EP1892468A1 - System and method for controlling thermodynamic parameters of a steam - Google Patents

Abstract

Described herein is a method for controlling thermodynamic parameters of a steam (ST) that is supplied to a steam-using unit (3), said steam (ST) being obtained by mixing a first regulation steam (ST₁) with a second regulation steam (ST₂), regulating the respective flow rates (Q _ST1, Q _ST2 ) of said first and second regulation steams (ST₁, ST₂), said method being characterized in that it comprises the steps of: controlling the thermodynamic parameters of said steam (ST) on the basis of said flow rates (Q_ST1, Q_ST2 ) of said first and second regulation steams (ST₁, ST₂ ) so that to one and the same variation of the flow rates (Q _ST1 , Q _ST2 ) of said first and second regulation steams (ST₁, ST₂ ) there always corresponds one and the same variation of said thermodynamic parameters of said steam (ST) and so that to a variation of one of said flow rates (Q _ST1 ,Q _ST2 ) there corresponds exclusively a variation of one of said thermodynamic parameters of steam (ST) that it is intended to control, maintaining all the other thermodynamic parameters of said steam (ST) constant.

Description

• The present invention relates to a system and a method for controlling thermodynamic parameters of a steam and, in particular, the temperature, pressure, and flow rate of a steam that is supplied to any steam using apparatus, for example a combustion chamber supplied with steam produced by a combined-cycle plant for the production of electric power.
• As is known, in industrial plants such as, for example, plants for the production of electric power or chemical plants, there is frequently the problem of having to control a set of thermodynamic parameters such as, for example, the pressure, temperature and flow rate of a fluid that flows within a duct or pipe and it supplied to a steam-using unit, for example a combustion chamber.
• In combined-cycle plants for the production of electric power, for example, it is known to control the temperature, pressure, and flow rate of the steam that is introduced into the combustion chamber of the gas turbine in order to reduce the emissions of the plant, appropriately mixing in the duct for supplying the combustion chamber a superheated steam, supplied, for example, by a superheater or by a steam turbine, with a saturated steam or water in conditions of saturation, coming, for example, from an evaporator.
• The amounts of saturated and superheated steam to be introduced into the duct for supplying the combustion chamber are determined according to the flow rate of steam at outlet from the duct, in order to regulate the temperature, pressure, and flow rate of supply steam so that the current values of said parameters always correspond to the desired ones.
• Said regulation is performed, generally, using two distinct regulators, one for the pressure, which controls the pressure of the supply steam, by regulating the flow rate of the first steam for example the saturated one, and one that controls the temperature of the steam, which acts by regulating the flow rate of the other steam, for example the superheated one.
• The regulation of the pressure and temperature of a supply steam for a plant by means of two separate regulators tends, however, to cause the values of the pressure and of the temperature of the steam at outlet from the supply duct to deviate from the desired values and to render the process of supply of the plant unstable principally on account of the fact that a fluid-dynamic system of this sort is nonlinear and presents a marked interaction between the variables involved in the process of regulation.
• Consequently, in the aforesaid type of control, the regulator of the pressure of the supply steam affects also the temperature of the supply steam, whilst the regulator of the temperature of the supply steam affects also the pressure of the supply steam, and there is thus created a static/dynamic coupling between the controlled variables, i.e., the pressure and temperature of the steam of the supply duct, and the control variables, i.e., the flow rate of saturated steam and the flow rate of superheated steam, a fact that tends to render the entire process unstable, above all in the case where the system for supply of steam presents characteristics of marked dynamicity, for example in the case where the flow rate of the outgoing steam varies continuously.
• Consequently, the control systems of a known type for controlling thermodynamic parameters of a fluid, in addition to presenting evident difficulties in the adjustment of the control variables, i.e., of the flow rates of the regulation fluids necessary for guaranteeing a sufficient stablity of the thermodynamic characteristics of the supply fluid of the plant, manage to achieve a good regulation of the thermodynamic parameters of the supply fluid only in the case where the flow rate of the supply fluid remains substantially constant, but are not able to manage in an optimal way the transient regimes, in which the flow rate of the supply fluid tends to vary.
• The aim of the present invention is to provide a system and a method for controlling thermodynamic parameters of a steam and, in particular, the temperature, pressure, and flow rate of a steam that is supplied to a steam-using unit, which will improve the systems and the methods of a known type.
• According to the present invention, a system and a method are provided for controlling thermodynamic parameters of a steam, as defined in the annexed claims.
• For a better understanding of the present invention, there is now described a preferred embodiment, purely by way of nonlimiting example, with reference to the attached drawings, wherein:
• Figure 1 shows a block diagram of the control system according to the invention; and
• Figure 2 shows a functional block diagram of the control method according to the invention.
• Designated as a whole by 1 in Figure 1 is the block diagram of a system for controlling thermodynamic parameters of a system 2 for supplying a fluid to a fluid-using unit 3, for example steam supplied to a combustion chamber, which implements the method according to the invention.
