CN115793432A - Space thermionic nuclear power supply control method based on model predictive control - Google Patents
Space thermionic nuclear power supply control method based on model predictive control Download PDFInfo
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Abstract
A space thermionic nuclear power supply control method based on model predictive control mainly comprises the following steps: 1. determining the structure of a space thermionic nuclear power supply system, dividing system nodes, establishing a differential equation set of a reactor core, a coolant and a radiation heat dissipation system, setting initial parameters 2 when the reactor core, the coolant and the radiation heat dissipation system run at a steady state and full power, calculating system parameters 3 of the space thermionic nuclear power supply at the current moment, inputting the system parameters of the space thermionic nuclear power supply and calculating control data 4 by a model prediction controller, calculating the angle and the reactivity of a control rotary drum by a control rotary drum module according to the control data 5, inputting the reactivity of the control rotary drum by the differential equation set of the space thermionic nuclear power supply system, returning to the step 2 to calculate the next time step, and obtaining the running parameters of the system at the next time step; the method can realize high-fidelity control of the thermionic space nuclear power supply, and the adopted model prediction controller has more excellent control performance.
Description
Technical Field
The invention relates to a space nuclear reactor power supply, in particular to a space thermionic nuclear power supply control method based on model predictive control.
Background
With the improvement of the demand of future Space exploration tasks, a Space Nuclear Reactor Power supply (Space Nuclear Reactor Power System) is a main research direction of future Space energy. Compared with the traditional solar power supply, the space nuclear reactor power supply can realize high-power supply and has good environmental adaptability. Since the 50 s of the 20 th century, major countries in the world have been researching space nuclear power sources, with the highest level of research in the united states and russia. The space nuclear power supply has two energy conversion modes: static conversion (thermocouple conversion, thermionic conversion, alkali metal conversion, etc.) and dynamic conversion (rankine cycle, brayton cycle, and stirling cycle), the former being well developed and the latter still in development. Russia successfully launched two TOPAZ-type thermionic space nuclear reactor power supplies in 1987, which were the most advanced design that operated successfully to date.
The space nuclear power supply operates in a space environment without human intervention, mostly adopts a control drum to realize power control, has larger difference with a common control rod of a ground reactor, and has no complete accident emergency system. In addition, the space nuclear power supply works in a low-gravity or zero-gravity environment, and cannot realize natural circulation by means of gravity. Therefore, the space nuclear power supply needs to be provided with a good automatic control system, power regulation in normal operation and emergency control under accident conditions are realized with smaller regulation time and overshoot, and the automatic control system based on the traditional PID controller is difficult to obtain good control performance.
Disclosure of Invention
In order to overcome the problems, the invention aims to provide a space thermionic nuclear power supply control method based on model predictive control, which adopts a high-precision space thermionic nuclear power supply system model and establishes a model predictive controller based on an incremental point reactor equation. By adopting the model prediction controller, the change of the controlled variable of the thermionic space nuclear power supply in a period of time in the future can be predicted, optimized control data can be given, and good control performance can be realized.
