Method for modeling new power system with virtual synchronous machine

Abstract

The application discloses a novel power system modeling method containing a virtual synchronous machine, and comprises the following steps: S1, constructing a reactive power control loop with feedback regulation, and deriving a state space equation of a single virtual synchronous machine (VSG) in a rotating coordinate system d-q axis by using a conventional power system modeling theory; S2, converting the state space equation of the single VSG from the rotating coordinate system d-q axis to a common coordinate system x-y axis by using a coordinate conversion theory, and constructing an overall state space equation of a novel power system dominated by the VSG in the common coordinate system x-y axis; and S3, combining a node voltage linearization equation and the overall state space equation of the system to derive a state matrix of the novel power system. The application constructs the reactive power control loop with the feedback regulation, realizes the novel power system modeling containing the VSG, and provides a model support for subsequent frequency stability analysis of the novel power system.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of new power systems, in particular to a new power system modeling method containing a virtual synchronous machine. BACKGROUND

[0002] With the acceleration of energy transformation and the development of distributed energy, the proportion of renewable energy generation in new power systems is increasing, leading to a decrease in system inertia level and a decline in anti-interference ability. At the same time, the random fluctuations of renewable energy equipment output and the uncertainty fluctuations of load will cause large voltage fluctuations in power grid operation and increase the complexity of power grid system. The virtual synchronous machine (VSG) technology can simulate the operating characteristics of synchronous generators, providing virtual inertia and damping for power systems, thereby improving the stability of the system. However, the modeling of virtual synchronous machines (VSG) is a complex problem, and traditional power system modeling methods cannot accurately describe the dynamic characteristics of virtual synchronous machines (VSG). Therefore, the present application proposes a new power system modeling method containing a virtual synchronous machine (VSG), which constructs a reactive power control loop with feedback regulation and realizes the modeling of new power systems containing virtual synchronous machines (VSG), providing model support for subsequent frequency stability analysis of new power systems. SUMMARY

[0003] To achieve the above-mentioned purpose, the technical solution provided by the present application is as follows:

[0004] S1: Construct a reactive power control loop with feedback regulation, and use traditional power system modeling theory to derive the state space equation of a single virtual synchronous machine (VSG) in the rotating coordinate system d-q axis.

[0005] S2: Use coordinate transformation theory to convert the state space equation of a single virtual synchronous machine (VSG) from the rotating coordinate system d-q axis to the common coordinate system x-y axis, and construct the overall state space equation of the new power system dominated by the virtual synchronous machine (VSG) in the common coordinate system x-y axis.

[0006] S3: Combine the node voltage linearization equation and the overall state space equation of the system to derive the state matrix of the new power system.

[0007] The step S1 includes:

[0008] S1-1: For the virtual synchronous machine (VSG), a reactive power control loop with feedback regulation is proposed, which includes: taking the difference between the reference reactive power Q ref and the output reactive power Q o as the input; the reactive power coefficient k QFor the forward path, the feedback coefficient k F The output of the feedback loop is summed with the reference electromotive force E ref to form the output electromotive force E

[0009] S1-2: Neglect the differential equation in the voltage-current double closed loop, reduce the influence of PI control parameters in the voltage-current double closed loop on the dynamic characteristics of the system, and construct the differential equation of the virtual synchronous generator VSG control link as follows:

[0010] (1)

[0011] In formula (1), δ is the output power angle, ω is the output angular frequency, ω ref is the reference angular frequency, P ref is the reference active power, P o is the output active power, H is the inertia, D is the damping;

[0012] S1-3: Small signal processing is performed on formula (1), and the linear equation of the virtual synchronous generator VSG control link is obtained as follows:

[0013] (2)

[0014] In formula (2), Δ δ is the power angle deviation, Δ ω is the angular frequency deviation, Δ E is the electromotive force deviation, Δ P o and Δ Q o are the active power deviation and the reactive power deviation, respectively, which are expressed by linear equations as follows:

[0015] (3)

[0016] In formula (3), Δ U d , Δ U q and Δ I d , Δ I q are the node voltage and node current deviation of the rotating coordinate system d-q axis, U d , U q ​With I d , I q Output voltage and output current of d-q axis of rotating coordinate system;

[0017] S1-4: using power system state space modeling theory, combining formula (1), formula (2), formula (3), the state space equation of a single virtual synchronous generator VSG under the d-q axis of the rotating coordinate system is constructed as follows:

[0018] (4)

[0019] In formula (4), A VSG , B IVSG , B VVSG , C VSG and D VSG are coefficient matrices, and their expressions are as follows:

[0020] (5)

[0021] In formula (5), A Z L is the line impedance between a single virtual synchronous generator VSG and a network node.

