CN111817359B - Micro-grid solvable boundary analysis method based on equivalent circuit - Google Patents

Micro-grid solvable boundary analysis method based on equivalent circuit Download PDF

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CN111817359B
CN111817359B CN202010597932.4A CN202010597932A CN111817359B CN 111817359 B CN111817359 B CN 111817359B CN 202010597932 A CN202010597932 A CN 202010597932A CN 111817359 B CN111817359 B CN 111817359B
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CN111817359A (en
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王冲
鞠平
吴峰
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Hohai University HHU
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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
    • H02J3/48—Controlling the sharing of the in-phase component
    • 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
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • 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
    • H02J3/50—Controlling the sharing of the out-of-phase component
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

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  • Power Engineering (AREA)
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Abstract

The invention relates to a method for analyzing a solvable boundary of a microgrid based on an equivalent circuit, and belongs to the technical field of the microgrid. The method comprises the following steps: 1) expanding a droop control equation of active power and reactive power to obtain a corresponding full power flow model; 2) obtaining an equivalent system model containing a virtual voltage source according to the full power flow model; 3) constructing a Jacobian matrix corresponding to an equivalent system containing a virtual voltage source; 4) and for the Jacobian matrix, obtaining whether the system can be solved or not by utilizing Wirtinger calculus and Levy-Desplanques theorem, and judging the solvable boundary of the micro-grid based on droop control by defining an index and the value of the index. The droop control method comprehensively considers the droop control of the micro-grid, expands the droop control equations of the active power and the reactive power to obtain an equivalent circuit containing the virtual power supply, and can directly utilize the online voltage and the injection power to judge the solvability of the original system based on the judgment basis.