In order to achieve the purpose, the invention adopts the following technical scheme:
a space thermionic nuclear power supply control method based on model predictive control comprises the following steps:
step 1: determining the structure of a space thermionic nuclear power supply system, dividing calculation nodes aiming at a reactor core, a coolant system and a radiation radiator, and respectively establishing a nonlinear differential equation set to obtain a physical model of the space thermionic nuclear power supply system;
the reactor core area of the space thermionic nuclear power system consists of a thermionic fuel element, a ZrH moderator and a BeO reflecting layer;
the thermionic fuel element is composed of fuel pellets, an emitter, a receiver, and a coolant jacket, and the fission power of the fuel pellets is calculated by the formula:
in the formula:
p-core power/W
rho-Total reactivity
Beta-total delayed neutron fraction
A-intermediate filial generation time/s
λ i -i group delayed neutron precursor nuclear decay constant
β i -first group delayed neutron precursor nucleus share
C i Concentration of precursor nucleus of delayed neutron in group i
The overall reactivity consists of temperature-reactivity feedback and drum reactivity, wherein the temperature-reactivity feedback includes the following seven components:
ρ T (T)＝ρ fuel (T)+ρ ec (T)+ρ mod (T)+ ρ ref (T)+ρ NaK (T)+ρ bam (T)+ρ BeO (T) (2)
in the formula:
ρ T (T) -temperature reactivity feedback
ρ fuel (T) -Fuel Doppler feedback
ρ ec (T) -electrode temperature feedback
ρ mod (T) -moderator temperature feedback
ρ ref (T) -reflective layer temperature feedback
ρ NaK (T) -Coolant temperature feedback
ρ bam (T) -support Structure temperature feedback
ρ BeO (T) -tip BeO temperature feedback
For the heat exchange calculation of the thermionic fuel element, the thermionic fuel element is divided into a plurality of control bodies along the axial direction and the radial direction, and the following heat balance relational expression is provided:
in the formula:
ρ i -ith control bulk density/kg m -3
c i -ith control body specific heat capacity/J.kg -1 ·K -1
V i -ith control volume/m 3
T i -ith control body temperature/K
Q gen -the ith control body generates heat/W
Q in -the ith control body inputting heat quantity/W
Q out -the ith control body outputs heat quantity/W
The coolant in the coolant system adopts sodium-potassium alloy, a plurality of control bodies are divided along the axial direction, and the following control equations are listed:
W i ＝W in (4)
in the formula:
W i -in the coolant channelMass flow/kg.s of i control bodies -1
W in -mass flow/kg-s at coolant channel inlet -1
In the formula:
Δp g，i -gravitational pressure drop/Pa
Δp a，i -acceleration pressure drop/Pa
Δp f，i -friction pressure drop/Pa
Δp c，i -local loss of resistance/Pa
l i Control body length/m
A i -control the volume flow area/m 2
In the formula:
ρ f -density of coolant/kg · m -3
Δ t-time step/s
q i -surface heat flux density/W.m of main control body i -2
U i -main control body i heating circumference/m
The radiation radiator adopts a heat pipe type design, a heat resistance network equation is established aiming at the heat pipe, and the radial heat conduction thermal resistance R of the pipe wall of the evaporation section is considered after simplification 1 Thermal conduction resistance R of evaporation section pipe wall and liquid absorption core 2 Heat conduction thermal resistance R of liquid absorption core and pipe wall of condensation section 3 Radial heat conduction thermal resistance R of pipe wall of condensation section 4 ：
In the formula:
D o -outer diameter of heat pipe wall/m
D i -inner diameter of heat pipe wall/m
λ c -heat pipe wall thermal conductivity/W.m -1 ·K -1
L eva -length of evaporation zone/m
In the formula:
D v -steam zone diameter/m
λ w -thermal conductivity of wick/W.m -1 ·K -1
In the formula: l is a radical of an alcohol con -length of condensation section/m
Obtaining a physical model of the space thermionic nuclear power supply system according to the formulas (1) to (10); setting initial operation conditions for a well established physical model of the space thermionic nuclear power supply system, wherein when t =0, the system is in a steady-state full-power operation state;
and 2, step: performing transient calculation of a time step aiming at a physical model of a space thermionic nuclear power supply system to obtain system parameters and controlled variables at the current moment;
and step 3: the space thermionic nuclear power supply system adopts a model prediction controller to realize power control; inputting a controlled variable of the space thermionic nuclear power supply system and a given controlled variable reference value by the model prediction controller, calculating by a simplified model in the model prediction controller to give control data, and transmitting the control data to the control drum module in the step 4;
