CN109066784A - A kind of micro-capacitance sensor stability control method based on bifurcation theory - Google Patents
A kind of micro-capacitance sensor stability control method based on bifurcation theory Download PDFInfo
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Abstract
The invention discloses a kind of micro-capacitance sensor stability control method based on bifurcation theory, comprising: according to micro-capacitance sensor circuit structure and electrical relation, establish the state equation of each distributed generation resource, transmission line of electricity and load respectively；Consider the frequency difference between the frequency difference and distributed generation resource and bulk power grid between distributed generation resource, establishes and consider that the micro-capacitance sensor of distributed generation resource output difference unifies state space equation；Under the unified state space equation of foundation, the leading factor for influencing micro-capacitance sensor stability is determined；When being changed based on bifurcation theory tracking leading factor, the equilibrium solution of micro-capacitance sensor steady operational status is popular, and then determines the boundary condition of micro-capacitance sensor stable operation.The dynamic characteristic of accurate description system of the present invention, the deficiency of Small Perturbation Analysis can only be used by compensating for current research；Whether occur the condition that bifurcation point determines system stable operation in parameter change by detection system, solves stability control method in the limitation of analysis high order system stability.
Description
Technical Field
The invention belongs to the technical field of microgrid control, and particularly relates to a microgrid stability control method based on a bifurcation theory.
Background
Currently, under the dual pressure of energy demand and environmental protection, a distributed power generation technology using clean and renewable energy has become a research hotspot at home and abroad. Most distributed power supplies have the characteristics of volatility and intermittence, and in order to realize access and consumption of large-scale distributed power supplies, the traditional control method cannot meet the requirements of users on power utilization reliability and safety, and the introduction of power electronic devices can aggravate the nonlinear characteristics of a power distribution network, so that the stability analysis of a micro-grid system becomes more difficult.
The micro-grid introduces a large number of power electronic devices, and the introduction of power electronic devices can aggravate the nonlinear characteristics of a power distribution network, so that the stability analysis of the micro-grid system becomes more difficult. Therefore, compared with the traditional generator set, the micro-grid inertia link is lost, and the stability performance is poor. The microgrid is a typical nonlinear power system, a stability controller of the microgrid is similar to a linear optimal controller, and the operation state of the microgrid is mostly selected to be linearly processed near the stable operation state of the microgrid, so that the result of stability analysis is more accurate only when the operation state of the microgrid is near; in other words, the method is only suitable for analyzing small disturbances near the balance point, and cannot well meet the requirement that the micro-grid keeps stable when large disturbances occur; meanwhile, the traditional stability control method such as the Lyapunov energy function method has the problem that the energy function is difficult to determine when the high-order nonlinear state space equation is faced. Theories and practices prove that the bifurcation theory is a powerful method for researching the nonlinear power system.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to solve the technical problems that the stability control method of the microgrid in the prior art cannot well meet the requirements of large disturbance of the microgrid and the difficulty in determining the high-order nonlinear state space equation energy function.
In order to achieve the above object, in one aspect, an embodiment of the present invention provides a microgrid stability control method based on a bifurcation theory, including the following steps:
s1, respectively establishing state equations of each distributed power supply, each power transmission line and each load according to a micro-grid circuit structure and an electrical relation;
s2, considering frequency difference among the distributed power supplies and frequency difference between the distributed power supplies and a large power grid, and establishing a micro-grid unified state space equation considering output difference of the distributed power supplies;
s3, determining dominant factors influencing the stability of the microgrid under the established unified state space equation;
and S4, tracking the change of the leading factors based on the bifurcation theory, wherein the balance solution of the stable operation state of the micro-grid is popular, and further determining the boundary condition of the stable operation of the micro-grid.