• In particular, for reasons of simplicity of illustration, the ensuing description refers to a system for controlling the temperature, pressure, and flow rate of a steam ST that supplies a combustion chamber 3 through a supply system 2 that comprises at least:
• a duct 4, flowing in which is the steam ST that supplies the combustion chamber 3 of a combined-cycle plant for the production of electric power (not illustrated in Figure 1);
• a valve 5, coupled to the combustion chamber 3 and the duct 4, for introduction, into the combustion chamber 3, of the steam ST that flows in the duct 4;
• a first steam source 6, for example of superheated steam ST₁ at outlet from a superheater;
• a valve 7, coupled to the first steam source 6 and to the duct 4, which regulates the flow rate Q_ST1 of the superheated steam ST₁ introduced into the duct 4;
• a second steam source 8, for example of saturated steam ST₂ at outlet from an evaporator;
• a valve 9, coupled to the second steam source 8 and to the duct 4, which regulates the flow rate Q_ST2 of the saturated steam ST₂ introduced into the duct 4.
• In particular, the supply system 2 illustrated in Figure 1 is a variable-regime fluid system, characterized by two incoming currents, namely, the flow of superheated steam ST₁ and the flow of saturated steam ST₂, and by an outgoing current, namely, the flow of steam ST that is the result of the sum of the two incoming currents ST₁ and ST₂. A fluid system of this sort is a markedly nonlinear system, i.e., one in which the dependence between the input variables and the output variables varies according to the working point, and is markedly coupled, i.e., one in which to a variation of the input variables there always corresponds a variation of all the thermodynamic parameters of the flows of steam ST₁, ST₂, and ST.
• Consequently, in order to be able to control in an optimal way in each working point the temperature, pressure, and rate of flow of steam ST, it is necessary to linearize the dependence between the input variables and the output variables of the supply system 2 so that to a variation of an input variable there always corresponds the same variation of the output variable, and to decouple each input variable from the output variables that it is not intended to control via the aforesaid input variable, so that to a variation of an input variable there corresponds exclusively a variation of the output variable associated thereto that it is intended to control.
• The control system 1 is configured for controlling the temperature, pressure, and rate of flow of steam ST in a control volume, in a linear and decoupled way and, for this purpose, comprises:
• a pressure sensor 10, set along the duct 4 downstream of the valve 5, for measuring the pressure P_ST of the steam ST that is introduced into the control volume;
• a temperature sensor 11, set along the duct 4 downstream of the valve 5, for measuring the temperature T_ST of the steam ST that is introduced into the control volume;
• a flow-rate sensor 12, set in the valve 5 or along the duct 4 downstream of the valve 5, for measuring the flow rate Q_ST of steam ST that is introduced into the control volume;
• a pressure sensor 13, set along the duct 4, upstream of the valve 7, for measuring the pressure P_S1 of the superheated steam S_T1;
• a temperature sensor 14, set along the duct 4, upstream of the valve 7, for measuring the temperature T_S1 of the superheated steam S_T1;
• a pressure sensor 15, set along the duct 4, upstream of the valve 9, for measuring the pressure P_S2 of the saturated steam ST₂ ;
• a temperature sensor 16, set along the duct 4, upstream of the valve 9, for measuring the temperature T_S2 of the saturated steam ST₂ ; and
• a microprocessor electronic control unit 17 and solid-state electronic circuits (neither of which are illustrated in the figures), connected to the sensors 10, 11, 12, 13, 14, 15 and 16 and to the valves 5, 7 and 9 and implementing the method for controlling thermodynamic parameters of a fluid according to the present invention, described in what follows with reference to the functional block diagram of Figure 2.
• In particular, the control system 1 is configured for controlling the temperature T_ST, the pressure P_ST, and the flow rate Q_ST of the steam ST, through the appropriate regulation of the flow rates Q_ST1 and Q_ST2 of the steams ST₁ and ST₂, and for generating signals for controlling the valves 5, 7 and 9 in order to obtain the desired regulation.
• In particular, the control system 1 is configured for controlling the temperature T_ST of the steam ST, regulating exclusively, in a linear and decoupled way, the flow rate of one of the two steams ST₁ or ST₂, for example the flow rate Q_ST1 of the superheated steam ST₁ introduced into the duct 4, and the pressure P_ST of the steam ST, regulating exclusively, in a linear and decoupled way, the flow rate of the other of the two steams ST₁ or ST₂, for example the flow rate Q_ST2 of the saturated steam ST₂ introduced into the duct 4.
• For this purpose, in the electronic control unit 17 are stored:
• a desired temperature T of the steam ST;
• a desired pressure P of the steam ST; and
• a desired flow rate Q of the steam ST;
• an enthalpy H₁ of the superheated steam ST₁, which is necessary for obtaining the desired temperature T of the steam ST; and
• an enthalpy H₂ of the saturated steam ST₂ necessary for obtaining the desired pressure P of the steam ST; all of which can be set by an operator.
• With reference to the functional block diagram of Figure 2, the electronic control unit 17 comprises:
• an electronic processing unit 18, designed to estimate a temperature T_EST and a pressure P_EST of the steam ST;
• an electronic processing unit 19, coupled to the electronic processing unit 18, designed to control the temperature T_ST of the steam ST;
• an electronic processing unit 20, coupled to the electronic processing unit 18, designed to control the pressure P_ST of the steam ST;