the model prediction controller mainly comprises an internal simplified model and a cost function; in each time step, the model prediction controller carries out pre-calculation based on the internal simplified model, and estimates the state of the space thermionic nuclear power supply system for a period of time in the future; evaluating the state of the space thermionic nuclear power supply system by adopting a cost function, and solving an optimization problem of minimizing the cost function to obtain control data;
the simplified model inside the model predictive controller uses a linearized dot-pile incremental equation as follows:
in the formula:
delta P-Nuclear Power increment/W
ρ 0 Initial reactivity
P 0 -initial thermal power/W
Δ ρ -increase in reactivity
ΔC i Increase in precursor concentration of delayed neutrons
Aiming at the reactive feedback, a system identification method is adopted to obtain a reactive feedback transfer function by fitting:
in the formula:
g(s) -reactive feedback transfer function
Combining equation (11) and equation (12), the simplified model inside the model predictive controller is expressed in the form of discrete state space:
in the formula:
x (k) -the state variables of the simplified model at time k;
x (k + 1) -the state variables of the simplified model at time k + 1;
u (k) -the control data of the model is simplified at time k;
y (k) -the output quantity of the model is simplified at time k;
a, B, C-state matrix corresponding to each variable
Considering the state variables of the simplified model at the future k + p moment and the control data input at the future k + c moment at the k moment, and defining the state variable sequence of the simplified model at the future k + p moment and the control data sequence at the future k + c moment by adopting a state space form:
X(k)＝[x(k|k)x(k+1|k)…x(k+c|k)…x(k+p|k)] T ((n+1)p×1) (14)
U(k)＝[u(k|k)u(k+1|k)…u(k+c-1|k)] T (c×1) (15)
in the formula:
x (k) -sequence of state variables of simplified model
U (k) -control data input sequence
And obtaining an output sequence and an error sequence of the simplified model according to the state variable sequence:
Y(k)＝F y x(k)+G y U(k) (16)
E(k)＝Y d (k)-Y(k) (17)
in the formula:
y (k) -output sequence of simplified model
E (k) — error sequence for simplified model
Y d (k) -simplifying the sequence of model output quantity reference values
F y And G y -coefficient matrix after iteration of the state matrix
F y ＝[C CA CA 2 CA 3 …CA p ] T ((n+1)p×1) (18)
And finally, constructing a cost function according to the state space expression:
J(k)＝E(k) T QE(k)+U(k) T RU(k) (20)
in the formula:
q-error weight diagonal matrix
R-input weight diagonal matrix
Substituting equations (16) and (17) into equation (20), the cost function is converted into a univariate quadratic problem with respect to the control data sequence, as in equation (21):
in the formula:
H(k)＝Y d (k)-F y x(k) (22)
solving the formula (21) to minimize the cost function to obtain a control data sequence U (k);
in order to improve the control performance and reduce errors caused by mismatch of a simplified model and a physical model of a thermionic space nuclear power supply system, a rolling optimization process is introduced: transmitting the first item of the control data sequence as control data to the control drum module at the moment k, and solving the formula (21) again by taking the moment k +1 as a starting point at the next time step;
and 4, step 4: the control drum module converts the control data input in the step 3 into a drum rotation angle and further converts the drum rotation angle into the control drum reactivity;
the calculation model for controlling the drum module is shown in equations (23) to (25):
in the formula:
omega-angular velocity/DEG.s of control drum -1
Control data of u-model predictive controller
θ＝θ 0 +∫ωdt，0≤θ≤180，0≤|ω|≤1 (24)
In the formula:
theta-controlling angle/° of the drum
θ 0 -controlling the initial angle/DEG of the drum
The rotating angle of the rotary drum of the control rotary drum has the following relation with the reactivity:
in the formula:
ρ θ (theta) — controlling the reactivity of the drum
And 5: and 4, returning the reactivity of the control rotary drum calculated in the step 4 to the space thermionic nuclear power supply system, returning to the step 2 to perform transient calculation of the next time step, updating system parameters of the space thermionic nuclear power supply system and the change condition of the controlled variable, and repeating the steps.
