CN114583685B - Method for improving stability of self-adaptive control direct-current micro-grid system - Google Patents
Method for improving stability of self-adaptive control direct-current micro-grid system Download PDFInfo
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Abstract
The invention belongs to the technical field of power information, and discloses a method for improving stability of a self-adaptive control direct current micro-grid system. The direct current micro-grid system comprises a power generation unit, a circuit, a public direct current bus and a load; the power generation unit consists of a direct current power supply and a Boost type converter, wherein the low-voltage side of the converter is connected with the direct current power supply, and the high-voltage side of the converter is connected with a public direct current bus through a line; a common direct current bus is connected with a voltage stabilizing capacitor in parallel; the constant-resistance load is connected in parallel to the public direct current bus. The direct current micro-grid operates independently, a double closed loop self-adaptive control strategy is adopted, the outer loop is droop control, and the inner loop is current control. According to the invention, the characteristic root is solved through the direct-current micro-grid system small signal equation, the effective interval of the stable sagging coefficient can be maintained according to the property of the characteristic root, and the sagging coefficient of the self-adaptive controller is directionally regulated in the effective interval, so that the stability of the micro-grid system is improved. The invention does not change the micro-grid structure and element parameters and does not cause adverse effect on the transient performance and steady state performance of the micro-grid system.
Description
Technical Field
The invention belongs to the technical field of power information, and particularly relates to a method for improving stability of a self-adaptive control direct current micro-grid system.
Background
The shortage of fossil energy has prompted the use of renewable energy. Renewable energy sources have the advantages of low cost, high environmental benefit and the like, and are applied in a plurality of fields. The renewable energy source is spread in the form of an alternating current micro-grid in early stage, and has the characteristics of high expansibility, reliability, portability and the like. However, the dc-ac conversion link necessary for using the dc power source increases energy costs and reduces operation efficiency.
The DC micro-grid has higher operation efficiency than the AC micro-grid. But its power balance control and the resulting system stability problems present significant challenges for microgrid operation management. For the direct current micro-grid system adopting self-adaptive control, the problem of stability in operation is more remarkable due to the lack of external energy support.
The existing method for improving the stability of the direct current micro-grid is basically implemented in two aspects. Firstly, from the structure and parameters of the system, the stability of the system is improved by increasing the parallel capacitance or reducing the equivalent inductance of each element of the system. The method increases additional problems, such as: poor matching degree of the capacitor and the inductor can influence the response speed of the system; the equivalent inductance of the circuit is very small, and the practical significance of improving the stability by further reducing the inductance is not great. Secondly, starting from the external condition of the system, the stability is improved by changing the equivalent operation parameters of the power supply or the load. The method can not influence the dynamic performance of the system while improving the stability, but can influence the steady-state performance of the system, such as: the mismatch of sagging coefficients causes circulation between parallel branches, significant bus voltage drop, and the like.
Therefore, it is necessary to design a method for improving the stability of the self-adaptive control direct current micro-grid system on the premise of not affecting the transient state characteristic and the steady state characteristic of the system.
Disclosure of Invention
The invention aims to provide a method for improving the stability of a self-adaptive control direct current micro-grid system so as to solve the technical problems.
In order to solve the technical problems, the specific technical scheme of the method for improving the stability of the self-adaptive control direct current micro-grid system is as follows:
A method for improving stability of self-adaptive control direct current micro-grid system, the direct current micro-grid system comprises a power generation unit, a circuit, a public direct current bus and a load; the power generation unit consists of a direct current power supply and a Boost type converter, wherein the low-voltage side of the converter is connected with the direct current power supply, and the high-voltage side of the converter is connected with a public direct current bus through a line; a common direct current bus is connected with a voltage stabilizing capacitor in parallel; the constant-resistance load is connected in parallel to a public direct current bus; the direct current micro-grid independently operates, adopts double closed-loop self-adaptive control, and comprises an inner ring and an outer ring, wherein the outer ring is a voltage-current sagging control ring, the feedback quantity is the output voltage of the converter, and the output quantity is the output current reference value of the converter; the inner loop is current control, the feedback quantity is the output current of the converter, the output quantity is the duty ratio of the carrier circuit of the converter, the method is realized by directionally adjusting the droop coefficient of the DG unit self-adaptive controller, and the specific steps are as follows:
Step 1: establishing a differential equation set of a direct current micro-grid system;
step 2: establishing a direct current micro-grid system small signal equation;
Step 3: solving a characteristic root of the system;
step 4: determining an effective adjustment interval of the droop coefficient of the adaptive controller;
Step 5: the droop coefficient of the adaptive controller is directionally adjusted to improve the stability of the system operation.