Specifically, the state equation of each transmission line and load is as follows:
wherein L isline_i、Rline_iThe inductive reactance and impedance, L, of the ith transmission lineload_i、Rload_iThe inductive reactance and the impedance of the ith load respectively; i.e. ilineD_i、ilineQ_iFor current i of ith transmission lineline_iD-axis, Q-axis components of (a); i.e. iloadD_i、iloadQ_iIs the current i of the ith loadload_iD-axis, Q-axis components of (a); w represents the angular velocity of the distributed power supply output voltage; u. ofoD_i、uoQ_iRespectively is the filtered output voltage u of the inverter in the ith distributed power supplyoiThe D-axis and Q-axis components of (1, 2) ·, and n, n are the number of distributed power sources in the microgrid.
Specifically, the distributed power supply is composed of a direct-current voltage source, a controller and a filter, and the state equation of the filter is as follows:
wherein Ls and C are respectively a filter inductor and a filter capacitor of the LC filter, iiD、iiQRespectively output current i for inverteriD-axis, Q-axis component of (u)iD、uiQRespectively an inverter output voltage uiD-axis, Q-axis component of (u)oD_i、uoQ_iRespectively is the filtered output voltage u of the inverter in the ith distributed power supplyoiD-axis, Q-axis component of (i)oD_i、ioQ_iRespectively is the filtered output current i of the inverter in the ith distributed power supplyoiThe component of D axis and Q axis, i is 1, 2.
Specifically, the controller comprises a power frequency controller and an excitation controller;
the control equation of the power frequency controller is as follows:
the control equation of the excitation controller is as follows:
u＝Mif·w
wherein,is a frequency reference value, e*For inverter voltage reference signal, P*And Q*Respectively an input active power reference value and a reactive power reference value, J, KpRespectively, the inertia constant of the frequency and the droop coefficient of the frequency, P is the actual active power of the line, Q is the actual reactive power of the line, and TeFor distributed power output torque, θ is the phase angle of the inverter output voltage, KqIs the voltage droop coefficient, K is the inertia constant of the voltage, MifTo simulate the magnetic flux in a synchronous generator, u is the magnitude of the inverter output voltage.
Specifically, step S2 specifically includes:
selecting a DQ coordinate system as a public DQ coordinate system, and converting other DQ coordinate systems into the public DQ coordinate system, wherein the conversion formula is as follows:
wherein,advancing the phase angle, w, of the common DQ axis for the kth inverter DQ axiskIs the k inverter DQ shaft angular velocity, w is the common DQ shaft angular velocity, α is the angle of large Grid leading the common DQ shaft, wgridFor large grid voltage angular velocity, fD、fQThe electrical quantities before conversion are D-axis and Q-axis components, FD、FQThe converted electrical quantity D axis component and Q axis component are respectively;
the microgrid unified state space equation is represented by the following formula:
y＝g(x)
where x represents a system state variable, y represents an intermediate variable, β is a system parameter,is the derivative of the system state variable x.
Specifically, step S3 specifically includes:
s301, carrying out linearization processing on the unified state space equation of the micro-grid to obtain a feature matrix A obtained after linearization;
s302, according to left and right eigenvector arrays u and v of the feature matrix A obtained after linearization, constructing a participation factor matrix P of a matrix feature root and a matrix element P of a participation factorijRepresents the ith state variable xiFor j characteristic root lambda of state equationjThe effect of the size of the particles,
λ1… λj… λn
and S303, performing per-unit processing on each column of the participation factor matrix, wherein the larger the participation factor is, the larger the influence of the state variable on the characteristic root is, and the dominant factor influencing the system stability can be determined by comparing the sizes of the participation factors.
Specifically, step S4 specifically includes:
s401, changing leading factors of a system, continuously tracking the balance solution popularity of the system by utilizing a homotopy continuation method, and obtaining a balance curve when the running state of the system changes along with parameters;
s402, linearizing the running state of the micro-grid system at a balance point according to the obtained system balance solution popularity;
s403, solving a characteristic value of a characteristic equation;
s404, judging whether the balance point (x, β) is a bifurcation point in the existing state by continuously judging whether the real part of the eigenvalue of the characteristic root matrix is positive, wherein the value of the system parameter β is a stable boundary condition when the bifurcation point occurs.