Compared with the prior art, the invention has the following advantages:
the space thermionic nuclear power supply is controlled and analyzed by adopting a high-precision system model, and a controlled object has a complete reactor core, a coolant system and a physical model of a radiation radiator, so that the reliability of control and analysis is improved; compared with the traditional PID controller, the model predictive controller has more excellent control performance. The method can be used for carrying out control analysis aiming at a universal space nuclear power supply system model, and provides a research method for automatic control of a space nuclear power supply in normal operation and accident conditions.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a comparison graph of the results of control simulation performed by the method.
Detailed Description
The invention is described in further detail below with reference to the following figures and detailed description:
the invention relates to a space thermionic nuclear power supply control method based on model predictive control, which adopts a high-precision physical model of a thermionic nuclear power supply system to carry out control analysis, adopts a linear point reactor incremental equation and a reactive feedback transfer function as an internal model of a controller, and solves an optimization problem on line at each time step to obtain an optimal control strategy. As shown in fig. 1, the specific process of the method includes the following steps:
step 1: determining the structure of a space thermionic nuclear power supply system, dividing calculation nodes aiming at a reactor core, a coolant system and a radiation radiator, and respectively establishing a nonlinear differential equation set to obtain a physical model of the space thermionic nuclear power supply system;
the reactor core region of the space thermionic nuclear power supply system consists of thermionic fuel elements, a ZrH moderator and a BeO reflecting layer;
the thermionic fuel element is composed of fuel pellets, an emitter, a receiver, and a coolant jacket, and the fission power of the fuel pellets is calculated by the formula:
in the formula:
p-core power/W
rho-Total reactivity
Beta-total delayed neutron fraction
Λ -middle filial generation time/s
λ i -i group delayed neutron precursor nuclear decay constant
β i -first group delayed neutron precursor nucleus share
C i Concentration of precursor nucleus of delayed neutron in group i
The total reactivity consists of temperature-reactive feedback and drum reactivity, wherein the temperature-reactive feedback comprises the following seven components:
ρ T (T)＝ρ fuel (T)+ρ ec (T)+ρ mod (T)+ ρ ref (T)+ρ NaK (T)+ρ bam (T)+ρ BeO (T) (2)
in the formula:
ρ T (T) -temperature reactivity feedback
ρ fuel (T) -Fuel Doppler feedback
ρ ec (T) -electrode temperature feedback
ρ mod (T) -moderator temperature feedback
ρ ref (T) -reflective layer temperature feedback
ρ NaK (T) -Coolant temperature feedback
ρ bam (T) -support Structure temperature feedback
ρ BeO (T) -tip BeO temperature feedback
The thermionic fuel element is composed of different materials, the different materials have different physical properties, for the heat exchange calculation of the thermionic fuel element, the thermionic fuel element is divided into a plurality of control bodies along the axial direction and the radial direction, and the following heat balance relational expression is provided:
in the formula:
ρ i -ith control bulk density/kg-m -3
c i -ith control body specific heat capacity/J.kg -1 ·K -1
V i -ith control volume/m 3
T i -ith individual control body temperature/K
Q gen -the ith control body generates heat/W
Q in -the ith control body inputting heat quantity/W
Q out -the ith control body outputs heat quantity/W
The coolant in the coolant system is made of sodium-potassium alloy, is single-phase incompressible liquid, only considers axial heat transfer, and is divided into a plurality of control bodies along the axial direction, and the following control equations are listed:
W i ＝W in (4)
in the formula:
W i -mass flow/kg · s of the ith control body in the coolant channel -1
W in -coolant channel inlet mass flow/kg · s -1
In the formula:
Δp g，i -gravitational pressure drop/Pa
Δp a，i -acceleration pressure drop/Pa
Δp f，i -frictional pressure drop/Pa
Δp c，i -local loss of resistance/Pa
l i -control body length/m
A i -control of the volume flow area/m 2
In the formula:
ρ f -density of coolant/kg · m -3
Δ t-time step/s
