CN109858129A - A kind of gas turbine dynamic emulation method about combined supply system - Google Patents
A kind of gas turbine dynamic emulation method about combined supply system Download PDFInfo
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Abstract
The invention discloses a kind of gas turbine dynamic emulation methods about combined supply system, which is characterized in that the described method includes: determining the composed structure of combined supply system；Gas turbine model is established, the mathematical model of component is established according to each characteristics of components；Gas turbine model is solved.Gas turbine is divided into different equipment, component by the method for the present invention, using lumped parameter model, initial static variable is sought using partial dynamic model, simulation efficiency is high, avoid repetition modeling, being conducive to dynamic model rapidly enters stable state simultaneously, ensure that model accuracy also with lumped parameter model and the small step-length solution of 10ms.
Description
Technical field
The invention belongs to energy internet simulation technical field, in particular to a kind of gas turbine about combined supply system
Dynamic emulation method.
Background technique
Dynamic simulation can be used for the verifying of energy internet design scheme, control strategy research, method of operation inspection, failure point
Recurrence, operations staff's emulation training etc. are analysed, there is important practical value.
Combined supply system based on gas turbine is the core component of energy internet, is electric power in energy internet
The dynamic characteristic of system, therrmodynamic system, the critical system coupled between fuel pipe network, combined supply system has weight to energy internet
The influence wanted.Combined supply system dynamic simulation is significant to the dynamic property of research energy internet.Gas turbine conduct
The core equipment of combined supply system, dynamic property directly affect the dynamic characteristic of combined supply system, combined supply system dynamic simulation
Middle gas turbine initial value has a significant impact to emulation, if re-establishing gas turbine static models, heavy workload, and research one
Kind is of practical meaning using the dynamic emulation method that gas turbine dynamic model seeks dynamic simulation initial value.
Summary of the invention
In view of the above-mentioned problems, the present invention provides a kind of gas turbine dynamic emulation method about combined supply system, it is described
Method the following steps are included:
Determine the composed structure of combined supply system；
Gas turbine model is established, the mathematical model of component is established according to each characteristics of components；
Gas turbine model is solved.
Further, the combined supply system includes gas turbine, waste heat boiler, lithium-bromide absorption-type refrigerating machine and phase transformation
Energy storage device.
Further, the gas turbine model includes static models and dynamic model.
Further, the static models include air intake duct model, compressor model, combustion chamber model, turbine model；
The dynamic model include air intake duct model, compressor model, combustion chamber model, turbine model, rotator model,
Revolving speed Controlling model.
Further, the relational expression of the air intake duct model are as follows:
P2=α1P1 T2=T1 (1)
P1、T1Respectively air intake duct air-source pressure, thermodynamic temperature, P2、T2Respectively air intake port atmospheric pressure,
Thermodynamic temperature, α1For Fighter Inlet total pressure recovery coefficient；
The compressor model includes:
According to compressor characteristic working curve, its pressure ratio, revolving speed are fitted, between four parameters of corrected flow and efficiency
Relational expression:
In formula,For compressor with respect to corrected flow,For relative efficiency,For relative rotation speed,For opposite pressure ratio,
fc1ForAboutWithNonlinear fitting relational expression, fc2ForAboutWithNonlinear fitting relational expression；
Conversion relation of the compressor with respect to corrected flow and compressor flow, expression formula are as follows:
In formula, GcinFor compressor air inlet machine flow；Pc0For compressor nominal pressure；Tc0For compressor operating temperature ratings；
Gc0For compressor metered flow；
Compressor relative efficiency pressure ratio opposite with compressor efficiency, relative rotation speed and revolving speed, compressor and compressor pressure ratio
Conversion relation, expression formula are as follows:
In formula, ηcFor compressor efficiency, ηc0For efficiency under compressor declared working condition；N is gas turbine rotary speed, n0To calm the anger
Machine rated speed；πcFor compressor pressure ratio, πc0For pressure ratio under declared working condition；
Relationship between compressor inlet variable and exported variable, expression formula are as follows:
In formula, P3For blower outlet air pressure；T3For blower outlet air themperature, k is adiabatic coefficent；cpcFor compressor
Pressurization by compressed air specific heat, WcFor the power of compressor consumption；GcoutFor blower outlet air mass flow；
The combustion chamber model includes:
One group is established using outlet pressure and specific enthalpy as the differential equation group of state variable according to quality and the conservation of energy, is expressed
Formula are as follows:
In formula, H3For combustion chamber inlet air specific enthalpy, G4、H4、P4、T4Respectively combustor exit gas flow, specific enthalpy, pressure
