CN110071514B - Consistency droop control method for power distribution and voltage frequency recovery - Google Patents
Consistency droop control method for power distribution and voltage frequency recovery Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/381—Dispersed generators
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
- H02J3/388—Islanding, i.e. disconnection of local power supply from the network
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Abstract
The invention provides a consistency droop control method for power distribution and voltage frequency recovery, which is used for an island micro-grid system, realizes accurate active and reactive power sharing, and simultaneously keeps frequency recovery and average voltage reaching a rated value. In the proposed control scheme, it is only necessary to exchange neighborhood reactive power information by using a sparse low bandwidth communication network, rather than transferring information of active power, reactive power and frequency over the communication links in existing consistency methods. The transmission data and data delay are significantly reduced compared to existing consistency-based methods, and a high reliability of the system can be achieved. Furthermore, even in the case of communication delays, accurate real/reactive power sharing and voltage frequency recovery can be ensured under disturbances of load and feeder impedance. And finally, a simulation result of the hardware in the loop is given, and the effectiveness of the control scheme is verified.
Description
Technical Field
The invention belongs to the technical field of micro-grids in a power system, and relates to a consistency droop control method for power distribution and voltage frequency recovery.
Background
In recent years, in Micro Grid (MG) of island mode, droop control methods have been widely used to establish system frequency and bus voltage and to share active power among Distributed Generation (DG) units simultaneously without using critical communication. However, in these methods, voltage and frequency deviations caused by the conventional droop control method are unavoidable, and reactive power sharing is poor under unequal feeder impedance conditions. To address such issues, typical secondary control strategies are often used in islanded micro-grids to restore voltage and frequency to nominal values to compensate for the limitations of the droop mechanism. While the secondary control strategy can eliminate voltage and frequency offsets, a microgrid central controller (MGCC) needs to connect each distributed DG unit, which increases system complexity and reduces scalability and reliability. In recent years, multi-agent control theory has been extensively studied in MG systems, and the main goal of multi-agent based coherence control is to implement a generic protocol between all agents in the network, which only requires interactions between nearby DGs, which is more reliable than the centralized control model based on MGCC. However, at least adjacent frequency, voltage, active power and reactive power information needs to be transmitted in the communication network for power sharing, in which case high density data will lead to challenges in data processing and analysis of large-scale microgrid systems. In addition, once there is a large delay in the communication network or the communication link fails, lacking any required data, the entire system is unstable.
According to the patent retrieval, chinese invention patent 201611074223.8 provides a secondary voltage unbalance control method for an island microgrid. The voltage of the distributed power supply is controlled through secondary control, the unbalanced voltage of the PCC points is compensated, and no static difference control of current and voltage is achieved. The method not only compensates the voltage deviation of the PCC points from the global perspective, but also realizes the accurate distribution of the reactive power. However, this method does not take into account the deviation in voltage frequency due to the droop control mechanism. The invention patent 201710979119.1 in China proposes a distributed coordination control method of a virtual power supply in a low-voltage microgrid based on MAS, which comprises primary control and secondary control, wherein the primary control is based on the matching use of virtual impedance and the virtual power supply, and the reactive power sharing of a micro source is improved to a certain extent. The secondary control is based on a consistency protocol, and the interaction of the voltage information of each virtual power supply among the micro-sources is carried out through the sparse communication network of the micro-grid, so that the voltages of the virtual power supplies are coordinated to be strictly consistent. However, this method requires a large amount of data information to be exchanged between the DGs, and once a communication link fails or there is a communication delay, the stability of the microgrid is easily affected.
In summary, the existing common secondary control and consistency control can realize active/reactive sharing, but the secondary control often depends on a central controller, so that the complexity of the system is increased and the reliability of the system is greatly reduced; in general consistency control, high-density data needs to be interacted to achieve a good control effect, if delay occurs in interaction of data of each DG unit, poor control is also caused, and moreover, an existing consistency control method lacks a droop mechanism, and performance of a plurality of DGs and stability of a system are also affected. Therefore, it is necessary to research a power equalization control method with high reliability, and to ensure that the voltage frequency is maintained at a rated value while achieving accurate active/reactive power equalization in complex power grids with different line impedances.
Disclosure of Invention
The invention aims to solve the problem that voltage/frequency deviation from a rated value is eliminated while active/reactive power average distribution of Distributed Generators (DGs) in a microgrid is carried out due to different line impedances and under the condition of load disturbance, and provides a consistency droop control method for power distribution and voltage frequency recovery.
