CN114784784B - Direct-current micro-grid stability optimization control method based on longitudinal and transverse intersection algorithm - Google Patents

Direct-current micro-grid stability optimization control method based on longitudinal and transverse intersection algorithm Download PDF

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CN114784784B
CN114784784B CN202210344826.4A CN202210344826A CN114784784B CN 114784784 B CN114784784 B CN 114784784B CN 202210344826 A CN202210344826 A CN 202210344826A CN 114784784 B CN114784784 B CN 114784784B
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黄泽杭
杨苓
陈璟华
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Abstract

The invention discloses a method for controlling the stability trend of a direct-current micro-grid based on a longitudinal and transverse intersection algorithm, which comprises the following steps: s1: solving a small signal model of the multi-source multi-load direct current micro-grid system; s2: the dominant mode of the system is solved through a characteristic root analysis method, and the influence degree of the state variable on the dominant mode is decoupled through a participation factor method; s3: applying a criss-cross algorithm to stability analysis of the direct-current microgrid, obtaining optimization-seeking parameters to achieve the optimal stability of the system, and enabling the direct-current microgrid to have larger stability margin, thereby realizing stability optimization-seeking control; the invention can realize global parallel search and has high convergence speed by utilizing the advantages of a crisscross algorithm, can quickly obtain the optimization solution of the parameters, effectively avoids the influence of the local solution of the parameters on stability analysis, enables the direct current micro-grid to have stability margin as large as possible, and realizes stability optimization control.

Description

Direct-current micro-grid stability optimization control method based on longitudinal and transverse intersection algorithm
Technical Field
The invention relates to the field of new energy distributed power generation, in particular to a method for controlling the stability trend of a direct-current micro-grid based on a crisscross algorithm.
Background
With the trend of high penetration of new energy, the water rises to the ship height, so that the direct-current micro-grid is widely concerned. Most loads are connected to the direct-current micro-grid through the power electronic interface circuit and are always represented as constant-power loads, the negative impedance characteristic of the loads easily causes system instability and reduces the quality of system electric energy, and therefore improvement of system stability becomes the key point of direct-current micro-grid operation research. The system parameter optimization is a mode capable of effectively improving the system stability, most of research system parameter optimization is to analyze the moving track of the characteristic root under the parameter change through a discrete form, and although the influence rule of the parameter adjustment trend on the system stability can be qualitatively analyzed, the quantitative result of the multi-parameter optimization control of the system cannot be obtained. Therefore, the invention provides a parameter Optimization control scheme based on a cross-bar Algorithm (CSO).
In order to achieve the purpose, the technical scheme provided by the invention is as follows:
a DC micro-grid stability optimization control method based on a criss-cross algorithm comprises the following steps:
s1: solving a small signal model of the multi-source multi-load direct current micro-grid system;
s2: the dominant mode of the system is solved through a characteristic root analysis method, and the influence degree of the state variable on the dominant mode is decoupled through a participation factor method;
s3: applying a criss-cross algorithm to stability analysis of the direct-current microgrid, obtaining optimization-seeking parameters to achieve the optimal stability of the system, and enabling the direct-current microgrid to have larger stability margin, thereby realizing stability optimization-seeking control;
further, in the step S1, the specific steps of obtaining the small signal model of the multi-source multi-load dc micro-grid system are as follows:
s1-1: small signal model of power module:
the power module utilizes a bidirectional DC/DC converter to perform voltage conversion, adopts a droop control method and a virtual inertia control method, wherein the droop control method ensures power equalization among multiple power supplies, the virtual inertia control method is a working principle similar to a capacitor, and aims to improve the voltage inertia of a direct-current bus and improve the dynamic performance when the voltage changes, and the state space model of the power module is as follows:
Figure BDA0003575995830000021
in the formula (1), d is the duty ratio of the bidirectional DC/DC converter in the power module, u b 、u oN And u o For the pre-conversion voltage, the post-conversion rated voltage and the post-conversion outlet voltage, i, of the bidirectional DC/DC converter in the power supply module b And i bref For converting the pre-current and its reference value, i, for a bidirectional DC/DC converter in a power supply module o For the outlet current, R, after conversion by a bidirectional DC/DC converter in a power supply module b 、L b And C s Parasitic resistance, filter inductance and support capacitance of the power supply module, S u Rated voltage u converted by bidirectional DC/DC converter in power module oN And an outlet voltage u o The squared difference of (a) is passed through a first-order inertia element and then a variable, k, is output p And k i Proportional and integral coefficients, S, for the power module PI controller i Current reference value i before conversion for bidirectional DC/DC converter in power module bref And current i b The difference is output as a variable k after an integration step droop As sag factor, C virb The method is characterized in that a virtual inertia coefficient is adopted, T is a time constant, s is a Laplace transform complex variable operator, the equation (1) is linearized near a steady state, and a small signal model of a power module is obtained as follows:
Figure BDA0003575995830000022