[0022] The step S2 comprises:

[0023] S2-1: the coordinate transformation formula of the state space equation of a single virtual synchronous generator VSG under the d-q axis of the rotating coordinate system to the common coordinate system x-y axis is as follows:

[0024] (6)

[0025] In formula (6), A U x , U y and B I x , I y are node voltage and node current of the common coordinate system x-y axis;

[0026] S2-2: combining formula (4) and formula (6), the state space equation of a single virtual synchronous generator VSG is converted from the d-q axis of the rotating coordinate system to the common coordinate system x-y axis, and the state space equation of a single virtual synchronous generator VSG under the common coordinate system x-y axis is as follows:

[0027] (7)

[0028] In formula (7), Δ U x , ΔU y ΔI I x ΔU I y are the deviation of node voltage and node current of the common coordinate system x-y axis, matrix , , and The expression of matrixes

[0029] (8)

[0030] S2-3: combine the state space equation of each virtual synchronous generator VSG in the common coordinate system x-y axis, and obtain the overall state space equation of the new type of power system dominated by the virtual synchronous generator VSG as:

[0031] (9)

[0032] In formula (9), matrix ΔI M and ΔU M are the node injection current and node voltage deviation vector matrix of all virtual synchronous generators VSG; the expressions of matrixes A M , B M , C M and D M are respectively:

[0033] (10)

[0034] In formula (10), j is the number of virtual synchronous generators.

[0035] The step S3 comprises:

[0036] S3-1: based on the power system modeling theory, the node voltage equation of the power system is expressed in the form of real part and imaginary part as:

[0037] (11)

[0038] In formula (11), Y G ii and Y B ii are the real part and imaginary part of the admittance matrix Y ii of the i-th node respectively, U xi , U yi and I xi , I yirespectively represent the real part and the imaginary part of the i-th node voltage and the i-th node current of the public coordinate system x-y axis, i=1, 2, …, r, r is the number of nodes of the power network;

[0039] S3-2: linearizing formula (11) to obtain the linear equation of the node voltage as:

[0040] (12)

[0041] In formula (12), ΔU gen , ΔI gen represents the node voltage and the injected current deviation vector matrix of all virtual synchronous machines VSG nodes, ΔU load , ΔI load is the node voltage and the injected current deviation vector matrix of all load nodes, the matrix Y GG represents the admittance matrix between the virtual synchronous machines VSG nodes, the matrix Y LL represents the admittance matrix between the load nodes, the matrix Y GL and Y LG is the admittance matrix between the virtual synchronous machines VSG nodes and the load nodes.

[0042] S3-3: combining formula (9), formula (12), and deducing the state matrix A of the new type of power system containing virtual synchronous machines VSG as:

[0043] (13).

[0044] Compared with the prior art, the principle and advantages of the scheme are as follows:

[0045] The application discloses a new type of power system modeling method containing virtual synchronous machines, comprising the following steps: S1: constructing a reactive power control loop with feedback regulation, and deducing the state space equation of a single virtual synchronous machine VSG under the d-q axis of the rotating coordinate system by using the traditional power system modeling theory; S2: converting the state space equation of the single virtual synchronous machine VSG from the d-q axis of the rotating coordinate system to the x-y axis of the public coordinate system by using the coordinate transformation theory, and constructing the overall state space equation of the new type of power system dominated by the virtual synchronous machine VSG under the x-y axis of the public coordinate system; and S3: combining the node voltage linearization equation and the overall state space equation of the system to deduce the state matrix of the new type of power system. The application constructs the reactive power control loop with feedback regulation, realizes the new type of power system modeling containing virtual synchronous machines VSG, and provides model support for subsequent frequency stability analysis of the new type of power system. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 It is a flow chart of the new type of power system modeling method containing virtual synchronous machines VSG in the embodiment of the application.

