Modeling method for novel electric power system containing virtual synchronous machine

Abstract

The invention discloses a virtual synchronous machine-containing novel power system modeling method, which comprises the following steps of S1, constructing a reactive power control ring with feedback regulation, and deducing a state-space equation of a single virtual synchronous machine VSG under a d-q axis of a rotating coordinate system by utilizing a traditional power system modeling theory; s2, converting a state-space equation of a single virtual synchronous machine VSG from a d-q axis of a rotating coordinate system to an x-y axis of a common coordinate system by using a coordinate transformation theory, and constructing an overall state-space equation of the novel power system dominated by the virtual synchronous machine VSG under the x-y axis of the common coordinate system; and S3, in combination with the node voltage linearization equation and the system overall state space equation, deducing to obtain a state matrix of the novel power system. According to the method, the reactive power control loop with feedback regulation is constructed, modeling of the novel power system containing the virtual synchronous machine VSG is realized, and model support is provided for subsequent frequency stability analysis of the novel power system.

Description

Technical Field

[0001] The present invention relates to the field of novel power systems, and in particular to a novel power system modeling method containing a virtual synchronous machine. Background Art

[0002] With the acceleration of energy transformation and the development of distributed energy, the proportion of renewable energy generation in new power systems continues to increase, resulting in a decrease in the system inertia level and a decrease in anti-interference ability. At the same time, the random fluctuations in the output of renewable energy equipment and the uncertain fluctuations in load will cause large fluctuations in the operating voltage of the power grid and increased complexity of the power grid system. Virtual synchronous machine VSG (Virtual Synchronous Generator) technology can simulate the operating characteristics of synchronous generators, provide virtual inertia and damping for the power system, and thus improve the stability of the system. However, the modeling of virtual synchronous machines VSG is a complex problem, and traditional power system modeling methods are difficult to accurately describe the dynamic characteristics of virtual synchronous machines VSG. Therefore, the present invention proposes a new power system modeling method containing a virtual synchronous machine VSG. The method constructs a reactive control loop with feedback regulation, realizes the modeling of a new power system containing a virtual synchronous machine VSG, and provides model support for the subsequent frequency stability analysis of the new power system. Summary of the Invention

[0003] To achieve the above objectives, the technical solutions provided by the present invention are:

[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 dq axis;

[0005] S2: Using coordinate transformation theory, the state space equation of a single virtual synchronous machine (VSG) is transformed from the rotating coordinate system (dq-axis) to the public coordinate system (xy-axis). This constructs the overall state space equation of the new power system dominated by the virtual synchronous machine (VSG) in the public coordinate system (xy-axis).

[0006] S3: Combining the node voltage linearization equation and the overall system state space equation, the state matrix of the new power system is derived.

[0007] The step S1 comprises:

[0008] S1-1: For the virtual synchronous machine VSG, a reactive power control loop with feedback regulation is proposed, whose structure includes: taking the reference reactive power Q ref and output reactive power Q o The difference is the input; the reactive coefficient k Q is the forward channel, and the feedback coefficient k FA negative feedback loop is formed; the output of the feedback loop is related to the reference electromotive force E ref The sum is the output electromotive force E;

[0009] S1-2: Ignore the differential equations in the voltage and current double closed loops, reduce the impact of the PI control parameters in the voltage and current double closed loops on the system dynamic characteristics, and construct the differential equations of the virtual synchronous machine VSG control link as follows:

[0010]

[0011] In formula (1), δ is the output power angle, ω is the output angular frequency, and 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, and D is the damping;

[0012] S1-3: Perform small signal processing on equation (1) to obtain the linearized equation of the virtual synchronous machine VSG control link:

[0013]

[0014] In formula (2), Δδ is the power angle deviation, Δω is the angular frequency deviation, ΔE is the electromotive force deviation, and ΔP o and ΔQ o are active power deviation and reactive power deviation respectively, which can be expressed as linear equations:

[0015]

[0016] In formula (3), ΔU d , ΔU q and ΔI d , ΔI q is the deviation between the node voltage and node current of the dq axis of the rotating coordinate system, U d 、U q with I d , I q are the output voltage and output current of the dq axis of the rotating coordinate system;