in the formula (2), Δ x b Being the state vector of the power supply module, Δ x b ＝[Δi b ,ΔS u ,ΔS i ,Δu o ] T ，Δi b Pre-conversion current i for a bidirectional DC/DC converter in a power supply module b State variable of, Δ S u Rated voltage u converted by bidirectional DC/DC converter in power module oN And an outlet voltage u o The squared difference of the first-order inertia element outputs a variable S u State variable of (a), Δ S i Current reference value i before conversion for bidirectional DC/DC converter in power module bref And current i b The difference is output as variable S after integral i State variable of (1), Δ u o For the outlet voltage u after conversion of the bidirectional DC/DC converter in the power supply module o A state variable of b Is a coefficient matrix of the power supply module, d 0 Is a steady-state quantity u of the duty cycle d of a bidirectional DC/DC converter in the power supply module o0 For the outlet voltage u after conversion of a bidirectional DC/DC converter in a power supply module o Steady state quantity of i b0 Current i before conversion for bidirectional DC/DC converter in power module b A steady state quantity of (c);
s1-2: small signal model of constant power load module:
the constant power load module utilizes a Buck converter to carry out voltage conversion, a voltage-current double-loop control strategy is adopted, and a state space model of the constant power load module is as follows:
Figure BDA0003575995830000031
in the formula (3), g is the duty ratio of the Buck converter in the constant-power load module, and u is F 、u LN And u L For the conversion of forward port voltage, constant power load rated voltage and constant power load actual voltage, i dc Conversion of forward port current, i, for Buck converters in constant-power load modules L And i Lref Is a constant power load current and its reference value, P L For constant power load power, R L 、L L And C L Parasitic resistance, filter inductance and filter capacitance of constant power load module, C F Supporting capacitor, k, for constant power load module pL_u And k iL_u Proportional and integral coefficients, k, of an outer loop PI controller for constant power load module voltage pL_i And k iL_i Proportional and integral coefficients, S, of a constant-power load module current inner loop PI controller uL And S iL Outputting variables for integral links of a voltage outer loop PI controller and a current inner loop PI controller of a constant power load module, wherein a small signal model of the constant power load module is as follows:
Figure BDA0003575995830000032
in the formula (4), Δ x L Is the state vector of the constant-power load module, Δ x L ＝[Δu F ,Δi L ,Δu L ,ΔS uL ,ΔS iL ] T ，Δu F Converting forward port voltage u for Buck converter in constant power load module F State variable of, Δ i L Is a constant power load current i L State variable of (1), Δ u L Is the actual voltage u of the load with constant power L State variable of (a), Δ S uL Outputting variable S for integral link of constant power load module voltage outer loop PI controller uL Shape of (1)State variable,. DELTA.S iL Outputting variable S for integral link of constant power load module current inner loop PI controller iL A state variable of L Is a coefficient matrix of the constant power load module, g 0 Is the steady-state quantity u of the duty ratio g of the Buck converter in the constant power load module F0 Conversion of forward port voltage u for Buck converter in constant power load module F Steady state quantity of i L0 Is a constant power load current i L A steady state quantity of;
s1-3: small signal model of the direct current transmission line:
a direct current transmission line is arranged between the power module and the constant power load module, and the state space model of the direct current transmission line is as follows:
Figure BDA0003575995830000041
in the formula (5), u DC And C DC For collecting bus voltage and supporting capacitance, R s And L s Resistance and inductance of the source side transmission line, R F And L F The small signal model of the direct current transmission line is as follows:
Figure BDA0003575995830000042
in the formula (6), Δ x d Is the state vector of the DC transmission line, Δ x d ＝[Δu o ,Δi o ,Δu DC ,Δi dc ,Δu F ] T ，Δi o For the outlet current i after conversion of a bidirectional DC/DC converter in a power supply module o State variable of (1), Δ u DC For converging bus voltage u DC State variable of, Δ i dc Converting forward port current i for Buck converter in constant power load module dc State variable of (D) d A coefficient matrix of the direct current transmission line is obtained;
s1-4: a small signal model of the direct-current micro-grid system:
the DC micro-grid system consists of threeThe power supply comprises a power supply module, three direct current transmission lines and three constant power load modules, the structure is in a conventional radiation type, the total length of the transmission lines at the source side and the load side is set as a certain value and is marked as 1, and the lengths of the transmission lines from the power supply modules 1,2 and 3 to a convergence bus are respectively l b1 、l b2 、l b3 The lengths from the convergent bus to the constant power load modules 1,2 and 3 are respectively l L1 、l L2 、l L3 The small signal model of the system is:
Figure BDA0003575995830000051
in the formula (7), Δ x sys Is a state vector of the DC micro-grid system, Δ x sys ＝[Δx bn ,Δx d123 ,Δx Ln ] T ，Δx bn Is the state vector of three power supply modules, n =1,2,3, Δ x Ln Is the state vector of three constant power load modules, n =1,2,3, Δ x d123 Is the state vector of three DC transmission lines, Δ x d123 ＝[Δu on ,Δi on ,Δu DC ,Δi dcn ,Δu Fn ] T ，Δu on And Δ i on The outlet voltage u after conversion of the bidirectional DC/DC converter in the three power supply modules on And an outlet current i on N =1,2,3, Δ i dcn And Δ u Fn Converting forward port current i for Buck converter in three constant power load modules dcn And inlet voltage u Fn N =1,2,3,a sys Is a coefficient matrix of the DC microgrid system, A bn Coefficient matrix for three power supply modules, n =1,2,3, D d123 Coefficient matrices for three DC transmission lines, A Ln A coefficient matrix of three constant power load modules, n =1,2,3;
further, the specific steps of step S2 are as follows:
s2-1: and (3) solving the dominant mode of the system through a characteristic root analysis method:
coefficient matrix according to direct current microgrid systemA sys Solving the characteristic value to obtain the oscillation mode of the system, wherein the leading mode is the mode closest to the virtual axis in the oscillation mode and plays a leading role in system response, and the leading mode solving expression is as follows:
Figure BDA0003575995830000052
in the formula (8), n is the nth oscillation mode with real part not being zero, D sys Coefficient matrix A of DC micro-grid system sys Characteristic root matrix of (n) 1 Root matrix D of features for dominant mode sys Position of (5), R (n) 1 ) And I (n) 1 ) Being the real and imaginary parts of the dominant mode, D M Coordinates that are the dominant modality;
s2-2: carrying out coupling analysis of a participation factor method on the dominant mode:
in order to research the relation between the dominant mode and the state variable, the influence degree of the state variable on the dominant mode is decoupled by a participatory factor method, and a mechanism influencing the stable operation characteristic of the system is obtained, wherein the expression is as follows:
Figure BDA0003575995830000053
in formula (9), pa (k, n) 1 ) To the extent that the state variable k affects the dominant modality,
Figure BDA0003575995830000054
is the k-th position in the left eigenvector of the system state matrix, phi (n) 1 K) is the kth position in the right eigenvector of the system state matrix;
introducing a state variable participation degree evaluation index eta on the basis of participation factor analysis k After the participation degree of the state variable k on the dominant mode is comprehensively considered for all the state variables, the expression is as follows:
Figure BDA0003575995830000061
further, the step S3 is as follows:
s3-1: determining parameters of the direct current micro-grid system needing to be optimized as population particles, and specifying upper and lower limits of the particles;
s3-2: setting maximum iteration times, population scale and penalty function; because of constraint relation among system parameters, the parameters can not be randomly selected, so a penalty function is defined to solve the problem of constraint conditions, and the objective function and the penalty function are as follows:
Figure BDA0003575995830000062
in the formula (11), f 1 (X) fitness of the objective function before penalty, f 2 (X) is the fitness of the objective function after punishment, P is a punishment coefficient, and P is X To constrain real-time values of variables, P ref Is a parameter constraint condition;
s3-3: performing vertical interleaving to generate a child population, wherein the vertical interleaving process is an arithmetic operation for interleaving particles with different dimensions:
X zc (i,d 1 )＝r·X(i,d 1 )+(1-r)·X(i,d 2 )+c·(X(i,d 1 )-X(i,d 2 )) (12)
in the formula (12), r is a random number between 0 and 1, c is a random number between 0 and 1, and X (i, d) 1 ) And X (i, d) 2 ) Being a parent of different dimensions, X zc (i,d 1 ) Offspring generated for longitudinal intersection of parents of different dimensions;
s3-4: substituting the population particles into a coefficient matrix A of the direct-current micro-grid system sys Solving the objective function value, checking whether constraint conditions are met, and if so, carrying out the next step; otherwise, adding a penalty function to the particle for calculation, and performing the step S3-5;
s3-5: executing a competition operator, storing the population particles with the best current fitness, wherein the competition operator is a mechanism for performing the relative elimination of parent generation and offspring generation, comparing the fitness of the parent generation and the offspring generation, and keeping the particles with stronger fitness to participate in the next iteration, so that the aim of making the whole population move towards the best direction is finally achieved;
s3-6: performing a horizontal crossing to generate a progeny population, wherein the horizontal crossing is an arithmetic operation for crossing all particles with different solutions, and performing steps S3-4 and S3-5:
Figure BDA0003575995830000063
in the formula (13), r 1 And r 2 Is a random number between 0 and 1, c 1 And c 2 Is a random number between-1 and 1, X (i, d) and X (j, d) are two different parent solutions, X hc (i, d) and X hc (j, d) child solutions generated by transversely crossing parent solutions;
s3-7: checking whether the maximum iteration times are reached, if so, selecting the population particles with the best fitness as the system trend optimal solution, and ending the iteration; otherwise, go to step S3-3.
Compared with the prior art, the principle and the advantages of the scheme are as follows:
according to the scheme, a small signal model of the multi-source multi-load direct-current micro-grid system is established, a dominant mode of the system is solved through a characteristic root analysis method, the influence degree of a state variable on the dominant mode is decoupled through a participation factor method, a vertical and horizontal cross algorithm is applied to stability analysis of the direct-current micro-grid, the optimization-oriented parameters are obtained to achieve the optimal stability of the system, the direct-current micro-grid has larger stability margin, and stability optimization-oriented control is achieved.
According to the scheme, the advantage that the vertical and horizontal cross algorithm can realize global parallel search and high convergence speed is utilized, the optimization approach solution of the parameters can be obtained quickly, the influence of the local solution of the parameters on stability analysis is effectively avoided, the direct-current micro-grid has the stability margin as large as possible, and stability optimization approach control is realized.
Drawings
Fig. 1 is a flow chart of the optimization trend control of the stability of the direct current microgrid in the embodiment of the invention;
FIG. 2 is a topological structure and a control block diagram of a multi-source multi-load direct-current micro-grid system in the embodiment of the invention;
FIG. 3 is a characteristic root analysis diagram of the DC micro-grid system in an embodiment of the invention;
FIG. 4 is a graph illustrating a droop coefficient optimization control curve according to an embodiment of the present invention;
FIG. 5 is a graph of source side line parameter optimization-seeking control curves in an embodiment of the present invention;
FIG. 6 is a graph showing the change of the voltage waveform of the DC bus before and after the droop coefficient control in the embodiment of the present invention;
fig. 7 is a diagram illustrating voltage waveform changes of the dc bus before and after the control of the source side line parameters according to the embodiment of the present invention.