[0047] Figure 2 a schematic diagram of a reactive power control loop with feedback regulation in an embodiment of the present application;

[0048] Figure 3 a system eigenvalue distribution diagram in an embodiment of the present application;

[0049] Figure 4 a participation factor analysis diagram of each virtual synchronous generator VSG in an oscillation mode in an embodiment of the present application. DETAILED DESCRIPTION

[0050] The present application will be further described below in conjunction with specific embodiments:

[0051] Figure 1 a flowchart of a novel power system modeling method with virtual synchronous generators VSGs, Figure 2 a schematic diagram of a reactive power control loop with feedback regulation, comprising the following steps:

[0052] S1: constructing a reactive power control loop with feedback regulation, and deriving a state space equation of a single virtual synchronous generator VSG in a rotating coordinate system d-q axis by using a conventional power system modeling theory;

[0053] S2: converting the state space equation of the single virtual synchronous generator VSG from the rotating coordinate system d-q axis to a common coordinate system x-y axis by using a coordinate transformation theory, and constructing an overall state space equation of a novel power system dominated by the virtual synchronous generator VSG in the common coordinate system x-y axis;

[0054] S3: combining a node voltage linearization equation and the overall state space equation of the system to derive a state matrix of the novel power system.

[0055] The step S1 comprises:

[0056] S1-1: proposing a reactive power control loop with feedback regulation for the virtual synchronous generator VSG, which has a structure comprising: taking a difference between a reference reactive power Q ref and an output reactive power Q o as an input; taking a reactive coefficient k Q as a forward channel, and taking a feedback coefficient k F as a negative feedback loop; taking a sum of a reference electromotive force E ref and an output electromotive force E as an output electromotive force

[0057] S1-2: Neglect the differential equation in the voltage and current double closed loop, reduce the influence of PI control parameters in the voltage and current double closed loop on the dynamic characteristics of the system, and construct the differential equation of the virtual synchronous generator VSG control link as:

[0058] (14)

[0059] In formula (14), δ is the output power angle, ω is the output angular frequency, ω ref is the reference angular frequency, P ref is the reference active power, P o is the output active power, H is the inertia, D is the damping;

[0060] S1-3: Small signal processing is performed on formula (14) to obtain the linear equation of the virtual synchronous generator VSG control link as:

[0061] (15)

[0062] In formula (15), Δ δ is the power angle deviation, Δ ω is the angular frequency deviation, Δ E is the electromotive force deviation, Δ P o and Δ Q o are the active power deviation and the reactive power deviation respectively, which are expressed by linear equations as:

[0063] (16)

[0064] In formula (16), Δ U d , Δ U q , Δ I d , Δ I q are the node voltage and node current deviation of the rotating coordinate system d-q axis, U d , U q and I d , I q are the output voltage and output current of the rotating coordinate system d-q axis;

[0065] S1-4: using the power system state space modeling theory, combining formula (14), formula (15), formula (16), the state space equation of a single virtual synchronous generator VSG under the d-q axis of the rotating coordinate system is constructed as follows:

[0066] (17)

[0067] In formula (17), A VSG , B IVSG , B VVSG , C VSG and D VSG are coefficient matrices, and their expressions are as follows:

[0068] (18)

[0069] In formula (18), A Z L is the line impedance between a single virtual synchronous generator VSG and a network node.

[0070] The step S2 includes:

[0071] S2-1: the coordinate transformation formula of the state space equation of a single virtual synchronous generator VSG under the d-q axis of the rotating coordinate system to the x-y axis of the common coordinate system is as follows:

[0072] (19)

[0073] In formula (19), A U x , U y , I x , I y are the node voltage and the node current of the x-y axis of the common coordinate system;

[0074] S2-2: combining formula (17) and formula (19), the state space equation of a single virtual synchronous generator VSG is converted from the d-q axis of the rotating coordinate system to the x-y axis of the common coordinate system, and the state space equation of a single virtual synchronous generator VSG under the x-y axis of the common coordinate system is as follows:

[0075] (20)

[0076] In formula (20), Δ U x , Δ U y , Δ I x , Δ I yThe expressions of the matrices , , and are respectively:

[0077] (21)

[0078] S2-3: Combining the state space equations of each virtual synchronous machine VSG in the common coordinate system x-y axis, the overall state space equation of the new type of power system dominated by the virtual synchronous machine VSG is obtained:

[0079] (22)

[0080] In equation (22), the matrices ΔI M and ΔU M are the node injection current and node voltage deviation vector matrices of all virtual synchronous machines VSG; the expressions of the matrices A M , B M , C M and D M are respectively:

[0081] (23)

[0082] In equation (23), j is the number of virtual synchronous machines.