Specifically, the saddle node is branched into:
wherein x represents system state variable, g (x) represents intermediate variable, β represents system parameter, A represents characteristic matrix obtained after linearization, q represents characteristic vector, q represents intermediate variable0Is a given vector, which is normalized to the feature vector q.
Specifically, the hopplev branches include:
wherein x represents a system state variable, g (x) represents an intermediate variable, β represents a system parameter, A represents a characteristic matrix obtained after linearization, q represents a characteristic vector, Aq ═ j χ represents that a pair of conjugate solutions of the equation occur, q represents a conjugate solution of the equation, and q represents a conjugate solution of the equation0Is a given vector, which is normalized to the feature vector q.
In order to achieve the above object, in another aspect, the embodiment of the present invention provides a computer-readable storage medium, on which a computer program is stored, and the computer program, when executed by a processor, implements the microgrid stability control method as described above.
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
(1) according to the method, the frequency difference between the distributed power supplies and the main power grid is considered, a uniform space state equation of the micro-grid comprising the distributed power supplies, the power transmission lines and the loads is established, the dynamic characteristics of the system can be accurately described, and the defect that only a small-disturbance analysis method can be adopted in the current research is overcome;
(2) the stability analysis based on the bifurcation theory can determine the dominant factors influencing the system stability; meanwhile, the balance solution popularity of the system can be tracked when the system parameters are changed, and the limitation of the traditional stability control method in analyzing the stability of a high-order system is solved by detecting whether a bifurcation point occurs when the system parameters are changed to determine the stable operation condition of the system.
Drawings
FIG. 1 is a schematic diagram of a microgrid topology provided by the present invention;
FIG. 2 shows a distributed generation DG according to an embodiment of the present inventioniA circuit topology schematic;
fig. 3 is a schematic structural diagram of a power frequency controller and an excitation controller according to an embodiment of the present invention, where fig. 3(a) is the power frequency controller, and fig. 3(b) is the excitation controller;
fig. 4 is a unified coordinate transformation diagram established in consideration of frequency differences of various electrical quantities according to an embodiment of the present invention;
FIG. 5 is a diagram of a distributed microgrid architecture for validation provided by the present invention;
FIG. 6 is a schematic diagram of a characteristic root distribution of a Jacobian matrix A;
fig. 7 is a graph showing the balance of the bifurcation parameter varying system, fig. 7(a) is a graph showing the balance of the bifurcation parameter J varying system, fig. 7(b) is a graph showing the balance of the bifurcation parameter K varying system, and fig. 7(c) is a graph showing the balance of the bifurcation parameter Ls varying system;
fig. 8 is a characteristic root distribution diagram of different bifurcation parameters, fig. 8(a) is a characteristic root distribution diagram with J being 10000, fig. 8(b) is a characteristic root distribution diagram with K being 1839, and fig. 8(c) is a characteristic root distribution diagram with Ls being 22.34;
fig. 9 is a graph of a voltage angular velocity curve of a distributed power supply and a D-axis voltage output by the distributed power supply after filtering according to the embodiment of the present invention, where fig. 9(a) is a graph of a voltage angular velocity curve of a distributed power supply after filtering, and fig. 9(b) is a graph of a voltage angular velocity curve of a distributed power supply;
fig. 10 is a graph of active and reactive power output of a distributed power supply according to an embodiment of the present invention, fig. 10(a) is a graph of active power output of the distributed power supply, and fig. 10(b) is a graph of reactive power output of the distributed power supply.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
A micro-grid stability control method based on a bifurcation theory comprises the following steps:
s1, respectively establishing state equations of each distributed power supply, each power transmission line and each load according to a micro-grid circuit structure and an electrical relation;
s2, considering frequency difference among the distributed power supplies and frequency difference between the distributed power supplies and a large power grid, and establishing a micro-grid unified state space equation considering output difference of the distributed power supplies;
s3, determining dominant factors influencing the stability of the microgrid under the established unified state space equation;
and S4, tracking the change of the leading factors based on the bifurcation theory, wherein the balance solution of the stable operation state of the micro-grid is popular, and further determining the boundary condition of the stable operation of the micro-grid.