Detailed Description
The invention is further illustrated by the following specific examples:
fig. 1 shows a stability optimization control flow chart of a direct current microgrid, and fig. 2 shows a topological structure and a control block diagram of a multi-source multi-load direct current microgrid system, and the stability optimization control method of the direct current microgrid based on a crossbar algorithm in the embodiment includes the following steps:
s1: solving a small signal model of the multi-source multi-load direct current micro-grid system; the specific process is as follows:
s1-1: small signal model of power module:
the power module utilizes a bidirectional DC/DC converter to perform voltage conversion, adopts a droop control method and a virtual inertia control method, wherein the droop control method ensures power equalization among multiple power supplies, the virtual inertia control method is a working principle similar to a capacitor, and aims to improve the voltage inertia of a direct-current bus and improve the dynamic performance when the voltage changes, and the state space model of the power module is as follows:
Figure BDA0003575995830000081
in the formula (14), d is the duty ratio of the bidirectional DC/DC converter in the power module, u b 、u oN And u o For the pre-conversion voltage, the post-conversion rated voltage and the post-conversion outlet voltage, i, of the bidirectional DC/DC converter in the power supply module b And i bref For a pre-conversion current and its reference value, i, of a bidirectional DC/DC converter in a power supply module o For the outlet current, R, after conversion by a bidirectional DC/DC converter in a power supply module b 、L b And C s Parasitic resistance, filter inductance and support capacitance of the power supply module, S u Rated voltage u converted by bidirectional DC/DC converter in power module oN And an outlet voltage u o The squared difference of (a) is passed through a first-order inertia element and then a variable, k, is output p And k i Proportional and integral coefficients, S, for power module PI controllers i Current reference value i before conversion for bidirectional DC/DC converter in power module bref And current i b The difference is output as a variable k after an integration step droop Is the sag factor, C virb The method is characterized in that a small signal model of a power supply module is obtained by linearizing a formula (1) in the vicinity of a steady state, wherein the model is a virtual inertia coefficient, T is a time constant, and s is a Laplace transform complex variable operator:
Figure BDA0003575995830000082
in the formula (15), Δ x b Being the state vector of the power supply module, Δ x b ＝[Δi b ,ΔS u ,ΔS i ,Δu o ] T ，Δi b Current i before conversion for bidirectional DC/DC converter in power module b State variable of, Δ S u Rated voltage u converted by bidirectional DC/DC converter in power module oN And an outlet voltage u o The squared difference of the first-order inertia element outputs a variable S u State variable of, Δ S i Current reference value i before conversion for bidirectional DC/DC converter in power module bref And current i b The difference is output as variable S after integral link i State variable of (1), Δ u o For the outlet voltage u after conversion of the bidirectional DC/DC converter in the power supply module o A state variable of b As a coefficient matrix of the power supply module, d 0 Is a steady-state quantity, u, of the duty cycle d of a bidirectional DC/DC converter in a power supply module o0 After being converted by a bidirectional DC/DC converter in a power supply moduleOutlet voltage u o Steady state quantity of i b0 Current i before conversion for bidirectional DC/DC converter in power module b A steady state quantity of;
s1-2: small signal model of constant power load module:
the constant power load module utilizes a Buck converter to carry out voltage conversion, a voltage-current double-loop control strategy is adopted, and a state space model of the constant power load module is as follows:
Figure BDA0003575995830000091
in the formula (16), g is the duty ratio of the Buck converter in the constant power load module, and u is F 、u LN And u L For the conversion of forward port voltage, constant power load rated voltage and constant power load actual voltage, i dc Conversion of forward port current, i, for Buck converters in constant-power load modules L And i Lref Is a constant power load current and its reference value, P L For constant power load power, R L 、L L And C L Parasitic resistance, filter inductance and filter capacitance of constant power load module, C F Supporting capacitor, k, for constant power load module pL_u And k iL_u Proportional and integral coefficients, k, of an outer loop PI controller for constant power load module voltage pL_i And k iL_i Proportional and integral coefficients of a constant power load module current inner loop PI controller, S uL And S iL Outputting variables for an integral link of a constant power load module voltage outer loop PI controller and a current inner loop PI controller, wherein a small signal model of the constant power load module is as follows:
Figure BDA0003575995830000092
in the formula (17), Δ x L Is the state vector of the constant-power load module, Δ x L ＝[Δu F ,Δi L ,Δu L ,ΔS uL ,ΔS iL ] T ，Δu F Conversion of forward port voltage u for Buck converter in constant power load module F State variable of, Δ i L Is a constant power load current i L State variable of (1), Δ u L Is the actual voltage u of the load with constant power L State variable of, Δ S uL Outputting variable S for integral link of constant power load module voltage outer loop PI controller uL State variable of, Δ S iL Outputting variable S for integral link of constant power load module current inner loop PI controller iL A state variable of L Is a coefficient matrix of the constant power load module, g 0 Is the steady-state quantity u of the duty ratio g of the Buck converter in the constant-power load module F0 Conversion of forward port voltage u for Buck converter in constant power load module F Steady state quantity of i L0 Is a constant power load current i L A steady state quantity of;
s1-3: small signal model of the direct current transmission line:
a direct current transmission line is arranged between the power module and the constant power load module, and the state space model of the direct current transmission line is as follows:
Figure BDA0003575995830000101
in the formula (18), u DC And C DC For collecting bus voltage and supporting capacitance, R s And L s Resistance and inductance of the source side transmission line, R F And L F The small signal model of the direct current transmission line is as follows:
Figure BDA0003575995830000102
in the formula (19), Δ x d Is the state vector, Δ x, of the DC transmission line d ＝[Δu o ,Δi o ,Δu DC ,Δi dc ,Δu F ] T ，Δi o For the outlet current i after conversion of a bidirectional DC/DC converter in a power supply module o State variable of (a), Δ u DC To convergeBus voltage u DC State variable of, Δ i dc Conversion of forward port current i for Buck converter in constant power load module dc State variable of (D) d A coefficient matrix of the direct current transmission line;