The specific technical scheme of the invention is as follows: aiming at an island microgrid system, a consistency droop control method for power distribution and voltage frequency recovery is provided, and the consistency droop control method specifically comprises a consistency droop controller which combines the advantages of a common consistency algorithm and droop control, can realize accurate active/reactive power sharing, and keeps the frequency of each DG at a rated value without neighborhood voltage, frequency and active information. Furthermore, the proposed controller can be used to share reactive power while regulating the average voltage of the MG to a nominal value, taking into account the capacity of the DG unit; the voltage-current controller ensures the stability of the voltage and current of each DG. By the control method provided by the invention, the islanding microgrid can be ensured to realize the equalization of active/reactive power under complex working conditions of different line impedances, load disturbance and the like, the voltage and the frequency are recovered to rated values, and the rapidity and the stability of the microgrid system are enhanced
The invention comprises the following steps:
s1, the invention adopts the following droop control technology without communication to represent the relation between the output voltage amplitude and the operating angular frequency of the micro-grid and the corresponding reactive power and active power:
in the formula, E i And omega i Which are the voltage amplitude and angular frequency of the actual operation of the microgrid, respectively. E i * And ω i * Rated voltage amplitude and rated angular frequency, m, respectively, for operation of the microgrid i And n i Respectively frequency and amplitude droop coefficients, P i And Q i Respectively, the measured average active power value and the reactive power value. However, voltage and frequency deviations caused by droop control are unavoidable, and reactive power cannot be shared in this approach.
And then a consistency algorithm is introduced and combined with a droop control algorithm to establish a consistency droop controller capable of realizing power distribution and voltage frequency recovery, wherein the specific expression of the equivalent consistency droop controller is as follows:
wherein s represents the Laplace operator, α ij Representing the communication relationship of node i and node j, p i Is instantaneous active power, omega i And E i Representing the frequency and amplitude of the output voltage, ω h And omega c Respectively representing the upper and lower cut-off frequencies, P, of the improved frequency controller i And Q i Respectively measured average active and reactive power values, Q j Represents the average reactive power of the j node; m is i ，k p ，k i And b is a positive gain, ω i * And E i * Rated angular frequency and voltage, χ i Hexix j Is to consider DG i The weighting factor of the capacity can be set equal to DG i The derivative of the droop coefficient of (c).
The improved frequency droop controller as shown in (2) can be used to achieve accurate active power sharing and maintain the frequency of each DG at a nominal value without the need for voltage and frequency information of the neighboring DG. Furthermore, a consistency-based reactive power controller may be used to divide the reactive power equally, while regulating the average voltage of the MGs to a nominal value, taking into account the capacity of the DG units.
And S2, further, carrying out steady-state performance analysis on the consistency droop control method. First, the reactive power is further analyzed, and in the time domain, the reactive power/voltage equation can be rewritten as follows:
by taking the derivative of each DG unit output voltage with respect to time, the dynamics of the reactive power unity control can be expressed as:
considering that the derivative of the output voltage is equal to zero at steady state, the following matrix can be derived:
note that the bold variables bolded in the derivation of the formula in the present invention all represent matrices or vectors, where Laplace matrix is used
Representing, diagonal matrices
Is defined as
Sum column vector
Are respectively represented as
And
according to two important theorems in graph theory: (1) if a picture
Containing a root node means that it has a spanning tree in which there is at least a direct path to each other node. (2)
Is a symmetric positive semi-definite matrix, zero is a vector with right characteristic
And if and only if
With directed spanning trees, all non-zero eigenvalues have a real positive part, i.e.
n represents the nth network node. So only have pairs
Is that
And k>The solution of 0, (5) can be obtained as follows:
therefore, the reactive power equalization can be realized through the consistency droop controller.
And S3, further, analyzing the corresponding steady-state performance of the average voltage regulation. In view of
(5) Where by multiplication
The following equation can be obtained:
then (7) can be simplified to:
further, the output voltage of each DG cell may be written as:
note that the average voltage of the microgrid distribution line is described as follows:
thus, in conjunction with (8) - (10), the average voltage magnitude can be written as:
wherein n represents the nth network node, E i d Is an initial electrical amplitude which can be flexibly adjusted according to the actual application, i.e. E i d Set to a nominal voltage amplitude, E * And k i Equal to 1, the average voltage can be adjusted as:
therefore, it can be concluded that the average voltage can be equal to the nominal value, as shown in (12).