• an electronic processing unit 21, designed to control the flow rate Q_ST of the steam ST;
• an electronic processing unit 22, coupled to the electronic processing unit 18, designed to calculate, on the basis of thermodynamic parameters of the superheated steam ST₁ and of the saturated steam ST₂ and of desired and estimated thermodynamic parameters of the steam ST, a linearization and decoupling function that enables linear and decoupled control of the thermodynamic parameters of the steam ST, and in particular the temperature T_ST , pressure P_ST , and flow rate Q_ST of the steam ST, as described in detail in what follows;
• an electronic processing unit 23, coupled to the electronic processing units 19, 20, 21 and 22, designed to calculate, on the basis of the aforesaid linearization and decoupling function, a flow rate Q_TS1 of superheated steam ST₁ and a flow rate Q_ST2 of saturated steam ST₂ to be introduced into the duct 4, and a flow rate Q_ST of the steam ST, which are necessary for the steam ST to have the desired temperature T and the desired pressure P, and to generate at output signals for controlling the valves 5, 7 and 9, as described in detail in what follows.
• In order to be able to calculate a precise linearization and decoupling function, the electronic processing unit 22 should know the instantaneous values of pressure P_ST and temperature T_ST of the steam ST. Said values cannot, however, be supplied directly to the electronic processing unit 22 on account of the delays introduced by the various elements of the control system 1, for example by the sensors 10 and 11.
• Consequently, it is necessary to estimate the value that the temperature T_ST and the pressure P_ST of the steam ST will assume at the instant when the electronic processing unit 22 calculates the linearization and decoupling function.
• For this purpose, the electronic processing unit 18 receives at input:
• the signal T_ST coming from the sensor 11, indicating the temperature of the steam ST,
• a signal U_T for regulation of the temperature T_ST, coming from the electronic processing unit 19, determined on the basis of the temperature T_EST-1 estimated in the preceding step of calculation and used for calculation of the preceding linearization and decoupling function;
• the signal P_ST coming from the sensor 10, indicating the pressure of the steam ST; and
• a signal U_P for regulation of the pressure P_ST, coming from the electronic processing unit 20 and determined on the basis of the pressure P_EST-1 estimated in the preceding step of calculation and used for calculation of the preceding linearization and decoupling function,
and on the basis of the signals T_ST and U_T estimates a temperature T_EST that the steam ST will assume at the instant when the electronic processing unit 22 calculates the linearization and decoupling function, whilst, on the basis of the signals P_ST and U_P , it estimates a pressure P_EST that the steam ST will assume at the instant when the electronic processing unit 22 calculates the linearization and decoupling function.
• The electronic processing unit 18 can be implemented in a way in itself known, for example via a so-called "Luenberger observer", or in the form of a single observer that estimates both the temperature and the pressure of the steam ST, or by means of two separate observers, one of which estimates the temperature and the other estimates the pressure of the steam ST.
• The estimated temperature T_EST is then supplied to the electronic processing unit 19, which calculates the difference ε _T between the desired temperature T and the estimated temperature T_EST of the steam ST and, on the basis of the difference ε_T , calculates a regulation function of a known proportional-integral type, expressed by the signal U_T, indicating the correction to be made to the estimated temperature T_EST of the steam ST to compensate for the difference ε_T .
• At the same time, the estimated pressure P_EST is supplied to the electronic processing unit 20, which calculates the difference ε _P between the desired pressure P and the estimated pressure PEST of the steam ST and, on the basis of the difference ε _P , calculates a regulation function of a known proportional-integral type, expressed by the signal U_P, indicating the correction to be made to the estimated pressure P_EST of the steam ST to compensate for the difference ε _P .
• The electronic processing unit 20 receives at input the signal coming from the sensor 12, indicating the flow rate Q_ST of the steam ST, calculates the difference ε _Q between the desired flow rate Q and the flow rate Q_ST of the steam ST and, on the basis of the difference ε _Q , calculates a regulation function of a known proportional-integral type, supplying at output a quantity U_Q indicating the correction to be made to the flow rate Q_ST of the steam ST to compensate for the difference ε _Q .
• In order to be able to calculate the aforesaid linearization and decoupling function, the electronic processing unit 22 receives at input:
• the signals P_S1 and T_S1, indicating, respectively, the pressure and temperature of the superheated steam ST₁;
• the signals P_S2 and T_S2, indicating, respectively, the pressure and temperature of the saturated steam ST₂ and;
• the signals P_EST and T_EST of the estimated pressure and of the estimated temperature
and, on the basis of the aforesaid quantities, calculates the dynamic equations of a known type, for a control volume of the steam-supply system 2, on the basis of which it calculates the aforesaid linearization and decoupling function.
• In particular, the electronic processing unit 22 calculates an equation that describes the evolution in time of the temperature T and of the pressure P of the steam ST according to the flow rates Q_ST1, Q_ST2 and Q_ST , for example an equation of the type: $$\frac{\partial }{\partial t}\left(\begin{array}{c}T\\ P\end{array}\right)=M\left(P_{\mathit{EST}}{T}_{\mathit{EST}}\right)\cdot \left[\begin{array}{c}{Q}_{\mathit{ST}1}\\ Q_{\mathit{ST}2}\end{array}\right]+G(P_{\mathit{EST}},T_{\mathit{EST}})\cdot Q_{\mathit{ST}}$$

