US20130238149A2

US20130238149A2 - System and method for maximising thermal efficiency of a power plant

Info

Publication number: US20130238149A2
Application number: US13/508,719
Authority: US
Inventors: Eli Yasni
Original assignee: Exergy Ltd
Current assignee: Exergy Ltd
Priority date: 2009-11-09
Filing date: 2010-11-08
Publication date: 2013-09-12
Also published as: EP2510441B1; EP2510441A4; CN102713859A; WO2011056081A2; US20120283886A1; JP5963677B2; JP2013510365A; US9436168B2; CN102713859B; EP2510441A1

Abstract

A method for maximising thermal efficiency of a power plant, the method comprising obtaining the current state of the plant from available measured data; obtaining a set of Variables representing a current state of the power plant; applying a set of constraints to the Variables; generating a revised set of Variables representing a revised state of the power plant; and testing the revised set of Variables within a mathematical model for convergence. Generating the revised set of Variable is based at least partly on Euler's equation, the conservation of mass equation; and a mathematical description of a reversible continuum. There are also provided a related power plant thermal efficiency maximisation system and computer program.

Description

CROSS-REFERENCE SECTION

This application claims the benefit of International Application No. PCT/NZ2010/000222, filed Nov. 8, 2010, and entitled “SYSTEM AND METHOD FOR MAXIMISING THERMAL EFFICIENCY OF A POWER PLANT”, which claims the benefit of U.S. Provisional Patent Application No. 61/259,516, filed Nov. 9, 2009, and entitled “SYSTEM AND METHOD FOR MAXIMIZING THERMAL EFFICIENCY OF A POWER PLANT,” which are hereby incorporated by reference in their entireties.

BACKGROUND

Experience shows that significant efficiency increase due to real time tuning of thermal power-plants is feasible. It would be helpful to provide a system that systematically yields the absolute maximum of thermal efficiency η of a plant with respect to a set of independent measured parameters. The parameters, also referred to as Variables, are preferably available to an operator or an engineer to manipulate, subject to operational, safety, structural, and environmental constraints. The technique would ideally be applicable to any type of energy-conversion plant in particular thermal power plants. Thermal power plants include, but are not restricted to steam-turbine, combined cycle, co-generation power-plants, Diesel cycles, and nuclear.
It is an object of the invention to go some way toward maximising thermal efficiency of a power plant, or to at least provide the public with a useful choice.

SUMMARY OF INVENTION

In one embodiment the invention comprises a method for maximising thermal efficiency of a power plant, the method comprising:

- obtaining the current state of the plant from available measured data;
- obtaining a set of Variables representing a current state of the power plant;
- applying a set of constraints to the Variables;
- generating a revised set of Variables representing a revised state of the power plant, the generation based at least partly on:

Euler's equation
$ρ \frac{\partial \vec{v}}{\partial t} = \frac{\partial (ρ \vec{v})}{\partial t} + ρ (\vec{v} \cdot V) \vec{v} = - \nabla P - \sum {\vec{F}}_{k} \cdot {\vec{j}}_{k} .;$
and the conservation of mass equation
$\frac{\partial (A ρ_{k})}{\partial t} + \nabla \cdot [A ({\vec{j}}_{k} + ρ_{k} \vec{v})] = \frac{\partial}{\partial t} [A \times M_{k} \sum_{j = 1}^{r} v_{kj} (ρ {\tilde{n}}_{j})];$
and

- a mathematical description of a reversible continuum; and
- testing the revised set of Variables within a mathematical model for convergence.

Preferably the mathematical description of the reversible continuum comprises:

- the reversible conservation of energy equation

$\frac{\partial}{\partial t} (ρ \frac{1}{2} {\vec{v}}^{2} + ψ) + \nabla \cdot (ρ \frac{1}{2} {\vec{v}}^{2} + ψ) + (\sum_{f = 1}^{R} \sum_{k = 1}^{K} μ_{k} v_{kj} J_{j} - ρ \dot{Q}) = - (\sum μ_{k} \frac{\partial ρ c_{k}}{\partial t} + \nabla \cdot ρ (h - T_{g}) \vec{v} - \nabla \cdot \sum μ_{k} {\vec{j}}_{k});$
and

- the thermodynamic equations of state

p=p(P,T,c _k),h−Ts=g=g(P,T,c _k),μ_k=μ_k(P,T,c _k),k=1 . . . N
Preferably the mathematical description of the reversible continuum comprises the geodesic equations
$\frac{\partial {\dot{R}}^{k}}{\partial R^{j}} {\dot{R}}^{j} + {\begin{matrix} k \\ ij \end{matrix}} {\dot{R}}^{i} {\dot{R}}^{j} = 0; \frac{\partial R^{k}}{\partial t} = {\dot{R}}^{k} .$
Preferably the method further comprises repeating the steps of generating the revised set of Variables and testing the revised set of Variables within the mathematical model until each of the revised set of Variables reaches a variance less than a threshold variance.
Preferably generating the revised set of variables is based at least partly on the equation
$\frac{1}{A} \frac{\partial A}{\partial x} = \frac{1}{ρ u^{2}} \frac{\partial P}{\partial x} (1 - u^{2} \frac{\partial ρ}{\partial P}) = \frac{1}{ρ u^{2}} \frac{\partial P}{\partial x (1 - {Ma}^{2})} .$
Preferably generating the revised set of variables is based at least partly on the equation
$\frac{\partial (A ρ_{k} u + j_{k})}{\partial x} = \frac{\partial}{\partial t} [A \times M_{k} \sum_{j = 1}^{r} v_{kj} (ρ {\tilde{n}}_{j})] .$
Preferably generating the revised set of variables is based at least partly on the equation
$\frac{\partial}{\partial x} (ρ \frac{1}{2} u^{2} + ψ) + (\sum_{j = 1}^{R} \sum_{k = 1}^{K} μ_{k} v_{kj} J_{j} - ρ \dot{Q}) = - [\frac{\partial}{\partial x} (ρ (h - T_{g}) u - \sum μ_{k} j_{k})]$
Preferably testing the revised set of variables for convergence includes:

- calculating the kinetic energy of each reversible continuum of the power plant at an initial state Aent;
- calculating the kinetic energy of each reversible continuum of the power plant at a subsequent state Aex; and
- calculating the difference between the kinetic energy at Aex and the kinetic energy at Aent.