s1-4: a small signal model of the direct-current micro-grid system:
the direct-current microgrid system is composed of three power modules, three direct-current transmission lines and three constant-power load modules, the structure is of a conventional radiation type, the total length of the transmission lines on the source side and the load side is set to be a certain value and is marked as 1, and the lengths of the transmission lines from the power modules 1,2 and 3 to a convergence bus are respectively marked as l b1 、l b2 、l b3 The lengths from the convergent bus to the constant power load modules 1,2 and 3 are respectively l L1 、l L2 、l L3 The small signal model of the system is:
Figure BDA0003575995830000111
in the formula (20), Δ x sys Is a state vector of the DC micro-grid system, Δ x sys ＝[Δx bn ,Δx d123 ,Δx Ln ] T ，Δx bn Is the state vector of three power supply modules, n =1,2,3, Δ x Ln Is the state vector of three constant power load modules, n =1,2,3, Δ x d123 Is the state vector of three DC transmission lines, Δ x d123 ＝[Δu on ,Δi on ,Δu DC ,Δi dcn ,Δu Fn ] T ，Δu on And Δ i on The outlet voltage u after conversion of the bidirectional DC/DC converter in the three power supply modules on And an outlet current i on N =1,2,3, Δ i dcn And Δ u Fn Conversion of forward port current i for Buck converter in three constant power load modules dcn And inlet voltage u Fn N =1,2,3,a sys Is a coefficient matrix of the DC microgrid system, A bn Coefficient matrix for three power supply modules, n =1,2,3, d d123 Series of three direct current transmission linesNumber matrix, A Ln A coefficient matrix of three constant power load modules, n =1,2,3;
step S2, a dominant mode of the system is obtained through a characteristic root analysis method, the influence degree of the state variable on the dominant mode is decoupled through a participation factor method, and the specific process is as follows:
s2-1: and (3) solving the dominant mode of the system through a characteristic root analysis method:
according to the coefficient matrix A of the direct current micro-grid system sys Solving the characteristic value to obtain the oscillation mode of the system, wherein the leading mode is the mode closest to the virtual axis in the oscillation mode and plays a leading role in system response, and the leading mode solving expression is as follows:
Figure BDA0003575995830000112
in the formula (21), n is the nth oscillation mode with real part not being zero, D sys Coefficient matrix A of DC micro-grid system sys Characteristic root matrix of (n) 1 Root matrix D of features for dominant mode sys Position of (5), R (n) 1 ) And I (n) 1 ) Are the real and imaginary parts of the dominant mode, D M Coordinates that are dominant modalities;
s2-2: carrying out decoupling analysis of a participation factor method on the dominant mode:
in order to research the relation between the dominant mode and the state variable, the influence degree of the state variable on the dominant mode is decoupled by a participatory factor method, and a mechanism influencing the stable operation characteristic of the system is obtained, wherein the expression is as follows:
Figure BDA0003575995830000121
in formula (22), pa (k, n) 1 ) To the extent that the state variable k affects the dominant modality,
Figure BDA0003575995830000122
is the k-th position in the left eigenvector of the system state matrix, phi (n) 1 K) is the kth position in the right eigenvector of the system state matrix;
introducing a state variable participation degree evaluation index eta on the basis of participation factor analysis k The participation degree of the state variable k to the dominant mode after the comprehensive consideration of all the state variables is expressed as follows:
Figure BDA0003575995830000123
step S3 is to apply the criss-cross algorithm to the stability analysis of the direct-current micro-grid, and the specific process is as follows:
s3-1: determining parameters of the direct current micro-grid system needing to be optimized as population particles, and specifying upper and lower limits of the particles;
s3-2: setting maximum iteration times, population scale and penalty function; because of the constraint relationship among the system parameters, the parameters can not be randomly selected, so a penalty function is defined to solve the problem of constraint conditions, and the target function and the penalty function are as follows:
Figure BDA0003575995830000124
in the formula (24), f 1 (X) target function fitness before penalty, f 2 (X) is the fitness of the objective function after punishment, P is a punishment coefficient, and P is X To constrain real-time values of variables, P ref Is a parameter constraint condition;
s3-3: performing vertical interleaving to generate a child population, wherein the vertical interleaving process is an arithmetic operation for interleaving particles with different dimensions:
X zc (i,d 1 )＝r·X(i,d 1 )+(1-r)·X(i,d 2 )+c·(X(i,d 1 )-X(i,d 2 )) (25)
in the formula (25), r is a random number between 0 and 1, c is a random number between 0 and 1, and X (i, d) 1 ) And X (i, d) 2 ) Being a parent of different dimensions, X zc (i,d 1 ) Child generation for longitudinal cross generation of parent generation with different dimensionality;
s3-4: substituting the population particles into a coefficient matrix A of the direct-current micro-grid system sys Solving the objective function value, checking whether constraint conditions are met, and if so, carrying out the next step; otherwise, adding a penalty function to the particle for calculation, and performing the step S3-5;
s3-5: executing a competition operator, storing the population particles with the best current fitness, wherein the competition operator is a mechanism for performing the relative elimination of parent generation and offspring generation, comparing the fitness of the parent generation and the offspring generation, and keeping the particles with stronger fitness to participate in the next iteration, so that the aim of making the whole population move towards the best direction is finally achieved;
s3-6: performing a horizontal crossing to generate a progeny population, wherein the horizontal crossing is an arithmetic operation for crossing all particles with different solutions, and performing steps S3-4 and S3-5:
Figure BDA0003575995830000125
in the formula (26), r 1 And r 2 Is a random number between 0 and 1, c 1 And c 2 Is a random number between-1 and 1, X (i, d) and X (j, d) are two different parent solutions, X hc (i, d) and X hc (j, d) child solutions generated by transversely crossing parent solutions;
s3-7: checking whether the maximum iteration times are reached, if so, selecting the population particles with the best fitness as the system trend optimal solution, and ending the iteration; otherwise, go to step S3-3.