  

  
  where:
• Q_ST, Q_ST1, and Q_ST2 are, respectively, the flow rates of the steams ST, ST₁ and S_T2;
• the product M (P_EST, T_EST)
• $\cdot \left[\begin{array}{c}{Q}_{\mathit{ST}1}\\ Q_{\mathit{ST}2}\end{array}\right]$
  
  describes the link between the thermodynamic parameters of the flows of steam ST₁, ST₂ and ST, and the flow rates Q_ST1 and Q_ST2 of the flows of steam ST₁ and ST₂; and
• the product G (P_EST, T_EST) ·Q_ST describes the link between the thermodynamic parameters and the flow rate Q_ST of the flow of steam ST.
• In particular, the matrix M (P_EST, T_EST) is a matrix of the transfer function of the supply system 2 of the steam ST, calculated on the basis of the estimated temperature T_EST and of the estimated pressure P_EST, of the type: $$M\left(P_{\mathit{EST}}{T}_{\mathit{EST}}\right)=\left(\begin{array}{cc}{m}_{11}& m_{12}\\ m_{21}& m_{22}\end{array}\right)$$

  

  which describes the link between the thermodynamic parameters of the flow of steam ST and the thermodynamic parameters of the flows of steam at input ST₁ and ST₂, the elements m₁₁, m₁₂, m₂₁ and m₂₂ of which are equal to: $$M\left(pT\right)=\left[\begin{array}{cc}-\mathrm{\rho }\left(pT\right)\frac{\partial }{\partial p}H\left(pT\right)+1+\left(H_1-H\left(pT\right)\right)\frac{\partial }{\partial p}\mathrm{\rho }(p,T)& -\mathrm{\rho }\left(pT\right)\frac{\partial }{\partial p}H\left(pT\right)+1+\left(H_2-H\left(pT\right)\right)\frac{\partial }{\partial p}\mathrm{\rho }(p,T)\\ \frac{\partial }{\partial T}\mathrm{\rho }\left(pT\right)\mathrm{.}\left(H_1-H\left(pT\right)\right)+\mathrm{\rho }\left(pT\right)\frac{\partial }{\partial T}H(p,T)& \frac{\partial }{\partial T}\mathrm{\rho }\left(pT\right)\mathrm{.}\left(H_2-H\left(pT\right)\right)+\mathrm{\rho }\left(pT\right)\frac{\partial }{\partial T}H(p,T)\end{array}\right]$$

  

  
  where with (P, T) are, respectively, the estimated pressure P_EST and the estimated temperature T_EST;
  and
• G (P_EST, TEST) is a vector that describes the thermodynamic parameters of the flow of steam ST at output, of the type: $$G(P_{\mathit{EST}},T_{\mathit{EST}})=\left(\begin{array}{c}{g}_1\\ {\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">g</figure-callout>}}_2\end{array}\right)$$
  
  the elements g₁ (P, T) and g₂ (P, T) of which are equal to: $$G\left(pT\right)=\left(\begin{array}{c}\mathrm{\rho }\left(pT\right)\frac{\partial }{\partial p}H\left(pT\right)-1\\ -\mathrm{\rho }\left(pT\right)\frac{\partial }{\partial p}H\left(pT\right)\end{array}\right)$$
  
  
  where (P, T) are, respectively, the estimated pressure P_EST and the estimated temperature T_EST;
  and where:
• ρ (P, T) and H (P, T) are, respectively, the density and the enthalpy of the steam ST calculated, in a way in itself known, as a function of the estimated temperature T_EST and of the estimated pressure P_EST of the steam ST, for example according to the known Koch and Van der Waals formulas;
• H₁ is the enthalpy of the superheated steam ST₁ stored, obtained by controlling in a way in itself known the temperature T_S1 and the pressure P_S1 of the superheated steam ST₁;
• H₂ is the enthalpy of the saturated steam ST₂ stored, obtained by controlling in a way in itself known the temperature T_S2 and the pressure P_S2 of the superheated steam S_T2;
• ∂/∂T·ρ (P, T) is the partial derivative of the density ρ (P, T) of the steam ST with respect to the estimated temperature T_EST, maintaining the estimated pressure P_EST constant;
• ∂/∂P·ρ (P, T) is the partial derivative of the density ρ (P, T) of the steam ST with respect to the estimated pressure P_EST, maintaining the estimated temperature T_EST constant;
• ∂/∂P·H (P, T) is the partial derivative of the enthalpy H (P, T) of the steam ST with respect to the estimated pressure P_EST, maintaining the estimated temperature T_EST constant; and
• ∂/∂T·H (P, T) is the partial derivative of the enthalpy H (P, T) of the steam ST with respect to the estimated temperature T_EST, maintaining the estimated pressure P_EST constant.
• The need to linearize the dependence between the input variables and the output variables of the supply system 2 derives principally precisely from the functions that describe the dependence of the density ρ (P, T) and of the enthalpy H (P, T) upon the pressure P_ST and the temperature T_ST. Said functions are in fact markedly nonlinear and consequently, in order to be able to control the pressure P_ST, and the temperature T_ST of the steam so that the control is the same in all the working points, it is necessary to linearize said functions.
• As may be noted moreover from the matrix M (P_EST, T_EST), both the density p (P, T) and the enthalpy H (P, T) of the flow of steam ST and, consequently, the desired temperature T and the desired pressure P of the steam ST, depend both upon the enthalpy H₁ of the flow of superheated steam ST₁ and upon the enthalpy H₂ of the flow of saturated steam ST₂.
• Consequently, as emerges clearly from the product $$M\left(P_{\mathit{EST}}{T}_{\mathit{EST}}\right)\cdot \left[\begin{array}{c}{Q}_{\mathit{ST}1}\\ Q_{\mathit{ST}2}\end{array}\right]$$

