CN117913962B - MPPT power supply control method for satellite based on improved BA-P & O hybrid algorithm - Google Patents
MPPT power supply control method for satellite based on improved BA-P & O hybrid algorithm Download PDFInfo
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- H—ELECTRICITY
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- H02J7/00—Circuit arrangements for charging or depolarising batteries or for supplying loads from batteries
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- H—ELECTRICITY
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- H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
- H02M3/00—Conversion of dc power input into dc power output
- H02M3/02—Conversion of dc power input into dc power output without intermediate conversion into ac
- H02M3/04—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters
- H02M3/10—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
- H02M3/145—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
- H02M3/155—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only
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- H02M3/158—Conversion of dc power input into dc power output without intermediate conversion into ac by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only with automatic control of output voltage or current, e.g. switching regulators including plural semiconductor devices as final control devices for a single load
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- Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02E10/00—Energy generation through renewable energy sources
- Y02E10/50—Photovoltaic [PV] energy
- Y02E10/56—Power conversion systems, e.g. maximum power point trackers
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Abstract
An MPPT power supply control method for satellites based on an improved BA-P & O hybrid algorithm belongs to the technical field of on-board power supply control. The invention aims at solving the problems that the existing MPPT power supply control method based on BA-P & O can cause premature convergence due to local extremum attraction and the bus voltage stability is poor. Comprising the following steps: the solar cell array regulates bus voltage to supply power for a load through a DC-DC unit; the storage battery is connected with a bus through a diode to supply power for a load; the bat algorithm iteration stage and the disturbance observation stage are used for tracking the maximum power of the solar cell array when the solar cell array and the storage battery jointly supply power; the bus voltage regulating stage is used for maintaining the bus voltage stable when the solar cell array is independently powered, and determining the updating direction of the current duty ratio according to the current bus voltage sampling value; and mutually jumping among three stages according to the set conditions. The MPPT power supply control method and device are used for MPPT power supply control.
Description
Technical Field
The invention relates to an MPPT power supply control method for a satellite based on an improved BA-P & O hybrid algorithm, and belongs to the technical field of on-board power supply control.
Background
From the energy transmission form distinction, the on-board power supply system is largely divided into two types, direct Energy Transmission (DET) and peak power tracking (MPPT). DET is a dissipative system, and the voltage and current output by the solar cell array are regulated through a shunt regulator. The space power supply control system based on peak power tracking (MPPT) is a non-dissipative system, an MPPT algorithm in the controller outputs a control signal to control the series switching regulator to regulate voltage, and the MPPT algorithm can track the maximum power output by the solar sailboard. The MPPT energy conversion efficiency is higher, and the solar sailboard does not need to be additionally provided with a redundant design.
When the temperature or illumination changes, the output power of the solar cell array of the DET power supply controller is affected to a certain extent; the MPPT power supply controller can track and output the current maximum power of the solar sailboard, so that power loss is avoided. Meanwhile, the MPPT technology can charge the storage battery more timely, so that the discharging depth of the storage battery is reduced, and the service life of the whole star can be prolonged.
Spatial power system infrastructure and power supply working mode analysis:
with reference to fig. 1, the MPPT algorithm logic is implemented by a hardware circuit or chip software, the sampling circuit is used to collect the voltage and current of the solar cell as input, and the output PWM controls the DC-DC unit via the driving circuit to implement the adjustment of the solar array.
The space power supply system without strict requirements on bus voltage can adopt a semi-regulated bus topological structure, a storage battery does not adopt a discharge controller, and the storage battery directly supplies power to a load through a diode connection bus in the ground shadow period, and the circuit block diagram is shown in figure 2.
According to the relation among the output power of the solar cell array, the charge and discharge power of the storage battery and the load power, the working modes of the space power supply system are 4 kinds of the following:
1) MPPT and battery charging:
The maximum output power of the solar cell array is larger than the load power, and the solar cell array can charge a storage battery and supply power to the load.
2) MPPT and battery discharge:
the maximum output power of the solar cell array is smaller than the load power, and the solar cell array and the storage battery supply power for the load together.
3) Constant-current charging of the storage battery:
The maximum output power of the solar cell array is larger than the constant current charging power and the load power of the storage battery, and the solar cell array can supply power for the constant current charging and the load of the storage battery.
4) The storage battery independently supplies power:
the spacecraft is positioned in the ground shadow area, and only the storage battery is used for supplying power to the load.
In summary, the MPPT unit will switch between the maximum power tracking mode and the voltage stabilizing mode during the on-orbit operation of the spacecraft. The conversion between the power tracking mode and the voltage stabilizing control mode depends on the output power of the solar battery, and the relation between the charge and discharge power of the storage battery and the load power is mostly logically judged by a lower computer.
MPPT algorithm analysis:
referring to fig. 3 and 4, the power voltage curve of the solar cell array under the condition of uniform illumination temperature is a single-peak value curve, and the algorithm mainly adjusts the bus according to the change of the output voltage and current of the solar cell array.
The traditional MPPT algorithm comprises a constant voltage method, a disturbance observation method, a conductance increment method, an interleaving disturbance method and the like. In the on-orbit running process of the spacecraft, the output characteristics of the multi-string solar cell array are characterized by multiple peak values due to partial shading, unbalanced temperature and illumination or partial solar cell damage, and the traditional MPPT algorithm based on a unimodal model is poor in global property and easy to sink into local peaks.
Heuristic algorithms such as a group intelligent iterative algorithm, a neural network, an evolutionary algorithm and the like generally do not need to increase external sensors of a spacecraft, and can better realize global tracking of the space solar cell array. The intelligent iterative algorithm applied to MPPT includes Particle Swarm Optimization (PSO), gray Wolf Optimization (GWO), bat swarm optimization (BA) and the like. Bats optimization algorithms are generally considered one of the best group intelligent iterative algorithms in terms of convergence time and avoiding premature convergence.
The BA algorithm has few parameters, strong robustness and high convergence speed, and is suitable for tracking the peak power of the solar cell array of the on-orbit spacecraft. However, the basic bat algorithm lacks an effective mutation mechanism, and individuals are easily attracted by local extrema to cause premature convergence. Therefore, the basic bat algorithm is required to make trade-off between convergence speed and convergence accuracy, and after iteration stabilization, new peak power generated by environmental change cannot be tracked.