[0017] S1-4: Using the power system state space modeling theory, combined with equations (1), (2), and (3), the state space equation of a single virtual synchronous machine VSG in the rotating coordinate system dq axis is constructed as follows:

[0018]

[0019] In formula (4), A VSG 、B IVSG 、B VVSG 、C VSG and DVSG is the coefficient matrix, and its expressions are:

[0020]

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

[0022] The step S2 comprises:

[0023] S2-1: The coordinate transformation formula for converting the state space equation of a single virtual synchronous machine VSG under the rotating coordinate system dq axis to the common coordinate system xy axis is:

[0024]

[0025] In formula (6), U x 、U y with I x , I y is the node voltage and node current of the common coordinate system xy axis;

[0026] S2-2: Combining equations (4) and (6), the state space equation of a single virtual synchronous machine VSG is converted from the rotating coordinate system dq axis to the public coordinate system xy axis. The state space equation of a single virtual synchronous machine VSG in the public coordinate system xy axis is obtained as follows:

[0027]

[0028] In formula (7), ΔU x , ΔU y and ΔI x , ΔI y is the deviation of the node voltage and node current of the common coordinate system xy axis, the matrix and The expressions are:

[0029]

[0030] S2-3: Combining the state space equations of each virtual synchronous machine VSG in the common coordinate system xy axis, the overall state space equation of the new power system dominated by the virtual synchronous machine VSG is obtained:

[0031]

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

[0033]

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

[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 and imaginary parts as follows:

[0037]

[0038] In formula (11), G ii With B ii Represents the admittance matrix Y of the i-th node ii The real and imaginary parts, U xi 、U yi with I xi , I yi denote the real and imaginary parts of the voltage and current at the ith node of the common coordinate system xy-axis, i = 1, 2, …, r, where r is the number of nodes in the power network;

[0039] S3-2: Linearize equation (11) to obtain the linearized equation of the node voltage:

[0040]

[0041] In formula (12), ΔU gen , ΔI gen Denotes the node voltage and injection current deviation vector matrix of all virtual synchronous machine VSG nodes, ΔU load , ΔI load The node voltage and injection 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 With Y LG is the admittance matrix between the virtual synchronous machine VSG node and the load node;

[0042] S3-3: Combining equations (9) and (12), the state matrix A of the new power system containing virtual synchronous generators VSG is derived as follows:

[0043]

[0044] Compared with the existing technology, the principles and advantages of this solution are as follows:

[0045] The present invention discloses a novel power system modeling method containing a virtual synchronous machine, comprising the following steps: S1: constructing a reactive control loop with feedback regulation, and using traditional power system modeling theory to derive the state space equation of a single virtual synchronous machine (VSG) under the dq axis of a rotating coordinate system; S2: using coordinate transformation theory, transforming the state space equation of a single virtual synchronous machine (VSG) from the dq axis of the rotating coordinate system to the xy axis of a common coordinate system, and constructing the overall state space equation of a novel power system dominated by the virtual synchronous machine (VSG) under the xy axis of the common coordinate system; S3: combining the node voltage linearization equation and the overall state space equation of the system to derive the state matrix of the novel power system. The present invention constructs a reactive control loop with feedback regulation, realizes the modeling of a novel power system containing a virtual synchronous machine (VSG), and provides model support for subsequent frequency stability analysis of the novel power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Flowchart of a novel power system modeling method including a virtual synchronous machine (VSG) according to an embodiment of the present invention;

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

[0048] Figure 3 This is a distribution diagram of system characteristic roots in an embodiment of the present invention;

[0049] Figure 4 3 is a diagram showing the participation factor analysis of each virtual synchronous machine VSG in the oscillation mode in an embodiment of the present invention. DETAILED DESCRIPTION

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

[0051] Figure 1 The figure shows a flow chart of a new power system modeling method including virtual synchronous generators (VSG). Figure 2 The following diagram shows a reactive power control loop with feedback regulation, which includes the following steps:

[0052] 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 dq axis;

[0053] S2: Using coordinate transformation theory, the state space equation of a single virtual synchronous machine (VSG) is transformed from the rotating coordinate system (dq-axis) to the public coordinate system (xy-axis). This constructs the overall state space equation of the new power system dominated by the virtual synchronous machine (VSG) in the public coordinate system (xy-axis).