By force, thermodynamic temperature, GfFor fuel flow rate, GaFor air mass flow needed for fuel and it is equal to Gcout, LHV is natural gas Lower heat value,
ηbFor efficiency of combustion, σbFor combustor total pressure recovery coefficient, VbIt is combustor exit combustion gas density for combustion chamber volume, ρ, k is exhausted
Heat number, RgFor gas constant, Rg=RM, R are universal gas constant, and M is the average molar mass of gas；
Relational expression between combustion chamber import variable and exported variable:
In formula, cpbFor combustion chamber inlet gas specific heat, GaFor air mass flow needed for fuel, TfFor combustion chamber inlet fuel heat
Mechanics temperature, with T3Close, α is excess air coefficient, Ga0For theoretical air flow needed for unit quality fuels；
The turbine model includes:
Fitted according to turbine rotor characteristic equation react the expansion ratio of its working condition, revolving speed, corrected flow and
Relationship between efficiency, expression formula are as follows:
In formula,For compressor with respect to corrected flow,For relative efficiency,For relative rotation speed,For relative expansion ratio,
ft1ForAboutWithNonlinear fitting relational expression, ft2ForAboutWithNonlinear fitting relational expression；
Conversion relation of the turbine with respect to corrected flow and turbine flow, expression formula are as follows:
GtinFor turbine inlet flow, Pt0For turbine nominal pressure；Tt0For turbine machine operating temperature ratings；Gt0For
Turbine metered flow；
Turbine relative efficiency and turbine efficiency, turbine relative expansion than the conversion relation with turbine expansion ratio,
Expression formula are as follows:
In formula, ηtFor turbine efficiency, ηt0For the efficiency under turbine declared working condition；πtFor turbine expansion ratio, πt0For
Expansion ratio under turbine declared working condition；
Relationship between turbine inlet variable and exported variable, expression formula are as follows:
In formula, P5For turbine outlet air pressure, T5For turbine outlet fuel gas temperature, WtPower, c are issued for turbineptFor
Turbine gas specific heat at constant pressure, GtoutFor turbine outlet gas flow；
Supplement working medium state equation:
Air Constitute equation are as follows:
In formula, t2、T2For compressor inlet Celsius temperature, thermodynamic temperature, t3、T3Respectively combustion chamber inlet air is taken the photograph
Family name's temperature, thermodynamic temperature, H3For combustion chamber inlet air specific enthalpy, cp,t,2For compressor inlet pressurization by compressed air specific heat, cp,t,3For
Blower outlet pressurization by compressed air specific heat；
Combustion gas Constitute equation are as follows:
In formula,Respectively N in turbine inlet combustion gas2、CO2、O2、H2O's
Specific heat at constant pressure, cp,t,4For turbine inlet combustion gas specific heat at constant pressure, Respectively turbine
N in outlet gas2、CO2、O2、H2The specific heat at constant pressure of O, cp,t,5For turbine outlet combustion gas specific heat at constant pressure,Respectively N in turbine inlet combustion gas2、CO2、O2、H2The specific enthalpy of O,It is N in combustion gas respectively2、CO2、O2、H2The mass fraction of O, need to be according to the component and fuel of fuel
It measures and is calculated with the mass ratio of air, specific formula is as follows:
The expression formula of the rotator model are as follows:
In formula, I is the rotary inertia of rotor, and n is rotor speed, WtPower, W are issued for turbinecFunction is consumed for compressor
Rate, WeFor generator power, ηmtFor turbine mechanical efficiency, π is pi；
The revolving speed Controlling model is for dynamic model described in rated speed, and revolution speed control system uses PI controlling party
Formula, expression formula are as follows:
In formula (23), Gf0For initial fuel flow, GfIt (t) is the fuel flow rate of t moment, KpFor proportional gain, TiFor integral
Time constant, Kp、TiNeed to suitably it be worth according to specific equipment debugging, e (t) is the revolving speed deviation of t moment, e (t)=n-nr, nr
For gas turbine rated speed.
Further, the fc1Expression formula are as follows:
The fc2Expression formula are as follows:
The ft1Expression formula are as follows:
The ft2Expression formula are as follows:
Further, the static models are lumped parameter mould when each differential term is 0 in dynamic model described in each component
Type obtains 3 common equations of gas turbine, it may be assumed that
In formula (20), Gcout、Gtout、Wc、WtIt is all about Gf、πc、πtNonlinear function, expression can be by above
The formula provided acquires, and enables:
In formula (21), (22), e1、e2、e3For the error of three common equations, f1(Gf,πc,πt)、f2(Gf,πc,πt)、f3
(Gf,πc,πt) it is about Gf、πc、πtNonlinear function, corresponding flow, power are substituted into formula (21), (22) can be in the hope of.
Further, the resolving process of the static models and the dynamic model the following steps are included:
Initial value setting, is arranged step-length 10ms, gives air-source parameter P1、T1, gas turbine rated speed nr, revolving speed initial value
n0, generated output WeWith gas turbine exhaust pressure P5, fuel flow rate G is setf, revolving speed n, compressor pressure ratio πc, turbine expansion ratio
πtInitial value；
Solve stable state initial value, that is, static models；
Judgement system disturbs if it exists with the presence or absence of disturbance, disturbance is added to dependent variable；
The Steady-state Initial G that will be acquiredf、P4、H4The initial value G calculated as dynamicf0、P40、H40Dynamic model is substituted into calculate.