  

  of Eq. (1), to a variation of the input variables Q _ST1 and/or Q _ST2 there always corresponds a variation of all the thermodynamic parameters of the flows of steam ST₁ and ST₂ and, consequentely, also a variation of all the thermodynamic parameters of the steam ST. For example, in the case where the flow rate Q_ST1 of the superheated steam ST₁ were varied in order to compensate for a possible variation of the temperature T_ST of the steam ST with respect to the desired temperature T, in addition to a variation of the temperature T_ST of the steam ST there would also occur a variation of the pressure P_ST of the steam ST, whilst in the case where the flow rate Q_ST2 of the saturated steam ST₂ were varied in order to compensate for a possible variation of the pressure P_ST of the steam ST with respect to the desired pressure P, in addition to a variation of the pressure P_ST of the steam ST there would also occur a variation of the temperature T_ST of the steam ST.
• Equation (1) moreover shows how the temperature T and the pressure P of the steam ST depend also upon the flow rate Q_ST and upon the thermodynamic parameters of the flow of steam ST.
• Consequently, from an analysis of Eq. (1) it may be deduced that, to obtain that to a variation of the flow rate Q_ST1 of the superheated steam ST₁ there corresponds exclusively a variation of the temperature T_ST of the steam ST at constant pressure P_ST, and that, likewise, to a variation of the flow rate Q_ST2 of the saturated steam ST₂ there corresponds exclusively a variation of the pressure P_ST of the steam ST at constant temperature T_ST, it is necessary to decouple:
• the flow rate Q_ST1 of the superheated steam ST₁ from the pressure P_ST of the steam ST;
• the flow rate Q_ST2 of the saturated steam ST₂ from the temperature T_ST of the steam ST; and
• the flow rate Q_ST of the steam ST from the temperature T_ST and from the pressure P_ST of the steam ST.
• In order to be able to obtain both the desired linearization and the desired decoupling, the electronic processing unit 21 calculates a matrix K (P_EST, T_EST) by right-handed diagonalizing of the matrix M (P_EST, T_EST), of the type: $$K\left(P_{\mathit{EST}}{T}_{\mathit{EST}}\right)=\left(\begin{array}{cc}1& K_{12}\\ {\mathrm{<figure-callout\; id="21"\; label="K"\; filenames="imgf0002.png"\; state="\{\{state\}\}">K</figure-callout>}}_{21}& 1\end{array}\right)$$

  

  
  where the elements K₁₁ and K₂₂ are equal to 1 and the elements K₁₂ and K₂₁ are equal, respectively, to:
• m₁₂ /m₁₁ and -m₂₁ /m₂₂, i.e., a matrix of the type: $$K\left(pT\right)=\left[\begin{array}{cc}1& \frac{-m_{21}\left(pT\right)}{m_{11}\left(pT\right)}\\ \frac{-m_{21}\left(pT\right)}{m_{22}\left(p\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">T</figure-callout>}\right)}& 1\end{array}\right]$$
  
where (P, T) are once again, respectively, the estimated pressure P_EST and the estimated temperature T_EST,
where the elements K₁₂ and K₂₁ are, respectively: $$K\left(pT\right)=\left[\begin{array}{cc}1& \frac{\mathrm{\rho }\left(pT\right)(\frac{\partial }{\partial p}H\left(pT\right){)}_T-1-(\frac{\partial }{\partial p}\mathrm{\rho }\left(pT\right){)}_T\cdot \left(H_2-H\left(pT\right)\right)}{-\mathrm{\rho }\left(pT\right)(\frac{\partial }{\partial p}H\left(pT\right){)}_T+1+{\left(H_1-H\left(pT\right)\right)}_T\cdot \left(\frac{\partial }{\partial p}\mathrm{\rho }\left(pT\right)\right)}\\ \frac{(\frac{\partial }{\partial T}\mathrm{\rho }\left(pT\right))p\cdot \left(H_1-H\left(pT\right)\right)-\mathrm{\rho }\left(pT\right)\cdot (\frac{\partial }{\partial T}H\left(pT\right))p}{-(\frac{\partial }{\partial T}\mathrm{\rho }\left(pT\right){)}_p\cdot \left(H_2-H\left(pT\right)\right)+\mathrm{\rho }\left(pT\right)\cdot (\frac{\partial }{\partial T}H\left(pT\right))\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">p</figure-callout>}}& 1\end{array}\right]$$