Description

Micro-grid solvable boundary analysis method based on equivalent circuit
Technical Field
The invention relates to a method for analyzing a solvable boundary of a microgrid based on an equivalent circuit, and belongs to the technical field of the microgrid.
Background
In recent years, with the development of renewable energy technology, the proportion of distributed power sources in a power system is higher and higher, distributed power generation has the advantages of economy, environmental protection and the like due to the development and utilization of renewable energy, and a microgrid is widely developed and applied as an efficient distributed power source integration mode. The micro-grid realizes self-management and control of the network mainly on the basis of a distributed power supply, electric energy conversion equipment, a load and a control strategy. In an island situation, a droop control strategy based on active power and reactive power is adopted in a common situation, and distribution of the active power and the reactive power is achieved.
The droop control strategy has great influence on the operation and control of the micro-grid, the set active reference value, the set reactive reference value and the droop control strategy coefficient have great influence on the safe operation of the micro-grid, and improper parameter setting can lead the micro-grid operating point to be closer to a safe and stable boundary, so that the risk of the micro-grid operation is increased. How to judge the safety of the operating point of the micro-grid by using the self information (such as voltage, power and parameter information) of the micro-grid is necessary. At present, the number of patents and documents for this convenience is relatively small, and intensive research and investigation are required.
Disclosure of Invention
Aiming at the problems, the invention provides a microgrid solvable boundary analysis method based on an equivalent circuit, which comprises the steps of expanding droop control to obtain a corresponding full power flow model, further obtaining an equivalent system model containing a virtual voltage source, and analyzing a Jacobian matrix of the equivalent system model by utilizing Wirtinger calculus and Levy-Desplanques theorem to obtain a basis for judging whether a system operation point is safe.
The invention adopts the following technical scheme for solving the technical problems:
a method for analyzing a solvable boundary of a microgrid based on an equivalent circuit comprises the following steps:
1) based on the collected active power and reactive power of the micro-grid, a droop control equation of the active power and the reactive power is expanded to obtain a corresponding full-power-flow model;
2) obtaining an equivalent system model containing a virtual voltage source based on the measured voltage of the microgrid and a full power flow model;
3) constructing a Jacobian matrix corresponding to an equivalent system containing a virtual voltage source;
4) and for the Jacobian matrix, whether the system can be solved is obtained by utilizing Wirtinger calculus and Levy-Desplanques theorem, and the solvable boundary of the micro-grid based on droop control is judged by defining an index and the value of the index.
The step 1) specifically comprises the following steps:
1-1) active control of droop control
Figure BDA0002557728400000021
In (1)
Figure BDA0002557728400000022
According to Vi1 and thetaiUnfolding with 0 to obtain
Figure BDA0002557728400000023
1-2) reactive control of droop control
Figure BDA0002557728400000024
In (1)
Figure BDA0002557728400000025
According to Vi1 and thetaiUnfolding with 0 to obtain
Figure BDA0002557728400000026
1-3) obtaining full power flow model of active control and reactive control based on expansion quantity
Figure BDA0002557728400000027
Figure BDA0002557728400000028
And
Figure BDA0002557728400000029
in the formula, thetaiThe phase angle of the voltage is represented,
Figure BDA00025577284000000210
reference value, P, representing the phase angle of the voltageiThe active power of the node is represented,
Figure BDA00025577284000000211
reference value, V, representing the active power of a nodeiWhich is indicative of the magnitude of the voltage at the node,
Figure BDA00025577284000000212
representing the node voltage amplitude reference, QiWhich represents the reactive power of the node(s),
Figure BDA00025577284000000213
a reference value representing the reactive power of the node,
Figure BDA00025577284000000214
and
Figure BDA00025577284000000215
are the corresponding coefficients.
The step 2) specifically comprises the following steps:
2-1) introducing a new parameter
Figure BDA00025577284000000216