Further, the step of solving the stable state initial value is as follows:
According to formula (1), P is substituted into1、T1, obtain P2、T2；
According to formula (2), (3), (4), (5), P is substituted into2、T2, gas turbine rotary speed n, compressor pressure ratio initial value πc, obtain
Gcout、ηc、P3、T3、Wc；
According to formula (8), (17), (18), P is substituted into3、T3, fuel flow rate initial value Gf, obtain P4、T4、Ga、H4；
According to formula (9), (10), (11), (12), P is substituted into4、T4、Ga, n, turbine expansion ratio initial value πt, drain pressure
P5, obtain Gtout、Wt、T5、ηt；
According to formula (21), G is substituted intocout、Gf、Ga、Gtout、Wc、Wt, given generated output We, acquire e1、e2、e3, then adopt
Formula (22) are solved with basic Newton-Raphson approach, obtain new πc、πt、Gf, convergence judgement is carried out, is come back for if not restraining
Iterative calculation, until convergence.
Further, the step of dynamic model calculates is as follows:
According to formula (1), given air-source parameter P is substituted into1、T1, obtain P2、T2；
According to formula (2), (3), (4), (5), (14), P is substituted into2、T2, gas turbine rotary speed n,Solve compressor mould
Type obtains Wc、Gcout、Gin、T3；
According to formula (17), (18), H is substituted into4、Gf、Ga, wherein GaEqual to Gcout, acquire T4, according to formula (9), (10), (11),
(12), T is substituted into4、P4、n、P5, turbine model is solved, W is obtainedt、Gtin、Gtout、T5, further according to formula (6), (7), (13),
(15), G is substituted intoa、T3、G4、Gf、H4, wherein G4Equal to Gtin, combustion chamber model is solved, differential variable is obtained's
Value；
According to formula (19), W is substituted intoc、Wt、We, rotator model is solved, is obtainedValue；
According to differential variableValue, integral obtain new P4、H4, n, in which:
New fuel flow rate G is calculated according to formula (23)f；
By variable P4、H4、n、GfUpdated value substitute into next time step and calculate.
Gas turbine is divided into different equipment, component by the method for the present invention, using lumped parameter model, utilizes partial dynamic
Model seeks initial static variable, and simulation efficiency is high, avoids repetition modeling, while being conducive to dynamic model and rapidly entering surely
State ensure that model accuracy also with lumped parameter model and the small step-length solution of 10ms.
Other features and advantages of the present invention will be illustrated in the following description, also, partly becomes from specification
It obtains it is clear that understand through the implementation of the invention.The objectives and other advantages of the invention can be by specification, right
Pointed structure is achieved and obtained in claim and attached drawing.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is this hair
Bright some embodiments for those of ordinary skill in the art without creative efforts, can be with root
Other attached drawings are obtained according to these attached drawings.
Fig. 1 shows the flow diagram of the embodiment of the present invention；
Fig. 2 shows the combined supply system figures of the embodiment of the present invention；
Fig. 3 shows the static models solution procedure of the embodiment of the present invention；
Fig. 4 shows the dynamical model solution process of the embodiment of the present invention.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical solution in the embodiment of the present invention clearly and completely illustrated, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without making creative work, shall fall within the protection scope of the present invention.
A kind of gas turbine dynamic emulation method about combined supply system as shown in figure 1, process are to determine first
The composed structure of combined supply system, illustratively, the combined supply system figure of the embodiment of the present invention as shown in Figure 2, trilogy supply system
System includes gas turbine, waste heat boiler and lithium-bromide absorption-type refrigerating machine, in addition, need to be assisted with phase-change energy storage equipment, to adjust
The equilibrium of supply and demand of hot and cold load.Specifically, natural gas is introduced into the compressor of gas turbine, then compressor is by natural conductance
Enter in the combustion chamber of gas turbine, natural gas burns in a combustion chamber, drives the rotating turbine in gas turbine, and then turbine
Machine drives engine operation to start to generate electricity, wherein waste gas residual heat after combustion of natural gas be used to after waste heat boiler heat supply or
By refrigeration machine cooling with cooling supply, carry out storing up cold and heat accumulation by phase-change energy storage equipment, it is hot and cold to refrigeration machine and waste heat boiler negative
The equilibrium of supply and demand of lotus is adjusted.
Secondly, establishing the mathematical model of gas turbine model and each component.
Specifically, gas turbine is divided into the components such as air intake duct, compressor, combustion chamber, turbine, rotor, according to each component
Characteristic establishes the governing equation group of component.
Specifically, air intake duct only considers its pressure loss, expression formula are as follows:
P2=α1P1 T2=T1 (1)
P1、T1Respectively air intake duct air-source pressure, thermodynamic temperature, P2、T2Respectively air intake port atmospheric pressure,
Thermodynamic temperature, α1For Fighter Inlet total pressure recovery coefficient, 0.99 is taken.