The intelligent iterative algorithm gives a feasible solution of the maximum power output after convergence, and the accurate maximum power can be obtained by adopting the traditional algorithm to refine and converge after the intelligent iterative algorithm is finished. Compared with a basic bat algorithm, the BA-P & O two-section MPPT algorithm shows better performance in environmental dynamic change.
Defects of the prior art:
1) Conventional MPPT algorithms may trap into local peaks, causing power loss. The basic bat algorithm lacks an effective mutation mechanism, and individuals are easily attracted by local extrema to cause premature convergence. And the bat algorithm needs to make trade-off between convergence speed and convergence accuracy, and can not track new peak power generated by environmental change after iteration stabilization. Existing BA-P & O two-stage hybrid algorithms may still fall into local peaks due to too fast convergence during bat iteration phases.
2) In space application, the output capacity of the spacecraft solar cell array is attenuated to a certain extent due to the influence of space irradiation, and the position of the maximum power point is shifted. The initial position of the bat optimization algorithm adopts a random generation mode, the individual initial position of the improved bat algorithm partially applied to the photovoltaic MPPT adopts a global maximum power prediction point of the solar cell array, the service life change of the on-orbit operation of the solar cell array is not considered, the iterative search range is large, and certain power loss can be caused.
3) The duty ratio of the intelligent iterative algorithm such as the bat algorithm, which is output to the DC-DC unit in the iterative process, may be suddenly changed, and a certain oscillation is generated on the bus voltage of the space power supply system.
4) The improper setting of the restarting condition after the existing BA-P & O hybrid algorithm is stabilized can cause the frequent restarting of the algorithm or the power loss caused by the long-term sinking of local peaks.
5) The algorithm lacks mode transition conditions. The conversion between the power tracking mode and the voltage regulating mode depends on the output power of the solar battery, the relation between the charge and discharge power of the storage battery and the load power is judged by the logic of the lower computer, the load is more, and the judgment logic is complex when the power relation is complex.
Disclosure of Invention
Aiming at the problems that the existing MPPT power supply control method based on BA-P & O can cause premature convergence due to local extremum attraction and the bus voltage stability is poor, the invention provides the MPPT power supply control method based on an improved BA-P & O hybrid algorithm for satellites.
According to the MPPT power supply control method for the satellite based on the improved BA-P & O hybrid algorithm, the solar cell array adjusts bus voltage to supply power for a load through the DC-DC unit; the storage battery is connected with a bus through a diode to supply power for a load;
the power supply control comprises three stages of bat algorithm iteration, disturbance observation and bus voltage regulation;
the bat algorithm iteration stage and the disturbance observation stage are used for tracking the maximum power of the solar cell array when the solar cell array and the storage battery jointly supply power;
The initial positions of a selected number of bat individuals are determined according to the voltage predicted value of the solar cell array at the maximum power point of the initial life period and the final life period and the working condition of the spacecraft in the bat algorithm iteration stage and used as the initial duty ratio of the DC-DC unit, and the DC-DC unit is controlled by the driving circuit; if the bus voltage corresponding to the initial duty ratio is greater than the mode conversion voltage threshold value, entering a bus voltage regulating stage; otherwise, adopting a greedy strategy to select the initial position of a half bat individual with larger current power of the solar cell array, performing random walk and then performing in-situ iterative update, and then combining the reverse bat individual positions after in-situ iterative update to obtain six updated duty ratios of the DC-DC unit, and controlling the DC-DC unit through a driving circuit; if the bus voltage corresponding to the updated optimal duty ratio is greater than the mode conversion voltage threshold value, entering a bus voltage regulation stage; otherwise, determining three new iterative bat individuals to continue to update the next position iteration until the maximum iteration times are reached; entering a disturbance observation stage;
The disturbance observation stage is used for calculating the current actual power of the solar cell array based on the currently determined duty ratio position corresponding to the iterative bat individual, and determining a disturbance direction to perform duty ratio disturbance according to the current actual power and the actual power change of the adjacent previous moment; after each time the DC-DC unit is controlled by adopting the duty ratio after disturbance, if the bus voltage corresponding to the duty ratio after disturbance is greater than the mode conversion voltage threshold value, entering a bus voltage regulation stage; otherwise, judging whether the restarting condition is met according to the current actual power and the current working time of the solar cell array, if so, entering a bat algorithm iteration stage, otherwise, calculating the current predicted power of the solar cell array according to the current post-disturbance duty ratio and comparing the current predicted power with the actual power, and determining the disturbance direction to continue to carry out duty ratio disturbance;
The bus voltage regulating stage is used for maintaining the bus voltage stable when the solar cell array is independently powered, and determining the updating direction of the current duty ratio according to the current bus voltage sampling value; if the corresponding bus voltage after the duty ratio is updated is still greater than the mode conversion voltage threshold, continuing to adjust the bus voltage, otherwise, entering into an iteration stage of the bat algorithm.
According to the MPPT power supply control method for the satellite based on the improved BA-P & O hybrid algorithm, firstly, the parameter initialization of the bat algorithm is carried out in the bat algorithm iteration stage, and the maximum iteration number is set as I;
duty cycle range at bat algorithm iteration stage The method comprises the following steps:
,
Wherein V bus is the bus voltage, and V oc is the open-circuit voltage of the solar cell array;
for out of duty cycle range in iteration Taking the duty ratio as a corresponding boundary value;
The method for determining the initial positions of six bat individuals comprises the following steps:
In the middle of To/>The initial positions of six bat individuals are in sequence,/>Is the voltage predicted value of the solar battery array at the maximum power point of the life beginningFor the predicted value of the voltage of the solar cell array at the maximum power point of the end of life,/>For searching the scale adjustment factor of the range under the high-temperature working condition of the spacecraft,/>Is the average temperature predicted value of the solar cell array under the high-temperature working condition of the spacecraft,/>Is the average temperature predicted value of the solar cell array under the low-temperature working condition of the spacecraft,/>For searching the scale regulating factor of the range under the low-temperature working condition of the spacecraft,/>The average temperature predicted value of the solar cell array is obtained when the spacecraft runs on orbit for a long time.