Preferably testing the revised set of variables for convergence includes minimizing the sum of individual calculated differences between the kinetic energy at Aex and the kinetic energy at Aent.
Preferably one or more of the calculated differences is determined by the normalized equation
$? = \sum \int_{P (- 1)}^{P (1)} \frac{1}{ρ} \partial P = \int_{- 1}^{1} A ρ u \frac{1}{2} u^{2} \partial x$ $? indicates text missing or illegible when filed$
In a further embodiment the invention comprises a computer readable medium on which is stored computer executable instructions that when executed by a processor cause the processor to perform any one of the above methods.
In a further embodiment the invention comprises a power plant thermal efficiency maximisation system comprising:

- a minimiser configured to apply a set of constraints to a set of Variables, the Variables representing a current state of a power plant;
- a solver configured to generate a revised set of Variables representing a revised state of the power plant, the generation based at least partly on:

Euler's equation
$ρ \frac{\partial \vec{v}}{\partial t} = \frac{\partial (ρ \vec{v})}{\partial t} + ρ (\vec{v} \cdot V) \vec{v} = - VP - \sum {\vec{F}}_{k} \cdot {\vec{j}}_{k} .;$
and

- the conservation of mass equation

$\frac{\partial (A ρ_{k})}{\partial t} + V \cdot [A ({\vec{j}}_{k} + ρ_{k} \vec{v})] = \frac{\partial}{\partial t} [A \times M_{k} \sum_{j = 1}^{r} v_{kj} (ρ {\tilde{n}}_{j})];$
and

- a mathematical description of a reversible continuum; and
- a convergence tester configured to test the revised set of Variables for convergence.

Preferably the mathematical description of the reversible continuum comprises:

- the reversible conservation of energy equation

$\frac{\partial}{\partial t} (ρ \frac{1}{2} {\vec{v}}^{2} + ψ) + \nabla \cdot (ρ \frac{1}{2} {\vec{v}}^{2} + ψ) + (\sum_{j = 1}^{R} \sum_{k = 1}^{K} μ_{k} v_{kj} J_{j} - ρ \dot{Q}) = - (\sum μ_{k} \frac{\partial ρ c_{k}}{\partial t} + \nabla \cdot ρ (h - T_{g}) \vec{v} - \nabla \cdot \sum μ_{k} {\vec{j}}_{k})$
and

- the thermodynamic equations of state

p=p(P,T,c _k),h−Ts=g=g(P,T,c _k),μ_k=μ_k(P,T,c _k),k=1 . . . N
Preferably the mathematical description of the reversible continuum comprises the geodesic equations
$\frac{\partial {\dot{R}}^{k}}{\partial R^{j}} {\dot{R}}^{j} + {\begin{matrix} k \\ ij \end{matrix}} {\dot{R}}^{i} {\dot{R}}^{j} = 0; \frac{\partial R^{k}}{\partial t} = {\dot{R}}^{k} .$
Preferably the solver is configured to repeat the steps of generating the revised set of Variables and testing the revised set of Variables within the mathematical model until each of the revised set of Variables reaches a variance less than a threshold variance.
Preferably generating the revised set of variables is based at least partly on the equation
$\frac{1}{A} \frac{\partial A}{\partial x} = \frac{1}{ρ u^{2}} \frac{\partial P}{\partial x} (1 - u^{2} \frac{\partial ρ}{\partial P}) = \frac{1}{ρ u^{2}} \frac{\partial P}{\partial x (1 - {Ma}^{2})} .$
Preferably generating the revised set of variables is based at least partly on the equation
$\frac{\partial (A ρ_{k} u + j_{k})}{\partial x} = \frac{\partial}{\partial t} [A \times M_{k} \sum_{j = 1}^{r} v_{kj} (ρ {\tilde{n}}_{j})] .$
Preferably generating the revised set of variables is based at least partly on the equation
$\frac{\partial}{\partial x} (ρ \frac{1}{2} u^{2} + ψ) + (\sum_{j = 1}^{R} \sum_{k = 1}^{K} μ_{k} v_{kj} J_{j} - ρ \dot{Q}) = - [\frac{\partial}{\partial x} (ρ (h - T_{g}) u - \sum μ_{k} j_{k})]$
Preferably the convergence tester is configured to test the revised set of variables for convergence, including:

Preferably testing the revised set of variables for convergence includes minimizing the sum of individual calculated differences between the kinetic energy at Aex and the kinetic energy at Aent.
Preferably one or more of the calculated differences is determined by the normalized equation
$? = \sum \int_{P (- 1)}^{P (1)} \frac{1}{ρ} \partial P = \int_{- 1}^{1} A ρ u \frac{1}{2} u^{2} \partial x$ $? indicates text missing or illegible when filed$
The term ‘comprising’ as used in this specification and claims means ‘consisting at least in part of’, that is to say when interpreting statements in this specification and claims which include that term, the features, prefaced by that term in each statement, all need to be present but other features can also be present. Related terms such as ‘comprise’ and ‘comprised’ are to be interpreted in similar manner.
As used herein the term “and/or” means “and” or “or”, or both.
As used herein “(s)” following a noun means the plural and/or singular forms of the noun.
This invention may also be said broadly to consist in the parts, elements and features referred to or indicated in the specification of the application, individually or collectively, and any or all combinations of any two or more of said parts, elements or features, and where specific integers are mentioned herein which have known equivalents in the art to which this invention relates, such known equivalents are deemed to be incorporated herein as if individually set forth.
In this description the following definitions are used:
A surface area
A_entexthe surface area across which matter enters and exits the control-volume
B,b exergy, specific exergy
C_kconcentration of chemical species k
${\begin{matrix} γ \\ α β \end{matrix}} Christoffel Symbols$
H, H_ƒ,h enthalpy, enthalpy of formation, specific enthalpy
{right arrow over (I)}_kdiffusion vector of chemical species k
J_jrate of chemical reaction j
{right arrow over (m)} unit vector normal to the surface
P pressure
{dot over (Q)} magnitude of heat interaction per volume
S,s entropy, specific entropy
Rⁱgeneral notation for intensive properties Rⁱ=T, etc.
T absolute temperature
t time
u velocity in the x direction
V volume
{right arrow over (v)} velocity vector
{dot over (W)} the rate of shaft work output (shaft power output), η thermal efficiency
p density
σ stress tensor
p_kdensity of species k
Ψ specific potential energy
μ chemical potential μ_kchemical potential of species k

BRIEF DESCRIPTION OF THE FIGURES

The present invention will now be described with reference to the accompanying drawings in which:

FIG. 1 shows a preferred form technique for maximising thermal efficiency.

FIG. 2 shows one implementation of a technique for maximising thermal efficiency.

FIG. 3 shows a preferred form computing device.

FIG. 4 shows the results of a first experiment.

FIG. 5 shows the results of a second experiment.