2-2) according to the obtained full power flow model and the introduced kiNode i with droop control is equivalent to a constant voltage source with a through reactance value of kiIs connected to node i, the constant voltage source has a voltage amplitude of
Figure BDA00025577284000000217
Phase angle of
Figure BDA00025577284000000218
At the same time, node i has reactive power
Figure BDA00025577284000000219
And active power
Figure BDA00025577284000000220
And injecting to obtain an equivalent system model containing a virtual voltage source.
The step 3) specifically comprises the following steps:
3-1) for an equivalent system containing virtual voltage sources, constructing the Jacobian matrix of the equivalent system
Figure BDA0002557728400000031
Wherein, P is an active vector, Q is a reactive vector, theta is a voltage phase angle vector, and V is a voltage amplitude vector;
3-2) for Jacobian matrix J, write to by transformation
Figure BDA0002557728400000032
In the formula IRIs the vector of the real part of the current, IIIs the imaginary vector of the current;
3-3) when J' is not singular, obtaining equivalent power flow energy solving of the system with the virtual voltage source, namely representing that the original system is within the energy solving boundary.
The step 4) specifically comprises the following steps:
4-1) Current, Voltage and admittance for an equivalent System with a virtual Voltage Source written as follows
Figure BDA0002557728400000037
Based on this, obtain
Figure BDA0002557728400000033
And
Figure BDA0002557728400000034
4-2) Jacobian matrix J using Wirtinger calculus and Levy-Desplanques theorem′Non-singular sufficiency conditions are
Figure BDA0002557728400000035
In the formula ISInjecting a current vector, I, for a power supply nodeDInjecting a current vector, V, into a node of a load nodeSNode voltage vector, V, of the power supply nodeDNode voltage vector, Y, of load nodeSSFormed as a matrix of elements of the admittance matrix associated with the power supply nodes, YSDMutual admittance matrix, Y, of load nodes and power supply nodes in the admittance matrixDDFor matrices formed by elements of the admittance matrix associated with the load nodes, ZDDFormed as a matrix of load node-related elements of the impedance matrix, VD(k) And VD(k') are each VDK and k' elements of (2), SD(k ') is the k' th element of the complex power vector of the load, ZDD(k, k') is ZDDK and k' represent count scalars, S and D represent power and load, respectively;
4-3) defining the index
Figure BDA0002557728400000036
Judging whether the micro-grid based on droop control is within the solvable boundary or not by judging the value of the index R, wherein R exists for all load nodes>1, illustrating that the power flow of an equivalent system containing a virtual voltage source can be solved, namely, indicating that a micro-grid based on droop control is within an solvable boundary; conversely, the representation is not within the solvable boundary.
The invention has the following beneficial effects:
the droop control method comprehensively considers the droop coefficient in the droop control of the micro-grid, expands the droop control equation of the active power and the reactive power to obtain an equivalent circuit containing the virtual power supply, and can directly utilize the online voltage and the injection power to judge the solvability of the original system based on the judgment basis.
Drawings
Fig. 1 is an original system diagram of a method for solving boundary analysis of a microgrid based on an equivalent circuit method.
Fig. 2 is an equivalent system diagram of the method for solving boundary analysis of the microgrid based on the equivalent circuit method.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Fig. 1 is an original system diagram of a method for solving boundary analysis of a microgrid based on an equivalent circuit method, wherein a node is connected with a control unit containing droop control. Fig. 2 is an equivalent system diagram of a method for solving boundary analysis of a microgrid based on an equivalent circuit method, wherein a control unit including droop control in fig. 1 is equivalent to a virtual voltage source and equivalent reactance.
The invention provides a method for analyzing a solvable boundary of a droop control microgrid based on an equivalent circuit method, which comprises the following steps of sequentially executing:
step 1: expanding a droop control equation of active power and reactive power to obtain a corresponding full power flow model;
1-1) active control of droop control
Figure BDA0002557728400000041
In (1)
Figure BDA0002557728400000042
According to Vi1 and thetaiUnfolding with 0 to obtain
Figure BDA0002557728400000043
1-2) reactive control of droop control
Figure BDA0002557728400000044
In (1)
Figure BDA0002557728400000045
According to Vi1 and thetaiUnfolding with 0 to obtain
Figure BDA0002557728400000046