S1, respectively establishing state equations of each distributed power source, each power transmission line and each load according to the micro-grid circuit structure and the electrical relation.
Fig. 1 is a schematic diagram of a topology of a microgrid structure provided by the present invention. As shown in fig. 1, the microgrid is composed of n distributed power sources DG1、DG2……DGnThe power transmission line, the load and the large power Grid. And respectively establishing state equations of each distributed power supply, each power transmission line and each load through the micro-grid circuit structure and the electrical relationship. The state equation of the transmission line and the load is as follows:
wherein L isline_i、Rline_iThe inductive reactance and impedance, L, of the ith transmission lineload_i、Rload_iThe inductive reactance and the impedance of the ith load respectively; i.e. ilineD_i、ilineQ_iFor current i of ith transmission lineline_iD-axis, Q-axis components of (a); i.e. iloadD_i、iloadQ_iIs the current i of the ith loadload_iD-axis, Q-axis components of (a); w represents the angular velocity of the distributed power supply output voltage; u. ofoD_i、uoQ_iRespectively is the filtered output voltage u of the inverter in the ith distributed power supplyoiD-axis, Q-axis components.
Considering kirchhoff's current law for each node i, a constraint equation for each node can be obtained:
ioi＝iline_i+iload_ii＝1
ioi＝iline_i-iline_i-1+iload_i1<i＜n
ioi＝igrid-iline_i-1+iload_ii＝n
wherein ioiThe current output for the ith distributed power supply; i.e. igridIs the current flowing through the large grid.
FIG. 2 shows a distributed generation DG according to an embodiment of the present inventioniA circuit topology schematic. The distributed power supply comprises a direct-current voltage source, a controller and a filter. As shown in fig. 2, the DC side is a distributed power supply, and for simplification of analysis, the main circuit is replaced by a DC voltage source, a DC/AC three-phase voltage-type inverter is used, and PWM rectification is used. U shapedcIs a direct current voltage, Ls,C is a filter inductor and a filter capacitor of the LC filter respectively and is used for reducing ripples caused by the closing of the switch,and e is a frequency reference value, e is an inverter voltage reference signal, and P and Q are an input active power reference value and a reactive power reference value respectively.
The controller comprises a power frequency controller and an excitation controller for receiving basic information of each line and given P*、Q*、e*、A signal is generated based on the control equation for controlling the switching of the switches in the inverter.
Inverter output voltage uiOutput current iiObtaining filtered output voltage u by LC filteroiAnd an output current ioi. The state equation of the filter is as follows:
fig. 3 is a schematic structural diagram of a power frequency controller and an excitation controller according to an embodiment of the present invention, where fig. 3(a) is the power frequency controller, and fig. 3(b) is the excitation controller. The power frequency controller mainly simulates the equation of motion of the rotor of the synchronous generator, the mathematicsThe establishment of the model aims to make the distributed power supply have the basic characteristics of a synchronous generator, and does not expect to introduce too many transient processes of the synchronous generator, so a second-order model of the synchronous generator is adopted. As shown in fig. 3(a), the power frequency controller is used to control the power frequency according to the active power reference value P of the line*And distributed power supply output torque TeAnd obtaining the phase angle theta of the output voltage of the inverter. As shown in fig. 3(b), the excitation controller is adapted to reference Q the reactive power of the line according to its value*And obtaining the amplitude u of the output voltage of the inverter by the actual reactive power Q of the line.