And S4, further, analyzing corresponding steady-state performance of active power average division and frequency recovery. The active power of each DG is regulated by a frequency droop controller in the consistency droop controller without the need for active and frequency information of the neighboring DG. By using the equivalence between the consistency droop control and the quadratic control, equation (2) can be rewritten as (13):
wherein k is p,ωi And k i,ωi Is DG i Δ ω is the control variable for frequency compensation, P is by low-pass filteringThe average active power measured by the machine.
Further, the matrix form of (13) can be derived as:
wherein
k pωi And k iωi Is DG i Positive gain of (1).
Under steady state conditions, (14) can be rewritten as:
in the formula (I), the compound is shown in the specification,
and
respectively represent
And
is measured at a steady-state value of (c),
and
are respectively
Proportional coefficient and integral coefficient. Considering that the time-dependent portion of (15) is equal to zero in the steady state, it can be obtained
Is a gain vector, t represents a time variable, t 0 Representing the initial time. Note that frequency is a global variable, and active power sharing can be ensured by a droop-based mechanism. Thus, an even sharing of active power can be achieved while maintaining the frequency of any DG unit at a nominal value.
The beneficial effects of the invention are:
1. if the existing consistency control strategy is adopted to realize the power equalization of the island MG system, the active information, the reactive power information, the voltage and the frequency information of each DG unit need to be exchanged, and if any one of the information is lacked or a communication line is disconnected, the power equalization of the system will fail. The consistency droop control method for power distribution and voltage frequency recovery provided by the invention can realize power sharing only by needing reactive power information among DGs. In an island MG system with a large number of distributed power supplies (namely under the condition that a large amount of information needs to be exchanged among DG units), the control method can effectively reduce the communication pressure of the system and improve the reliability of the system.
2. In case of a communication failure, the system cannot exchange any information between DGs, nor naturally can it achieve power averaging, under existing consistency control strategies. Under the same conditions, although the system cannot realize reactive power sharing through a consistent droop control method, active power sharing can still be realized. In addition, the frequency can still be stabilized at the rated value, which indicates that the system is not affected by communication faults.
Drawings
Fig. 1 is a parallel DG unit circuit structure of an island micro grid in an embodiment of the present invention.
Fig. 2 is a control schematic diagram of an islanded microgrid employing a consistent droop control method for power distribution and voltage frequency recovery.
Fig. 3 is a diagram of a dynamic response effect of an island microgrid under a traditional droop control strategy.
Fig. 4 is a dynamic response effect diagram of an island microgrid under the control of a consistency droop control strategy.
Fig. 5 is a diagram of a dynamic response effect of an island microgrid under a consistency droop control strategy in the presence of time delay.
Detailed Description
The embodiments of the invention are described in detail below with reference to the drawings: the present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following embodiments.
Fig. 1 is a parallel DG unit circuit structure of an island microgrid in an embodiment of the present invention, which is composed of 4 DG and 3 loads, each DG unit is connected to the microgrid through a PCC point, and includes a line impedance, a load unit and a static switch, wherein each DG unit is composed of a three-phase full-bridge inverter, an LCL filter and a local controller of the DG unit. In addition, unequal feed line impedances and different power ratings of the DG units are taken into account, with DG1 and DG2 having twice the rated power as DG3 and DG4, the complete parameters being given in table I.
TABLE I
The invention comprises the following steps:
s1, the invention adopts the following droop control technology without communication to represent the relation between the output voltage amplitude and the operating angular frequency of the micro-grid and the corresponding reactive power and active power:
in the formula of Chinese，E i And ω i Which are the voltage amplitude and angular frequency of the actual operation of the microgrid, respectively. E i * And ω i * Rated voltage amplitude and rated angular frequency, m, respectively, for operation of the microgrid i And n i Respectively, frequency and amplitude droop coefficients, P i And Q i Respectively, the measured average active power value and the reactive power value. However, voltage and frequency deviations caused by droop control are unavoidable, and reactive power cannot be shared in this approach. The present invention therefore proposes a consistent droop control scheme for power distribution and voltage frequency recovery, as shown in fig. 2, in which a VSI-based MG inner loop including voltage and current controllers is built to regulate the output voltage and current while maintaining system stability. It can be seen that the reference of the voltage control loop is generated by the proposed unity droop controller.