According to the MPPT power supply control method for the satellite based on the improved BA-P & O hybrid algorithm, the method for performing original position iteration update in the bat algorithm iteration stage comprises the following steps:
Initial position for six bat individuals To/>Selecting by greedy strategy according to the current power of the solar cell array corresponding to each other, and reserving the initial positions/>, of three bat individuals with larger current power under the same calculation ruleFor an iterative process;
,
,
,
wherein I represents the number of iterations, i=1, 2,3, … … I; for the speed of three bat individuals for the ith iteration, ω is the inertial weight,/> For bat individual history optimal position,/>For the pulse frequencies of three bat individuals for the ith iteration,Is the minimum pulse frequency of bat/(The maximum pulse frequency of the bat, beta is a random number between (0, 1);
The bat random walk causes position change, and the random walk formula is:
,
In the middle of New positions of three bat individuals for the ith iteration, i.e., random walk on the basis of original positionsIs a random walk direction coefficient, is a random number between [ -1,1]For the scaling factor of loudness,/>Loudness of three bat individuals for the ith iteration;
the conditions for the bat individuals to walk randomly are:
,
In the middle of Representing a random number one,/>, randomly generated between 0 and 1Pulse emission rate representing the ith-1 th iteration of the kth individual bat, k=1, 2,3; for individual bats where random walk occurs, new locations/>, where random walk will occurFinal bat individual location/>, obtained as current iterative processAnd (5) finishing the iterative updating of the home position.
According to the MPPT power supply control method for the satellite based on the improved BA-P & O hybrid algorithm, the method for obtaining the updated duty ratio of the DC-DC unit after iterative updating by combining the reverse bat individual position of the bat individual position after the initial iterative updating comprises the following steps:
In the iterative updating of I less than or equal to I/2, a reverse learning mechanism is introduced to increase the searching range, and the positions of three bat individuals after the ith iterative updating are updated The corresponding reverse bat individual position is/>:
;
For the followingThe conditions for updating the corresponding bat individual positions are as follows:
And/> ,
In the middle ofFor the power of the solar cell array corresponding to the kth bat individual of the ith iteration,/>A random number two randomly generated between 0 and 1; /(I)Loudness for the ith-1 th iteration for the kth individual bat;
if the position updating condition is met, updating the bat individuals with reserved positions to new positions, wherein the parameter updating formula is as follows:
,
,
Where alpha is the loudness attenuation parameter, Initial pulse emission rate for three bat individuals,/>Enhancing parameters for pulse transmission rate; /(I)Three bat individual pulse emission rates for the ith iteration;
The bat individual position obtained after the position is updated And reverse bat individual location/>Six updated duty cycles of the DC-DC unit as the current iterative process, and determining the optimal duty cycle.
According to the MPPT power supply control method for satellite based on the improved BA-P & O hybrid algorithm of the invention,
And selecting three bat individual positions with larger power corresponding to the solar cell array by adopting a greedy strategy to perform next iteration update on the six updated duty ratios of the DC-DC unit in the bat algorithm iteration stage.
According to the MPPT power supply control method for the satellite based on the improved BA-P & O hybrid algorithm, after the duty ratio is updated each time, the relation between the bus voltage V bus and the mode conversion voltage threshold value is judged; the mode switching voltage threshold determining method comprises the following steps:
,
In the middle of For mode switching voltage threshold,/>Is the maximum discharge voltage of the storage battery.
According to the MPPT power supply control method for the satellite based on the improved BA-P & O hybrid algorithm, six update duty ratios of the DC-DC unit are updated in the order from small to large when the duty ratio is updated before the update, and the duty ratio is updated in the order from large to small when the duty ratio is updated after the update.
According to the MPPT power supply control method for the satellite based on the improved BA-P & O hybrid algorithm, in the disturbance observation stage, the current predicted power calculation method comprises the following steps:
,
In the middle of For/>Predicted/>, with constant time-to-time duty cycleThe power is predicted at the moment in time,For/>Real power of moment,/>For/>The actual power at the moment;
in the disturbance observation stage, the optimal duty ratio finally determined in the bat algorithm iteration stage is used as the DC-DC unit Initial duty cycle of time according to/>Real power of time/>And/>Real power of time/>Determining a disturbance direction from the change in (a); at the same time by/>Real power of time/>And/>Real power of time/>Prediction/>Predicted power of time/>; Taking the corresponding duty ratio after the adjacent previous disturbance direction determination as the DC-DC unit in/>The duty cycle of the moment in time is again according to/>Real power of time/>And/>Predicted power of time/>And judging the next disturbance direction, and continuing to perform duty ratio disturbance until the end.
According to the MPPT power supply control method for the satellite based on the improved BA-P & O hybrid algorithm, the restarting condition in the disturbance observation stage is set to meet one of the following conditions:
1) And/> ,
In the middle ofFor the maximum power of population history in the bat algorithm iteration stage, limit is the minimum power variation of a restarting algorithm,/>For the current working time of disturbance observation stage,/>The maximum stable duration of the disturbance observation stage;
2),
In the middle of Is the maximum working time of the disturbance observation stage.
According to the MPPT power supply control method for the satellite based on the improved BA-P & O hybrid algorithm, the DC-DC unit is realized by adopting a BUCK type voltage reduction circuit.
The invention has the beneficial effects that: the MPPT improved algorithm provided by the method can meet the global requirement of power tracking, improves convergence accuracy, adapts to environmental changes caused by satellite operation, and improves the stability of bus voltage. In actual use, the method of the invention can integrate the power tracking and voltage stabilizing mode conversion logic into the same algorithm to adapt to the space power supply system of the semi-regulated bus. The design of an independent MPPT electric interface unit can meet the requirement of direct control of a comprehensive electronic computer of a microminiature spacecraft.