DETAILED DESCRIPTION OF PREFERRED FORMS

Thermal efficiency of a power-plant is defined as
$\begin{matrix} η = \frac{\dot{W}}{\dot{H}} = \frac{\dot{W}}{{\dot{H}}_{f} + {\dot{H}}^{'}} = \frac{\dot{W}}{{\dot{m}}_{f} h_{f} + {\dot{H}}^{'}} = \frac{\dot{W}}{{\dot{m}}_{f} Cv + {\dot{H}}^{'}} & (1) \end{matrix}$
where {dot over (W)} is the rate of shaft work output (shaft power output), {dot over (H)}_fis the rate of fuel energy input, {dot over (H)}^Fis the rate of other energy inputs, h_jis fuel specific enthalpy which is the same as fuel calorific value Cv, {dot over (m)}_fis fuel mass-flow rate; η is measured in %.
For turbine plants the inverse
$HRT = \frac{1}{η}$
called heat-rate is used; the units of HRT are Kwh/Kj or Kj/Kj.
The techniques maximize η (minimize HRT) with respect to a set of independent measured parameters called Variables. The Variables are available to an operator or an engineer to manipulate subject to operational, safety, and structural constraints. In addition to these structural constraints there are external constraints like the environment. The Variables are independent in the sense that one or more can be varied without affecting the others. If the load {dot over (W)} and C_v, {dot over (H)}^Fare externally dictated, then {dot over (m)}_fis to be minimized; however, one can invert this to a dictated {dot over (H)}_f, {dot over (H)}^Fthen {dot over (W)} is to be maximised.
It is intended that the technology below apply to both scenarios
It is well known that max(η) is equivalent to min (T₀Δ{dot over (S)}) where Δ{dot over (S)} is the total rate of entropy production, T₀is the temperature of the sink, normally the environment (atmosphere, ocean) and T₀Δ{dot over (S)} is total plant's exergy-loss. A given T₀is an example of an environmental constraint. The techniques below do not require that T₀be fixed. Rather the related quantity of reversible work is used.
FIG. 1 shows a preferred form technique for maximising thermal efficiency. The system 100 operates iteratively. It takes as input the current actual state 105 of a physical power plant 100. A data acquisition system 115 obtains available measured data. Conventional mass and energy balance calculations are carried out 120. The intention is that substantially every meaningful cross-section of the mass flow rate, temperature, pressure and chemical composition are known. In this way the current state of the plant is obtained from available measured data. The actual state of the plant constitutes all relevant thermodynamic properties throughout the plant. It is fed to the Solver 125 at the start of the first iteration. The initial control set or Variables 130 include temperatures, pressures and flows. These are typically determined by the user, who decides what the variables should be. The settings of each variable are subject to constraints 135. These constraints 135 are sent to a minimizer 140 and then to Solver 125.
The Solver 125 outputs a numerical solution 145 at least partly from a mathematical model 150. The Solver 125 is used to generate the value of an objective function 155 which is then tested against a convergence criterion by a convergence tester 160. The tester 160 determines whether the values of the objective function 155 at the (current) jth iteration are “sufficiently close” to its value at jth-1 iteration. If yes then the criterion is satisfied and the Algorithm displays the Variables' values that maximise the plant's efficiency. Otherwise these are fed back into the minimizer 140 which feeds the jth set of Variables into the Solver 125. Solver 125 then feeds the jth numerical 145 solution into the objective function 155 and the process is repeated.
The final values of the Variables generated by the system 100 can also be fed to the plant's control system and so render the maximizing of η fully automatic.
System 100 further includes a simulator 165. One can show that the numerical solution given by the Solver 125 at any iteration, say the jth, corresponds to an actual state of the plant dictated by the jth set of the Variables. The Variables are the only plant parameters that can be varied independently. Hence one can tabulate the plant's actual states against all the combinations of Variables generated by the minimizer 140 (this is of course, a multi-dimensional table). Furthermore one can take the minimizer 140 out of the loop, and generate the said table for any number of arbitrary combinations of the Variables. Either way, for any set of values of the Variables the table yields the corresponding plant's actual state. Such a table is a simulator by conventional definition. It makes a prediction of the state of the plant if one changes the value of the Variable(s).
A plant, no matter how complex, constitutes a finite number of continuities separated by boundaries also know as discontinuities. Such a system is called semi-continuous. In a power plant these continuities are flows of the working fluids governed by the laws of Fluid-Mechanics. The most fundamental of these are the balances of momentum, mass, energy entropy, and electrical charge. The last of these is irrelevant to the techniques described below. These balances can be written both in integral and differential forms. The differential balance equations for mass and energy and momentum can always be written in a divergent form which renders them Conservation Laws. The name comes from the fact because of the divergent the integral form of the said balance is a vanishing surface integral. This can be put more simply as “what goes in goes out.” Because of its importance to what follows consider for example the general balance of momentum:
$\begin{matrix} ρ \frac{\partial \vec{v}}{\partial t} = \frac{\partial ρ \vec{v}}{\partial t} + \nabla \cdot (p \vec{v} \vec{v}) = \nabla \cdot \overset{\vec{_}}{σ} - \sum {\vec{F}}_{k} \cdot {\vec{j}}_{k} & (2) \end{matrix}$
The above mentioned system of partial differential equations (PDEs) is undetermined. Constituent (or phenomenological) equations complement these PDEs. The fundamental constitutent coefficients and the symmetries they obey are already known. The numerical values of the phenomenological coefficients are not normally known; for the most important ones there are tabulated empirical values which are by no means standards. Whichever the method, the assumption that the phenomenological coefficients even exist, is enabled by a balance of entropy equation which is not a conservation law.
Balance of entropy can be reduced to a conservation law only for reversible flows. For such a fluid the rate of entropy production is zero, ie it satisfies:
$\begin{matrix} \nabla (\frac{1}{T}) \cdot \vec{Q} = 0, \frac{1}{T^{\overset{\vec{_}}{τ}}} : \nabla \vec{v} = 0, \sum_{h} (\frac{F_{k}}{T} - \nabla \frac{μ_{k}}{T}) \cdot {\vec{j}}_{k} = 0 & (3) \end{matrix}$
For a reversible fluid the phenomenological coefficients all vanish. A fluid for which σ=0 is known as a perfect fluid. For a perfect fluid the balance of momentum equation reduces to Euler's equation of motion. It is well known that even under the assumption of perfect fluid the set of Euler's equations and conservation of mass are underdetermined in the 3 components of the velocity field, pressure field, and density field. Hence for various applications some other assumptions are added to well-pose the system of PDEs. The best known are isentropic or isothermal flow, or some truncated equation of state. The term p=p(P) is one of the most commonly used.
Referring to FIG. 1 the mathematical model 150 comprises Euler's equation, conservation of mass and either the equation of Thermodynamic Geodesic Field (TGF) in the thermodynamic metric, or a direct Reversible Energy Conservation (REC) equation. This mathematical model accurately represents a reversible flow. Either TGF or REC can be used. The two equations TGF and REC are equivalent for the techniques described here. Other equations which are best described as different flavours of REC or TGF can also be used. The numerical solution of the mathematical model 150 is an accurate state of a reversible equivalent of the actual plant. The power output of the reversible equivalent is the maximum possible, subject to the given thermodynamic boundary conditions of the plant. The actual power is dictated as a constraint. The intention is to minimize the reversible power by manipulating the Variables, because the loss is simply the reversible power minus the actual power.
