbance variables. Here, this applies to the injected mass flows. Although injected mass flows are measured, an estimate by the EKF 13 is preferred in this case due to the lack of accuracy. The same applies to the output mass flow m(P).sub.FD, which is likewise estimated.

(96) The observed state variables and the estimated disturbance variables are, simultaneously, the output variables of the observer 10.

(97) The diagonally occupied covariance matrix Q.sub.obs specifies the covariance of the state noise of the observer model. A small value is selected for states that are well-described by the model equations. States that are modeled less exactly and pure disturbance variables are assigned higher values in the covariance matrix due to the higher stochastic deviations.

(98) The covariance matrix of the measurement noise R.sub.obs is likewise occupied diagonally. Large values mean very noisy measurements, and so trust is more likely to be put into prediction by the model. In the case of small values (and therefore reliable measurements), observer errors can accordingly be corrected more sharply.

(99) Here, the entries of Q.sub.obs and R.sub.obs are themselves diagonal matrices in each case, the dimensions of which depend on the number of states or the number of temperature measurement points.

(100) In order to set the speed of the observer 10, the ratio of the covariance matrices to one another is varied by the factor .sub.obs. In theory, the weightings of the individual states and measured variables within the matrices can also be trimmed. However, the interplay is complex such that, for reasons of simple parameterizability, tuning should be carried out only by way of the factor .sub.obs.

(101) Multi-Variable State Controller 3 (Cf. FIG. 2) Concept

(102) The closed-loop control concept of the multi-variable state controller 3 (FIG. 2) is based on concepts of individual LQG observer controllers of/for the fresh steam pressure, evaporator output enthalpy and (via the injections) (cf. FIGS. 8 to 10) superheater output temperature individual controls, which were extended appropriately to the present multi-variable system (the overall observer 10 is put in place of the observers of the individual LQR observer controllers).

(103) The controlled variables are fresh steam pressure, evaporator output enthalpy and superheater output temperatures.

(104) The power (or the fresh steam mass flow) is controlled by the turbine valve, which is assumed to be ideal. Therefore, the fresh steam mass flow is predetermined and hence an input variable of the system.

(105) In addition to the fuel mass flow and the feedwater mass flow, a plurality of injections (into the superheaters 5, 6) serve as manipulated variables. Moreover, for the injection mass flows there exists a reference value which is intended to be maintained in the stationary state.

(106) Individual Controls (Fresh Steam Pressure, Evaporator Output Enthalpy and Superheater Output Temperatures (Via the Injections) (Cf. FIGS. 8 to 10)

(107) Superheater Output Temperature Controller/(Abbreviated) Temperature Controller (FIG. 8)

(108) In a cascaded structure of temperature control (superheater output temperature control), the temperature controller generates, as shown by FIG. 8, the reference value for the underlying closed-loop control of the injection cooling of each superheater stage.

(109) The temperature controller operates using enthalpy variables, and so, initially, it is necessary to calculate these (to the extent that these are measured/measurable, otherwise by the observer) from the measured/observed temperature values and the associated pressures with the aid of a water/steam table.

(110) For the observer estimate, the steam enthalpy is reconstructed at three points in the superheater 4, 5, 6 by the observer (where the length of the superheater is spatially divided into three).

(111) FIG. 8 shows the temperature controller (closed-loop control-technical process model (with controller elements 14)), wherein the observed variables used by the temperature controller are marked by dashes.

(112) The steam enthalpy after the injection cooling h.sub.NK and after the evaporator h.sub.VD and also the output enthalpy h.sub.FD (or h.sub.1) are still available as measured variables; the intermediate variables h.sub.2 and h.sub.3 are variables estimated by the observer.

(113) However, there is a difference in respect of the thermal output of the flue gas q.sub.F. It is not determined as a specific variable by the observer, but as an absolute value. However, since the temperature controller expects a specific variable, the value must initially be calculated with the aid of the mass flows m(P) between the volume elements VE, which mass flows are likewise observed.