1-3) based on the expansion quantity, a full power flow model for active control and reactive control can be obtained
Figure BDA0002557728400000047
Figure BDA0002557728400000048
And
Figure BDA0002557728400000049
in the formula, thetaiThe phase angle of the voltage is represented,
Figure BDA00025577284000000410
reference value, P, representing the phase angle of the voltageiThe active power of the node is represented,
Figure BDA00025577284000000411
reference value, V, representing the active power of a nodeiWhich is indicative of the magnitude of the voltage at the node,
Figure BDA00025577284000000412
representing the node voltage amplitude reference, QiWhich represents the reactive power of the node(s),
Figure BDA00025577284000000413
a reference value representing the reactive power of the node,
Figure BDA00025577284000000414
and
Figure BDA00025577284000000415
are the corresponding coefficients. Step 2: obtaining an equivalent system model containing a virtual voltage source according to the full power flow model;
2-1) introducing a new parameter
Figure BDA00025577284000000416
2-2) based on the parameter kiThe full power flow can be re-expressed as
Figure BDA0002557728400000051
And
Figure BDA0002557728400000052
2-3) based on
Figure BDA0002557728400000053
And
Figure BDA0002557728400000054
Figure BDA0002557728400000055
droop control can be equivalent to a constant voltage source with a through reactance value of kiIs connected to node i, the constant voltage source has a voltage amplitude of
Figure BDA0002557728400000056
Phase angle of
Figure BDA0002557728400000057
At the same time, node i has reactive power
Figure BDA0002557728400000058
And active power
Figure BDA0002557728400000059
And injecting to obtain an equivalent system model containing a virtual voltage source. As shown in fig. 1.
And step 3: and constructing a corresponding Jacobian matrix for an equivalent system containing a virtual voltage source.
3-1) for an equivalent system containing virtual voltage sources, constructing the Jacobian matrix of the equivalent system
Figure BDA00025577284000000510
3-2) for Jacobian matrix J, it can be written by equivalent transformation
Figure BDA00025577284000000511
3-3) when J' is not singular, the equivalent tidal current energy of the system with the virtual voltage source can be obtained to solve, namely, the original system is shown to be within the energy solving boundary.
Wherein P is an active vector, Q is a reactive vector, θ is a voltage phase angle vector, V is a voltage magnitude vector, IRIs the vector of the real part of the current, IIIs the imaginary vector of the current.
And 4, step 4: and analyzing the singularity of the Jacobian matrix by utilizing the Wirtinger calculus and the Levy-Desplanques theorem to obtain whether the system can solve or not.
4-1) for an equivalent system with virtual voltage sources the currents, voltages and admittances as shown in FIG. 2 are written in the form of a matrix
Figure BDA00025577284000000512
Based on this matrix equation, one can obtain
Figure BDA00025577284000000513
Figure BDA00025577284000000514
And
Figure BDA00025577284000000515
4-2) judging whether the Jacobian matrix J' is singular or not, namely judging whether the system can solve or not, namely judging whether the system is in a boundary capable of solving or not. Judging whether the matrix J' is singular or not by utilizing Wirtinger calculus and Levy-Desplanques theorem to obtain the non-singular sufficient condition of the matrix J
Figure BDA00025577284000000516
In the formula ISInjecting a current vector, I, for a power supply nodeDInjecting a current vector, V, into a node of a load nodeSNode voltage vector, V, of the power supply nodeDNode voltage vector, Y, of load nodeSSFormed as a matrix of elements of the admittance matrix associated with the power supply nodes, YSDMutual admittance matrix, Y, of load nodes and power supply nodes in the admittance matrixDDFor matrices formed by elements of the admittance matrix associated with the load nodes, ZDDFormed as a matrix of load node-related elements of the impedance matrix, VD(k) And VD(k') are each VDK and k' elements of (2), SD(k ') is the k' th element of the complex power vector of the load, ZDD(k, k') is ZDDK and k' represent count scalars, and S and D represent power and load, respectively.
4-3) non-singular sufficiency condition based on matrix J' is
Figure BDA0002557728400000061
Defining an index
Figure BDA0002557728400000062
And 4-4) collecting the system state (voltage, power and system network parameters) and calculating the index R. R >1 is provided for all load nodes, and the equivalent power flow energy solving of the system with the virtual voltage source is illustrated, namely the micro-grid based on droop control is shown to be within the energy solving boundary; conversely, the representation is not within the solvable boundary.