The improved BA-P & O algorithm of the invention determines global stable feasible solutions through a plurality of bat individuals in the BA stage, and carries out local dynamic update based on the feasible solutions output in the BA stage in the P & O stage. When the solar cell array power is enough, the algorithm can jump out from the BA or P & O stage to enter the bus voltage regulating stage, so that the storage battery does not participate in power supply after the bus voltage exceeds the threshold value. The invention combines the advantages of BA algorithm and P & O algorithm.
The MPPT algorithm improved by the method disclosed by the invention meets the global performance of maximum power tracking, has good dynamic performance of adapting to environmental changes, improves the stability of bus voltage, can be directly sampled and controlled by a comprehensive electronic computer, and improves the software integration level of the comprehensive electronic computer.
The method is an MPPT (maximum power point tracking) hybrid algorithm based on BA and P & O, is suitable for multi-peak global power tracking, can improve convergence accuracy, improves bus stability, and is suitable for illumination change of satellite operation. The working mode conversion logic based on the bus voltage is reliable, the implementation is simple, and the number of independent electrical interfaces of the MPPT unit and the control computer is reduced. The MPPT algorithm can be operated on the satellite comprehensive electronic computer, and the integration level of satellite software is improved. And by the bypass design, the power supply reliability is improved.
Drawings
FIG. 1 is a block diagram of a typical MPPT based spatial power supply system circuit; in the figure, PV_I is a solar cell array output current sampling signal, and PV_V is a solar cell array output voltage sampling signal;
FIG. 2 is a block diagram of an MPPT space power supply system of a semi-regulated bus;
FIG. 3 is a graph of the single peak of a solar array under uniform illumination temperature conditions;
FIG. 4 is a graph of power voltage for a solar array under uniform illumination temperature conditions;
FIG. 5 is a schematic flow chart of the iterative phase of the bat algorithm;
FIG. 6 is a schematic flow diagram of a disturbance observation phase;
FIG. 7 is a schematic flow chart of a bus voltage regulation phase;
FIG. 8 is a circuit block diagram of a control system of the method of the present invention;
fig. 9 is an MPPT unit and bypass circuit diagram;
FIG. 10 is a bypass drive circuit diagram;
FIG. 11 is a graph of solar array output power for a multi-peak power;
Fig. 12 is a graph of tracking output power of a solar array based on a modified BA-P & O algorithm, wherein 83.32 represents the output power value.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The invention is further described below with reference to the drawings and specific examples, which are not intended to be limiting.
The invention provides an MPPT power supply control method for a satellite based on an improved BA-P & O hybrid algorithm, which is shown in the specific embodiment of the invention with reference to fig. 2 and 5-7, wherein a solar cell array adjusts bus voltage to supply power for a load through a DC-DC unit; the storage battery is connected with a bus through a diode to supply power for a load;
the power supply control comprises three stages of bat algorithm iteration, disturbance observation and bus voltage regulation;
the bat algorithm iteration stage and the disturbance observation stage are used for tracking the maximum power of the solar cell array when the solar cell array and the storage battery jointly supply power;
The initial positions of a selected number of bat individuals are determined according to the voltage predicted value of the solar cell array at the maximum power point of the initial life period and the final life period and the working condition of the spacecraft in the bat algorithm iteration stage and used as the initial duty ratio of the DC-DC unit, and the DC-DC unit is controlled by the driving circuit; if the bus voltage corresponding to the initial duty ratio is greater than the mode conversion voltage threshold value, entering a bus voltage regulating stage; otherwise, adopting greedy strategy to select half bat individuals with larger current power of the solar cell array, namely, carrying out initial position iteration update after three bat individuals randomly walk, and then obtaining six updated duty ratios of the DC-DC unit by combining the reverse bat individual positions of the bat individual positions after initial position iteration update and controlling the DC-DC unit through a driving circuit; if the bus voltage corresponding to the updated optimal duty ratio is greater than the mode conversion voltage threshold value, entering a bus voltage regulation stage; otherwise, determining three new iterative bat individuals to continue to update the next position iteration until the maximum iteration times are reached; entering a disturbance observation stage;
The disturbance observation stage is used for calculating the current actual power of the solar cell array based on the currently determined duty ratio position corresponding to the iterative bat individual, and determining a disturbance direction to perform duty ratio disturbance according to the current actual power and the actual power change of the adjacent previous moment; after each time the DC-DC unit is controlled by adopting the duty ratio after disturbance, if the bus voltage corresponding to the duty ratio after disturbance is greater than the mode conversion voltage threshold value, entering a bus voltage regulation stage; otherwise, judging whether the restarting condition is met according to the current actual power and the current working time of the solar cell array, if so, entering a bat algorithm iteration stage, otherwise, calculating the current predicted power of the solar cell array according to the current post-disturbance duty ratio and comparing the current predicted power with the actual power, and determining the disturbance direction to continue to carry out duty ratio disturbance;
The bus voltage regulating stage is used for maintaining the bus voltage stable when the solar cell array is independently powered, and determining the updating direction of the current duty ratio according to the current bus voltage sampling value; if the corresponding bus voltage after the duty ratio is updated is still greater than the mode conversion voltage threshold, continuing to adjust the bus voltage, otherwise, entering into an iteration stage of the bat algorithm.
In the embodiment, the DC-DC unit (voltage regulating unit of MPPT) has two main effects, namely, when the solar cell array has enough power, the voltage of the bus can be maintained stable when power is supplied separately; and secondly, tracking the maximum power of the solar array when the solar battery array is not high enough in power and the storage battery and the solar array are required to supply power together.
Further, firstly initializing parameters of the bat algorithm in the bat algorithm iteration stage, and setting the maximum iteration number as I; loudness is a, frequency is r, etc.
And initializing the bat group after initializing the parameters, and determining the bat quantity and the duty ratio of the corresponding BUCK circuit of the bat initial position. For a space power supply system of a semi-regulated bus, a storage battery is directly connected to the bus through a diode to supply power to a load, and in order to reduce the power loss of an iterative process of a bat group algorithm, the duty ratio range of the iterative process is determined according to the voltage of the bus. For individuals in the iteration that exceed the duty cycle range, the duty cycle is taken as a boundary value.