q i -surface heat flux/W.m of main control body i -2
U i -main control body i heating circumference/m
The radiation radiator adopts a heat pipe type design, and because the working medium thawing working condition when the heat pipe is started is not considered in the steady-state operation, the heat pipe is equivalent to a plurality of heatEstablishing a thermal resistance network equation aiming at the heat pipe, and considering the radial heat conduction thermal resistance R of the pipe wall of the evaporation section after simplification 1 Thermal conduction resistance R of evaporation section pipe wall and liquid absorption core 2 Heat conduction thermal resistance R of liquid absorption core and pipe wall of condensation section 3 Radial heat conduction thermal resistance R of pipe wall of condensation section 4 ：
In the formula:
D o -outer diameter of heat pipe wall/m
D i -inner diameter of heat pipe wall/m
λ c -heat pipe wall thermal conductivity/W.m -1 ·K -1
L eva Length of evaporation zone/m
In the formula:
D v -steam zone diameter/m
λ w -thermal conductivity of wick/W.m -1 ·K -1
In the formula: l is con -length of condensation section/m
Obtaining a physical model of the space thermionic nuclear power supply system according to the formulas (1) to (10); setting initial operation conditions for a well established physical model of the space thermionic nuclear power supply system, wherein when t =0, the system is in a steady-state full-power operation state;
and 2, step: performing transient calculation of a time step aiming at a physical model of a space thermionic nuclear power supply system to obtain system parameters and controlled variables at the current moment;
and 3, step 3: the space thermionic nuclear power system adopts a model prediction controller to realize power control; inputting a controlled variable of the space thermionic nuclear power supply system and a given controlled variable reference value by the model prediction controller, calculating by a simplified model in the model prediction controller to give control data, and transmitting the control data to the control drum module in the step 4;
the model prediction controller mainly comprises an internal simplified model and a cost function; in each time step, the model prediction controller carries out pre-calculation based on an internal simplified model, and estimates the state of the space thermionic nuclear power supply system for a period of time in the future; evaluating the state of the space thermionic nuclear power supply system by adopting a cost function, and solving an optimization problem of minimizing the cost function to obtain control data;
the simplified model inside the model predictive controller uses a linearized dot-pile incremental equation as follows:
in the formula:
delta P-Nuclear Power increment/W
ρ 0 Initial reactivity
P 0 -initial thermal power/W
Δ ρ -increase in reactivity
ΔC i Increase in precursor concentration of delayed neutrons
Aiming at the reactive feedback, a system identification method is adopted to obtain a reactive feedback transfer function by fitting:
in the formula:
g(s) -reactive feedback transfer function
Combining equation (11) and equation (12), the simplified model inside the model predictive controller is expressed as a discrete state space form:
in the formula:
x (k) -the state variables of the simplified model at time k;
x (k + 1) -the state variables of the simplified model at time k + 1;
u (k) -the control data of the model is simplified at time k;
y (k) -the output quantity of the model is simplified at time k;
a, B, C-state matrix corresponding to each variable
Considering the state variables of the simplified model at the future k + p moment and the control data input at the future k + c moment at the k moment, and defining the state variable sequence of the simplified model at the future k + p moment and the control data sequence at the future k + c moment by adopting a state space form:
X(k)＝[x(k|k)x(k+1|k)…x(k+c|k)…x(k+p|k)] T ((n+1)p×1) (14)
U(k)＝[u(k|k)u(k+1|k)…u(k+c-1|k)] T (c×1) (15)
in the formula:
x (k) -sequence of state variables of a simplified model
U (k) -control data input sequence
And obtaining an output sequence and an error sequence of the simplified model according to the state variable sequence:
Y(k)＝F y x(k)+G y U(k) (16)
E(k)＝Y d (k)-Y(k) (17)
in the formula:
y (k) -output sequence of simplified model
E (k) -error sequence of simplified model
Y d (k) -simplifying the sequence of model output quantity reference values
F y And G y -coefficient matrix after iteration of the state matrix