(114) Evaporator Output Enthalpy Controller/(Abbreviated) Enthalpy Controller (FIG. 9)

(115) The enthalpy controller has the object of controlling the enthalpy at the evaporator output to a reference value with the aid of the feedwater mass flow.

(116) Analogously to the temperature controller, the enthalpy controller requires the enthalpy values at three points in the evaporator 7. In addition to the measured value at the evaporator output, the existing observer reconstructs the values of the enthalpy at and of the length of the evaporator 7.

(117) So that the overall system observer 10 of the multi-variable state control 3 also knows the corresponding enthalpy values, the model must be parameterized with multiples of three states (i.e. volume elements).

(118) FIG. 9 shows the closed-loop control-technical process model of the enthalpy controller, wherein the observed variables used thereby are marked by dashes.

(119) The input and output enthalpies h.sub.vECO and x.sub.1 are available to the controller as measured variables; the intermediate enthalpies x.sub.2 and x.sub.3 and the mass flows m(P).sub.i, m(P).sub.2, m(P).sub.3 are estimated by the observer.

(120) Fresh Steam Pressure Controller/(Abbreviated) Pressure Controller (FIG. 10)

(121) The fuel mass flow m(P).sub.b serves as manipulated variable for controlling the fresh steam pressure. The fresh steam mass flow m(P).sub.FD guided onto the turbine acts as a disturbance variable on the pressure.

(122) The dynamics of converting fuel into thermal output is represented by third order delay elements 14.

(123) FIG. 10 shows the closed-loop control-technical process model of the pressure controller, wherein the observed variables used thereby are marked by dashes.

(124) These individual LQG observer state controllers are adapted in such a way that these can be simulated by the overall system observer 10 instead of their dedicated observer. Only relatively small modifications are required since these are based on comparable models.

(125) The closed-loop control concept of the multi-variable state controller 3 provides a controller consisting of two independent modules, namely the static pre-controller 8 and the (actual) multi-variable state controller 12 (abbreviated to state controller 12 only below) (cf. FIG. 3).

(126) In this manner, the advantages of the state control in respect of compensating for disturbances are combined with the stationary accuracy of conventional PI control.

(127) Pre-Control 8/Central Reference Value Default 11

(128) As elucidated by FIG. 3, the central reference value default 11 satisfies two objects.

(129) Firstly, it consists of a static guide and disturbance variable application. This generates the manipulated variables (u.sub.open-loop control), which bring 8 the system into the reference state, on the basis of the guide variables and the observer outputs.

(130) Secondly, the associated reference value is calculated for each state of the model, once again on the basis of the guide variables and the estimated disturbance variables. These reference values comprise the states of the firing model, the pressure and the enthalpies of the volume elements. These reference values are required for the reference value/actual value compensation in the state control 12.

(131) In conclusion, the following outputs therefore emerge from the central reference value default 11:

(132) $u_{\mathrm{open}\text{-}\mathrm{loop}\mathrm{control}}=\left[\begin{array}{c}{\stackrel{.}{m}}_{b,\mathrm{open}\text{-}\mathrm{loop}\mathrm{control}}\\ {\stackrel{.}{m}}_{i,\mathrm{open}\text{-}\mathrm{loop}\mathrm{control}}\\ \end{array}\right],x_{\mathrm{reference}}=\left[\begin{array}{c}{x}_{f,\mathrm{reference}}\\ p_{\mathrm{reference}}\\ h_{\mathrm{reference}}\end{array}\right],$
where:
{dot over (m)}.sub.b,open-loop control.sup.11, {dot over (m)}.sub.i,open-loop control.sup.i1,
x.sub.f,reference.sup.31, p.sub.reference.sup.11, h.sub.reference.sup.n1.