The control equation of the power frequency controller is as follows:
wherein,
control equation of the excitation controller:
wherein u is Mif·w，
Wherein, J, KpRespectively, the inertia constant of the frequency and the droop coefficient of the frequency, P is the actual active power of the line, KqIs the voltage droop coefficient, K is the inertia constant of the voltage, MifTo simulate the magnetic flux in a synchronous generator, iiD、iiQRespectively output current i for inverteriD-axis, Q-axis components.
And S2, considering the frequency difference between the distributed power supplies and the large power grid, and establishing a micro-grid unified state space equation considering the output difference of the distributed power supplies.
Fig. 4 is a unified coordinate transformation diagram established in consideration of frequency differences of the electrical quantities according to an embodiment of the present invention. As shown in fig. 4, when considering that the microgrid includes a plurality of distributed power sources, it is necessary to unify the DQ axes, select a common DQ coordinate system, and establish a unified spatial coordinate:
wherein,advancing the phase angle, w, of the common DQ axis for the kth inverter DQ axiskIs the k inverter DQ shaft angular velocity, w is the common DQ shaft angular velocity, α is the angle of large Grid leading the common DQ shaft, wgridFor large grid voltage angular velocity, fd、fqThe electrical quantities before conversion are D-axis and Q-axis components, Fd、FqThe converted electrical quantities are respectively the D-axis component and the Q-axis component.
Taking the filtered output voltage obtained by the output voltages of the two inverters through the LC filter as an example, how to consider the unified coordinate transformation established by the frequency difference will be described. 1 st inverter output voltage u1The filtered equation is
2 nd inverter output voltage u2The filtered equation is
Because the two inverter output voltages have frequency difference, the selected DQ axes are not uniform, and therefore, the two DQ axes need to be uniform. With 1 st DQ axis as a common DQ coordinate system, 2 nd inverter output voltage u2Filtered output voltage u0Transformation to the common DQ coordinate system is done by:
the microgrid unified state space equation is represented by the following formula:
y＝g(x)
where x represents a system state variable, y represents an intermediate variable, β is a system parameter,for the differentiation of the system state variable x, the above equation is linearized:and A is a characteristic matrix obtained after linearization.
And S3, determining the leading factors influencing the stability of the micro-grid under the established unified state space equation.
And a set of stable operation parameters of the system is given, and the dominant factors influencing the stability of the system are determined according to the characteristic root distribution of the stable operation state of the system. Assuming that u and v are left and right eigenvector arrays of the feature matrix a (n × n), respectively, the participation factor matrix of the matrix feature root can be obtained.
λ1… λj… λn
Matrix element p of participation factorijRepresents the ith state variable xiFor j characteristic root lambda of state equationjAnd the influence of the size is to perform per-unit processing on each column of the participation factor matrix, the larger the participation factor is, the larger the influence of the state variable on the characteristic root is, and the dominant factor influencing the system stability can be determined by comparing the sizes of the participation factors.
And S4, tracking the change of the leading factors based on the bifurcation theory, wherein the balance solution of the stable operation state of the micro-grid is popular, and further determining the boundary condition of the stable operation of the micro-grid.
Before voltage instability, a power system may experience Hopflug Bifurcation (HB) and Saddle Node Bifurcation (SNB), wherein the HB bifurcation is essentially that a pair of conjugate pure virtual solutions appear at the characteristic root of a Jacobian matrix of the system, and the SNB bifurcation is essentially that a zero solution appears at the Jacobian matrix of the system.
If the system satisfies saddle node bifurcation or Hopff bifurcation at the equilibrium point (x, β), the Jacobian matrix in the system corresponds to having a 0 eigenroot and a pair of conjugate pure imaginary roots at that point, respectively.
The saddle node is bifurcated with:
in the formula, q0Is a given vector, which is normalized to the feature vector q.