Duty cycle range at bat algorithm iteration stageThe method comprises the following steps:
,
Wherein V bus is the bus voltage, and V oc is the open-circuit voltage of the solar cell array;
for out of duty cycle range in iteration Taking the duty ratio as a corresponding boundary value;
To speed convergence and avoid trapping local peaks, the initial position of a portion of the bat individual should be as close as possible to the maximum power point. For a space power supply system, the power output characteristics change greatly due to the influence of space irradiation on the service life attenuation of the solar cell array, and the maximum power point at the initial stage and the end stage of the service life changes. Therefore, considering the performance and the working temperature of the solar battery, six bat individuals are selected, and the initial positions of the six bat individuals are determined by the following steps:
In the middle of To/>The initial positions of six bat individuals are in sequence,/>Is the voltage predicted value of the solar battery array at the maximum power point of the life beginningFor the predicted value of the voltage of the solar cell array at the maximum power point of the end of life,/>For searching the scale adjustment factor of the range under the high-temperature working condition of the spacecraft,/>Is the average temperature predicted value of the solar cell array under the high-temperature working condition of the spacecraft,/>Is the average temperature predicted value of the solar cell array under the low-temperature working condition of the spacecraft,/>For searching the scale regulating factor of the range under the low-temperature working condition of the spacecraft,/>The average temperature predicted value of the solar cell array is obtained when the spacecraft runs on orbit for a long time.
In this embodiment, the method for performing the initial position iteration update in the bat algorithm iteration stage includes:
the duty ratio of the initial bat position is brought into the DC-DC unit, and the power corresponding to each initial bat is recorded. Selecting initial and final bat individuals at the same temperature by greedy strategy, namely, selecting initial positions of six bat individuals To/>Selecting by greedy strategy according to the current power of the solar cell array corresponding to each other, and reserving the initial positions/>, of three bat individuals with larger current power under the same calculation ruleFor an iterative process;
,
,
,
Wherein I represents the number of iterations, i=1, 2,3, … … I; for the speeds of three bat individuals for the ith iteration, ω is the inertial weight, For bat individual history optimal position,/>Pulse frequency of three bat individuals for the ith iteration, between [0,1 ]/>Is the minimum pulse frequency of bat/(The maximum pulse frequency of the bat should be gradually increased in the iteration; beta is a random number between (0, 1);
The bat random walk causes position change, and the random walk formula is:
,
In the middle of New positions of three bat individuals for the ith iteration, i.e., random walk on the basis of original positionsIs a random walk direction coefficient, is a random number between [ -1,1]The size of the step of the random walk can be controlled for the proportional adjustment coefficient of the loudness; /(I)Loudness of three bat individuals for the ith iteration;
the conditions for the bat individuals to walk randomly are:
,
In the middle of Representing a random number one,/>, randomly generated between 0 and 1Pulse emission rate representing the ith-1 th iteration of the kth individual bat, k=1, 2,3; for individual bats where random walk occurs, new locations/>, where random walk will occurFinal bat individual location/>, obtained as current iterative processAnd (5) finishing the iterative updating of the home position.
Still further, the method for obtaining the updated duty ratio of the iteratively updated DC-DC unit by combining the reverse bat individual position of the original iteratively updated bat individual position comprises:
in the previous iteration process, in order to avoid trapping in local peak values, a reverse learning mechanism is introduced to increase the search range, and in the iterative updating of I < I/2, the positions of three bat individuals after the ith iterative updating are updated The corresponding reverse bat individual position is/>:
;
RecordingAnd/>Determining the optimal duty ratio according to the corresponding maximum power;
For the following The conditions for updating the corresponding bat individual positions are as follows:
And/> ,
In the middle ofFor the power of the solar cell array corresponding to the kth bat individual of the ith iteration,/>A random number two randomly generated between 0 and 1; /(I)Loudness for the ith-1 th iteration for the kth individual bat;
if the position updating condition is met, updating the bat individuals with reserved positions to new positions, wherein the parameter updating formula is as follows:
,
,
Where alpha is the loudness attenuation parameter, Initial pulse emission rate for three bat individuals,/>Enhancing parameters for pulse transmission rate; /(I)Three bat individual pulse emission rates for the ith iteration;
The bat individual position obtained after the position is updated And reverse bat individual location/>And determining the optimal duty ratio according to the corresponding maximum power as six updated duty ratios of the DC-DC unit in the current iteration process.
The trend of the loudness a is gradually decreasing, and the value of the pulse emission rate r gradually increases. The loudness A is larger, so that the global searching capability of iteration is improved, and the local optimizing capability of iteration is improved when r is larger. γ=0.9, α=0.9 is preferable.
And selecting three bat individual positions with larger power corresponding to the solar cell array by adopting a greedy strategy to perform next iteration update on the six updated duty ratios of the DC-DC unit in the bat algorithm iteration stage. And (3) carrying out greedy strategy selection on the original bat individuals and the corresponding opposite individuals, and reserving the positions of the better individuals for the next iteration, so that the number of the bat individuals reserved in each iteration is 3.
The DC-DC unit of the MPPT of the space power supply system of the semi-regulated bus has the function of regulating the bus voltage, so that the relationship between the bus voltage V bus and the mode conversion voltage threshold value is judged after the duty ratio is updated to the DC-DC unit each time; the mode switching voltage threshold determining method comprises the following steps:
,
In the middle of For mode switching voltage threshold,/>Is the maximum discharge voltage of the storage battery.
If the bus voltage V bus is greater than the mode switching voltage thresholdAnd entering a bus voltage stabilizing adjustment mode. In order to reduce the discharge of the accumulator during the voltage regulation, the mode switching voltage threshold should be slightly higher than the maximum discharge voltage of the accumulator.
If the bus voltage V bus is smaller than the mode switching voltage thresholdThe bat group iterative process continues.
In the bat algorithm iteration stage, six update duty ratios of the DC-DC unit are updated from small to large when the duty ratio is updated before the update, and from large to small when the duty ratio is updated after the update.
Since the partial load is directly connected to the bus, bus voltage fluctuations should be minimized. In order to reduce the influence of abrupt change of the duty ratio on the bus voltage, the bat positions in the iterative process are subjected to individual sequencing and then the duty ratio is output. On the basis of not affecting the intelligent iteration capacity of the algorithm group, the bat group can output the duty ratio in the order from low to high when updating the positions for odd times, and the bat group can output the duty ratio in the order from high to low when updating the positions for even times.