which, multiplied by the matrix M (P_EST, T_EST), would yield a matrix M (P_EST, T_EST) ·K (P_EST, T_EST) equal to: $$K\left(pT\right)=\left[\begin{array}{cc}\frac{\begin{array}{c}M(p,T{)}_{1,1}\mathrm{.}M(p,T{)}_{2,2}-M(p,T{)}_{2,1}\mathrm{.}M(p,T{)}_{1,2}\end{array}}{M(p,T{)}_{2,2}}& 0\\ 0& \frac{\begin{array}{c}M(p,T{)}_{1,1}\mathrm{.}M(p,T{)}_{2,2}-M(p,T{)}_{2,1}\mathrm{.}M(p,T{)}_{1,2}\end{array}}{M(p,T{)}_{1,1}}\end{array}\right]$$


where the elements (M·K) ₁₁, (M·K) ₂₂ are much greater than the elements (M · K) ₁₂ and (M·K) ₂₁ which, in this case, would be approximately equal to zero.
Introducing the matrix (9) in Eq. (1), we thus obtain: $$\frac{\partial }{\partial t}\left(\begin{array}{c}T\\ P\end{array}\right)=\left(\begin{array}{cc}[M\left(P_{\mathit{EST}}{T}_{\mathit{EST}}\right)\cdot K\left(P_{\mathit{EST}}{T}_{\mathit{EST}}\right){]}_{11}& 0\\ 0& [M\left(P_{\mathit{EST}}{T}_{\mathit{EST}}\right)\cdot K\left(P_{\mathit{EST}}{T}_{\mathit{EST}}\right){]}_{22}\end{array}\right)\cdot \left[\begin{array}{c}{Q}_{\mathit{ST}1}\\ Q_{\mathit{ST}2}\end{array}\right]+G(P_{\mathit{EST}},T_{\mathit{EST}})\cdot Q_{\mathit{ST}}$$

Equation (10) shows clearly how, but for the component G (P_EST, TEST) .Q_ST, to a variation of the flow rate Q_ST1 of the steam ST₁ there corresponds exclusively a variation of the thermodynamic parameters of the flow of superheated steam ST₁, whilst a variation of the flow rate Q_ST2 of the saturated steam ST₂ involves only a variation of the thermodynamic parameters of the flow of saturated steam S_T2 .
• In order to obtain a linearization and a decoupling corresponding to the one expressed in the Eq. (10), and eliminate also the dependence of the output variables T and P upon the flow rate Q_ST of the steam ST, the electronic processing unit 21 calculates, in a way in itself known, a matrix M (P_EST, T_EST) ^-1 , which is the inverse of the matrix M (P_EST, T_EST), multiplies the inverse matrix -M (P_EST, T_EST) ^-1 with change of sign by the vector G (P_EST, T_EST), and calculates a matrix K' (P_EST, TEST) of the type: $$\mathit{Kʹ}\left(P_{\mathit{EST}}{T}_{\mathit{EST}}\right)=\left(\begin{array}{cc}\left[K\right]& -\left[M(P_{\mathit{EST}},T_{\mathit{EST}}{)}^{-1}\cdot G\left(P_{\mathit{EST}}{T}_{\mathit{EST}}\right)\right]\\ 0& 1\end{array}\right)$$

  