Specifically, compressor is a non-linear very strong component, according to its characteristic working curve, its opposite pressure is fitted
Than, the relational expression between relative rotation speed, corrected flow and four parameters of relative efficiency.It is calculated according to compressor both ends pressure
Pressure ratio finds out opposite pressure ratio, then calculates relative rotation speed by revolving speed, so as to find out opposite corrected flow and relative efficiency.It is quasi-
Conjunction relational expression is Groebner Basis, expression formula are as follows:
In formula,For compressor with respect to corrected flow,For relative efficiency,For relative rotation speed,For opposite pressure ratio,
fc1ForAboutWithNonlinear fitting relational expression, fc2ForAboutWithNonlinear fitting relational expression.
Wherein, conversion relation of the compressor with respect to corrected flow and compressor flow are as follows:
In formula, GcinFor compressor air inlet machine flow；Pc0For compressor nominal pressure, 101.325kPa is taken；Tc0For compressor
Operating temperature ratings take 288K；Gc0For compressor metered flow, 0.5kg/s is taken.
Compressor relative efficiency pressure ratio opposite with compressor efficiency, relative rotation speed and revolving speed, compressor and compressor pressure ratio
Conversion relation are as follows:
In formula, ηcFor compressor efficiency, ηc0For efficiency under compressor declared working condition, 0.81 is taken；N is gas turbine rotary speed,
n0For compressor rated speed, 96000r/min is taken；πcFor compressor pressure ratio, πc0For pressure ratio under declared working condition, 3.2 are taken.
Further, the relational expression between compressor inlet variable and exported variable is as follows:
In formula, P3For blower outlet air pressure；T3For blower outlet air themperature, k is adiabatic coefficent, takes 1.4；cpcFor
Compressor air specific heat at constant pressure, WcFor the power of compressor consumption；GcoutFor blower outlet air mass flow.
Specifically, combustion chamber model when need to consider its volume inertia, thermal inertia, efficiency of combustion and crushing, ignore its to
Extraneous heat dissipation capacity.In view of burning chamber volume is smaller, burning is considerably complicated with flow process, lumped parameter model is established,
One group is established using outlet pressure and specific enthalpy as the differential equation group of state variable, expression formula according to quality and the conservation of energy are as follows:
In formula, H3For combustion chamber inlet air specific enthalpy, G4、H4、P4、T4Respectively combustor exit gas flow, specific enthalpy, pressure
By force, thermodynamic temperature, GfFor fuel flow rate, GaFor air mass flow needed for fuel and it is equal to Gcout, LHV is natural gas Lower heat value,
Take 48101.53kJ/kg, ηbFor efficiency of combustion, 0.98, σ is takenbFor combustor total pressure recovery coefficient, 0.97, V is takenbFor combustion chamber
Product, takes 0.05m3, ρ is combustor exit combustion gas density, and k is adiabatic exponent, takes 1.4, RgFor gas constant, Rg=RM, R are logical
It with gas constant, takes 8.314510 × 10-3kJ/ (molK), M is the average molar mass of gas, takes 28.03 × 10-3kg/
mol。
Further, the relational expression between combustion chamber import variable and exported variable are as follows:
In formula, cpbFor combustion chamber inlet gas specific heat, 1.01kJ/ (kgK), G are takenaFor air mass flow needed for fuel, Tf
For combustion chamber inlet fuel thermodynamic temperature, with T3Close, α is excess air coefficient, takes 1.5, Ga0For unit flow fuel institute
The theoretical air flow needed, takes 18.23kg/s.
Specifically, turbine can also go out react according to working characteristics equation model the expansion ratio of its working condition, revolving speed,
Relationship between corrected flow and efficiency, expression formula are as follows:
In formula,For compressor with respect to corrected flow,For relative efficiency,For relative rotation speed,For relative expansion ratio,
ft1ForAboutWithNonlinear fitting relational expression, ft2ForAboutWithNonlinear fitting relational expression.
Wherein, conversion relation of the turbine with respect to corrected flow and turbine flow are as follows:
GtinFor turbine inlet flow, Pt0For turbine nominal pressure, 310kPa is taken；Tt0For turbine machine nominal operation
Temperature takes 1113K；Gt0For turbine metered flow, 0.5kg/s is taken.
Turbine relative efficiency and turbine efficiency, turbine relative expansion are than the conversion relation with turbine expansion ratio
Are as follows:
In formula, ηtFor turbine efficiency, ηt0For the efficiency under turbine declared working condition, 0.82 is taken；πtFor turbine expansion
Than πt0For the expansion ratio under turbine declared working condition, 3 are taken.
Further, the relational expression between turbine inlet variable and exported variable are as follows:
In formula, P5For turbine outlet air pressure, T5For turbine outlet fuel gas temperature, WtPower, c are issued for turbineptFor
Turbine gas specific heat at constant pressure, GtoutFor turbine outlet gas flow.