Claims (5)

1. A method for analyzing a solvable boundary of a microgrid based on an equivalent circuit is characterized by comprising the following steps:
1) based on the collected active power and reactive power of the micro-grid, a droop control equation of the active power and the reactive power is expanded to obtain a corresponding full-power-flow model:
Figure FDA0003249973780000011
and
Figure FDA0003249973780000012
in the formula, thetaiThe phase angle of the voltage is represented,
Figure FDA0003249973780000013
reference value, P, representing the phase angle of the voltageiThe active power of the node is represented,
Figure FDA0003249973780000014
reference value, V, representing the active power of a nodeiWhich is indicative of the magnitude of the voltage at the node,
Figure FDA0003249973780000015
representing the node voltage amplitude reference, QiWhich represents the reactive power of the node(s),
Figure FDA0003249973780000016
a reference value representing the reactive power of the node,
Figure FDA0003249973780000017
and
Figure FDA0003249973780000018
is the corresponding coefficient;
2) obtaining an equivalent system model containing a virtual voltage source based on the measured voltage of the microgrid and a full power flow model;
3) constructing a Jacobian matrix corresponding to an equivalent system containing a virtual voltage source;
4) for the Jacobian matrix, whether the system can be solved is obtained by utilizing Wirtinger calculus and Levy-Desplanques theorem, and the solvable boundary of the micro-grid based on droop control is judged by defining an index R and the value of the index; the index R is defined as
Figure FDA0003249973780000019
In the formula, VD(k) And VD(k ') are the kth and kth' elements, Z, respectively, of the load node voltage vectorDD(k, k ') is the k-th row and k' -th column crossing element of the impedance matrix, SD(k') denotes the node injecting the kth element of the apparent power vector; by judging the value of the index R, whether the micro-grid based on droop control is within the solvable boundary can be judged; with R for all load nodes>1, illustrating that the micro-grid based on droop control is within the solvable boundary; conversely, the representation is not within the solvable boundary.
2. The method for analyzing the resolvable boundary of the microgrid based on the equivalent circuit as claimed in claim 1, wherein the step 1) specifically comprises the following steps:
1-1) active control of droop control
Figure FDA00032499737800000110
In (1)
Figure FDA00032499737800000111
According to Vi1 and thetaiUnfolding with 0 to obtain
Figure FDA00032499737800000112
1-2) reactive control of droop control
Figure FDA00032499737800000113
In (1)
Figure FDA00032499737800000114
According to Vi1 and thetaiUnfolding with 0 to obtain
Figure FDA00032499737800000115
1-3) obtaining full power flow model of active control and reactive control based on expansion quantity
Figure FDA0003249973780000021
Figure FDA0003249973780000022
And
Figure FDA0003249973780000023
in the formula, thetaiThe phase angle of the voltage is represented,
Figure FDA0003249973780000024
reference value, P, representing the phase angle of the voltageiThe active power of the node is represented,
Figure FDA0003249973780000025
reference value, V, representing the active power of a nodeiWhich is indicative of the magnitude of the voltage at the node,
Figure FDA0003249973780000026
representing the node voltage amplitude reference, QiRepresenting reactive power of a nodeThe ratio of the total weight of the particles,
Figure FDA0003249973780000027
a reference value representing the reactive power of the node,
Figure FDA0003249973780000028
and
Figure FDA0003249973780000029
are the corresponding coefficients.
3. The method for analyzing the resolvable boundary of the microgrid based on the equivalent circuit as claimed in claim 2, wherein the step 2) specifically comprises the following steps:
2-1) introducing a new parameter
Figure FDA00032499737800000210
2-2) according to the obtained full power flow model and the introduced kiNode i with droop control is equivalent to a constant voltage source with a through reactance value of kiIs connected to node i, the constant voltage source has a voltage amplitude of
Figure FDA00032499737800000211
Phase angle of
Figure FDA00032499737800000212
At the same time, node i has reactive power
Figure FDA00032499737800000213
And active power
Figure FDA00032499737800000214
And injecting to obtain an equivalent system model containing a virtual voltage source.
4. The method for analyzing the resolvable boundary of the microgrid based on the equivalent circuit as claimed in claim 1, wherein the step 3) specifically comprises the following steps:
3-1) for an equivalent system containing virtual voltage sources, constructing the Jacobian matrix of the equivalent system
Figure FDA00032499737800000215
Wherein, P is an active vector, Q is a reactive vector, theta is a voltage phase angle vector, and V is a voltage amplitude vector;
3-2) for Jacobian matrix J, write to by transformation
Figure FDA00032499737800000216
In the formula IRIs the vector of the real part of the current, IIIs the imaginary vector of the current;
3-3) when J' is not singular, obtaining equivalent power flow energy solving of the system with the virtual voltage source, namely representing that the original system is within the energy solving boundary.
5. The method for analyzing the resolvable boundary of the microgrid based on the equivalent circuit as claimed in claim 1, wherein the step 4) specifically comprises the following steps:
4-1) Current, Voltage and admittance for an equivalent System with a virtual Voltage Source written as follows
Figure FDA00032499737800000217
Based on this, obtain
Figure FDA00032499737800000218
And
Figure FDA00032499737800000219
4-2) utilizing Wirtinger calculus and Levy-Desplanques theorem, wherein the nonsingular sufficient condition of the Jacobian matrix J' is
Figure FDA0003249973780000031
In the formula ISInjecting a current vector, I, for a power supply nodeDInjecting a current vector, V, into a node of a load nodeSNode voltage vector, V, of the power supply nodeDNode voltage vector, Y, of load nodeSSFormed as a matrix of elements of the admittance matrix associated with the power supply nodes, YSDMutual admittance matrix, Y, of load nodes and power supply nodes in the admittance matrixDDFor matrices formed by elements of the admittance matrix associated with the load nodes, ZDDFormed as a matrix of load node-related elements of the impedance matrix, VD(k) And VD(k') are each VDK and k' elements of (2), SD(k ') is the k' th element of the complex power vector of the load, ZDD(k, k') is ZDDK and k' represent count scalars, S and D represent power and load, respectively;
4-3) defining the index
Figure FDA0003249973780000032
Judging whether the micro-grid based on droop control is within the solvable boundary or not by judging the value of the index R, wherein R exists for all load nodes>1, illustrating that the power flow of an equivalent system containing a virtual voltage source can be solved, namely, indicating that a micro-grid based on droop control is within an solvable boundary; conversely, the representation is not within the solvable boundary.
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CN105514971A (en) * 2015-11-02 2016-04-20 湘潭大学 Flow calculation method suitable for microgrids in various operation modes
CN109274116A (en) * 2018-09-12 2019-01-25 湘潭大学 A kind of alternating current-direct current mixing micro-capacitance sensor continuous tide calculation method
CN109617079A (en) * 2018-12-18 2019-04-12 华南理工大学 A kind of existence and method for analyzing stability of direct-flow distribution system flow solution

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CN105514971A (en) * 2015-11-02 2016-04-20 湘潭大学 Flow calculation method suitable for microgrids in various operation modes
CN109274116A (en) * 2018-09-12 2019-01-25 湘潭大学 A kind of alternating current-direct current mixing micro-capacitance sensor continuous tide calculation method
CN109617079A (en) * 2018-12-18 2019-04-12 华南理工大学 A kind of existence and method for analyzing stability of direct-flow distribution system flow solution

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