(133) The reference values or the control components are in this case calculated on the basis of the model equations. All mass flows between the volume elements VE and the feedwater mass flow emerge from the (given) fresh steam mass flow and the reference values for the injection mass flows. This is described in the following equation (in the following, the dimensions of the matrices are specified in part):

(134) $\left[\underset{\underset{nn}{}}{\begin{array}{cc}F& F_i\left(:,1\right)\end{array}}\right].Math.\left[\begin{array}{c}{\stackrel{.}{m}}_m\\ \underset{\underset{n1}{}}{{\stackrel{.}{m}}_{\mathrm{Spw}}}\end{array}\right]=\underset{\underset{n\left(o+i-1\right)}{}}{\left[\begin{array}{cc}{F}_o& -F_i\left(:,2\text{:}\mathrm{end}\right)\end{array}\right]}.Math.\left[\begin{array}{c}{\stackrel{.}{m}}_o\\ \underset{\underset{\left(o+i-1\right)1}{}}{{\stackrel{.}{m}}_{\mathrm{Einsp},\mathrm{reference}}}\end{array}\right].$

(135) From this, the enthalpy reference values of all VEs can be calculated with the aid of the estimated heat flows Q(P). To this end, the mass flows are initially brought into matrix form:

(136) $\underset{\underset{nn}{}}{M^{*}}=\underset{\underset{\left(nm\right)\left(mm\right)\left(mn\right)}{}}{F.Math.M_m.Math.F_{-}^{}}-\underset{\underset{\left(no\right)\left(oo\right)\left(on\right)}{}}{F_o.Math.{\stackrel{.}{m}}_o.Math.F_o^{}},$
whereby all enthalpy reference values (hreference) can be calculated using the enthalpy balance:

(137) $\left[\underset{\underset{n\left(n-1\right)}{}}{M^{*}\left(:,1\text{:}\mathrm{end}-1\right)}\underset{\underset{n1}{}}{\begin{array}{cc}& \stackrel{.}{Q}\end{array}}\right].Math.\left[\begin{array}{c}{h}_{\mathrm{reference}}\left(1\text{:}\mathrm{end}-1\right)\\ \underset{\underset{n1}{}}{{\hat{x}}_{f,\mathrm{reference}}}\end{array}\right]=\left[\underset{\underset{n1}{}}{-M^{*}\left(:,\mathrm{end}\right)}\right].Math.\underset{\underset{11}{}}{h_{\mathrm{FD},\mathrm{reference}}}-\left[\underset{\underset{ni}{}}{F_i}\right].Math.\left(\underset{\underset{i1}{}}{{\stackrel{.}{m}}_{{}_{i,\mathrm{reference}}}}\underset{\underset{i1}{}}{.Math.h_i}\right).$

(138) Consequently, the enthalpy reference values emerge as:

(139) $h_{\mathrm{reference}}=\left[\begin{array}{c}{h}_{\mathrm{reference}}\left(1\text{:}\mathrm{end}-1\right)\\ \underset{\underset{n1}{}}{h_{\mathrm{FD},\mathrm{reference}}}\end{array}\right].$

(140) The reference value for the pressure (p.sub.reference) is predetermined from the outside and therefore does not need to be calculated. The three states of the firing model 18 have the same reference value in the stationary case, and so the following applies:

(141) $x_{f,\mathrm{reference}}={\hat{x}}_{f,\mathrm{reference}}.Math.x_{f,\mathrm{obs}}.Math.\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right].$

(142) The control components are the calculated input mass flows m(P).sub.spw and m(P).sub.i,reference. For the fuel mass flow, the control component equals the reference value of the firing model 18 multiplied by the observed output of the firing model 18:

(143) 0${\stackrel{.}{m}}_{i,\mathrm{open}\text{-}\mathrm{loop}\mathrm{control}}=\left[\begin{array}{c}{\stackrel{.}{m}}_{\mathrm{Spw}}\\ \underset{\underset{i1}{}}{{\stackrel{.}{m}}_{i,\mathrm{reference}}}\end{array}\right],{\stackrel{.}{m}}_{b,\mathrm{open}\text{-}\mathrm{loop}\mathrm{control}}={\hat{x}}_{f,\mathrm{reference}}.Math.x_{f,\mathrm{obs}}.$

(144) State Controller 12

(145) In the case of a perfect model and an undisturbed system, the central reference value default 11 would be sufficient. However, since this is not the case, the pre-control 8 is, as shown in FIG. 3, complemented by the (actual) multi-variable state controller 12 (also abbreviated to state controller 12 only below).