The hopfu branches include:
the method can track the bifurcation point of an equation, change the leading factor of the system, continuously track the balance solution popularity of the system by utilizing the homotopy continuation method, obtain a balance curve when the system running state changes along with the parameters, judge whether the balance point (x, β) is the bifurcation point in the existing state by continuously judging whether the real part of the eigenvalue of the characteristic root matrix is positive, and the value of the system parameter β is the stable boundary condition when the bifurcation point occurs.
And (3) according to the obtained system balance solution popularity, linearizing the running state of the microgrid system at a balance point, and according to the characteristic value of the solved characteristic equation, researching the change condition of the characteristic root of the microgrid state equation in the parameter change process by using a Lyapunov function so as to determine the boundary condition of the system stability.
In order to verify the micro-grid stability analysis strategy based on the bifurcation theory, the micro-grid stability analysis is simulated and verified on a PSCAD simulation platform, and fig. 5 is a structural diagram of a distributed micro-grid for verification provided by the invention. As shown in fig. 5. Simulation parameters: the effective value of the rated line voltage of the power supply is 380V; the active and reactive reference values and the voltage and frequency reference values are selected to be 20kW, 20Kvar, 380V and 314 rad/s; the load resistance was selected to be 3.63 omega.
The specific implementation flow is as follows:
taking table 1 as an example, a simulation model is built, and a uniform state space equation of the system is built; simulating to obtain a stable operation state of the system as shown in table 2;linearization was performed at the equilibrium point. FIG. 6 is a schematic diagram of the characteristic root distribution of the Jacobian matrix A. As shown in FIG. 6, there are 3 clusters of feature roots λ in this case1、λ2、λ3Wherein λ is3Nearest to the imaginary axis, λ2Second, λ1The farthest. Thus, λ3Is the dominant feature root affecting stability.
And acquiring dominant factors influencing a stable operation system based on a characteristic root analysis method.
TABLE 1
TABLE 2
Taking the parameters in table 1 as an example to construct a system, selecting a frequency inertia constant J as a bifurcation parameter, and researching the influence of the change of the frequency inertia constant on the stability of the system. Changing the numerical value of the bifurcation parameter J, tracking the balance solution popularity of the system by utilizing Matcont software, and drawing a balance curve of the bifurcation parameter changing system; and similarly, selecting K and Ls as bifurcation parameters of the system respectively, and drawing the equilibrium solution popularity when the K and Ls change. Fig. 7 is a graph showing the balance of the bifurcation parameter varying system, fig. 7(a) is a graph showing the balance of the bifurcation parameter J varying system, fig. 7(b) is a graph showing the balance of the bifurcation parameter K varying system, and fig. 7(c) is a graph showing the balance of the bifurcation parameter Ls varying system; fig. 8 is a characteristic root distribution diagram of different bifurcation parameters, fig. 8(a) is a characteristic root distribution diagram with J being 10000, fig. 8(b) is a characteristic root distribution diagram with K being 1839, and fig. 8(c) is a characteristic root distribution diagram with Ls being 22.34; fig. 9 is a graph of a D-axis voltage output by the filtered distributed power supply and a voltage angular velocity of the distributed power supply according to the embodiment of the present invention, where fig. 9(a) is a graph of a D-axis voltage output by the filtered distributed power supply, and fig. 9(b) is a graph of a voltage angular velocity of the distributed power supply.
As can be seen from fig. 7(a), in the process of changing the bifurcation parameter J, no bifurcation point occurs in the system, which indicates that the system can be always stable in the process of changing J, and when J is 10000, the characteristic root of the system is plotted in fig. 8(a), and it can be seen that the real part of all the characteristic roots of the system is still less than zero; according to Lyapunov's law, the system can remain stable during changes in J.
As can be seen from fig. 7(b), with 5500 as an initial value, K is gradually decreased, and the system has a Hopf bifurcation point when K is 1839; in fig. 8(b), the characteristic root of the system is plotted when K is 1839, and when the system appears a pair of conjugate characteristic roots with zero real part, the system begins to be unstable.