Specifically, supplement working medium state equation, air Constitute equation and combustion gas Constitute equation are as follows:
Specifically, can be obtained according to air physical property:
In formula (14), (15), t2、T2For compressor inlet Celsius temperature, thermodynamic temperature, t3、T3Respectively combustion chamber into
Mouth air Celsius temperature, thermodynamic temperature, H3For combustion chamber inlet air specific enthalpy, cp,t,2For compressor inlet pressurization by compressed air ratio
Heat, cp,t,3For blower outlet pressurization by compressed air specific heat.
Specifically, can be obtained according to combustion gas physical property:
In formula (16), (17),Respectively N in turbine inlet combustion gas2、
CO2、O2、H2The specific heat at constant pressure of O, cp,t,4For turbine inlet combustion gas specific heat at constant pressure,
Respectively N in turbine outlet combustion gas2、CO2、O2、H2The specific heat at constant pressure of O, cp,t,5For turbine outlet combustion gas specific heat at constant pressure.Respectively N in turbine inlet combustion gas2、CO2、O2、H2The specific enthalpy of O.It is N in combustion gas respectively2、CO2、O2、H2The mass fraction of O, need to be according to the component and fuel of fuel
It measures and is calculated with the mass ratio of air, specific formula is as follows:
When excess air coefficient α is certain, takes α=1.5,Respectively 76.29%,
9.44%, 6.75%, 7.52%.
Specifically, rotor is the rotation axis for making compressor, turbine and generator connect together, turbine issues function, and
Compressor, generator consume function.The equation of motion of rotor are as follows:
In formula, I is the rotary inertia of rotor, takes 0.003kgm2, n is rotor speed, WtPower, W are issued for turbinec
Power, W are consumed for compressoreFor generator power, ηmtFor turbine mechanical efficiency, π is pi.
Further, it is each component dynamic lumped parameter model above, when each differential term is 0, then constitutes gas turbine
Static lumped parameter model obtains 3 common equations of gas turbine, it may be assumed that
In formula (20), Gcout、Gtout、Wc、WtIt is all about Gf、πc、πtNonlinear function, expression can be by above
The formula provided acquires, and enables:
In formula (21), (22), e1、e2、e3For the error of three common equations, f1(Gf,πc,πt)、f2(Gf,πc,πt)、f3
(Gf,πc,πt) it is about Gf、πc、πtNonlinear function, corresponding flow, power are substituted into formula (21), (22) can be in the hope of.
Specifically, compressor, turbine ignore the influence of temperature comparisons' heat, c in static lumped parameter modelpc、cptTake perseverance
Value, cpcTake 1.01kJ/ (kgK), cptTake 1.3kJ/ (kgK).
Further, for the dynamic model of rated speed, revolution speed control system uses PI control mode, specifically, PI
Control is a kind of Linear Control, it constitutes control deviation according to given value and real output value, and the ratio of deviation and integral is logical
It crosses linear combination and constitutes control amount, controlled device is controlled, expression formula are as follows:
In formula (23), Gf0For initial fuel flow, GfIt (t) is the fuel flow rate of t moment, KpFor proportional gain, TiFor integral
Time constant, Kp、TiNeed to suitably it be worth according to specific equipment debugging, e (t) is the revolving speed deviation of t moment, e (t)=n-nr, nr
For gas turbine rated speed.
Finally, resolved to emulation mode proposed by the present invention, resolve process the following steps are included:
1, initial value is arranged.Step-length 10ms is set, air-source parameter P is given1、T1, gas turbine rated speed nr, at the beginning of revolving speed
Value n0, generated output WeWith gas turbine exhaust pressure P5.Fuel flow rate G is setf, revolving speed n, compressor pressure ratio πc, turbine expansion
Compare πtInitial value.
2, stable state initial value solves, and specific Steady-state Initial solution procedure is as follows:
2.1, according to formula (1), substitute into P1、T1, obtain P2、T2。
2.2, according to formula (2), (3), (4), (5), substitute into P2、T2, gas turbine rotary speed n, compressor pressure ratio initial value πc, obtain
To Gcout、ηc、P3、T3、Wc。
2.3, according to formula (8), (17), (18), substitute into P3、T3, fuel flow rate initial value Gf, obtain P4、T4、Ga、H4。
2.4, according to formula (9), (10), (11), (12), substitute into P4、T4、Ga, n, turbine expansion ratio initial value πt, exhaust pressure
Strong P5, obtain Gtout、Wt、T5、ηt。
2.5, according to formula (21), substitute into Gcout、Gf、Ga、Gtout、Wc、Wt, given generated output We, acquire e1、e2、e3, then
Formula (22) are solved using basic Newton-Raphson approach, obtain new πc、πt、Gf, convergence judgement is carried out, goes to step if not restraining
Rapid 2.2 iterative calculation is until convergence.
3, judge that system with the presence or absence of disturbance, disturbs if it exists, disturbance is added to dependent variable.