The simulator 165 tabulates the numerical outputs of the Solver 125 for different sets of Variables. These tables correspond to predictions of the state of the actual plant. This is surprising, since the many models of continuous fluid-flow all call upon Navier-Stokes equations (also a balance of momentum), which depend upon 2 empirical phenomenological coefficients, and the solving of which involves further ad-hoc assumptions. These equations are heavy on computer resources, may not even be solvable, or are very difficult to integrate for an entire plant, which is the main reason why there is no efficiency maximize for a power plant at present.
The techniques also claim to accurately predict actual parameters of the continuum through the mathematical model of the reversible flow, but only at the terminals (i.e. at Aent, Aex) of the continuum. This is the price paid for the simplification. However these are the only ones where properties are measurable by power-plant engineers.
Consider a steam-turbine as a subprocess of a power plant. It can be described as a single continuum. The ordered pairwhich is the Clausius notion of a process, are the states on steam entering and existing cross-sections (Aentex) of the turbine.
The maximum possible magnitude of work interaction subject to the given end states is delivered by a reversible process which can be an isentropic turbine, diverting part of its power to drive a Carnot heat-pump, which in turn maintains the Aentex (end) states of the actual turbine by drawing heat from reservoirs (the environment).
The total rate of entropy production of the isentropic turbine, the Carnot heat-pump and reservoirs is zero; hence the process is reversible. In other words the actual turbine is replaced by an isentropic one plus a Carnot heat-pump which is compensated to maintain the Aent, Aex thermodynamic states.
These techniques apply the said principle to a continuum. The general statement is that for every given (irreversible) continuum there exists a reversible continuum which delivers maximum work, such that values of the thermodynamic properties at the boundary of the original continuum are maintained. Such a substitution of a reversible continuum for an actual irreversible continuum is referred to here as Reversible Masking.
These techniques establish that the converse is also true, that is, one can recover the original continuum from the reversible one. It is the inversion from predicted reversible to predicted actual, which enables the function of simulator 165.
Mathematical model 150 does not require any prior knowledge of plant's dimensions, or any other (plant component's) characteristics, or any empirical tabulated data save thermodynamic properties h,s,v, of the working fluids. The model is also free of ad-hoc assumption, hence its accuracy. The same mathematical model can be used as a stand-alone to predict variations of the plant parameters other than maximum work, both for dynamics and steady-state.
The model has the potential to be fast, light on computer resources, and universal. The key to the success of the mathematical model lies with an augmentation to Euler's balance-of-momentum equations as presented below.
This augmentation is an energy conservation equation for a reversible process (REC) without reference to external systems like the environment. The techniques described below include a number of such augmenting equations, all equivalent.
The full, well-posed system of PDEs is set out below. For a reversible flow the shear stress components τ_ijare zero hence equation (2) reduces to the Euler equation.
$\begin{matrix} ρ \frac{\partial \vec{v}}{\partial t} = \frac{\partial (ρ \vec{v})}{\partial t} + ρ (\vec{v} \cdot \nabla) \vec{v} = - \nabla P - Σ {\vec{F}}_{k} \cdot {\vec{j}}_{k} & (4) \end{matrix}$
Conservation of mass of a continuum subject to a variable cross section area
$\begin{matrix} \frac{\partial (A ρ_{k})}{\partial t} + \nabla \cdot [A ({\vec{j}}_{k} + ρ_{k} \vec{v})] = \frac{\partial}{\partial t} [A \times M_{k} \sum_{j = 1}^{r} v_{kj} (ρ {\tilde{n}}_{j})] & (5) \end{matrix}$
In the above equation:
M_kis the mass of species k,
{right arrow over (I)}_k=p_k{right arrow over (v)} is the diffusion flux of species k, and ñ_jis the number of Kmoles of chemical reaction j per Kg of total mass.
The rate of chemical reaction j is
$J_{j} = \frac{\partial (ρ {\tilde{n}}_{j})}{\partial t} .$
Conservation of energy for a reversible flow (REC) equation.
$\begin{matrix} \frac{\partial}{\partial t} (ρ \frac{1}{2} {\vec{v}}^{2} + ψ) + \nabla \cdot (ρ \frac{1}{2} {\vec{v}}^{2} + ψ) + (\sum_{j = 1}^{R} \sum_{k = 1}^{K} μ_{k} v_{kj} J_{j} - ρ \dot{Q}) = - (\sum μ_{k} \frac{\partial ρ c_{k}}{\partial t} + \nabla \cdot ρ (h - T_{0}) \vec{v} - \nabla \cdot \sum μ_{k} {\vec{j}}_{k}) & (6) \end{matrix}$
In addition there are the thermodynamic equations of state
p=p(P,T,c _k),h−Ts=g=g(P,T,c _k), μ_k=μ_k(P,T,c _k), k=1 . . . N
For the system to be well-posed the number of unknown functions must equal the number of differential equations. The unknown functions are the 3 components of the velocity {right arrow over (v)}, the density p, the Gibbs function g, the pressure P, the temperature T, altogether 7 unknowns. Plus the N densities p_k, the N chemical potentials μ_k, altogether 2N+7 unknowns. There are 3 Euler conservation of momentum equations, 1 equation of reversible conservation of energy, N equations of conservation of mass, N equations of state μ_k=μ_k(P,T,p), 2 equations of state
$g = g (P, T, ρ_{j}), ρ = ρ (P, T, ρ_{j}), and ρ = \sum_{k} ρ_{k} . Altogether 3 + 1 + 2 N + 2 + 1 = 2 N + 7.$
Discussion is initially limited to 2 spatial dimensions x,y and time t (2 d+1), that is, the unknown functions do not vary in the direction. Given the distribution of the cross-sectional area A(x,y,t), and the initial (at time t=t₀) values of the unknown functions on a region f(x(t₀),y(t₀),t₀)=0 on the spatial x-y plane, then the set of equations (4) to (6) is well posed and can be solved yielding the spatial distribution of the unknown functions at any time t i.e. the values of {right arrow over (v)}(x,y,t),P(x,y,t),T(x,y,t),p_k(x,y,t), μ_k(x,y,t), p(x,y,t), g(x,y,t) for all x,y,t varying between predetermined limits. The cross-sectional area A is such that the spatial vector {right arrow over (n)} normal to A lies on the spatial x,y,t∀x,y, t plane. In other words the A intersects the x-y plane along a curve that can be of any shape. If the said intersecting curve is a straight line perpendicular to the x axis everywhere, then the flow is 1 d+1. This is known as cylindrically symmetric.
Alternatively, one can replace the 3 equations of the conservation of momentum (Euler) by the geodesic equations (TGF) in the spatial coordinates (the summation convention applies)
$\begin{matrix} \frac{\partial v^{γ}}{\partial q^{S}} v^{S} + {\begin{matrix} γ \\ a, s \end{matrix}} v^{α} v^{β} = 0 & (7) \end{matrix}$
where the q coordinates are in the Galilean 2+1 space, and the Christoffel Symbols are in an induced metric. This induced metric is described in Weinhold F. 1975 Metric Geometry of Equilibrium Thermodynamics (followed by II,III,IV,V) Journal of Chemical Physics 63: 2479-2483. It is referred to as the Weinhold metric. This metric is not commonly known hence it is rather preferable to replace the N equations of conservation of mass plus the equation of reversible conservation of energy plus the equation of state g=g(P,T,c_k) by N+2 geodesics equations in the thermodynamic coordinates, in this case P,T,p_k, here the Christoffel Symbols are in the Weinhold metric which can be derived from standard thermodynamic properties functions and the knowledge of the chemical reaction
$\begin{matrix} \frac{\partial {\dot{R}}^{k}}{\partial R^{j}} {\dot{R}}^{j} + {\begin{matrix} k \\ ij \end{matrix}} {\dot{R}}^{i} {\dot{R}}^{j} = 0; \frac{\partial R^{k}}{\partial t} = {\dot{R}}^{k} & (8) \end{matrix}$