And when the iteration times reach the set maximum iteration times I, exiting the iteration process, and entering a disturbance observation link.
Still further, in the disturbance observation stage, after the disturbance observation link is started, initializing a time parameter to determine the disturbance observation time. The disturbance observation link realizes the disturbance to the solar cell array voltage by increasing or decreasing the duty ratio, determines the disturbance direction according to the power change, and if the power after the disturbance is larger than the power before the disturbance, the disturbance direction is kept, otherwise, the disturbance is carried out in the opposite direction.
Because the traditional disturbance observation method may have misjudgment when the illumination environment changes, the power prediction disturbance observation method is adopted in the embodiment. The power judgment of the disturbance observation method of power prediction is carried out by adding a sample, and the difference between the predicted power value P F (t-1) and the current actual power value P (t) is calculated, so that the influence of environmental change is eliminated.
The current prediction power calculation method comprises the following steps:
,
In the middle of For/>Predicted/>, with constant time-to-time duty cycleThe power is predicted at the moment in time,For/>Real power of moment,/>For/>The actual power at the moment;
in the disturbance observation stage, the optimal duty ratio finally determined in the bat algorithm iteration stage is used as the DC-DC unit Initial duty cycle of time according to/>Real power of time/>And/>Real power of time/>Determining a disturbance direction from the change in (a); at the same time by/>Real power of time/>And/>Real power of time/>Prediction/>Predicted power of time/>; Taking the corresponding duty ratio after the adjacent previous disturbance direction determination as the DC-DC unit in/>The duty cycle of the moment in time is again according to/>Real power of time/>And/>Predicted power of time/>And judging the next disturbance direction, and continuing to perform duty ratio disturbance until the end.
And (3) bringing the duty ratio of the disturbance observation link into a BUCK voltage regulating unit, and judging the magnitude relation between the bus voltage and a mode conversion voltage threshold value, wherein the mode conversion voltage threshold value is at least larger than the maximum discharge voltage of the storage battery. If the bus voltage is greater than the threshold voltageAnd entering a bus voltage stabilizing adjustment mode. If the bus voltage is less than the threshold voltage, the perturbation is continued.
In the present embodiment, the restart condition in the disturbance observation stage is set to satisfy one of the following conditions:
1) And/> ,
In the middle ofFor the maximum power of population history in the bat algorithm iteration stage, limit is the minimum power variation of a restarting algorithm,/>For the current working time of disturbance observation stage,/>The maximum stable duration of the disturbance observation stage; after the disturbance observation stage is stable, the method has a certain tracking capability on illumination change, and if the power change is large, the algorithm is restarted.
2) In order to prevent the long-term sinking into the local peak value, the periodic algorithm is added for restarting, the time judgment is carried out on the disturbance link, whether the bat swarm algorithm needs to be restarted is determined, and the judgment conditions are as follows:
,
In the middle of Is the maximum working time of the disturbance observation stage.
In the bus voltage regulating stage, the duty ratio is adjusted only depending on the bus voltage, the duty ratio is reduced when the bus voltage is higher than V a, and the duty ratio is increased when the bus voltage is lower than V a. And restarting the bat swarm algorithm when the bus voltage is lower than V bat, and entering a power tracking mode.
As an example, the DC-DC unit is implemented using a BUCK circuit.
The control circuit design of the method comprises the following steps:
based on the space power supply system of the semi-regulated bus, the MPPT unit increases bus voltage sampling. The sampling bus voltage is input into a satellite comprehensive electronic computer, an electrical interface is designed to realize direct control of the comprehensive electric computer on the MPPT unit, and an MPPT algorithm can be directly operated on the comprehensive electric computer.
With reference to fig. 8, the corresponding electrical interface has three sampling signals, namely, a solar cell array output voltage, a solar cell array output current, a bus voltage, two complementary PWM waves and a bypass switch control signal. The integrated electronic computer can control the MPPT unit through an independent electrical interface. For small-volume satellites such as cube satellites, the integrated electronic computer can be directly connected with the MPPT unit through a connector, and high-frequency PWM wave control is supported.
With reference to fig. 9, the bus regulating DC-DC unit adopts a synchronous rectifying BUCK circuit, and adds a bypass design adapted to the control of a comprehensive electronic computer. The S1 and the S2 of the BUCK circuit are two NMOS tubes, the two NMOS tubes are driven by a half-bridge driving chip, the S3 of the BUCK circuit is a PMOS tube, and the MPPT circuit can be automatically switched to a bypass to directly connect the output of the solar cell array to a bus when the MPPT circuit fails or a comprehensive computer fails, so that the whole star power supply is ensured.
As shown in connection with fig. 10, the bypass switch is directly controlled by the satellite integrated electronic computer. When the comprehensive electronic computer is stopped accidentally, the chip pins of the comprehensive electronic computer corresponding to the bypass switch signals are connected with the pull-down resistor to ensure the whole star power supply. The bypass switch circuit is designed, when the bypass switch is turned off in the case of high level signals, and when the bypass switch is turned on in the case of low level signals. The bypass switch driving signal is directly supplied by the output voltage of the solar cell array through resistor voltage division, so that the reliability is improved.
The comprehensive electronic computer controls the bypass switch through the high and low level. When the MPPT function is used, the bypass switch corresponding interface always outputs a high level. If the comprehensive electronic computer is stopped accidentally, the corresponding pins will output low level, the bypass switch is turned on, the solar cell array will be directly connected with the bus for power supply, and the reliability of power supply is improved.
Simulation verification:
simulations were performed based on SIMULINK to verify the performance of the improved BA-P & O hybrid algorithm. The modeling and output characteristics of a solar array with multi-peak power are shown in fig. 11. The output power curve of the solar cell array obtained by simulation is shown in fig. 12.
Therefore, the improved BA-P & O algorithm can avoid sinking local peaks, reduces voltage oscillation, reduces the influence of abrupt change of duty ratio on bus voltage, and has faster convergence time.