Further, the step1 comprises the following specific steps:
the differential equation of the DG unit, the adaptive controller and the line is constructed as follows:
In the above formula: n is the number of DG units; n=1, 2, …, N; u n、In is the output voltage and output current of the converter; u n,ref、kn is the voltage reference value and droop coefficient of the self-adaptive controller; u dc is the DC bus voltage; u s,n、Ib,n is the DC source voltage and output current; l b,n、Cn is the filter inductance and the voltage stabilizing capacitance of the converter respectively; k P,n、KI,n is the proportional and integral coefficient of the PI controller in the self-adaptive controller; m n is the sawtooth peak value of the pulse generator; u b,n is the integral term output of the PI controller in the adaptive controller; r n、Ln is the resistance and equivalent inductance of the line, and a differential equation for constructing the DC bus voltage stabilizing capacitor according to kirchhoff current law is as follows:
In the above formula, C dc is a capacitance value; r load is the resistance value of the DC bus load.
Further, the step2 comprises the following specific steps:
according to differential equations of all DG units, the self-adaptive controller and the circuit and differential equations of the voltage stabilizing capacitor, a direct current micro-grid differential equation set is established, and according to a first method of a Liapunov stability criterion, linearizing is carried out on a nonlinear differential equation set near a steady-state operation point, so that a small signal model of the micro-grid system can be obtained as follows:
Wherein ,ΔX＝[ΔU1,ΔIb,1,ΔI1,ΔUb,1,…,ΔUN,ΔIb,N,ΔIN,ΔUb,N,ΔUdc]T,AEIG is a feature matrix of a small signal equation, and the expression is:
Wherein 0 represents zero in the elements of the corresponding positions; a c is a subarray formed by row vectors, a l,n is a subarray formed by column vectors, a n is a 4×4 order subarray, and each subarray expression is as follows:
Ac＝[0 0 -1/Cdc 0] (5)
Al,n＝[0 0 -1/Ln 0]T (6)
Wherein, The initial value of the output voltage of the converter; /(I)For the initial value of the output current of the direct current power supply, alpha n is the duty ratio of the nth converter.
Further, the step 3 comprises the following specific steps:
According to the feature matrix A EIG determined by the formulas (4) to (7), a feature equation is constructed as follows:
det[λI-AEIG]＝(λ-λ1)(λ-λ2)…(λ-λ4N+1)＝0 (8)
Solving a characteristic root lambda 1,λ2,…,λ4N+1, wherein when all characteristic values are positioned on the left half plane of the s domain, the system is stable; when the characteristic value is in the right half plane of the s domain, the system is unstable; when the characteristic root with the real part being zero exists, further judgment is made according to the high-order remainder.
Further, the step 4 includes the following specific steps:
For a certain DG unit, the initial droop coefficient is changed in an oriented manner, if the dominant characteristic root of the system always moves to the left half plane of the s domain, the stability of the system can be improved by increasing the droop coefficient; if the dominant characteristic root of the system moves to the left half plane of the s domain and then moves to the right half plane, the system stability can be improved by increasing the sagging coefficient within a certain range, and if the dominant characteristic root of the system exceeds the range, the system stability is reduced; the sagging coefficient corresponding to the characteristic root when being positioned at the leftmost position is an inflection point value;
If the dominant characteristic root of the system moves to the right half plane of the s domain, the increase of the droop coefficient is not beneficial to improving the stability of the system; and when the real part of the characteristic root is zero, the corresponding droop coefficient is a critical value.