[0083] The step S3 includes:

[0084] S3-1: Based on the power system modeling theory, the node voltage equation of the power system is expressed in the form of real part and imaginary part as:

[0085] (24)

[0086] In equation (24), G ii and B ii represent the real part and imaginary part of the admittance matrix Y ii of the i-th node, U xi , U yi and I xi , I yi respectively represent the real part and imaginary part of the i-th node voltage and the i-th node current in the common coordinate system x-y axis, i=1, 2, …, r, r is the number of nodes of the power network;

[0087] S3-2: Linearizing formula (24), the linearized equation of the node voltage is obtained as follows:

[0088] (25)

[0089] In formula (25), ΔU gen , ΔI gen represents the node voltage and injected current deviation vector matrix of all virtual synchronous machine VSG nodes, ΔU load , ΔI load is the node voltage and injected current deviation vector matrix of all load nodes, matrix Y GG represents the admittance matrix between virtual synchronous machine VSG nodes, matrix Y LL represents the admittance matrix between load nodes, matrix Y GL and Y LG is the admittance matrix between virtual synchronous machine VSG nodes and load nodes.

[0090] S3-3: Combining formula (22) and formula (25), the state matrix A of the new power system containing virtual synchronous machine VSG is derived as follows:

[0091] (26).

[0092] Figure 3 The system eigenvalue distribution diagram is shown, for the new power system of 10 virtual synchronous machines 39 nodes, the system state matrix A as shown in formula (26) is derived, and the system eigenvalue distribution diagram is drawn, wherein the parameter settings of each virtual synchronous machine VSG are: reactive voltage coefficient k Q =1, feedback coefficient k F =10, line impedance Z L =0.02; the system has 10 pairs of conjugate eigenvalues and 10 eigenvalues on the real axis, and all the eigenvalues of the system are in the left half plane, the system is in a stable state, Figure 3 The enlarged view in the upper left plane is marked.

[0093] Figure 4 The participation factor analysis diagram of each virtual synchronous machine VSG in the oscillation mode is shown, and the participation factor analysis diagram of each virtual synchronous machine VSG in the corresponding oscillation mode is obtained by using the conjugate eigenvalues in Figure 3 , wherein each oscillation mode contains participation factors of at least two virtual synchronous machines VSG, each oscillation mode is affected by multiple virtual synchronous machines VSG, therefore, each virtual synchronous machine VSG has coupling, which makes the inertia and damping optimization design of the virtual synchronous machine VSG very complex.

[0094] The above-described embodiments are only preferred embodiments of the present application and are not intended to limit the scope of the present application. Any change made in the shape, principle or the like of the present application should be covered by the scope of the present application.