The application scene of the method is as follows:
The LEO satellite has the characteristics of short period and rapid alternation of a photo-shadow area, the charging time of a storage battery is short during on-orbit running, the charging time can be shortened by improving the output power of a solar cell array, and the space power supply control system based on MPPT can better meet task requirements. The output power of the solar battery array is large in change range in the initial and final life stages when the deep space detectors are in track operation, and the MPPT technology is used for a large number of deep space detectors.
The invention is suitable for a semi-regulated bus power supply system of a microminiature spacecraft.
The method of the invention is in an improved BA stage: the initial bat position selection of the solar cell on-orbit service life is considered. Reverse learning is introduced, and convergence and the ability to jump out local peaks are improved. The iteration sequence of the bat group iteration process is improved, and after each round of bat group iteration is finished, individual sequencing is carried out on the population, so that the influence of duty ratio mutation on the busbar voltage is reduced.
Improved disturbance observation phase: and the power prediction is introduced, so that the accuracy of power tracking is improved. Setting two restarting conditions of time judgment and power judgment. When the illumination temperature is greatly mutated, the MPPT can restart the algorithm. In order to prevent MPPT from being trapped into local peaks for a long time, long-time power loss is caused, and the algorithm is restarted after a period of operation in a disturbance observation stage.
Algorithm design based on bus voltage: initial individual bat selections based on bus voltage are set. The MPPT algorithm is added with the mode conversion judgment based on the bus voltage, the mode conversion logic is simple and easy to realize, and the algorithm independently realizes the functions of bus voltage regulation and power tracking.
MPPT independent electrical interface and bypass design: the MPPT unit is suitable for the independent electric interfaces of the MPPT unit directly controlled by the on-orbit comprehensive electronic computer, and the number of the interfaces is small, and 6 paths are totally used. The microminiature spacecraft has small volume, the integrated electronic computer outputs high-frequency PWM waves through the connector or the short-distance cable to independently control the MPPT unit, and the MPPT algorithm can be operated on the integrated electronic computer, so that the integration level of software is improved. The power supply device is suitable for bypass design in the case of faults of an on-track comprehensive electric cutting machine or MPPT, and improves the power supply reliability.
The method considers the BA algorithm bat individual initial position selection of the solar cell on-orbit service life change. Reverse learning and individual sequencing are introduced in the BA stage, so that the algorithm convergence capacity and the bus stability are improved. Power prediction and increased time restart conditions are introduced to improve the disturbance observation phase. Mode conversion based on bus voltage. The mode switching logic is simplified, and the power supply system is suitable for a semi-regulated bus. MPPT independent electrical interface design and bypass design can be performed.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.
Claims (10)
1. A satellite MPPT power supply control method based on an improved BA-P & O hybrid algorithm is characterized in that,
The solar cell array regulates bus voltage to supply power for a load through a DC-DC unit; the storage battery is connected with a bus through a diode to supply power for a load;
the power supply control comprises three stages of bat algorithm iteration, disturbance observation and bus voltage regulation;
the bat algorithm iteration stage and the disturbance observation stage are used for tracking the maximum power of the solar cell array when the solar cell array and the storage battery jointly supply power;
The initial positions of a selected number of bat individuals are determined according to the voltage predicted value of the solar cell array at the maximum power point of the initial life period and the final life period and the working condition of the spacecraft in the bat algorithm iteration stage and used as the initial duty ratio of the DC-DC unit, and the DC-DC unit is controlled by the driving circuit; if the bus voltage corresponding to the initial duty ratio is greater than the mode conversion voltage threshold value, entering a bus voltage regulating stage; otherwise, adopting a greedy strategy to select the initial position of a half bat individual with larger current power of the solar cell array, performing random walk and then performing in-situ iterative update, and then combining the reverse bat individual positions after in-situ iterative update to obtain six updated duty ratios of the DC-DC unit, and controlling the DC-DC unit through a driving circuit; if the bus voltage corresponding to the updated optimal duty ratio is greater than the mode conversion voltage threshold value, entering a bus voltage regulation stage; otherwise, determining three new iterative bat individuals to continue to update the next position iteration until the maximum iteration times are reached; entering a disturbance observation stage;
The disturbance observation stage is used for calculating the current actual power of the solar cell array based on the currently determined duty ratio position corresponding to the iterative bat individual, and determining a disturbance direction to perform duty ratio disturbance according to the current actual power and the actual power change of the adjacent previous moment; after each time the DC-DC unit is controlled by adopting the duty ratio after disturbance, if the bus voltage corresponding to the duty ratio after disturbance is greater than the mode conversion voltage threshold value, entering a bus voltage regulation stage; otherwise, judging whether the restarting condition is met according to the current actual power and the current working time of the solar cell array, if so, entering a bat algorithm iteration stage, otherwise, calculating the current predicted power of the solar cell array according to the current post-disturbance duty ratio and comparing the current predicted power with the actual power, and determining the disturbance direction to continue to carry out duty ratio disturbance;
The bus voltage regulating stage is used for maintaining the bus voltage stable when the solar cell array is independently powered, and determining the updating direction of the current duty ratio according to the current bus voltage sampling value; if the corresponding bus voltage after the duty ratio is updated is still greater than the mode conversion voltage threshold, continuing to adjust the bus voltage, otherwise, entering into an iteration stage of the bat algorithm.
2. The improved BA-P & O hybrid algorithm based MPPT power control method for satellites of claim 1 wherein,
Firstly initializing parameters of the bat algorithm in the bat algorithm iteration stage, and setting the maximum iteration number as I;
duty cycle range at bat algorithm iteration stage The method comprises the following steps:
,
Wherein V bus is the bus voltage, and V oc is the open-circuit voltage of the solar cell array;
for out of duty cycle range in iteration Taking the duty ratio as a corresponding boundary value;
The method for determining the initial positions of six bat individuals comprises the following steps:
In the middle of To/>The initial positions of six bat individuals are in sequence,/>Is the voltage predicted value of the solar battery array at the maximum power point of the life beginningFor the predicted value of the voltage of the solar cell array at the maximum power point of the end of life,/>For searching the scale adjustment factor of the range under the high-temperature working condition of the spacecraft,/>Is the average temperature predicted value of the solar cell array under the high-temperature working condition of the spacecraft,/>Is the average temperature predicted value of the solar cell array under the low-temperature working condition of the spacecraft,/>For searching the scale regulating factor of the range under the low-temperature working condition of the spacecraft,/>The average temperature predicted value of the solar cell array is obtained when the spacecraft runs on orbit for a long time.