Further, the step 5 comprises the following specific steps:
When the system has an inflection point, the stability of the system operation can be improved by changing the droop coefficient from the current droop coefficient to the inflection point direction; when the system does not have inflection points, the stability of the system can be improved by adjusting the droop coefficient according to the direction of the dominant characteristic root moving to the left half plane of the s domain.
The method for improving the stability of the self-adaptive control direct current micro-grid system has the following advantages: according to the method for improving the stability of the self-adaptive control direct current micro-grid system, the sagging coefficient of the self-adaptive controller is directionally regulated, so that the sagging coefficient is reasonably set in a stable interval determined by an inflection point and a critical point, and the running stability of the system is improved. Compared with the existing method for improving the stability of the system, the method provided by the invention does not change the micro-grid structure and element parameters and does not cause adverse effects on the transient performance and steady-state performance of the micro-grid system.
Drawings
FIG. 1 is an equivalent circuit diagram of a DC micro-grid system of the present invention;
FIG. 2 is a schematic diagram of an adaptive controller of the DC micro-grid system of the present invention;
FIG. 3 is a schematic diagram of a DC micro-grid structure used in an embodiment of the present invention;
FIG. 4 is a root locus diagram of a feature root for k 1 as varied between [ 0.3-10 ] V/A;
FIG. 5 is a root locus diagram of a feature root for k 2 as varied between [ 0.3-10 ] V/A;
FIG. 6 is a root locus diagram of a feature root for k 3 as varied between [ 0.3-10 ] V/A;
FIG. 7 is a root locus diagram of a feature root for k 4 as varied between [ 0.3-10 ] V/A;
FIG. 8 is a graph of the real part values of the characteristic root 10 at different droop coefficient adjustment intervals;
FIG. 9 is a graph of various bus voltage waveforms for time domain simulation;
fig. 10 is a graph of the DG unit output current waveform in a time domain simulation.
Detailed Description
For a better understanding of the objects and functions of the present invention, a method for improving the stability of an adaptively controlled dc micro-grid system according to the present invention is described in further detail below with reference to the accompanying drawings.
As shown in fig. 1, the dc micro-grid system includes a power generation unit, a line, a common dc bus, and a load; the power generation unit consists of a direct current power supply and a Boost type converter, wherein the low-voltage side of the converter is connected with the direct current power supply, and the high-voltage side of the converter is connected with a public direct current bus through a line; a common direct current bus is connected with a voltage stabilizing capacitor in parallel; the constant-resistance load is connected in parallel to the public direct current bus.
The direct current micro-grid independently operates and adopts double closed loop self-adaptive control, and comprises an inner ring and an outer ring. As shown in fig. 2. The outer ring is a voltage-current sagging control ring, the feedback quantity is the output voltage of the converter, and the output quantity is the output current reference value of the converter; the inner loop is current control, the feedback quantity is the output current of the converter, and the output quantity is the duty ratio of the carrier circuit of the converter.
The method for improving the stability of the self-adaptive control direct current micro-grid system is realized by directionally adjusting the droop coefficient of the DG unit self-adaptive controller, and is implemented specifically according to the following steps:
① And establishing a differential equation set of the direct current micro-grid system.
According to fig. 1 and 2, differential equations for DG units, adaptive controllers and lines are constructed as follows:
In the above formula: n is the number of DG units; n=1, 2, …, N; u n、In is the output voltage and output current of the converter; u n,ref、kn is the voltage reference value and droop coefficient of the self-adaptive controller; u dc is the DC bus voltage; u s,n、Ib,n is the DC source voltage and output current; l b,n、Cn is the filter inductance and the voltage stabilizing capacitance of the converter respectively; k P,n、KI,n is the proportional and integral coefficient of the PI controller in the self-adaptive controller; m n is the sawtooth peak value of the pulse generator; u b,n is the integral term output of the PI controller in the adaptive controller; r n、Ln is the resistance and equivalent inductance of the line.
The differential equation of the DC bus voltage stabilizing capacitor constructed according to kirchhoff current law is as follows:
In the above formula, C dc is a capacitance value; r load is the resistance value of the DC bus load.
② And establishing a direct-current micro-grid small signal model.