4, dynamic model calculates.The Steady-state Initial G that will be acquiredf、P4、H4The initial value G calculated as dynamicf0、P40、H40。
4.1, according to formula (1), substitute into given air-source parameter P1、T1, obtain P2、T2。
4.2, according to formula (2), (3), (4), (5), (14), substitute into P2、T2, gas turbine rotary speed n,Solve compressor
Model obtains Wc、Gcout、Gin、T3。
4.3, according to formula (17), (18), substitute into H4、Gf、Ga, wherein GaEqual to Gcout, acquire T4.According to formula (9), (10),
(11), (12) substitute into T4、P4、n、P5, turbine model is solved, W is obtainedt、Gtin、Gtout、T5.Further according to formula (6), (7),
(13), (15) substitute into Ga、T3、G4、Gf、H4, wherein G4Equal to Gtin, combustion chamber model is solved, differential variable is obtainedValue.
4.4, according to formula (19), substitute into Wc、Wt、We, rotator model is solved, is obtainedValue.
4.5 according to differential variableValue, integral obtain new P4、H4、n。
4.6 new fuel flow rate G is calculated according to formula (23)f。
4.7 go to step 3, by variable P4、H4、n、GfUpdated value substitute into next time step (i.e. step 3) calculate.
Illustratively, as shown in figure 3, setting step-length is 10ms, P1For known air-source pressure, T1For known heating power
Learn temperature, generated output WeWith gas turbine exhaust pressure P5, fuel flow rate G is setf, revolving speed n, compressor pressure ratio πc, turbine it is swollen
It is swollen to compare πtInitial value.By P1、T1Value substitute into formula (1) in, P is calculated2、T2, by P2、T2、n、πcValue substitute into formula (2),
(3), (4), in (5), obtain Gcout、ηc、P3、T3、Wc, by P3、T3、GfSubstitution formula (8), in (18), obtains P at (17)4、T4、Ga,
By P4、T4、n、πt、P5Substitution formula (9), (11), in (12), obtains G at (10)tout、Wt、T5、ηt, by Gcout、Wc、Gf、Ga、We、
Gtout、WtIn substitution formula (21), formula (22) are solved using basic Newton-Raphson approach.Specifically, Newton-Raphson approach, that is, ox
Iterative method, it is a kind of method of approximate solution equation in real number field and complex field.Formula (22) obtains new π after solvingc、
πt、GfValue, judge πc、πt、GfValue whether restrain, gone to if not restraining step 2.2 be iterated calculating until πc、πt、Gf
Value convergence.Judge that system with the presence or absence of disturbance, is disturbed if it exists, disturbance is added to dependent variable, illustratively, such as G againf
Disturbance occur leads to GfFlow changes, and variable quantity is Δ Gf, then new flow should be G after disturbingf+ΔGf.As shown in figure 4,
The Steady-state Initial G that will be acquiredf、P4、H4As the initial value that dynamic calculates, gas turbine rated speed n is givenr, by P1、T1Value
In substitution formula (1), P is calculated2、T2, by P2、T2、n、Substitution formula (2), (4), (5), in (14), obtains W at (3)c、
Gcin、Gcout、T3, by H4、Gf、GaIn substitution formula (17), (18), wherein GaEqual to Gcout, acquire T4.According to formula (9), (10),
(11), (12) substitute into T4、P4、n、P5, turbine model is solved, W is obtainedt、Gtin、Gtout、T5, further according to formula (6), (7),
(13), (15) substitute into Ga、T3、G4、Gf、H4, wherein G4Equal to Gtin, combustion chamber model is solved, differential variable is obtainedValue, by Wc、Wt、WeIn substitution formula (19), rotator model is solved, is obtainedValue.Wherein,For the output quantity and differential variable of each component, integrated to obtain new P according to differential variable4、H4, n, root
New fuel flow rate G is calculated according to formula (23)f.Finally by variable P4、H4、n、GfUpdated value continue to substitute into next time step (i.e.
Step 3) calculates.
The identical meaning of identical symbology in the present invention.
Although the present invention is described in detail referring to the foregoing embodiments, those skilled in the art should manage
Solution: it is still possible to modify the technical solutions described in the foregoing embodiments, or to part of technical characteristic into
Row equivalent replacement；And these are modified or replaceed, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The spirit and scope of scheme.
Claims (10)
1. a kind of gas turbine dynamic emulation method about combined supply system, which is characterized in that the method includes following steps
It is rapid:
Determine the composed structure of combined supply system；
Gas turbine model is established, the mathematical model of component is established according to each characteristics of components；
Gas turbine model is solved.
2. emulation mode according to claim 1, it is characterised in that: the combined supply system includes gas turbine, waste heat
Boiler, lithium-bromide absorption-type refrigerating machine and phase-change energy storage equipment.
3. emulation mode according to claim 1, it is characterised in that: the gas turbine model includes static models and moves
States model.
4. emulation mode according to claim 3, it is characterised in that: the static models include air intake duct model, calm the anger
Machine model, combustion chamber model, turbine model；
The dynamic model includes air intake duct model, compressor model, combustion chamber model, turbine model, rotator model, revolving speed
Controlling model.