As can be seen from fig. 7(c), with 2 as an initial value, Ls is gradually increased, and the system has an SNB bifurcation point when Ls is 22.34; in fig. 8(c), the characteristic root of the system is plotted when Ls is 22.34, and when the system has a characteristic root with zero real part, the system starts to be unstable.
Respectively constructing a system simulation model when the K is 1800 and 1900 for verifying the system stable boundary condition of the bifurcation parameter K in the change process; fig. 9(a) and 9(b) show the D-axis voltage output by the distributed power supply after filtering and the voltage angular velocity of the distributed power supply, respectively, and it can be seen that: when K is 1900, the voltage is stabilized at about 302V, and when K crosses a Hopf bifurcation point to reach 1800, the voltage has a constant amplitude oscillation phenomenon; the frequency was stabilized at 50Hz when K did not cross the bifurcation point, and oscillation around 0.2Hz occurred when K reached 1800.
In order to verify the stable boundary condition of the system in the variation process of the bifurcation parameter Ls, a system simulation model of Ls at 22 and 23 is respectively constructed. Fig. 10 is a graph of active and reactive power output of a distributed power supply according to an embodiment of the present invention, fig. 10(a) is a graph of active power output of the distributed power supply, and fig. 10(b) is a graph of reactive power output of the distributed power supply. As shown in fig. 10: when Ls is 22, namely Ls does not exceed the saddle node bifurcation point, the active power output and the reactive power output of the system are stabilized at about 20 kW; when the value of Ls is 23mH (exceeds the saddle node bifurcation point), a characteristic root with a positive real part appears in the system, the system is unstable, and irregular fluctuation appears in the active and reactive power output of the distributed power supply.
The above description is only for the preferred embodiment of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present application should be covered within the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (10)
1. A micro-grid stability control method based on a bifurcation theory is characterized by comprising the following steps:
s1, respectively establishing state equations of each distributed power supply, each power transmission line and each load according to a micro-grid circuit structure and an electrical relation;
s2, considering frequency difference among the distributed power supplies and frequency difference between the distributed power supplies and a large power grid, and establishing a micro-grid unified state space equation considering output difference of the distributed power supplies;
s3, determining dominant factors influencing the stability of the microgrid under the established unified state space equation;
and S4, tracking the change of the leading factors based on the bifurcation theory, wherein the balance solution of the stable operation state of the micro-grid is popular, and further determining the boundary condition of the stable operation of the micro-grid.
2. The microgrid stability control method of claim 1, characterized in that the state equations of each transmission line and load are as follows:
wherein L isline_i、Rline_iThe inductive reactance and impedance, L, of the ith transmission lineload_i、Rload_iThe inductive reactance and the impedance of the ith load respectively; i.e. ilineD_i、ilineQ_iFor current i of ith transmission lineline_iD-axis, Q-axis components of (a); i.e. iloadD_i、iloadQ_iIs the current i of the ith loadload_iD-axis, Q-axis components of (a); w represents the angular velocity of the distributed power supply output voltage; u. ofoD_i、uoQ_iRespectively is the filtered output voltage u of the inverter in the ith distributed power supplyoiThe D-axis and Q-axis components of (1, 2) ·, and n, n are the number of distributed power sources in the microgrid.
3. The microgrid stability control method of claim 1, wherein the distributed power supply is composed of a direct current voltage source, a controller and a filter, and the state equation of the filter is as follows:
wherein Ls and C are respectively a filter inductor and a filter capacitor of the LC filter, iiD、iiQRespectively output current i for inverteriD-axis, Q-axis component of (u)iD、uiQRespectively an inverter output voltage uiD-axis, Q-axis component of (u)oD_i、uoQ_iRespectively is the filtered output voltage u of the inverter in the ith distributed power supplyoiD-axis, Q-axis component of (i)oD_i、ioQ_iRespectively is the filtered output current i of the inverter in the ith distributed power supplyoiThe component of D axis and Q axis, i is 1, 2.