And establishing a direct current micro-grid differential equation set according to differential equations of all DG units, the self-adaptive controller and the circuits and differential equations of the voltage stabilizing capacitors. The system of equations is nonlinear and requires approximation to obtain a linearization model of the system near steady state operating points. According to the first method of the Liapunov stability criterion, linearizing the nonlinear differential equation set near a steady-state operating point to obtain a small signal model of the micro-grid system, wherein the small signal model is as follows:
Wherein ,ΔX＝[ΔU1,ΔIb,1,ΔI1,ΔUb,1,…,ΔUN,ΔIb,N,ΔIN,ΔUb,N,ΔUdc]T,AEIG is a feature matrix of a small signal equation, and the expression is:
Wherein 0 represents zero in the elements of the corresponding positions; a c is a subarray formed by a row vector, a l,n is a subarray formed by a column vector, and a n is a 4×4-order subarray. The expressions of each subarray are respectively as follows:
Ac＝[0 0 -1/Cdc 0] (5)
Al,n＝[0 0 -1/Ln 0]T (6)
Wherein, The initial value of the output voltage of the converter; /(I)For the initial value of the output current of the direct current power supply, alpha n is the duty ratio of the nth converter.
③ And solving the characteristic root of the system.
According to the feature matrix A EIG determined by the formulas (4) to (7), a feature equation is constructed as follows:
det[λI-AEIG]＝(λ-λ1)(λ-λ2)…(λ-λ4N+1)＝0 (8)
And solving a characteristic root lambda 1,λ2,…,λ4N+1. When all the characteristic values are positioned on the left half plane of the s domain, the system is stable; when the characteristic value is in the right half plane of the s domain, the system is unstable; when the characteristic root with the real part being zero exists, further judgment is made according to the high-order remainder.
④ An effective adjustment interval for the droop coefficient of the adaptive controller is determined.
For a certain DG unit, from its initial droop coefficient orientation change, if the dominant feature root of the system always moves to the s-domain left half plane, it is explained that increasing the droop coefficient can improve the stability of the system. If the dominant characteristic root of the system moves to the left half plane of the s domain and then moves to the right half plane, the system stability can be improved by increasing the sagging coefficient within a certain range, and if the dominant characteristic root of the system exceeds the range, the system stability is reduced; and the droop coefficient corresponding to the characteristic root at the leftmost position is an inflection point value. If the dominant characteristic root of the system moves to the right half plane of the s domain, the increase of the droop coefficient is not beneficial to improving the stability of the system; and when the real part of the characteristic root is zero, the corresponding droop coefficient is a critical value.
⑤ The droop coefficient of the adaptive controller is directionally adjusted to improve the running stability of the system.
When the system has an inflection point, the stability of the system operation can be improved by changing the droop coefficient from the current droop coefficient to the inflection point direction; when the system does not have inflection points, the stability of the system can be improved by adjusting the droop coefficient according to the direction of the dominant characteristic root moving to the left half plane of the s domain.
Examples
As shown in fig. 3, the dc micro-grid system that operates independently includes 4 DG units, each DG unit is composed of a dc voltage source and a Boost converter, and is connected to a common dc bus through a line; the rated voltage of the common direct current bus is 200V, and the voltage stabilizing capacitance of the common direct current bus is 0.09mF;2 constant-resistance loads are connected into a public direct current bus, and R load,1 is input and R load,2 is not input under the initial operation condition; each DG unit adopts a double closed-loop self-adaptive controller shown in FIG. 2, and initial values of droop coefficients are 1.0V/A, 2.1V/A, 1.4V/A and 1.8V/A respectively. Other component parameters are shown in table 1.