Due to the defects of the droop controller, a consistency algorithm is introduced and combined with the droop control algorithm to establish a consistency droop controller capable of realizing power distribution and voltage frequency recovery, and the specific expression of the equivalent consistency droop controller is as follows:
wherein p is i Is instantaneous active power, ω i And E i Representing the frequency and amplitude, ω, of the output voltage h And omega c Respectively representing the upper and lower cut-off frequencies, P, of the improved frequency controller i And Q i Respectively measured average active power and reactive power values. m is a unit of i ，k p ，k i And b is a positive gain, ω i * And E i * Rated angular frequency and voltage, χ i Hexix- j Is to consider DG i The weighting coefficient of the capacity can be set equal to DG i The derivative of the droop coefficient.
As shown in fig. 2 and (2), the improved frequency droop controller shown can be used to achieve accurate active power sharing and maintain the frequency of each DG at a nominal value without the need for voltage and frequency information of the neighboring DG. Furthermore, a consistency-based reactive power controller may be used to divide the reactive power evenly while regulating the average voltage of the MG to a nominal value, taking into account the capacity of the DG units.
And S2, further, carrying out steady-state performance analysis on the consistency droop control method. First, the reactive power is further analyzed, and in the time domain, the reactive power/voltage consistent equation can be rewritten as follows:
by taking the derivative of each DG unit output voltage with respect to time, the dynamics of the reactive power unity control can be expressed as:
considering that the derivative of the output voltage is equal to zero in the steady state, the following matrix can be derived:
wherein the Laplace matrix is used
Representing, diagonal matrices
Is defined as
Sum column vector
Are respectively represented as
And
according to two important theorems in graph theory: (1) if a graph is available
Containing a root node means that it has a spanning tree in which there is at least a direct path to each other node. (2)
Is a symmetric positive semi-definite matrix, zero is a vector with right feature
And if and only if
With directed spanning trees, all non-zero eigenvalues have a positive real part, i.e.
So only have pairs
Is that
And k>The solution of 0, (5) can be obtained as follows:
therefore, the reactive power equalization can be realized through the consistency droop controller.
Further, the average voltage adjustment is analyzed for corresponding steady state performance. In view of
(5) Where by multiplication
The following equation can be obtained:
then (7) can be simplified to:
further, the output voltage of each DG unit may be written as follows:
note that the average voltage of the microgrid distribution lines is described as follows:
thus, in conjunction with (8) - (10), the average voltage magnitude can be written as:
wherein E i d Is an initial voltage amplitude which can be flexibly adjusted according to the actual application, i.e. E i d Set to a nominal voltage amplitude, E * And k i Equal to 1, the average voltage can be adjusted as:
therefore, it can be concluded that the average voltage can be equal to the nominal value, as shown in (12).
And further, performing corresponding steady-state performance analysis on active power average division and frequency recovery. The active power of each DG is regulated by a frequency droop controller in the consistency droop controller without the need for active and frequency information of the neighboring DG. By using the equivalence between the consistency droop control and the quadratic control, equation (2) can be rewritten as (13):
wherein k is p,ωi And k i,ωi Is DG i Δ ω is the control variable for frequency compensation and P is the average active power measured by the low pass filter.
Further, the matrix form of (13) can be derived as:
wherein
k pωi And k iωi Is DG i Positive gain of (c).
Under steady state conditions, (14) can be rewritten as:
in the formula (I), the compound is shown in the specification,
and
respectively represent
And
the steady-state value of (a) is,
and
are respectively
Proportional coefficient and integral coefficient. Considering that the time-dependent portion of (15) is equal to zero in the steady state, it can be obtained
Is a gain vector. Note that frequency is a global variable, and active power sharing can be ensured by a droop-based mechanism. Thus, an equal division of active power can be achieved while maintaining the frequency of any DG unit at a nominal value.
In order to verify the accuracy of the proposed consistency droop control strategy under the complex working condition, fig. 3 and fig. 4 are respectively a dynamic response effect diagram of an island micro-grid under the traditional droop control and the consistency droop control strategy, and fig. 5 is a dynamic response effect diagram of the island micro-grid under the consistency droop control strategy under the condition of time delay. In fig. 3, 4 and 5, (a), (b), (c) and (d) show the active power and reactive power of each DG of the microgrid, respectively. Voltage and frequency dynamic response conditions.
Based on the above description of the operating conditions of fig. 3, 4 and 5, the following describes the dynamic effects of fig. 3, 4 and 5 in detail.