Claims

1. A method of modeling a power system containing virtual synchronous machines, characterized in that, The method comprises the following steps: S1: Constructing a reactive power control loop with feedback regulation, using traditional power system modeling theory to derive the state space equation of a single virtual synchronous generator VSG in the rotating coordinate system d-q axis: S1-1: for a virtual synchronous machine VSG, a reactive power control loop with feedback regulation is proposed, the structure of which comprises: the difference between the reference reactive power Q ref and the output reactive power Q o is input; the reactive coefficient k Q is a forward channel, and the feedback coefficient k F forms a negative feedback loop; The output of the feedback loop is compared to a reference electromotive force E ref The sum of which is the output electromotive force E ; S1-2: Neglecting the differential equation in the voltage and current double closed loop, reducing the influence of PI control parameters in the voltage and current double closed loop on the dynamic characteristics of the system, and constructing the differential equation of the virtual synchronous generator VSG control link as: (1) in formula (1), δ is the output power angle, ω is the output angular frequency, ω ref is the reference angular frequency, P ref is the reference active power, P o is the output active power, H is the inertia, D is the damping; S1-3: Small signal processing is performed on formula (1) to obtain the linear equation of the virtual synchronous generator VSG control link as: (2) In formula (2), Δ δ is a power angle deviation, Δ ω is an angular frequency deviation, Δ E is an electromotive force deviation, Δ P o and Δ Q o are active power deviation and reactive power deviation, respectively, and are expressed by linear equations. (3) In formula (3), Δ U d , Δ U q , Δ I d , Δ I q is a deviation amount of a node voltage and a node current of a d-q axis of a rotating coordinate system, U d , U q , and I d , I q is an output voltage and an output current of a d-q axis of a rotating coordinate system; S1-4: Using power system state space modeling theory, combining formula (1), formula (2) and formula (3), the state space equation of a single virtual synchronous generator VSG in the rotating coordinate system d-q axis is constructed as: (4) In formula (4), A VSG , B IVSG , B VVSG , C VSG , and D VSG are coefficient matrices, whose expressions are as follows, respectively: (5) In formula (5), Z L is the line impedance between the single virtual synchronous machine VSG and the network node of the power system. S2: Using coordinate transformation theory, the state space equation of a single virtual synchronous generator VSG is converted from the rotating coordinate system d-q axis to the common coordinate system x-y axis, and the overall state space equation of the power system dominated by the virtual synchronous generator VSG in the common coordinate system x-y axis is constructed: S2-1: The coordinate transformation formula for converting the state space equation of a single virtual synchronous generator VSG in the rotating coordinate system d-q axis to the common coordinate system x-y axis is: (6) In formula (6), U x , U y and I x , I y are the node voltage and node current of the x-y axis of the common coordinate system. S2-2: Combining formula (4) and formula (6), the state space equation of a single virtual synchronous generator VSG is converted from the rotating coordinate system d-q axis to the common coordinate system x-y axis, and the state space equation of a single virtual synchronous generator VSG in the common coordinate system x-y axis is obtained as: (7) In formula (7), Δ U x , Δ U y , Δ I x , Δ I y are the deviation amounts of the node voltages and the node currents of the x-y axes of the common coordinate system, and the matrix , , and are expressed as follows, respectively. (8) S2-3: Combining the state space equations of each virtual synchronous generator VSG in the common coordinate system x-y axis, the overall state space equation of the power system dominated by the virtual synchronous generator VSG is obtained as: (9) In formula (9), the matrix ΔI M and the matrix ΔU M are the node injection current and the node voltage deviation vector matrix of all virtual synchronous machines VSG; the expressions of the matrices A M , B M , C M and D M are as follows: (10) In formula (10), j is the number of virtual synchronous generators; S3: Combining the node voltage linear equation and the overall state space equation of the system, the state matrix A of the power system is derived as: (11) In formula (11), the matrix Y GG represents the admittance matrix between the virtual synchronous machine VSG nodes.

2. The virtual synchronous machine contained power system modeling method according to claim 1, characterized in that, The process of deriving the state matrix A of the power system comprises: S3-1: Based on the power system modeling theory, the node voltage equation of the power system is expressed in the form of real part and imaginary part as: (12) In formula (12), G ii and B ii respectively represent the real part and the imaginary part of the admittance matrix Y ii of the i-th node, U xi , U yi and I xi , I yi respectively represent the real part and the imaginary part of the i-th node voltage and the i-th node current of the x-y axis of the common coordinate system, i=1, 2, …, r, and r is the number of nodes of the power network. S3-2: Linearizing formula (12) to obtain the linear equation of the node voltage as: (13) In formula (13), ΔU gen , ΔI gen represents the node voltage and injected current deviation vector matrix of all virtual synchronous generator VSG nodes, ΔU load , ΔI load is the node voltage and injected current deviation vector matrix of all load nodes, matrix Y LL represents the admittance matrix between load nodes, matrix Y GL is the admittance matrix between load nodes and virtual synchronous generator VSG nodes; and LG is the admittance matrix between virtual synchronous generator VSG nodes. S3-3: Combining formula (9) and formula (13), the state matrix A of the power system containing the virtual synchronous generator VSG is derived.

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