In order to verify the effectiveness of the optimization-seeking control method, a direct-current micro-grid system model shown in the figure 2 is established on an RT-LAB experimental platform. The root-of-feature analysis of the dc microgrid system is depicted in fig. 3. Setting algorithm parameters: the iteration number is 200, the initial solution population size is 30, and the penalty coefficient is 0.5. The droop coefficient is used as an optimization-approaching control object, the voltage deviation of the direct current bus is 5% and is used as a constraint condition, the algorithm is used for solving the optimization-approaching solutions of the droop coefficient, namely 0.3903, 0.2077 and 0.3897, the droop coefficient optimization-approaching control curve is plotted in a graph of fig. 4, and the voltage waveform change of the direct current bus before and after control is plotted in a graph of fig. 6; the source side line parameters are taken as optimization-seeking control objects, the total length of the three source side lines is equal to 1 and taken as constraint conditions, the optimization-seeking solutions of the source side line parameters obtained by the algorithm are 0.5058, 0.4924 and 0.0018 respectively, the source side line parameter optimization-seeking control curve is plotted in fig. 5, and the voltage waveform change of the direct current bus before and after control is plotted in fig. 7.
As can be seen from fig. 3 to 7, in the implementation example, the real part of the dominant mode under the initial parameters of the system is-34.95, the real part of the dominant mode of the system after the droop coefficient optimization control is-49.92, the stability margin of the system is improved by 42.83% compared with the initial value, the best effect is achieved after iteration for 44 times, the oscillation degree of the dc bus voltage before control is larger, and the control is more stable; the real part of the dominant mode of the system after the optimization control of the source side line parameters is-42.62, the stability margin of the system is improved by 21.95% compared with the initial value, the optimal effect is achieved after 13 iterations, the direct current bus voltage oscillation degree before control is larger, and the control is more stable. The method shows that in the process of improving the stability of the direct-current micro-grid, the convergence speed of the criss-cross algorithm is high, the optimization approach solution of the parameters can be quickly obtained, the direct-current micro-grid has the stability margin as large as possible, and the stability optimization approach control is realized.
The above-mentioned embodiments are merely preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, so that variations based on the shape and principle of the present invention should be covered within the scope of the present invention.

Claims (3)

1. A DC micro-grid stability optimization control method based on a criss-cross algorithm is characterized by comprising the following steps:
s1: solving a small signal model of the multi-source multi-load direct current micro-grid system;
s2: the dominant mode of the system is solved through a characteristic root analysis method, and the influence degree of the state variable on the dominant mode is decoupled through a participation factor method;
s3: applying a criss-cross algorithm to stability analysis of the direct-current micro-grid to obtain optimization parameters to achieve the optimal stability of the system, so that the direct-current micro-grid has larger stability margin, and stability optimization control is realized;
in the step S1, the specific steps of solving the small signal model of the multi-source multi-load direct current micro-grid system are as follows:
s1-1: small signal model of power module:
the power module utilizes a bidirectional DC/DC converter to perform voltage conversion, adopts a droop control method and a virtual inertia control method, wherein the droop control method ensures power equalization among multiple power supplies, the virtual inertia control method is a working principle similar to a capacitor, and aims to improve the voltage inertia of a direct-current bus and improve the dynamic performance when the voltage changes, and the state space model of the power module is as follows:
Figure FDA0003905998760000011
in the formula (1), d is the duty ratio of the bidirectional DC/DC converter in the power module, u b 、u oN And u o For the pre-conversion voltage, the post-conversion rated voltage and the post-conversion outlet voltage, i, of the bidirectional DC/DC converter in the power supply module b And i bref For a pre-conversion current and its reference value, i, of a bidirectional DC/DC converter in a power supply module o For the outlet current, R, after conversion by a bidirectional DC/DC converter in a power supply module b 、L b And C s Parasitic resistance, filter inductance and support capacitance of the power supply module, S u Rated voltage u converted by bidirectional DC/DC converter in power module oN And an outlet voltage u o The squared difference of (a) is passed through a first-order inertia element and then a variable, k, is output p And k i Proportional and integral coefficients, S, for power module PI controllers i Pre-conversion current reference i for a bidirectional DC/DC converter in a power supply module bref And current i b The difference is output as a variable k after an integration step droop Is the sag factor, C virb The method is characterized in that a virtual inertia coefficient is adopted, T is a time constant, s is a Laplace transform complex variable operator, the equation (1) is linearized near a steady state, and a small signal model of a power module is obtained as follows:
Figure FDA0003905998760000021