As shown in fig. 3 (a), initially the load is connected to the MG system, and the steady state active power of each DG is 1000W, 500W and 500W, respectively. When t =1.5s, the load 1 is disconnected from the MG system, and the active power of each DG is reduced to 750W, 380W and 380W, respectively. The maximum active power fluctuation is about 30W, and the system can stably operate in a short regulation time (about 0.3 s) under the interference condition of a feeder line and a load. At t =3.5s, the load 1 is reconnected, and the active power returns to the normal value within the time of small fluctuation and short regulation, indicating that the system can achieve the active power sharing under the load disturbance through the traditional droop control. However, due to the inherent drawbacks of the conventional droop control, as shown in fig. 3 (b) - (d), the reactive power, voltage and frequency deviation respectively drop by 31.527var, 0.913v and 0.158hz under steady state conditions, which indicates that the stability of the island microgrid under the conventional droop control is not good.
The dynamic response of the proposed load perturbed uniform droop controller in the present invention is shown in fig. 4. In this case, the active and reactive power can be apportioned while the average voltage is regulated to the nominal value, as shown in fig. 4 (a) and (b). Note that in the case of feeder and load disturbances, the reactive power (less than 15.517 var) has only small dynamic fluctuations, as shown in fig. 4 (b). It is recommended that the individual bus voltages should deviate slightly from the nominal values (less than 5%) to achieve an accurate reactive power distribution per DG unit. As shown in fig. 4 (c), when the active and reactive power of the island MG system are divided equally, the maximum voltage difference is less than 0.09V (about 0.15% of the rated voltage amplitude). Furthermore, fig. 4 (d) shows that the frequency can be restored to the nominal value without voltage and frequency information of the domain DG unit. Compared to the conventional control strategy of fig. 3, the fluctuations in fig. 4 are smaller (about 0.028 Hz) and the settling time is shorter (about 0.51 s).
In addition, the influence of the communication delay on the proposed control method is also studied, and a continuous 400 ms delay is added to the DG low-bandwidth sparse communication network of the system. The improved uniformity droop controller is not affected by time delays because the scheme does not require neighborhood active power, frequency and voltage information. Thus, accurate reactive power distribution and frequency recovery can be achieved in the event of communication delays and even a communication system crash. Thus, as can be seen from fig. 5 (a) and 5 (d), the active power sharing and frequency recovery of the system is the same as the dynamic response without communication delay (as in fig. 4 (a) and 4 (d)). Although a slight fluctuation of the output voltage of about 0.2V can be seen in fig. 5 (c), the adjustment can be performed in a short time (less than 1 s). As shown in fig. 5 (b), even in the case of communication delay, accurate reactive power distribution is not affected, and the result of reactive power distribution is substantially the same as that in the case of no delay, indicating that the reliability of the MG system is high.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art, having the benefit of this disclosure, may effect numerous modifications thereto and changes may be made without departing from the scope of the invention in its aspects.
Claims (1)
1. A method for consistent droop control for power distribution and voltage frequency recovery, comprising the steps of:
s1, the following droop control technology without communication is adopted to represent the relation between the output voltage amplitude and the operating angular frequency of the micro-grid and the corresponding reactive power and active power:
in the formula, E i And ω i The voltage amplitude and the angular frequency of actual operation of the micro-grid are respectively; e i * And ω i * Respectively is a rated voltage amplitude value and a rated angular frequency of the micro-grid operation; m is i And n i Frequency and amplitude droop coefficients, respectively; p is i And Q i Respectively the measured average active power value anda reactive power value; however, voltage and frequency deviations caused by droop control are unavoidable, and reactive power cannot be shared in this approach;
and then a consistency algorithm is introduced and combined with a droop control algorithm to establish a consistency droop controller capable of realizing power distribution and voltage frequency recovery, wherein the specific expression of the equivalent consistency droop controller is as follows:
wherein s represents the Laplace operator, α ij Representing the communication relationship of node i and node j, p i Is the instantaneous active power; omega i And E i Representing the frequency and amplitude of the output voltage; omega h And omega c Respectively representing the upper and lower cut-off frequencies of the improved frequency controller; p is i And Q i Measured average active and reactive power values, respectively; q j Represents the average reactive power of the j node; m is i ，k p ，k i And b is a positive gain; omega i * And E i * Rated angular frequency and voltage, respectively; chi-type food processing machine i Hexix j Is to consider DG i The weighting factor of the capacity can be set equal to DG i The derivative of the droop coefficient of;