TABLE 1 parameters of the elements of the system
| Rated capacity of converter (kW) | Pra,1＝2.0,Pra,2＝1.0,Pra,3＝1.5,Pra,4＝1.25 |
| Line resistance (omega) | R1＝1.5,R2＝2.0,R3＝1.4,R4＝1.8 |
| Line equivalent inductance (mH) | L1＝0.25,L2＝0.33,L3＝0.20,L4＝0.30 |
| Filter inductor of converter (mH) | Lb,1＝0.33,Lb,2＝0.11,Lb,3＝0.22,Lb,4＝0.17 |
| Voltage stabilizing capacitor of converter (mF) | C1＝0.38,C2＝0.52,C3＝0.45,C4＝0.49 |
| Constant resistance load (omega) | Rload,1＝18,Rload,2＝36 |
For the direct current micro-grid system with the equivalent circuit of fig. 1 and the structure of fig. 3, system characteristic root calculation is performed under the operation parameters of table 1, and the results are shown in table 2. All feature roots have negative real parts and the system is stable at the initial operating point.
TABLE 2 System characterization root at initial run conditions
The influence of sagging coefficient on the system operation stability is further analyzed. The system feature root is computed as k 1 varies from 0.3V/a to 10V/a, the root trace of which is shown in fig. 4. For clarity only the root trajectories of the dominant feature roots 10, 11, 17 are shown in the figure. As can be seen from fig. 4, when k 1 increases, the feature root 17 moves to the right half plane but the movement amplitude is small, so that the stability is not greatly affected; the characteristic roots 10 and 11 always move leftwards, the movement amplitude is obvious, and the system stability is obviously influenced. When k 1 =0.432, the real parts of the 10 th and 11 th characteristic roots are zero, and the value is a sag coefficient critical value. It can thus be determined that when k 1 e (0.432, ++), the system can remain stable and that increasing k 1 in this interval can effectively improve the stability of the system operation.
The same analysis method was used to analyze the other three sag factors:
The sag factor k 2 has a threshold of 0.661. When k 2 epsilon (0.661 and infinity), the system can be kept stable, and the increase of k 2 in the interval can effectively improve the running stability of the system. The root trace as k 2 changes is shown in figure 5.
The sag factor k 3 has a threshold of 0.613. When k 3 epsilon (0.613 and infinity) is adopted, the system can be kept stable, and the increase of k 3 in the interval can effectively improve the running stability of the system. The root trace as k 3 changes is shown in figure 6.
The sag factor k 4 has a threshold of 3.308. When k 4 epsilon (- ≡3.308), the system can be kept stable, and the reduction of k 4 in the interval can effectively improve the running stability of the system. The root trace as k 4 changes is shown in figure 7.
For the dc micro-grid system of the embodiment, there is no sag factor inflection point, but the rule of the feature root variation with sag factor varies. The characteristic root change rule is related to a specific network structure and operation parameters, and analysis is needed according to a specific operation state. The invention provides the method for improving the running stability of the direct current micro-grid system, which is favorable for reasonably setting the system parameters.
And further performing time domain simulation on the direct current micro-grid system to verify the effectiveness of the method. According to the droop coefficient effective interval determined by the method, as shown in fig. 8, a group of values are randomly selected for simulation: k 1＝1.00,k2＝2.64,k3＝1.71,k4 =1.93. The bus voltage and DG output current are shown in fig. 9 and 10. The voltage and current of each bus remain stable under the initial operating conditions. And R load,2 is put into the system after 2s, and the system enters a new stable running state after a transient process.
It will be understood that the application has been described in terms of several embodiments, and that various changes and equivalents may be made to these features and embodiments by those skilled in the art without departing from the spirit and scope of the application. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the application without departing from the essential scope thereof. Therefore, it is intended that the application not be limited to the particular embodiment disclosed, but that the application will include all embodiments falling within the scope of the appended claims.