in the formula (2), Δ x b Is the state vector of the power supply module, Δ x b ＝[Δi b ,ΔS u ,ΔS i ,Δu o ] T ，Δi b Current i before conversion for bidirectional DC/DC converter in power module b State variable of, Δ S u Rated voltage u converted by bidirectional DC/DC converter in power module oN And an outlet voltage u o The squared difference of the first order inertia element outputs a variable S u State variable of, Δ S i Current reference value i before conversion for bidirectional DC/DC converter in power module bref And current i b The difference is output as variable S after integral i State variable of (1), Δ u o For the outlet voltage u after conversion of the bidirectional DC/DC converter in the power supply module o A state variable of b As a coefficient matrix of the power supply module, d 0 Is a steady-state quantity u of the duty cycle d of a bidirectional DC/DC converter in the power supply module o0 For the outlet voltage u after conversion of a bidirectional DC/DC converter in a power supply module o Steady state quantity of (ii), i b0 Current i before conversion for bidirectional DC/DC converter in power module b A steady state quantity of;
s1-2: small signal model of constant power load module:
the constant power load module utilizes a Buck converter to carry out voltage conversion, a voltage-current double-loop control strategy is adopted, and a state space model of the constant power load module is as follows:
Figure FDA0003905998760000022
in the formula (3), g is the duty ratio of the Buck converter in the constant-power load module, and u is F 、u LN And u L For the conversion of forward port voltage, constant power load rated voltage and constant power load actual voltage, i dc Conversion of forward port current, i, for Buck converters in constant-power load modules L And i Lref For constant power load current and its reference value, P L Is of constant powerLoad power, R L 、L L And C L Parasitic resistance, filter inductance and filter capacitance of constant power load module, C F Supporting capacitor, k, for constant power load module pL_u And k iL_u Proportional and integral coefficients, k, of an outer loop PI controller for constant power load module voltage pL_i And k iL_i Proportional and integral coefficients, S, of a constant-power load module current inner loop PI controller uL And S iL Outputting variables for integral links of a voltage outer loop PI controller and a current inner loop PI controller of a constant power load module, wherein a small signal model of the constant power load module is as follows:
Figure FDA0003905998760000031
in the formula (4), Δ x L Is the state vector of the constant-power load module, Δ x L ＝[Δu F ,Δi L ,Δu L ,ΔS uL ,ΔS iL ] T ，Δu F Conversion of forward port voltage u for Buck converter in constant power load module F State variable of, Δ i L Is a constant power load current i L State variable of (a), Δ u L Is a constant power load actual voltage u L State variable of (a), Δ S uL Outputting variable S for integral link of constant power load module voltage outer loop PI controller uL State variable of, Δ S iL Output variable S for integral link of constant power load module current inner loop PI controller iL A state variable of L Is a coefficient matrix of the constant power load module, g 0 Is the steady-state quantity u of the duty ratio g of the Buck converter in the constant-power load module F0 Conversion of forward port voltage u for Buck converter in constant power load module F Steady state quantity of i L0 Is a constant power load current i L A steady state quantity of;
s1-3: small signal model of the direct current transmission line:
a direct current transmission line is arranged between the power module and the constant power load module, and the state space model of the direct current transmission line is as follows:
Figure FDA0003905998760000032
in the formula (5), u DC And C DC For collecting bus voltage and supporting capacitance, R s And L s Resistance and inductance of the source side transmission line, R F And L F The small signal model of the direct current transmission line is as follows:
Figure FDA0003905998760000041
in the formula (6), Δ x d Is the state vector of the DC transmission line, Δ x d ＝[Δu o ,Δi o ,Δu DC ,Δi dc ,Δu F ] T ，Δi o For the outlet current i after conversion of a bidirectional DC/DC converter in a power supply module o State variable of (1), Δ u DC For converging bus voltage u DC State variable of, Δ i dc Conversion of forward port current i for Buck converter in constant power load module dc State variable of (D) d A coefficient matrix of the direct current transmission line;
s1-4: a small signal model of the direct-current micro-grid system:
the direct-current micro-grid system is composed of three power modules, three direct-current transmission lines and three constant-power load modules, the structure is in a conventional radiation type, the total length of the transmission lines on the source side and the load side is set to be a certain value and is marked as 1, and the lengths of the transmission lines from the power modules 1,2 and 3 to a convergence bus are respectively l b1 、l b2 、l b3 The lengths from the convergent bus to the constant power load modules 1,2 and 3 are respectively l L1 、l L2 、l L3 The small signal model of the system is:
Figure FDA0003905998760000042
in the formula (7), Δ x sys Is a state vector of the DC micro-grid system, Δ x sys ＝[Δx bn ,Δx d123 ,Δx Ln ] T ，Δx bn Is the state vector of three power supply modules, n =1,2,3, Δ x Ln Is the state vector of three constant power load modules, n =1,2,3, Δ x d123 State vectors, Δ x, for three direct current transmission lines d123 ＝[Δu on ,Δi on ,Δu DC ,Δi dcn ,Δu Fn ] T ，Δu on And Δ i on Outlet voltage u converted by bidirectional DC/DC converter in three power supply modules on And outlet current i on N =1,2,3, Δ i dcn And Δ u Fn Conversion of forward port current i for Buck converter in three constant power load modules dcn And inlet voltage u Fn N =1,2,3,a sys Is a coefficient matrix of the DC micro-grid system, A bn Coefficient matrix for three power supply modules, n =1,2,3, D d123 Coefficient matrices for three DC transmission lines, A Ln N =1,2,3, a matrix of coefficients for three constant power load modules.