Strictly speaking equations (4,5,6,8) are (2N+2)×2 equations with the additional 2N+2 variables {dot over (H)}^k.
Equation (8) is equivalent to the 2^ndorder system in the parameter t.
$\begin{matrix} \frac{\partial^{2} R^{1}}{\partial t^{2}} + {\begin{matrix} i \\ jk \end{matrix}} \frac{\partial R^{j}}{\partial t} \frac{\partial R^{k}}{\partial t} = 0 R^{1} = T, R^{2} = P, R^{3} = ρ (1), R^{4} = ρ (2) \dots R^{N + 2} = ρ (N) R^{1} (t = 0) = R_{0}^{1}, R^{1} (t = t_{2}) = R_{2}^{4}, ρ_{2} = ρ (T, T (P)) & (9) \end{matrix}$
Clearly equation (8) is an augmentation to Euler's equations replacing both energy and mass conservation equations. The solutions are in fact the same. The left hand side structure of both equations is the same i.e. the covariant derivative of the velocity {right arrow over (v)}, however in different metrics. Even though the right hand sides differ the solution is still the same. Either way, the solution is valid only for reversible flows. Described below is how this applies to real irreversible flows.
A plant is commissioned with measuring instruments such that it is possible to compute all stationary-state relevant mass-flow-rates by integral energy and mass balances alone. This is so because the efficiency monitoring is most important for stationary-state which is where a power plant normally is. To minimize the cost of instrumentation, manufacturers arrange measuring instruments across the power plant such that the basic continuums assume cylindrical symmetry, hence are in effect one-dimensional. For example there is normally one thermometer at a turbine inlet main stream pipe and one at its exhaust, implicitly assuming that this single theremometer(s) represent the cross-sectional temperature distribution.
If the actual continuum is in one-dimensional stationary-state then so is its Reversible Masking, that is, all
$\frac{\partial}{\partial t}$
of equations (4) to (6) vanish, and velocities and other properties vary only in the x-direction. Hence the reversible conservation PDEs can be reduced to ODEs, or even be reduced further to algebraic equations. The time independent 1 d balance of momentum
$\begin{matrix} \frac{\partial (ρ uu)}{\partial x} = - \frac{\partial P}{\partial x} - Σ {\vec{F}}_{k} \cdot {\vec{J}}_{k} \Rightarrow u \frac{\partial u}{\partial x} = - ρ^{- 1} \frac{\partial P}{\partial x} - Σ {\vec{F}}_{k} \cdot {\vec{j}}_{k} & (10) \end{matrix}$
For 1 d stationary-state it is more convenient to work with the “diffuser-nozzle theory”
$\begin{matrix} \frac{dA}{A} = \frac{dP}{ρ u^{2}} - \frac{d ρ}{ρ} = \frac{dP}{ρ u^{2}} (1 - u^{2} \frac{\partial ρ}{\partial P}) = \frac{dP}{ρ u^{2}} (1 - {Ma}^{2}) & (11) \end{matrix}$
where Ma is the Mach number. Writing this in one-dimension in the direction of x
$\begin{matrix} \frac{1}{A} \frac{\partial A}{\partial x} = \frac{1}{ρ u^{2}} \frac{\partial P}{\partial x} (1 - u^{2} \frac{\partial ρ}{\partial P}) = \frac{1}{ρ u^{2}} \frac{\partial P}{\partial x (1 - {Ma}^{2})} & (12) \end{matrix}$
Equations (11, 12) are a resultant of combining momentum and continuity, hence one can use equation (12) instead of Euler's equation.
The conservation of mass equation (5) in 1 d, is
$\begin{matrix} \frac{\partial (A ρ \vec{v})}{\partial t} + \nabla \cdot A (ρ \vec{v} + {\vec{j}}_{k}) = \frac{\partial (A ρ_{k} u)}{\partial t} + \frac{\partial (A ρ_{k} u + j_{k})}{\partial x} = \frac{\partial}{\partial t} [A \times M_{k} \sum_{j = 1}^{r} v_{kj} (ρ {\tilde{n}}_{j})] & (13) \end{matrix}$
With chemical reaction but otherwise stationary state this reduces to
$\begin{matrix} \frac{\partial (A ρ_{k} u + j_{k})}{\partial x} = \frac{\partial}{\partial t} [A \times M_{k} \sum_{j = 1}^{r} v_{kj} (ρ {\tilde{n}}_{j})] & (14) \end{matrix}$
Conservation of energy for a reversible flow (REC) (6) for ld stationary-state with chemical reaction is
$\begin{matrix} \frac{\partial}{\partial x} (ρ \frac{1}{2} u^{2} + ϕ) + (\sum_{j = 1}^{R} \sum_{k = 1}^{K} μ_{k} v_{kj} J_{j} - ρ \dot{Q}) = - [\frac{\partial}{\partial x} (ρ (h - Ts) u - {Σμ}_{k} j_{k})] & (15) \end{matrix}$
The geodesic equations (8,9) remain unchanged because they are in the thermodynamic space. Spatial coordinates are not normally known for a given plant. However for performance calculation these are irrelevant. One normalizes to an interval (−1;1). To solve the N+3 first order ODEs (12, 14, 15) and N Equations-of State in the 2N+3 functions
P(x),T(x),g(x),p(x),p_k(x),μ_k(x), u(x).
To solve these equations, one needs to know the cross sectional area A(x) for the reversible continuum. This is obtained by combining the system (12,14,15) and the N Equations-of-State together with the integral energy and mass balances of the actual (real, irreversible) continuum e.g. {dot over (M)}Δh={dot over (W)}+{dot over (Q)}.
A delicate but important point to note here, is, that necessarily the mass-flow-rate is common to both the Masked (reversible) and actual continuum. The extra magnitude of work interaction manifests itself as differences in velocities only. Hence {dot over (M)}=[Apu]_Aent=[Apu]_Aexer, {dot over (W)}, {dot over (Q)} are the actual magnitudes of work and heat interactions (load). Δh are the given enthalpies difference at Aentex of the plant's continuums. The additional actual energy balance equation combines with (12,14,15) and Equations-of-State is well-posed in the 2N+3 unknown functions plus A(x), which is then kept fixed through the iterations following the loop shown in FIG. 1.
By varying the initial conditions at Aent (x=−1) for first order ODEs (12,14,15) P(x₀), T(x₀), g(x₀),p(x₀), μ_k(x₀), one obtains new values for the functions P(x),T(x),g(x),p(x),p_k(x),μ_k(x), as well as for u(x). In particular one obtains the values at Aex(x=1). These predictions are the essence of the mathematical model of a reversible continuum in 1 d.
It follows therefore, that the state of the entire Masked (reversible) plant is determined by the values of the free Variables. These decide the initial conditions of the plant's terminal continuums Aent.
Solving the mathematical model for terminal continuums gives the state at their Aex, which, in turn, is the state of the next cascading continuum and so on until the functions of P(x),T(x),g(x),p(x),p_k(x),μ_k(x)u(x), are known for all continuums that make up the plant. That is, the state of the entire Masked (reversible) plant is deduced. If it so happens that one or more continuums are not included in the cascade, then either there are more free variables, or the excluded set of continuums is indifferent to the Variables.
It follows, that varying the free Variables yields a new state of the reversible plant, as one would expect from a mathematical model. Each iteration around the loop shown in FIG. 1 generates a new state of the reversible plant which yields a new value of maximum work—the objective function to be minimized.
The objective of maximizing is equivalent to minimizing the sum of all plant's exergy-losses. These techniques focus on the more primitive concept of Maximum Work or maximum power. The very definition of losses is the Lost Work, i.e. the difference between the maximum power, (which corresponds to the rate of work delivered in a reversible plant), and the actual electrical power output. Since the latter is predetermined, then minimizing the Reversible Work will minimize the losses.
The maximum rate of work delivered by the Masked (reversible) continuum, i.e. its Reversible
Work, is the difference in kinetic energy at its Aent, Aex. That is
$\begin{matrix} ? = Σ \int_{P (- 1)}^{P (1)} \frac{1}{ρ} \partial P = \int_{- 1}^{1} Apu \frac{1}{2} u^{2} \partial x ? indicates text missing or illegible when filed & (16) \end{matrix}$
where the summing up is over all continuums; the summation yields the reversible work of the entire plant. It is this sum which is the objective function to be minimized, which for given electrical load will minimize the plant's fuel flow-rate subject to the operational and environmental constraints.
The techniques and systems described above comprise 2 main parts:

- 1. The objective function to be minimized which is the rate of kinetic energy delivered by a reversible representation of the actual plant. This minimization is equivalent to minimization of thermodynamic losses.
- 2. An accurate mathematical model that accurately determines how variations in losses in one or more part(s) of the plant affect the rest of it. Such variations can, in turn, be caused by manipulating the Variables. The accuracy of the model is facilitated by the Reversible Energy Conservation equation or the Thermodynamic Geodesic Field equation, augmenting Euler's equations. It is in essence a mathematical model of the reversible plant which assumes the same thermodynamic values at each cross-section as the actual plant.

The accuracy of the mathematical model combined with the built-in constraints guarantees that the system-generated values for the 7₁-maximising Variables are in fact attainable in practice.
The mathematical model can in fact simulate a real plant even though the equations as such correspond to a reversible process. There is no need for ad-hoc assumptions and empirically derived tabulated data other than thermodynamic properties of working fluids. The model is fast, light on computer resources, and universal.
FIG. 2 shows at 200 one example of implementation of the techniques described above. Power plant 205 includes any one or more of a steam turbine, combined cycle, cogeneration power plant, diesel cycle, and nuclear.
Plant 205 has associated with it a plant archive 210. This plant archive is maintained in computer memory or secondary storage. The plant archive comprises time stamped efficiency data for some or all components of plant 205. The plant archive 210 is used to determine the current plant state.
A server configuration 215 carries out the functions described above performed by the solver 125 of FIG. 1. The server configuration 215 includes for example at least one display device, a processor, computer memory, and computer network components.
The results of analysing efficiencies can be displayed on display devices associated with the server configuration 215. The results can also be transmitted over a data network 220 to one or more client processing devices 225 operated by an operator. The results can be displayed on display devices associated with client device 225. The data can also be produced in hard copy on an associated printer device or saved in a data file on associated secondary storage.
A further embodiment of the system 200 transmits data from plant archive 210 to server configuration 215. The server 215 then automatically adjusts parameters of the plant 205 based on convergence calculations it has determined.
FIG. 3 shows a simplified block diagram of a machine in the example form of a computing device 300. The server configuration 215 is one example of computing device 300. In one embodiment the server configuration 215 operates as a standalone computing device with network connections allowing it to access current values of client instrumentation. The server configuration 215 reports recommendations on both the device itself and via a network to other clients. In an alternative embodiment the techniques described above are executed entirely within a control system computing device associated with the plant 205.
Sets of computer executable instructions are executed within device 300 that cause the device 300 to perform the methods described above. Preferably the computing device 300 is connected to other devices. Where the device is networked to other devices, the device is configured to operate in the capacity of a server or a client machine in a server-client network environment. Alternatively the device can operate as a peer machine in a peer-to-peer or distributed network environment. The device may also include any other machine capable of executing a set of instructions that specify actions to be taken by that machine. These instructions can be sequential or otherwise.
A single device 300 is shown in FIG. 3. The term “computing device” also includes any collection of machines that individually or jointly execute a set or multiple sets of instructions to perform any one or more of the methods described above.
The example computing device 300 includes a processor 302. One example of a processor is a central processing unit or CPU. The device further includes main system memory 304 and static memory 306. The processor 302, main memory 304 and static memory 306 communicate with each other via data bus 308.
Computing device 300 further includes a data input device 310. In one embodiment the data input device includes a computer keyboard. The device 310 includes both a physical keyboard and/or a representation of a keyboard displayed on a touch sensitive display for example display device 312.
Computing device 300 may also include reader unit 314, network interface device 316, display device 312, optical media drive 318, cursor control device 320, and signal generation device 322.
Reader unit 314 is able to receive a machine readable medium 324 on which is stored one or more sets of instructions and data structures, for example computer software 326. The software 326 uses one or more of the methods or functions described above. Reader unit 314 includes a disc drive and/or a USB port. In these cases the machine readable medium includes a floppy disc and a static storage device such as a thumb drive. Where the optical media drive 318 is used, the machine readable medium includes a CD Rom.
Software 326 may also reside completely or at least partially within main system memory 304 and/or within processor 302 during execution by the computing device 300. In this case main memory 304 and processor 302 constitute machine-readable tangible storage media. Software 326 may further be transmitted or received over network 328 via network interface device 316. The data transfer uses any one of a number of well known transfer protocols. Once example is hypertext transfer protocol (http).
Machine-readable medium 324 is shown in an example embodiment to be a single medium. This term should however be taken to include a single medium or multiple media. Examples of multiple media include a centralised or distributed database and/or associated caches. These multiple media store the one or more sets of computer executable instructions. The term “machine readable medium” should also be taken to include any medium that is capable of storing, encoding or carrying a set of instructions for execution by the machine and that cause the machine to perform any one or more of the methods described above. The machine-readable medium is also capable of storing, encoding or carrying data structures used by or associated with these sets of instructions. The term “machine-readable medium” includes solid-state memories, optical media, magnetic media and carrier wave signals.
In one embodiment the software is installed and operating at a client site on a computing device 300. Network interface device 316 is required to communicate with an offsite central server for example to submit data results and licence validations.
In some cases the network interface device 316 and network 328 are not required as the system can run in a stand alone mode. This means that no data results are submitted to the offsite central server.
The techniques described above have been tested on a power station in normal operating conditions. While the power plant was running at a constant power output, the instrument data was analysed by the invention and new recommendations for operating parameters measurements calculated. The plant operators then adjusted the plant parameters to these recommendations and efficiency was observed to improve.
FIG. 4 shows a first experiment run at a Huntly power station on 7 Dec. 2007 from 13:30 to 21:00.
The system described above recommended changes which required an operator to change attemperator flow-rates, main steam temperature, reheater temperature, and burner angle of tilting. Operator intervention began around 15:50. The heat rate was observed to improve or drop by close to 2%.
FIG. 5 shows a second experiment that was run at the Huntly power station from 16 May 2008 starting at 18:00 to 17 May 2008 at 04:00.
The techniques described above recommended another combination of attemperator flow-rates, main steam and reheater temperature and the burner tilt angle.
Operator intervention commenced at 22:00 and heat-rate improvements of 1.5 to 2% were observed.
The techniques described above result in changes made to thermal efficiency of a power plant. In one embodiment the results of the equations above are applied manually to the plant by a user such as a plant operator. This is known as an open loop application. Alternatively the changes to the plant are applied automatically by a control system associated with the plant. This is known as a closed loop system.
The foregoing describes the invention including preferred forms thereof. Modifications and improvements as would be obvious to those skilled in the art are intended to be incorporated in the scope hereof, as defined by the accompanying claims.