5. emulation mode according to claim 4, it is characterised in that: the relational expression of the air intake duct model are as follows:
P2=α1P1 T2=T1 (1)
P1、T1Respectively air intake duct air-source pressure, thermodynamic temperature, P2、T2Respectively air intake port atmospheric pressure, thermodynamics
Temperature, α1For Fighter Inlet total pressure recovery coefficient；
The compressor model includes:
According to compressor characteristic working curve, its pressure ratio, revolving speed, the pass between four parameters of corrected flow and efficiency are fitted
It is expression formula:
In formula,For compressor with respect to corrected flow,For relative efficiency,For relative rotation speed,For opposite pressure ratio, fc1ForAboutWithNonlinear fitting relational expression, fc2ForAboutWithNonlinear fitting relational expression；
Conversion relation of the compressor with respect to corrected flow and compressor flow, expression formula are as follows:
In formula, GcinFor compressor air inlet machine flow；Pc0For compressor nominal pressure；Tc0For compressor operating temperature ratings；Gc0For
Compressor metered flow；
Compressor relative efficiency pressure ratio opposite with revolving speed, compressor with compressor efficiency, relative rotation speed and compressor pressure ratio change
Calculation relationship, expression formula are as follows:
In formula, ηcFor compressor efficiency, ηc0For efficiency under compressor declared working condition；N is gas turbine rotary speed, n0For compressor volume
Determine revolving speed；πcFor compressor pressure ratio, πc0For pressure ratio under declared working condition；
Relationship between compressor inlet variable and exported variable, expression formula are as follows:
In formula, P3For blower outlet air pressure；T3For blower outlet air themperature, k is adiabatic coefficent；cpcFor compressor air
Specific heat at constant pressure, WcFor the power of compressor consumption；GcoutFor blower outlet air mass flow；
The combustion chamber model includes:
One group is established using outlet pressure and specific enthalpy as the differential equation group of state variable, expression formula according to quality and the conservation of energy
Are as follows:
In formula, H3For combustion chamber inlet air specific enthalpy, G4、H4、P4、T4Respectively combustor exit gas flow, specific enthalpy, pressure,
Thermodynamic temperature, GfFor fuel flow rate, GaFor air mass flow needed for fuel and it is equal to Gcout, LHV is natural gas Lower heat value, ηb
For efficiency of combustion, σbFor combustor total pressure recovery coefficient, VbIt is combustor exit combustion gas density for combustion chamber volume, ρ, k is insulation
Index, RgFor gas constant, Rg=R/M, R are universal gas constant, and M is the average molar mass of gas；
Relational expression between combustion chamber import variable and exported variable:
In formula, cpbFor combustion chamber inlet gas specific heat, GaFor air mass flow needed for fuel, TfFor combustion chamber inlet fuel thermodynamics
Temperature, with T3Close, α is excess air coefficient, Ga0For theoretical air flow needed for unit quality fuels；
The turbine model includes:
Expansion ratio, revolving speed, corrected flow and the efficiency for reacting its working condition are fitted according to turbine rotor characteristic equation
Between relationship, expression formula are as follows:
In formula,For compressor with respect to corrected flow,For relative efficiency,For relative rotation speed,For relative expansion ratio, ft1
ForAboutWithNonlinear fitting relational expression, ft2ForAboutWithNonlinear fitting relational expression；
Conversion relation of the turbine with respect to corrected flow and turbine flow, expression formula are as follows:
GtinFor turbine inlet flow, Pt0For turbine nominal pressure；Tt0For turbine machine operating temperature ratings；Gt0For turbine
Machine metered flow；
Turbine relative efficiency and turbine efficiency, turbine relative expansion are than the conversion relation with turbine expansion ratio, expression
Formula are as follows:
In formula, ηtFor turbine efficiency, ηt0For the efficiency under turbine declared working condition；πtFor turbine expansion ratio, πt0For turbine
Expansion ratio under machine declared working condition；
Relationship between turbine inlet variable and exported variable, expression formula are as follows:
P5=P4/πt
Wt=Gtin·cpt·(T4-T5)
Gtout=Gtin=G4
In formula, P5For turbine outlet air pressure, T5For turbine outlet fuel gas temperature, WtPower, c are issued for turbineptFor turbine
Machine gas specific heat at constant pressure, GtoutFor turbine outlet gas flow；
Supplement working medium state equation:
Air Constitute equation are as follows:
In formula, t2、T2For compressor inlet Celsius temperature, thermodynamic temperature, t3、T3Respectively combustion chamber inlet air temperature Celsius
Degree, thermodynamic temperature, H3For combustion chamber inlet air specific enthalpy, cp,t,2For compressor inlet pressurization by compressed air specific heat, cp,t,3To calm the anger
Machine outlet air specific heat at constant pressure；
Combustion gas Constitute equation are as follows:
cpt=(cp,t,4+cp,t,5)/2 (16)
In formula,Respectively N in turbine inlet combustion gas2、CO2、O2、H2The level pressure of O
Specific heat, cp,t,4For turbine inlet combustion gas specific heat at constant pressure, Respectively turbine outlet
N in combustion gas2、CO2、O2、H2The specific heat at constant pressure of O, cp,t,5For turbine outlet combustion gas specific heat at constant pressure,Respectively N in turbine inlet combustion gas2、CO2、O2、H2The specific enthalpy of O,It is N in combustion gas respectively2、CO2、O2、H2The mass fraction of O, need to be according to the component and fuel of fuel
It measures and is calculated with the mass ratio of air, specific formula is as follows:
The expression formula of the rotator model are as follows:
In formula, I is the rotary inertia of rotor, and n is rotor speed, WtPower, W are issued for turbinecPower is consumed for compressor,
WeFor generator power, ηmtFor turbine mechanical efficiency, π is pi；
The revolving speed Controlling model is for dynamic model described in rated speed, and revolution speed control system uses PI control mode, table
Up to formula are as follows:
In formula (23), Gf0For initial fuel flow, GfIt (t) is the fuel flow rate of t moment, KpFor proportional gain, TiFor the time of integration
Constant, Kp、TiNeed to suitably it be worth according to specific equipment debugging, e (t) is the revolving speed deviation of t moment, e (t)=n-nr, nrFor combustion
Gas-turbine rated speed.