  which contains the right-handed diagonalizing matrix [K] of the matrix M (P_EST, T_EST), which enables decoupling of the pressure P_ST of the steam ST from the flow rate Q_ST1 of the superheated steam ST₁ and the temperature T_ST of the steam ST from the flow rate Q_ST2 of the saturated steam ST₂, and the matrix - [M (P_EST, T_EST) ^-1. G (P_EST, T_EST) ], which enables elimination also of the dependence of the output variables T and P upon the flow rate Q_ST of the steam ST.
  Developing the matrix K' (P_EST, T_EST) , we obtain: $$\mathrm{Kʹ}\left(\mathrm{p}\mathrm{T}\right)\mathrm{simplify}\mathrm{\to }\left(\begin{array}{ccc}\mathrm{1}& \frac{\mathrm{-}{\mathrm{m}}_{\mathrm{12}}\left(\mathrm{p}\mathrm{T}\right)}{{\mathrm{m}}_{\mathrm{11}}\left(\mathrm{p}\mathrm{T}\right)}& \frac{\mathrm{-}{\mathrm{g}}_{\mathrm{1}}\left(\mathrm{p}\mathrm{T}\right)\mathrm{\cdot }{\mathrm{m}}_{\mathrm{11}}\left(\mathrm{p}\mathrm{T}\right)\mathrm{+}{\mathrm{m}}_{\mathrm{12}}\left(\mathrm{p}\mathrm{T}\right)\mathrm{\cdot }{\mathrm{g}}_{\mathrm{2}}\left(\mathrm{p}\mathrm{T}\right)}{{\mathrm{m}}_{\mathrm{11}}\left(\mathrm{p}\mathrm{T}\right)}\\ \frac{\mathrm{-}{\mathrm{m}}_{\mathrm{21}}\left(\mathrm{p}\mathrm{T}\right)}{{\mathrm{m}}_{\mathrm{22}}\left(\mathrm{p}\mathrm{T}\right)}& \mathrm{1}& \frac{{\mathrm{m}}_{\mathrm{21}}\left(\mathrm{p}\mathrm{T}\right)\mathrm{\cdot }{\mathrm{g}}_{\mathrm{1}}\left(\mathrm{p}\mathrm{T}\right)\mathrm{-}{\mathrm{g}}_{\mathrm{2}}\left(\mathrm{p}\mathrm{T}\right)\mathrm{\cdot }{\mathrm{m}}_{\mathrm{22}}\left(\mathrm{p}\mathrm{T}\right)}{{\mathrm{m}}_{\mathrm{22}}\left(\mathrm{p}\mathrm{T}\right)}\\ \mathrm{0}& \mathrm{0}& \mathrm{2}\end{array}\right)$$

  

  The quantities U_T, U_P and U_Q and the coefficients of the linearization and decoupling matrix K' (P_EST, T_EST) are then supplied to the electronic processing unit 22, which, on the basis of the aforesaid quantities, calculates:
• a flow rate Q_ST1 of superheated steam ST₁ to be introduced into the duct 4 to compensate for the difference of temperature ε_T and re-establish the desired temperature T of the steam ST, without varying the pressure P_ST of the steam ST;
• a flow rate Q_ST2 of saturated steam ST₂ to be introduced into the duct 4 to compensate for the difference of temperature ε _P and re-establish the desired pressure P of the steam ST, without varying the temperature T_ST of the steam ST; and
• a flow rate Q_ST of steam ST at outlet from the duct 4 to compensate for the difference of flow rate ε_Q and re-establish the desired flow rate Q of the steam ST, without varying the temperature T_ST and the pressure P_ST of the steam ST; and
generating respectively, on the basis of the flow rates Q_ST1, Q_ST2 and Q_ST , signals for controlling the valves 5, 7 and 9.
• The main advantage of the device according to the invention is that it enables an optimal regulation of the thermodynamic parameters of a fluid for supply of a plant and, in particular, of the temperature, pressure, and flow rate of the fluid, in so far as it enables control of said thermodynamic parameters in a linear and decoupled way.
• Finally, it is clear that modifications and variations can be made to the method and system described and illustrated herein, without thereby departing from the sphere of protection of the present invention, as defined in the annexed claims.
• The algorithms implemented by the electronic processing units 18-23 could, for example, be integrated in a single centralized calculating unit.

Claims (12)

1. A method for controlling thermodynamic parameters of a steam (ST) that is supplied to a steam-using unit(3), said steam (ST) being obtained by mixing a first regulation steam (ST₁ ) with a second regulation steam (ST₂ ), regulating the respective flow rates (Q _ST1 , Q _ST2 ) of said first and second regulation steams (ST₁, ST₂ ), said method being characterized in that it comprises the step of:

   • controlling said thermodynamic parameters of said steam (ST) on the basis of said flow rates (Q_ST1, Q_ST2 ) of said first and second regulation steams (ST₁, ST₂ ) so that to one and the same variation of the flow rates (Q_ST1, Q_ST2 ) of said first and second regulation steams (ST₁, ST₂ ) there always corresponds one and the same variation of said thermodynamic parameters of said steam (ST) and so that to a variation of one of said flow rates (Q_ST1, Q_ST2 ) there corresponds exclusively a variation of one of said thermodynamic parameters of steam (ST) that it is intended to control, maintaining constant all the other thermodynamic parameters of said steam (ST).
2. The control method according to Claim 1, in which said thermodynamic parameters of said steam comprise a temperature (T_ST, T_EST ), a pressure (P_ST, P_EST ), and a flow rate (Q_ST ) of said steam (ST) that it supplied to said steam-using unit (3).
3. The control method according to Claim 2 moreover comprising:

   • controlling said temperature (T_ST, T_EST ) of said steam (ST) by controlling exclusively said flow rate (Q_ST1 ) of said first regulation steam (ST₁ );

   • controlling said pressure (P_ST, P_EST ) of said steam (ST) by controlling exclusively said flow rate (Q_ST1 ) of said second regulation steam (ST₂ ); and

   • controlling said flow rate (Q_ST ) of said steam (ST) on the basis of the flow rates (Q _ST1 , Q _ST2 ) of said first and second regulation steams (ST₁, ST₂ ) .
4. The control method according to Claim 3, in which controlling said temperature (T_ST, T_EST ), said pressure (P_ST, P_EST ), and said flow rate (Q _ST ) of said steam (ST) comprises:

   • determining a function (U_T ) for regulation of said temperature (T_ST, T_EST ) ;

   • determining a function (U_P ) for regulation of said pressure (P_ST, P_EST ) ;

   • determining a function (U_Q ) for regulation of said flow rate (Q_ST ) ;

   • determining a function (K' (P_EST, T_EST ) ) that linearizes the relation that links said temperature (T_EST ), pressure (P_EST ) and flow rate (Q_ST ) with said flow rates (Q_ST1, Q_ST2 ) of said first and second regulation steams (ST₁, ST₂ ) and that decouples: said temperature (T_EST ) of said steam (ST) from a variation of said flow rate (Q_ST2 ) of said second regulation steam (ST₂ ), said pressure (P_EST ) of said steam (ST) from a variation of said flow rate (Q_ST1) of said first regulation steam (ST₁ ), and said temperature (T_EST ) and pressure (P_EST ) from a variation of said flow rate (Q_ST ) of said steam (ST); and
   on the basis of said functions of regulation (U_T, U_P, U_Q ) and of said linearization and decoupling function (K' (P_EST, T_EST ) ), determining:

   • a flow rate (Q_ST1 ) of said first regulation steam such as to compensate for a possible deviation of said temperature (T_EST ) with respect to a pre-set temperature (T), and such as to maintain the pressure (P_EST ) of the steam (ST) constant;

   • a flow rate (Q_ST2 ) of said second regulation steam such as to compensate for a possible deviation of said pressure (P_EST ) with respect to a pre-set pressure (P), and such as to maintain the temperature (T_EST ) of the steam (ST) constant; and

   • a flow rate (Q_ST ) of said steam (ST) such as to compensate for a possible deviation of said flow rate (Q_ST ) with respect to a pre-set flow rate (Q), and such as to maintain the temperature (T_EST ) and the pressure (P_EST ) of the steam (ST) constant.
5. The control method according to Claim 4, in which determining said functions (U_T, U_P ) for regulation of said temperature (T_ST, T_EST ) and pressure (P_ST, P_EST ) comprises:

   • estimating a temperature (T_EST ) and a pressure (P_EST ) of said steam (ST) at the instant when calculation of said linearization and decoupling function (K' (P_EST, T_EST ) ) is made; and

   • determining said function (U_T ), for regulation of said temperature on the basis of said estimated temperature (T_EST ), and said function (U_P ) for regulation of said pressure (P_ST ) on the basis of said estimated pressure (P_EST ).
6. The control method according to Claim 4, in which determining said functions (U_T , U _P ) for regulation of said temperature (T_ST, T_EST ) and pressure (P_ST, P_EST ) comprises:

   • estimating a temperature (T_EST ) and a pressure (P_EST ) of said steam (ST) at the instant when calculation of said linearization and decoupling function (K' (P_EST, T_EST ) ) is made;

   • calculating the difference (ε _T ) between said estimated temperature (T_EST ), and said desired temperature (T) and the difference (ε _P ) between said estimated pressure (P_EST ), and said desired pressure (P); and

   • determining said function (U_T ), for regulation of said temperature (T_ST ) on the basis of said difference of temperature (ε _T ), and said function (U_P ) for regulation of said pressure (P_ST ) on the basis of said difference of pressure (ε _P ).
7. The control method according to Claim 6, in which determining said function (U_Q ) for regulation of said flow rate (Q_ST ) comprises:

   • acquiring said flow rate (Q_ST ) of the steam (ST);

   • calculating the difference (ε _Q ) between said flow rate (Q_ST ), and said desired flow rate (Q); and

   • determining said function (U_Q ), for regulation of said flow rate (Q_ST ) on the basis of said difference of flow rate (ε _Q ).
8. The control method according to Claims 5 and 6, in which estimating a temperature (T_EST ) and a pressure (P_EST ) of said steam (ST) at the instant when calculation of said linearization and decoupling function is made comprises:

   • acquiring said temperature (T_ST ) and flow rate (Q_ST ) of the steam (ST); and

   • acquiring a function (U_T ) for regulation of temperature calculated on the basis of an estimated temperature (T_EST-1 ) of said steam (ST) used for calculating the preceding linearization and decoupling function (K' (P_EST, T_EST ) ).
9. The control method according to any one of the preceding claims, in which said steam-using unit (3) is a combustion chamber of a plant for the production of electric power.
10. A system for controlling thermodynamic parameters of a steam (ST) that supplies a combustion chamber of a plant for the production of electric power, said steam (ST) being obtained by mixing a first regulation steam (ST₁ ) and a second regulation steam (ST₂ ), regulating the respective flow rates (Q _ST1 , Q _ST2 ) of said first and second regulation steams (ST₁, ST₂ ), comprising electronic processing means (22, 23) that are configured for implementing the control method according to Claims 1 to 9.
11. A computer product that can be loaded into the memory of a digital processor, said computer product comprising portions of software code that are able to implement the method according to any one of Claims 1 to 7 when said computer product is run on said digital processor.
12. A plant for the production of electric power equipped with the control system implementing the method, as described in Claims 1 to 9.

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