3. The improved BA-P & O hybrid algorithm based MPPT power control method for satellites of claim 2 wherein the iterative update of the original location at the iterative stage of the bat algorithm is:
Initial position for six bat individuals To/>Selecting by greedy strategy according to the current power of the solar cell array corresponding to each other, and reserving the initial positions/>, of three bat individuals with larger current power under the same calculation ruleFor an iterative process;
,
,
,
wherein I represents the number of iterations, i=1, 2,3, … … I; for the speed of three bat individuals for the ith iteration, ω is the inertial weight,/> For bat individual history optimal position,/>Pulse frequency of three bat individuals for the ith iteration,/>Is the minimum pulse frequency of bat/(The maximum pulse frequency of the bat, beta is a random number between (0, 1);
The bat random walk causes position change, and the random walk formula is:
,
In the middle of New positions of three bat individuals for the ith iteration, i.e., random walk on the basis of original positionsIs a random walk direction coefficient, is a random number between [ -1,1]For the scaling factor of loudness,/>Loudness of three bat individuals for the ith iteration;
the conditions for the bat individuals to walk randomly are:
,
In the middle of Representing a random number one,/>, randomly generated between 0 and 1Pulse emission rate representing the ith-1 th iteration of the kth individual bat, k=1, 2,3; for individual bats where random walk occurs, new locations/>, where random walk will occurFinal bat individual location/>, obtained as current iterative processAnd (5) finishing the iterative updating of the home position.
4. The improved BA-P & O hybrid algorithm based MPPT power control method for satellites of claim 3 wherein the method of iteratively updated back-to-back duty cycle of the DC-DC unit in combination with the back-to-back bat individual position of the original position iteratively updated bat individual position is:
In the iterative updating of I less than or equal to I/2, a reverse learning mechanism is introduced to increase the searching range, and the positions of three bat individuals after the ith iterative updating are updated The corresponding reverse bat individual position is/>:
;
For the followingThe conditions for updating the corresponding bat individual positions are as follows:
And/> ,
In the middle ofFor the power of the solar cell array corresponding to the kth bat individual of the ith iteration,/>A random number two randomly generated between 0 and 1; /(I)Loudness for the ith-1 th iteration for the kth individual bat;
if the position updating condition is met, updating the bat individuals with reserved positions to new positions, wherein the parameter updating formula is as follows:
,
,
Where alpha is the loudness attenuation parameter, Initial pulse emission rate for three bat individuals,/>Enhancing parameters for pulse transmission rate; /(I)Three bat individual pulse emission rates for the ith iteration;
The bat individual position obtained after the position is updated And reverse bat individual location/>Six updated duty cycles of the DC-DC unit as the current iterative process, and determining the optimal duty cycle.
5. The improved BA-P & O hybrid algorithm-based MPPT power supply control method for a satellite of claim 4, wherein,
And selecting three bat individual positions with larger power corresponding to the solar cell array by adopting a greedy strategy to perform next iteration update on the six updated duty ratios of the DC-DC unit in the bat algorithm iteration stage.
6. The improved BA-P & O hybrid algorithm based MPPT power control method for satellites of claim 5 wherein each update of duty cycle is followed by determining a relationship of bus voltage V bus to a mode transition voltage threshold; the mode switching voltage threshold determining method comprises the following steps:
,
In the middle of For mode switching voltage threshold,/>Is the maximum discharge voltage of the storage battery.
7. The improved BA-P & O hybrid algorithm based MPPT power control method for satellites of claim 6 wherein,
In the bat algorithm iteration stage, six update duty ratios of the DC-DC unit are updated from small to large when the duty ratio is updated before the update, and from large to small when the duty ratio is updated after the update.
8. The improved BA-P & O hybrid algorithm based MPPT power control method for satellites of claim 7 wherein during the disturbance observation phase the current predicted power calculation method is:
,
In the middle of For/>Predicted/>, with constant time-to-time duty cyclePredicted power at time,/>Is thatReal power of moment,/>For/>The actual power at the moment;
in the disturbance observation stage, the optimal duty ratio finally determined in the bat algorithm iteration stage is used as the DC-DC unit Initial duty cycle of time according to/>Real power of time/>And/>Real power of time/>Determining a disturbance direction from the change in (a); at the same time by/>Real power of time/>And/>Real power of time/>Prediction/>Predicted power of time/>; Taking the corresponding duty ratio after the adjacent previous disturbance direction determination as the DC-DC unit in/>The duty cycle of the moment in time is again according to/>Real power of time/>And/>Predicted power of time/>And judging the next disturbance direction, and continuing to perform duty ratio disturbance until the end.
9. The improved BA-P & O hybrid algorithm based MPPT power control method for satellites of claim 8 wherein,
The restart condition in the disturbance observation stage is set to satisfy one of the following conditions:
1) And/> ,
In the middle ofFor the maximum power of population history in the bat algorithm iteration stage, limit is the minimum power variation of a restarting algorithm,/>For the current working time of disturbance observation stage,/>The maximum stable duration of the disturbance observation stage;
2),
In the middle of Is the maximum working time of the disturbance observation stage.
10. The improved BA-P & O hybrid algorithm based MPPT power control method for satellites of claim 9 wherein the DC-DC unit is implemented using BUCK-type step-down circuitry.
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Optimization of the P&O-MPPT controller by the adaptive method (Ad-P&O) for stand-alone PV systems;O. A. Ba, A. Ndiaye, A. Ba, E. H. M. Ndiaye and M. A. Tankari;2023 11th International Conference on Smart Grid (icSmartGrid);20230606;第1-8页 * |
航天器能源管理技术研究进展;陈洪伟 等;空间控制技术与应用;20191031;第45卷(第05期);第63-71页 * |
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