(146) FIG. 3 shows the interconnection thereof with the steam generator model 9, the overall system observer 10 and the central reference value default 11.

(147) The reference values of the states are balanced with the observed states and the control error is formed thereby. Consequently, the control error is not a scalar variable, as is the case in e.g. conventional PI control, but a vector variable.

(148) As elucidated by FIG. 3, manipulated variables (u.sub.closed-loop control) are calculated from this vector, which manipulated variables are applied to the control components in an additive manner. Here, control law consists of a weighted sum of the control errors 8 in accordance with the following equation:
u.sub.closed-loop control=K
where
K.sup.(3+1+n)(1+1+i1)
u.sub.closed-loop control.sup.(1+i)(1).

(149) Here, the control gain K is calculated by solving an optimization problem, in which a compromise is found between high control quality and low manipulation complexity. In this optimization problem, a quality functional satisfying the following equation is minimized:
J=.sub.0.sup.(xQ.sub.lqrx+uR.sub.lqru)dt

(150) The state controller 12 is parameterized by two weighting matrices Q.sub.lqr and R.sub.lqr.

(151) The two weighting matrices Q.sub.lqr and R.sub.lqr are components of a square quality functional. The controller 12 or the feedback matrix K is the result of an optimization problem, in which a compromise is found between control quality and manipulation complexity. Here, Q.sub.lqr evaluates the control quality and R.sub.lqr evaluates the manipulation complexity.

(152) A stronger weighting of Q.sub.lqr (smaller weighting of R.sub.lqr) accordingly leads to smaller square deviations of the actual state values from the reference values. However, this is bought by an increased manipulation complexity. Conversely, smaller values of Q.sub.lqr lead to worse control quality but, at the same time, a smoother manipulated variable profile is also achieved.

(153) The weighting matrices are diagonal matrices, the dimensions of which correspond to the number of state variables or the number of manipulated variables. The order of magnitude of the state variables (or manipulated variables) also plays a role when selecting the weightings in the non-normalized case. In principle, all weightings are selectable individually; however, the weightings within one system section (e.g. evaporator 7) are expediently evaluated the same.

(154) In a manner analogous to the observer design, a matrix Riccati differential equation is also solved here (22):

(155) $-\frac{d{P}_{\mathrm{lqr}}}{dt}=A^{}{P}_{\mathrm{lqr}}+P_{\mathrm{lqr}}A-P_{\mathrm{lqr}}{\mathrm{BR}}_{\mathrm{lqr}}^{-1}{B}^{}{P}_{\mathrm{lqr}}+Q_{\mathrm{lqr}}$

(156) The solution renders it possible to determine the controller gain K
K=R.sub.lqr.sup.1BP.sub.lqr,
where P.sub.lqr is the solution of the matrix Riccati differential equation.

(157) Although the present invention has been disclosed in the form of preferred embodiments and variations thereon, it will be understood that numerous additional modifications and variations could be made thereto without departing from the scope of the invention.

(158) For the sake of clarity, it is to be understood that the use of a or an throughout this application does not exclude a plurality, and comprising does not exclude other steps or elements. The mention of a unit or a module does not preclude the use of more than one unit or module.

LIST OF REFERENCE SIGNS

(159) 1 Steam generator 2 Thermal power plant 3 Multi-variable state controller/control, LQR multi-variable state controller 4 (First) superheater 5 (Second) superheater 6 (Third) superheater 7 Evaporator 8 Static pre-control 9 (Spatially discretized) steam generator model 9 Extended steam generator model (from (9)) 10 (Overall) observer, state/disturbance variable observer 11 Central reference value default 12 State control (in (3)) 13 Kalman filter, extended Kalman filter 14 Controller, control element, third-order delay element, PT3 element 15 (First) injection 16 (Second) injection 17 Linearization (about a work point), linearized model 18 Firing model 19 Disturbance variable model 20 Observer model 21 Linear Kalman filter, linear model/observer 22 Riccati solver DSP Pressure storage VE Volume element L Observer gain [/] State variable [\] Input variable P Process