[0054] S3: Combining the node voltage linearization equation and the overall system state space equation, the state matrix of the new power system is derived.

[0055] The step S1 comprises:

[0056] S1-1: For the virtual synchronous machine VSG, a reactive power control loop with feedback regulation is proposed, whose structure includes: taking the reference reactive power Q ref and output reactive power Q o The difference is the input; the reactive coefficient k Q is the forward channel, and the feedback coefficient k F A negative feedback loop is formed; the output of the feedback loop is related to the reference electromotive force E ref The sum is the output electromotive force E;

[0057] S1-2: Ignore the differential equations in the voltage and current double closed loops, reduce the impact of the PI control parameters in the voltage and current double closed loops on the system dynamic characteristics, and construct the differential equations of the virtual synchronous machine VSG control link as follows:

[0058]

[0059] In formula (14), δ is the output power angle, ω is the output angular frequency, and 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, and D is the damping;

[0060] S1-3: Perform small signal processing on equation (14) to obtain the linearized equation of the virtual synchronous machine VSG control link:

[0061]

[0062] In formula (15), Δδ is the power angle deviation, Δω is the angular frequency deviation, ΔE is the electromotive force deviation, and ΔP o and ΔQ o are active power deviation and reactive power deviation respectively, which can be expressed as linear equations:

[0063]

[0064] In formula (16), ΔU d , ΔU q and ΔI d , ΔI q is the deviation between the node voltage and node current of the dq axis of the rotating coordinate system, U d 、U q with I d , Iq are the output voltage and output current of the dq axis of the rotating coordinate system;

[0065] S1-4: Using the power system state space modeling theory, combined with equations (14), (15), and (16), the state space equation of a single virtual synchronous machine VSG in the rotating coordinate system dq axis is constructed as follows:

[0066]

[0067] In formula (17), A VSG 、B IVSG 、B VVSG 、C VSG and D VSG is the coefficient matrix, and its expressions are:

[0068]

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

[0070] The step S2 comprises:

[0071] S2-1: The coordinate transformation formula for converting the state space equation of a single virtual synchronous machine VSG under the rotating coordinate system dq axis to the common coordinate system xy axis is:

[0072]

[0073] In formula (19), U x 、U y with I x , I y is the node voltage and node current of the common coordinate system xy axis;

[0074] S2-2: Combining equations (17) and (19), the state space equation of a single virtual synchronous machine VSG is converted from the rotating coordinate system dq axis to the public coordinate system xy axis. The state space equation of a single virtual synchronous machine VSG in the public coordinate system xy axis is obtained as follows:

[0075]

[0076] In formula (20), ΔU x , ΔU y and ΔI x , ΔI y is the deviation of the node voltage and node current of the common coordinate system xy axis, the matrix and The expressions are:

[0077]

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

[0079]

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

[0081]

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

[0083] The step S3 comprises:

[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 and imaginary parts as follows:

[0085]

[0086] In formula (24), G ii With B ii Represents the admittance matrix Y of the i-th node ii The real and imaginary parts, U xi 、U yi with I xi , I yi denote the real and imaginary parts of the voltage and current at the ith node of the common coordinate system xy-axis, i = 1, 2, …, r, where r is the number of nodes in the power network;

[0087] S3-2: Linearize equation (24) to obtain the linearized equation of the node voltage:

[0088]

[0089] In formula (25), ΔU gen , ΔI gen Denotes the node voltage and injection current deviation vector matrix of all virtual synchronous machine VSG nodes, ΔU load , ΔI loadThe node voltage and injection 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 With Y LG is the admittance matrix between the virtual synchronous machine VSG node and the load node;

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

[0091]

[0092] Figure 3 The system characteristic root distribution diagram is shown. For the new power system with 10 virtual synchronous machines and 39 nodes, the system state matrix A shown in formula (26) is derived and the system characteristic root distribution diagram is drawn. The parameters of each virtual synchronous machine VSG are set as follows: reactive voltage coefficient k Q =1, feedback coefficient k F =10, line impedance Z L =0.02; the system has 10 pairs of conjugate characteristic roots and 10 characteristic roots on the real axis, and all the characteristic roots of the system are in the left half plane, the system is in a stable state, Figure 3 The enlarged image in the middle marks the characteristic root of the upper left plane.