4. The microgrid stability control method of claim 3, wherein the controller comprises a power frequency controller and an excitation controller;
the control equation of the power frequency controller is as follows:
the control equation of the excitation controller is as follows:
u＝Mif·w
wherein, w*For the frequency reference, e is the inverter voltage reference, P and Q are the input active and reactive power references, respectively, J, KpRespectively, the inertia constant of the frequency and the droop coefficient of the frequency, P is the actual active power of the line, Q is the actual reactive power of the line, and TeFor distributed power output torque, θ is the phase angle of the inverter output voltage, KqIs the voltage droop coefficient, K is the inertia constant of the voltage, MifTo simulate the magnetic flux in a synchronous generator, u is the magnitude of the inverter output voltage.
5. The microgrid stability control method according to claim 1, wherein the step S2 specifically includes:
selecting a DQ coordinate system as a public DQ coordinate system, and converting other DQ coordinate systems into the public DQ coordinate system, wherein the conversion formula is as follows:
wherein,advancing the phase angle, w, of the common DQ axis for the kth inverter DQ axiskIs the k inverter DQ shaft angular velocity, w is the common DQ shaft angular velocity, α is the angle of large Grid leading the common DQ shaft, wgridFor large grid voltage angular velocity, fD、fQThe electrical quantities before conversion are D-axis and Q-axis components, FD、FQThe converted electrical quantity D axis component and Q axis component are respectively;
the microgrid unified state space equation is represented by the following formula:
y＝g(x)
where x represents a system state variable, y represents an intermediate variable, β is a system parameter,is the derivative of the system state variable x.
6. The microgrid stability control method according to claim 1, wherein the step S3 specifically includes:
s301, carrying out linearization processing on the unified state space equation of the micro-grid to obtain a feature matrix A obtained after linearization;
s302, according to left and right eigenvector arrays u and v of the feature matrix A obtained after linearization, constructing a participation factor matrix P of a matrix feature root and a matrix element P of a participation factorijRepresents the ith state variable xiFor j characteristic root lambda of state equationjThe effect of the size of the particles,
and S303, performing per-unit processing on each column of the participation factor matrix, wherein the larger the participation factor is, the larger the influence of the state variable on the characteristic root is, and the dominant factor influencing the system stability can be determined by comparing the sizes of the participation factors.
7. The microgrid stability control method according to claim 1, wherein the step S4 specifically includes:
s401, changing leading factors of a system, continuously tracking the balance solution popularity of the system by utilizing a homotopy continuation method, and obtaining a balance curve when the running state of the system changes along with parameters;
s402, linearizing the running state of the micro-grid system at a balance point according to the obtained system balance solution popularity;
s403, solving a characteristic value of a characteristic equation;
s404, judging whether the balance point (x, β) is a bifurcation point in the existing state by continuously judging whether the real part of the eigenvalue of the characteristic root matrix is positive, wherein the value of the system parameter β is a stable boundary condition when the bifurcation point occurs.
8. The microgrid stability control method of claim 7, characterized in that saddle nodes are branched with:
wherein x represents system state variable, g (x) represents intermediate variable, β represents system parameter, A represents characteristic matrix obtained after linearization, q represents characteristic vector, q represents intermediate variable0Is a given vector, which is normalized to the feature vector q.
9. The microgrid stability control method of claim 7, characterized in that the hopplev branches have:
wherein x represents a system state variable, g (x) represents an intermediate variable, β represents a system parameter, A represents a characteristic matrix obtained after linearization, q represents a characteristic vector, Aq ═ j χ represents that a pair of conjugate solutions of the equation occur, q represents a conjugate solution of the equation, and q represents a conjugate solution of the equation0Is a given vector, which is normalized to the feature vector q.
10. A computer-readable storage medium, having stored thereon a computer program which, when executed by a processor, implements a microgrid stability control method according to any one of claims 1 to 9.
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