Claims

1. A computer implemented method of controlling any energy conversion plant, in particular power plants of all kinds, having a plurality of measured parameters (which may include temperatures, pressures, partial pressures, mole numbers, as well as flows ,in and out electrical and/or mechanical powers, position of valves, and other actuators), that maximizes the plant's thermal efficiency with respect to a subset of the plant's measured parameters which can be manipulated, hence termed Variables, subject to operational structural financial and environmental constraints; this constrained maximization is called optimizing; said computer is either integral part of the plant's control system (DCS or other) in the sense that it both reads measured parameter from the DCS's Data Acquisition System (DAS) and writes the Variables maximizing values into the DSC as set-points (closed loop optimization), or just reads measured parameter from the DAS whilst human operators apply maximizing value of the Variables as set-points or by modifying the plant itself (open loop optimization), said method constitutes the following steps:

(a) Determine set of all relevant measured thermodynamic properties throughout the plant (e.g. temperatures, pressures, partial pressures, mole number, liquid and gas flows and electrical input and output values position of valves and other actuators), and its Variables subset (that is, those measured parameters which can be independently manipulated), by reading them via an interface with the DAS, or manual input,

(b) derive from the measured parameters in accordance to step (1a) and corresponding thermodynamic properties (e.g. specific volume enthalpy and entropy), the state of the plant which constitutes all relevant thermodynamic properties throughout the plant, as well as energy mass and entropy flows, temperatures, pressures, partial pressures, mole numbers, liquid and gas flows and electrical input and output values, real velocity vector fields, by way of relevant balance equations and particular expressions;

(c) from the plant state determined in step (1b) partition the plant into a finite number of real, irreversible physical continuums in the context of continuum-mechanics, which may or may not deliver useful work, and which correspond to discontinuities of measured and derived parameters making up the state of the plant as established in step (1b), and satisfying conservation-of-mass condition(s),

(d) construct an isometric (in the thermodynamic metric) map in the context of differential geometry, of each real continuum as established in step (1c) from the thermodynamic manifold which is spanned by thermodynamic coordinates (for example pressure temperature and chemical potentials) and time, to a region of the Galilean manifold spanned by the spatial and time coordinates (for example Cartesian x,y,z,t),

(e) construct the plant model using the partition into physical continuums determined in accordance to step (1c) and in accordance of the physical real arrangement of the plant's actual hardware, as interfacing (i.e. incedenting) physical continuums, exhibited as a graph in the context of graph theory which can be reduced to a planar graph, wherein each boundary plays the role of an edge and each continuum the role of a node,