F y ＝[C CA CA 2 CA 3 …CA p ] T ((n+1)p×1) (18)
And finally, constructing a cost function according to the state space expression:
J(k)＝E(k) T QE(k)+U(k) T RU(k) (20)
in the formula:
q-diagonal matrix of error weights
R-input weight diagonal matrix
Substituting equations (16) and (17) into equation (20), the cost function is converted into a univariate quadratic problem with respect to the control data sequence, as in equation (21):
in the formula:
H(k)＝Y d (k)-F y x(k) (22)
solving the formula (21) to minimize the cost function to obtain a control data sequence U (k);
the simplified model in the model prediction controller and the nonlinear physical model of the space thermionic nuclear power supply have certain difference, and the U (k) is directly utilized to adopt open-loop control to generate larger error, so that the error caused by mismatch of the simplified model and the physical model of the thermionic space nuclear power supply system is reduced for improving the control performance, and the rolling optimization process is introduced: only the first item of the control data sequence U (k) is taken as control data at the moment k and is transmitted to the control drum module, and the solution (21) is solved again by taking the moment k +1 as a starting point at the next time step;
and 4, step 4: the control drum module converts the control data input in the step 3 into a drum rotation angle and further converts the drum rotation angle into the control drum reactivity;
the calculation model for controlling the drum module is shown in equations (23) to (25):
in the formula:
omega-controlling angular velocity/°. S of the drum -1
Control data of u-model predictive controller
θ＝θ 0 +∫ωdt，0≤θ≤180，0≤|ω|≤1 (24)
In the formula:
theta-controlling angle/° of the drum
θ 0 -controlling the initial angle/° of the drum
The rotating angle of the rotary drum of the control rotary drum has the following relation with the reactivity:
in the formula:
ρ θ (theta) — controlling the reactivity of the rotating drum
And 5: and 4, returning the reactivity of the control rotary drum calculated in the step 4 to the space thermionic nuclear power supply system, returning to the step 2 to perform transient calculation of the next time step, updating system parameters of the space thermionic nuclear power supply system and the change condition of the controlled variable, and repeating the steps.
The method is adopted to carry out control simulation on the space thermionic nuclear power supply system, and the following transient working conditions are designed: selecting the nuclear power as a controlled variable, introducing-5% target nuclear power step at 20s, wherein the initial working condition is steady-state full power.
The control effect of the model predictive controller was compared with the conventional PID controller, and the result is shown in fig. 2. As can be seen from fig. 2, the model predictive controller built by the above method can track the change of the core power reference value and provide a control signal, so as to implement fast non-overshoot core power control, and has a better control performance compared with the conventional PID controller.
Claims (1)
1. A space thermionic nuclear power supply control method based on model predictive control is characterized in that: the method comprises the following steps:
step 1: determining the structure of a space thermionic nuclear power supply system, dividing calculation nodes aiming at a reactor core, a coolant system and a radiation radiator, and respectively establishing a nonlinear differential equation set to obtain a physical model of the space thermionic nuclear power supply system;
the reactor core region of the space thermionic nuclear power supply system consists of thermionic fuel elements, a ZrH moderator and a BeO reflecting layer;
the thermionic fuel element is composed of fuel pellets, an emitter, a receiver, and a coolant jacket, and the fission power of the fuel pellets is calculated by the following formula:
in the formula:
p-core power/W
rho-Total reactivity
Beta-total delayed neutron fraction
Λ -middle filial generation time/s
λ i -i group delayed neutron precursor nuclear decay constant
β i -first group delayed neutron precursor nucleus share
C i Concentration of delayed neutron precursor nuclei in the ith group
The overall reactivity consists of temperature-reactivity feedback and drum reactivity, wherein the temperature-reactivity feedback includes the following seven components:
ρ T (T)＝ρ fuel (T)+ρ ec (T)+ρ mod (T)+ρ ref (T)+ρ NaK (T)+ρ bam (T)+ρ BeO (T) (2)
in the formula:
ρ T (T) -temperature reactivity feedback
ρ fuel (T) -Fuel Doppler feedback
ρ ec (T) -electrode temperature feedback
ρ mod (T) -moderator temperature feedback
ρ ref (T) -reflective layer temperature feedback
ρ NaK (T) -Coolant temperature feedback
ρ bam (T) -support Structure temperature feedback
ρ BeO (T) -end BeO temperature feedback
For the heat exchange calculation of the thermionic fuel element, the thermionic fuel element is divided into a plurality of control bodies along the axial direction and the radial direction, and the following heat balance relational expression is provided:
in the formula:
ρ i -ith control bulk density/kg m -3
c i -ith control body specific heat capacity/J.kg -1 ·K -1
V i -ith control volume/m 3
T i -ith individual control body temperature/K
Q gen -the ith control body generates heat/W
Q in -the ith control body inputs heat/W
Q out -the ith control body outputs heat quantity/W
The coolant in the coolant system adopts sodium-potassium alloy, a plurality of control bodies are divided along the axial direction, and the following control equations are listed:
W i ＝W in (4)
in the formula:
W i -mass flow/kg-s of ith control body in coolant channel -1
W in -coolant channel inlet mass flow/kg · s -1
In the formula:
Δp g，i -gravitational pressure drop/Pa
Δp a，i -acceleration pressure drop/Pa
Δp f，i -frictional pressure drop/Pa
Δp c，i -local resistance loss/Pa
l i -control body length/m
A i -control the volume flow area/m 2
In the formula:
ρ f -density of coolant/kg-m -3
Δ t-time step/s
q i -surface heat flux/W.m of main control body i -2
U i -main control body i heating circumference/m
The radiation radiator adopts a heat pipe type design, a heat resistance network equation is established aiming at the heat pipe, and the radial heat conduction thermal resistance R of the pipe wall of the evaporation section is considered after simplification 1 Thermal conduction resistance R of evaporation section pipe wall and liquid absorption core 2 Heat conduction thermal resistance R of liquid absorption core and pipe wall of condensation section 3 Radial thermal conduction resistance R of pipe wall of condensation section 4 ：
In the formula:
D o -outside diameter/m of heat pipe wall
D i -inner diameter of heat pipe wall/m
λ c -heat pipe wall thermal conductivity/W.m -1 ·K -1
L eva Length of evaporation zone/m
In the formula:
D v -steam zone diameter/m
λ w -thermal conductivity of wick/W.m -1 ·K -1
In the formula: l is a radical of an alcohol con Length of condensing section/m
Obtaining a physical model of the space thermionic nuclear power supply system according to the formulas (1) to (10); setting initial operation conditions for a well established physical model of the space thermionic nuclear power supply system, wherein when t =0, the system is in a steady-state full-power operation state;
and 2, step: performing transient calculation of a time step aiming at a physical model of a space thermionic nuclear power supply system to obtain system parameters and controlled variables at the current moment;
and 3, step 3: the space thermionic nuclear power system adopts a model prediction controller to realize power control; inputting a controlled variable of the space thermionic nuclear power supply system and a given controlled variable reference value by the model prediction controller, calculating by a simplified model in the model prediction controller to give control data, and transmitting the control data to the control drum module in the step 4;
the model prediction controller mainly comprises an internal simplified model and a cost function; in each time step, the model prediction controller carries out pre-calculation based on the internal simplified model, and estimates the state of the space thermionic nuclear power supply system for a period of time in the future; evaluating the state of the space thermionic nuclear power supply system by adopting a cost function, and solving an optimization problem of minimizing the cost function to obtain control data;
the simplified model inside the model predictive controller uses a linearized dot-pile incremental equation as follows:
in the formula:
Δ P-Nuclear Power increment/W
ρ 0 Initial reactivity
P 0 -initial thermal power/W
Δ ρ -increase in reactivity
ΔC i Increase in precursor concentration of delayed neutrons
Aiming at the reactive feedback, a system identification method is adopted to obtain a reactive feedback transfer function by fitting:
in the formula:
g(s) -reactive feedback transfer function
Combining equation (11) and equation (12), the simplified model inside the model predictive controller is expressed as a discrete state space form:
in the formula:
x (k) -state variables of the simplified model at time k
Simplifying the state variables of the model at x (k + 1) -k +1 moments
u (k) -time k simplifying control data of model
y (k) -k time simplifying the output of the model
A, B, C-state matrix corresponding to each variable
Considering the state variables of the simplified model at the future k + p moment and the control data input at the future k + c moment at the k moment, and defining the state variable sequence of the simplified model at the future k + p moment and the control data sequence at the future k + c moment by adopting a state space form:
X(k)＝[x(k|k) x(k+1|k)…x(k+c|k)…x(k+p|k)] T ((n+1)p×1) (14)
U(k)＝[u(k|k) u(k+1|k)…u(k+c-1|k)] T (c×1) (15)
in the formula:
x (k) -sequence of state variables of a simplified model
U (k) -control data input sequence
And obtaining an output sequence and an error sequence of the simplified model according to the state variable sequence:
Y(k)＝F y x(k)+G y U(k) (16)
E(k)＝Y d (k)-Y(k) (17)
in the formula:
y (k) -output sequence of simplified model
E (k) -error sequence of simplified model
Y d (k) -simplifying the sequence of model output quantity reference values
F y And G y -coefficient matrix after iteration of the state matrix
F y ＝[C CA CA 2 CA 3 …CA p ] T ((n+1)p×1) (18)
And finally, constructing a cost function according to the state space expression:
J(k)＝E(k) T QE(k)+U(k) T RU(k) (20)
in the formula:
q-diagonal matrix of error weights
R-input weight diagonal matrix
Substituting equations (16) and (17) into equation (20), the cost function is converted into a univariate quadratic problem with respect to the control data sequence, as in equation (21):
in the formula:
H(k)＝Y d (k)-F y x(k) (22)
solving the formula (21) to minimize the cost function to obtain a control data sequence U (k);
in order to improve the control performance and reduce errors caused by mismatch of a simplified model and a physical model of a thermionic space nuclear power supply system, a rolling optimization process is introduced: transmitting the first item of the control data sequence as control data to the control drum module at the moment k, and solving the formula (21) again by taking the moment k +1 as a starting point at the next time step;
and 4, step 4: the control drum module converts the control data input in the step 3 into a drum rotation angle and further converts the drum rotation angle into the control drum reactivity;
the calculation model for controlling the drum module is shown in equations (23) to (25):
in the formula:
omega-controlling angular velocity/° s of rotating drum -1
Control data of u-model predictive controller
θ＝θ 0 +∫ωdt，0≤θ≤180，0≤|ω|≤1 (24)
In the formula:
theta-controlling the angle/DEG of the drum
θ 0 -controlling the initial angle/DEG of the drum
The rotating angle of the rotary drum is controlled to have the following relation with the reactivity:
in the formula:
ρ θ (theta) — controlling the reactivity of the drum
And 5: and 4, returning the reactivity of the control rotary drum calculated in the step 4 to the space thermionic nuclear power supply system, returning to the step 2 to perform transient calculation of the next time step, updating system parameters of the space thermionic nuclear power supply system and the change condition of the controlled variable, and repeating the steps.
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| US20110264426A1 (en) * | 2008-02-11 | 2011-10-27 | Westinghouse Electric Company Llc | Methodology for modeling the fuel rod power distribution within a nuclear reactor core |
| CN110598304A (en) * | 2019-09-06 | 2019-12-20 | 西安交通大学 | Physical and thermal coupling analysis method for space nuclear power propulsion system pebble bed reactor |
| CN115270660A (en) * | 2022-08-04 | 2022-11-01 | 上海交通大学 | Multi-scale multi-physical field coupling analysis method for transient behavior of space thermionic reactor |
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| CN110598304A (en) * | 2019-09-06 | 2019-12-20 | 西安交通大学 | Physical and thermal coupling analysis method for space nuclear power propulsion system pebble bed reactor |
| CN115270660A (en) * | 2022-08-04 | 2022-11-01 | 上海交通大学 | Multi-scale multi-physical field coupling analysis method for transient behavior of space thermionic reactor |
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