6. emulation mode according to claim 5, it is characterised in that: the fc1Expression formula are as follows:
The fc2Expression formula are as follows:
The ft1Expression formula are as follows:
The ft2Expression formula are as follows:
7. emulation mode according to claim 5, it is characterised in that: the static models are dynamic model described in each component
In each differential term be 0 when lumped parameter model, obtain 3 common equations of gas turbine, it may be assumed that
In formula (20), Gcout、Gtout、Wc、WtIt is all about Gf、πc、πtNonlinear function, expression can be by being given above
Formula acquire, enable:
In formula (21), (22), e1、e2、e3For the error of three common equations, f1(Gf,πc,πt)、f2(Gf,πc,πt)、f3(Gf,πc,
πt) it is about Gf、πc、πtNonlinear function, corresponding flow, power are substituted into formula (21), (22) can be in the hope of.
8. emulation mode according to claim 7, it is characterised in that: the resolving of the static models and the dynamic model
Process the following steps are included:
Initial value setting, is arranged step-length 10ms, gives air-source parameter P1、T1, gas turbine rated speed nr, revolving speed initial value n0, hair
Electrical power WeWith gas turbine exhaust pressure P5, fuel flow rate G is setf, revolving speed n, compressor pressure ratio πc, turbine expansion ratio πtJust
Initial value；
Solve stable state initial value, that is, static models；
Judgement system disturbs if it exists with the presence or absence of disturbance, disturbance is added to dependent variable；
The Steady-state Initial G that will be acquiredf、P4、H4The initial value G calculated as dynamicf0、P40、H40Dynamic model is substituted into calculate.
9. emulation mode according to claim 8, it is characterised in that: the step of solving the stable state initial value is as follows:
According to formula (1), P is substituted into1、T1, obtain P2、T2；
According to formula (2), (3), (4), (5), P is substituted into2、T2, gas turbine rotary speed n, compressor pressure ratio initial value πc, obtain Gcout、
ηc、P3、T3、Wc；
According to formula (8), (17), (18), P is substituted into3、T3, fuel flow rate initial value Gf, obtain P4、T4、Ga、H4；
According to formula (9), (10), (11), (12), P is substituted into4、T4、Ga, n, turbine expansion ratio initial value πt, drain pressure P5, obtain
To Gtout、Wt、T5、ηt；
According to formula (21), G is substituted intocout、Gf、Ga、Gtout、Wc、Wt, given generated output We, acquire e1、e2、e3, then using basic
Newton-Raphson approach solve formula (22), obtain new πc、πt、Gf, convergence judgement is carried out, comes back for iteration meter if not restraining
It calculates, until convergence.
10. emulation mode according to claim 8, it is characterised in that: the step of dynamic model calculates is as follows:
According to formula (1), given air-source parameter P is substituted into1、T1, obtain P2、T2；
According to formula (2), (3), (4), (5), (14), P is substituted into2、T2, gas turbine rotary speed n,Compressor model is solved, is obtained
To Wc、Gcout、Gin、T3；
According to formula (17), (18), H is substituted into4、Gf、Ga, wherein GaEqual to Gcout, acquire T4, according to formula (9), (10), (11),
(12), T is substituted into4、P4、n、P5, turbine model is solved, W is obtainedt、Gtin、Gtout、T5, further according to formula (6), (7), (13),
(15), G is substituted intoa、T3、G4、Gf、H4, wherein G4Equal to Gtin, combustion chamber model is solved, differential variable is obtained's
Value；
According to formula (19), W is substituted intoc、Wt、We, rotator model is solved, is obtainedValue；
According to differential variableValue, integral obtain new P4、H4, n, in which:
New fuel flow rate G is calculated according to formula (23)f；
By variable P4、H4、n、GfUpdated value substitute into next time step and calculate.
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