(f) convert each partitioned real, irreversible physical continuum into a (virtual) corresponding reversible continuum or Reversible Masking of the real continuum, subject to the constraint(s) that the real continuum and reversible continuum assume the same boundary values of thermodynamic properties in accordance to all previous steps and that their derivatives are continuous and equal at the boundaries, as well as mass-flow-rate, such that the partitioned irreversible real continuums which are governed by a system of conventional balance equations and constituent (phenomenological) equations, are converted into partitioned Reversible Maskings substitute which are governed by a system of (partial) differential equations excluding any constituent equations, but including either the equation of Thermodynamic Geodesic Field (TGF) in the thermodynamic metric, or a direct Reversible Energy Conservation (REC), uniquely describing the reversible continuum (called a Mathematical Model of the reversible continuum),

(g) construct an equivalent reversible (virtual) plant by mapping the partitioned Reversible Masking substitute equations from step (1f) into the plant model constructed in step (1e), such that the graph of step (1e) is maintained, that is, map the partition of the real plant of irreversible real continuums, into a partition of Reversible Maskings substitute equations, with the same incidence matrix in the context of graph theory,

(h) solve the mapped equations from step (1g) for the current plant state in terms of velocity (vector) fields across the reversible continuums and store the values of the solutions within the spaces defined by the reversible continuums,

(i) construct the objective function (called Loss) to be minimized by a surface integral of kinetic energy obtained from the velocity field derived according to step (1h) over the boundary of each Reversible Masking, inputting to the (numerical) integration the velocity field, density field(s) of (1e) values at the boundary, outputting the difference in kinetic energy between boundaries where matter leaves and enters the Reversible Masking, subtracting from the sum of all kinetic energy increment the actual work delivered by the real plant,

(j) simulate the plant using the solved equations from step (1g) using the reversible model and adjust the control set-points in the simulation to determine the Variables (control inputs) defined in 1 that correspond to the minimization of the Loss constructed in step (1i) resulting in maximizing the efficiency of the plant according to a predetermined objective function,

(k) apply the Variables (control inputs) derived according to step (1j) that minimize the objective function constructed according to step (1i) to the real thermal power plant.

2. A method to generate a revised state of the plant and reversible velocity fields due to varying the Variables subset defined in claim 1), based at least partly on a (power) plant configuration in accordance to step (le), superimposed by the Reversible Masking in accordance to step (1f), and consequent reversible plant in accordance to step (1g) comprising a solver as follows:

(a) Euler's balance of momentum equation; and

(b) the conservation of mass equation; and

(c) the reversible conservation of energy (REC) equation; and

(d) the thermodynamic equations of state; or

(e) the thermodynamic geodesic field (TGF) equations,

(f) and a module to carry out the numerical solution of the simultaneous equations (2a) to (2e) subject to revised boundary conditions based at least partly on Central Schemes methods, Method of Lines, or reduced versions thereof.

3. A simulator constituting a readable media module storing the data that flows from the numerical solution module defined in (2f) which simulates the thermodynamic properties of the real plant.

4. A method to derive kinetic energy differences across each of the reversible continuums defined in step (1f), from the data flow of the reversible velocity field(s) computed by the solver defined in claim 2), which is fed into a module of numerical integration of kinetic energy around the surface of each reversible continuum.

5. A method to obtain the objective function constituting the sum of all kinetic energy integrals, of all Reversible Maskings defined in step (1f).

6. An apparatus for any one of the preceding claims herein comprising a (power) plant thermal efficiency constrained-maximization (optimization), the apparatus configured to implement the method of claim 1, that is, configured to obtain the current state of the plant from available measured data; obtain the Variables subset of the measured data defined in claim 1; apply a set of constraints to the Variables; generate a revised state of the reversible power plant, where the reversible plant is defined in step (1g), as a function of the revised set of Variables, the generation based at least partly on mathematical model of the reversible continuum (or Reversible Masking) of step (1f);and test the revised set of Variables for convergence, comprising the following modules and data flows:

(a) interfacing module with the DAS or exercising manual input in accordance with claim 1), to determine initial values of the set of all relevant measured thermodynamic properties throughout the plant in accordance to step (1a); the measured data and the Variables subset flow to readable media modules;

(b) a module that generates the initial (current) state of the plant as defined in step (1b), from the measured parameters in accordance to step (1a) which is stored in a module depicted in (6a) and the corresponding thermodynamic properties (e.g. specific volume, enthalpy and entropy),

(c) a module constructing the partition into physical continuums in accordance to step (1c), based at least partly on checking each combination of boundary-surfaces of mass-flow entering the continuum against all combinations of boundary-surfaces of mass-flow leaving the continuum for conservation of mass; as a result each continuum is reduced to cylindrical symmetry (1-dimensional), and furthermore the plant is exhibited as a planar graph in the context of graph theory, wherein each boundary of interfacing (i.e. incedenting) physical continuum plays the role of an edge, and each continuum the role of a node, and furthermore the resultant plant model is as defined in step (1e),

(d) a convergence tester module which can be part of the minimizer procedure (like Cobyla), within which the solver of claim 2), the simulator of claim 3), and the objective function in accordance to claim 5), are applied in that order to the plant model of module (6c) and the revised set of Variables, which is then examined to reach a variance less than a threshold variance; if the convergence test fails, then the revised numerical values of the objective function and the Variables and state of the plant which are stored in the simulator module of claim 3) above, are fed into

(e) a minimizer module like Cobyla which generates revised values of the set of Variables defined in claim 1) which are fed into the mathematical model of the reversible plant (that is the solver of claim 2)), and

(f) repeating convergence testing described in (6d) of generating yet another revised state of the plant and reversible velocity field, and testing the resultant revised objective function as defined in step (1i) and generated in accordance to claim 5), and testing the revised set of Variables for a variance less than a threshold variance in the convergence tester module (6d); if achieved, then

(g) physically applying continuously the Variables values generated in module (6f) which is the Optimizer output, to the (real) energy conversion plant, by way of closed loop optimization or open loop optimization in accordance with claim 1), necessarily resulting in minimizing the objective function (Losses) defined in step (1i), and generated in accordance to (6d), resulting in the maximizing of the thermal efficiency of the real plant; if a constraint in the context of claim 1) is a given power output then said maximizing of thermal efficiency will manifest itself as the minimizing of fuel consumption, whilst if the fuel consumption is rather dictated as an external constraint, then said maximizing of thermal efficiency will manifest itself as the maximizing of power output.