Claims (1)
1. A method for improving stability of self-adaptive control direct current micro-grid system, the direct current micro-grid system comprises a power generation unit, a circuit, a public direct current bus and a load; the power generation unit consists of a direct current power supply and a Boost type converter, wherein the low-voltage side of the converter is connected with the direct current power supply, and the high-voltage side of the converter is connected with a public direct current bus through a line; a common direct current bus is connected with a voltage stabilizing capacitor in parallel; the constant-resistance load is connected in parallel to a public direct current bus; the direct current micro-grid independently operates, adopts double closed-loop self-adaptive control, and comprises an inner ring and an outer ring, wherein the outer ring is a voltage-current sagging control ring, the feedback quantity is the output voltage of the converter, and the output quantity is the output current reference value of the converter; the method is characterized by comprising the following specific steps of:
Step 1: establishing a differential equation set of a direct current micro-grid system;
the differential equation of the DG unit, the adaptive controller and the line is constructed as follows:
In the above formula: n is the number of DG units; n=1, 2, …, N; u n、In is the output voltage and output current of the converter; u n,ref、kn is the voltage reference value and droop coefficient of the self-adaptive controller; u dc is the DC bus voltage; u s,n、Ib,n is the DC source voltage and output current; l b,n、Cn is the filter inductance and the voltage stabilizing capacitance of the converter respectively; k P,n、KI,n is the proportional and integral coefficient of the PI controller in the self-adaptive controller; m n is the sawtooth peak value of the pulse generator; u b,n is the integral term output of the PI controller in the adaptive controller; r n、Ln is the resistance and equivalent inductance of the line, and a differential equation for constructing the DC bus voltage stabilizing capacitor according to kirchhoff current law is as follows:
In the above formula, C dc is a capacitance value; r load is the resistance value of the direct current bus load;
step 2: establishing a direct current micro-grid system small signal equation;
according to differential equations of all DG units, the self-adaptive controller and the circuit and differential equations of the voltage stabilizing capacitor, a direct current micro-grid differential equation set is established, and according to a first method of a Liapunov stability criterion, linearizing is carried out on a nonlinear differential equation set near a steady-state operation point, so that a small signal model of the micro-grid system can be obtained as follows:
Wherein ,ΔX＝[ΔU1,ΔIb,1,ΔI1,ΔUb,1,…,ΔUN,ΔIb,N,ΔIN,ΔUb,N,ΔUdc]T,AEIG is a feature matrix of a small signal equation, and the expression is:
Wherein 0 represents zero in the elements of the corresponding positions; a c is a subarray formed by row vectors, a l,n is a subarray formed by column vectors, a n is a 4×4 order subarray, and each subarray expression is as follows:
Ac＝[0 0 -1/Cdc 0] (5)
Al,n＝[0 0 -1/Ln 0]T (6)
Wherein, The initial value of the output voltage of the converter; /(I)Outputting a current initial value for a direct current power supply; alpha n is the duty cycle of the nth converter;
Step 3: solving a characteristic root of the system;
According to the feature matrix A EIG determined by the formulas (4) to (7), a feature equation is constructed as follows:
det[λI-AEIG]＝(λ-λ1)(λ-λ2)…(λ-λ4N+1)＝0 (8)
Solving a characteristic root lambda 1,λ2,…,λ4N+1, wherein when all characteristic values are positioned on the left half plane of the s domain, the system is stable; when the characteristic value is in the right half plane of the s domain, the system is unstable; when the characteristic root with the real part being zero exists, further judging according to the high-order remainder;
step 4: determining an effective adjustment interval of the droop coefficient of the adaptive controller;
For a certain DG unit, the initial droop coefficient is changed in an oriented manner, if the dominant characteristic root of the system always moves to the left half plane of the s domain, the stability of the system can be improved by increasing the droop coefficient; if the dominant characteristic root of the system moves to the left half plane of the s domain and then moves to the right half plane, the system stability can be improved by increasing the sagging coefficient within a certain range, and if the dominant characteristic root of the system exceeds the range, the system stability is reduced; the sagging coefficient corresponding to the characteristic root when being positioned at the leftmost position is an inflection point value;
If the dominant characteristic root of the system moves to the right half plane of the s domain, the increase of the droop coefficient is not beneficial to improving the stability of the system;
when the real part of the characteristic root is zero, the corresponding sagging coefficient is a critical value;
step 5: the droop coefficient of the self-adaptive controller is directionally regulated to improve the stability of the system operation;
When the system has an inflection point, the stability of the system operation can be improved by changing the droop coefficient from the current droop coefficient to the inflection point direction; when the system does not have inflection points, the stability of the system can be improved by adjusting the droop coefficient according to the direction of the dominant characteristic root moving to the left half plane of the s domain.
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