2. The method for controlling the trend of the stability of the direct-current microgrid based on the criss-cross algorithm of claim 1 is characterized in that the step S2 is used for solving a dominant mode of a system through a characteristic root analysis method, and decoupling the degree of influence of a state variable on the dominant mode through a participation factor method; the specific steps of step S2 are as follows:
s2-1: and (3) solving the dominant mode of the system through a characteristic root analysis method:
according to the coefficient matrix A of the direct current micro-grid system sys Solving the characteristic value to obtain the oscillation mode of the system, wherein the leading mode is the mode closest to the virtual axis in the oscillation mode and plays a leading role in system response, and the leading mode solving expression is as follows:
Figure FDA0003905998760000051
in the formula (8), n is the nth oscillation mode with real part not being zero, D sys Coefficient matrix A of DC micro-grid system sys Characteristic root matrix of (n) 1 Root matrix D of features for dominant mode sys Position of (5), R (n) 1 ) And I (n) 1 ) Being the real and imaginary parts of the dominant mode, D M Coordinates that are dominant modalities;
s2-2: carrying out coupling analysis of a participation factor method on the dominant mode:
in order to research the relation between the dominant mode and the state variable, the influence degree of the state variable on the dominant mode is decoupled by a participatory factor method, and a mechanism influencing the stable operation characteristic of the system is obtained, wherein the expression is as follows:
Figure FDA0003905998760000052
in formula (9), pa (k, n) 1 ) To the extent that the state variable k affects the dominant modality,
Figure FDA0003905998760000053
is the k-th position in the left eigenvector of the system state matrix, phi (n) 1 K) is the kth position in the right eigenvector of the system state matrix;
introducing a state variable participation degree evaluation index eta on the basis of participation factor analysis k The participation degree of the state variable k to the dominant mode after the comprehensive consideration of all the state variables is expressed as follows:
Figure FDA0003905998760000054
3. the method for controlling the trend of the stability of the direct-current microgrid based on the crisscross algorithm of claim 2, wherein the step S3 of applying the crisscross algorithm to the stability analysis of the direct-current microgrid comprises the following specific steps:
s3-1: determining parameters of the direct current micro-grid system needing to be optimized as population particles, and specifying upper and lower limits of the particles;
s3-2: setting maximum iteration times, population scale and penalty function; because of constraint relation among system parameters, the parameters can not be randomly selected, so a penalty function is defined to solve the problem of constraint conditions, and the objective function and the penalty function are as follows:
Figure FDA0003905998760000061
in the formula (11), f 1 (X) target function fitness before penalty, f 2 (X) is the fitness of the objective function after punishment, P is a punishment coefficient, and P is X To constrain real-time values of variables, P ref Is a parameter constraint condition;
s3-3: performing vertical interleaving to generate a filial population, wherein the vertical interleaving process is an arithmetic operation for interleaving particles with different dimensions:
X zc (i,d 1 )＝r·X(i,d 1 )+(1-r)·X(i,d 2 )+c·(X(i,d 1 )-X(i,d 2 )) (12)
in the formula (12), r is a random number between 0 and 1, c is a random number between 0 and 1, and X (i, d) 1 ) And X (i, d) 2 ) Being a parent of different dimensions, X zc (i,d 1 ) Offspring generated for longitudinal intersection of parents of different dimensions;
s3-4: substituting the population particles into a coefficient matrix A of the direct-current micro-grid system sys Solving the objective function value, checking whether constraint conditions are met, and if so, carrying out the next step; otherwise, adding a penalty function to the particle for calculation, and performing the step S3-5;
s3-5: executing a competition operator, storing the population particles with the best current fitness, wherein the competition operator is a mechanism for performing the relative elimination of parent generation and offspring generation, comparing the fitness of the parent generation and the offspring generation, and keeping the particles with stronger fitness to participate in the next iteration, so that the aim of making the whole population move towards the best direction is finally achieved;
s3-6: performing a horizontal crossing to generate a progeny population, wherein the horizontal crossing is an arithmetic operation for crossing all particles with different solutions, and performing steps S3-4 and S3-5:
Figure FDA0003905998760000062
in the formula (13), r 1 And r 2 Is a random number between 0 and 1, c 1 And c 2 Is a random number between-1 and 1, X (i, d) and X (j, d) are two different parent solutions, X hc (i, d) and X hc (j, d) child solutions generated by transversely crossing parent solutions;
s3-7: checking whether the maximum iteration times are reached, if so, selecting the population particles with the best fitness as a system trend optimal solution, and ending the iteration; otherwise, go to step S3-3.
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