the improved frequency droop controller as shown in (2) can be used to achieve accurate active power sharing and maintain the frequency of each DG at a nominal value without the need for voltage and frequency information of the neighborhood DG; furthermore, a consistency-based reactive power controller may be used to average the reactive power while regulating the average voltage of the MGs to a nominal value, taking into account the capacity of the DG units;
s2, further, carrying out steady-state performance analysis on the consistency droop control method; first, the reactive power is further analyzed, and in the time domain, the reactive power/voltage consistent equation can be rewritten as follows:
by taking the derivative of each DG unit output voltage with respect to time, the dynamics of the reactive power unity control can be expressed as:
considering that the derivative of the output voltage is equal to zero at steady state, the following matrix can be derived:
it is noted that the bold variables bolded during the derivation of the formula in the present invention all represent matrices or vectors, where the laplacian matrix is denoted by L and the diagonal matrix K is defined as K = diag { K } 1 ,k 2 ,..,k N And column vectors
Q/χ are respectively represented by
And Q χ -1 ＝[Q 1 /χ 1 ,Q 2 /χ 2 ,…,Q N /χ N ] T ；
According to two important theorems in graph theory: (1) if a picture
Containing a root node means that it has a spanning tree in which there is at least a direct path to each other node; (2) l is a symmetric positive semi-definite matrix; zero is a vector with a right feature1And if and only if
With directed spanning trees, all non-zero eigenvalues have a real positive part, L1 n ＝0 n ,1 T n L＝0 T n N represents the nth network node; so the only non-zero solution for lx =0 is X = k1And k>The solution of 0, (5) can be obtained as follows:
Q＝k(χ) -1 1，k＞0 (6)
therefore, the reactive power equalization can be realized through the consistency droop controller;
s3, further, analyzing corresponding steady-state performance of the average voltage regulation; in view of1 T n L＝0 T n In the formula (5), by multiplying1 T n K -1 The following equation can be obtained:
then (7) can be simplified to:
further, the output voltage of each DG unit may be written as follows:
note that the average voltage of the microgrid distribution line is described as follows:
thus, in conjunction with (8) - (10), the average voltage magnitude can be written as:
where n represents the nth network node,
is an initial voltage amplitude which can be flexibly adjusted according to practical application, i.e.
Set to a nominal voltage amplitude, E * And k i Equal to 1, the average voltage can be adjusted as:
therefore, it can be concluded that the average voltage can be equal to the nominal value, as shown in (12);
s4, further, analyzing corresponding steady-state performance of active power average and frequency recovery; the active power of each DG is adjusted by a frequency droop controller in the consistency droop controller, and the active and frequency information of the adjacent DGs is not needed; by using the equivalence between the consistency droop control and the quadratic control, equation (2) can be rewritten as (13):
wherein k is p,ωi And k i,ωi Is DG i Δ ω is the control variable for frequency compensation, P is the average active power measured by the low-pass filter;
further, the matrix form of (13) can be derived as:
ω＝ω * -mP+J(ω * -ω) (14)
wherein J = diag { k } pωi +k iωi /s},i∈[1,N]，k pωi And k iωi Is DG i A positive gain of (d); omega * ＝ω * 1,ω＝[ω 1 ,ω 2 ,…,ω N ] T ,m＝diag{m i }，P＝[P 1 ,P 2 …P N ] T ；
Under steady state conditions, (14) can be rewritten as:
ω s ＝ω s,* -nP s +J p (ω s,* -ω s )+J I (ω s,* -ω s )(t-t 0 )+K ω (t 0 ) (15)
in the formula, omega s ，ω s,* And P s Respectively represent omega, omega * And steady state values of P; j. the design is a square p And J I Are the proportionality and integration coefficients of J, K ω Is a gain vector, t represents a time variable, t 0 Represents an initial time; in consideration of the fact that the time-dependent portion of (15) is equal to zero in the steady state, ω can be obtained s ＝ω s,* (ii) a Note that frequency is a global variable, and active power averaging can be ensured through a droop-based mechanism; thus, a sharing of active power can be achieved while keeping the frequency of any DG unit at a nominal value.
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| CN112821413A (en) * | 2021-01-27 | 2021-05-18 | 哈尔滨工业大学（威海） | Method, device, equipment and storage medium for controlling secondary voltage of micro-grid |
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| CN115001055B (en) | 2022-08-03 | 2022-11-08 | 深圳市德兰明海科技有限公司 | Multi-inverter parallel connection self-adaptive control method and device and multi-inverter parallel connection system |
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