[0093] Figure 4 The figure shows the participation factor analysis diagram of each virtual synchronous machine VSG in the oscillation mode. Figure 3 The conjugate characteristic roots in the oscillation mode are used to obtain the participation factor analysis diagram of each virtual synchronous machine VSG in the corresponding oscillation mode. Each oscillation mode contains the participation factors of at least two virtual synchronous machines VSG. Each oscillation mode is affected by multiple virtual synchronous machines VSG. Therefore, there is coupling between each virtual synchronous machine VSG, which makes the inertia and damping optimization design of the virtual synchronous machine VSG very complicated.

[0094] The embodiments described above are only preferred embodiments of the present invention and are not intended to limit the scope of implementation of the present invention. Therefore, any changes made based on the shape and principle of the present invention should be included in the scope of protection of the present invention.

Claims

1. A novel power system modeling method including virtual synchronous machines, characterized in that: The following steps are involved: S1: Construct a reactive power control loop with feedback regulation, and use the traditional power system modeling theory to derive the state space equation of a single virtual synchronous machine VSG under the dq axis of the rotating coordinate system; S2: Using the coordinate transformation theory, the state space equation of a single virtual synchronous machine VSG is transformed from the rotating coordinate system dq axis to the public coordinate system xy axis, and the overall state space equation of the new power system dominated by the virtual synchronous machine VSG in the public coordinate system xy axis is constructed; S3: Combining the node voltage linearization equation and the overall system state space equation, the state matrix of the new power system is derived.

2. The novel power system modeling method including virtual synchronous machines according to claim 1 is characterized in that: The step S1 comprises: S1-1: For the virtual synchronous machine VSG, a reactive power control loop with feedback regulation is proposed, whose structure includes: taking the reference reactive power Q ref And the output reactive power Q o The difference is the input; the reactive power coefficient k Q is the forward channel, and the feedback coefficient k F A negative feedback loop is formed; the output of the feedback loop is related to the reference electromotive force E ref The sum is the output electromotive force E; S1-2: Ignore the differential equations in the voltage and current double closed loops, reduce the impact of the PI control parameters in the voltage and current double closed loops on the dynamic characteristics of the system, and construct the differential equations of the virtual synchronous machine VSG control link as follows: In formula (1), δ is the output power angle, ω is the output angular frequency, and 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, and D is the damping; S1-3: Perform small signal processing on equation (1) to obtain the linearized equation of the virtual synchronous machine VSG control link: In formula (2), Δδ is the power angle deviation, Δω is the angular frequency deviation, ΔE is the electromotive force deviation, and ΔP o and ΔQ o They are active power deviation and reactive power deviation respectively, which can be expressed by linear equations as follows: In formula (3), ΔU d , ΔU q With ΔI d , ΔI q is the deviation of the node voltage and node current of the dq axis of the rotating coordinate system, U d , U q with I d ,I q are the output voltage and output current of the dq axis of the rotating coordinate system; S1-4: Using the power system state space modeling theory, combined with equations (1), (2), and (3), the state space equation of a single virtual synchronous machine VSG under the dq axis of the rotating coordinate system is constructed as follows: In formula (4), A VSG , B IVSG , B VVSG , C VSG and D VSG is the coefficient matrix, and its expressions are: In formula (5), Z L It is the line impedance between a single virtual synchronous machine VSG and the power system network node.

3. The novel power system modeling method including virtual synchronous machines according to claim 2 is characterized in that: The step S2 comprises: S2-1: The coordinate transformation formula for converting the state space equation of a single virtual synchronous machine VSG under the rotating coordinate system dq axis to the common coordinate system xy axis is: In formula (6), U x , U y with I x ,I y is the node voltage and node current of the common coordinate system xy axis; S2-2: Combining equations (4) and (6), the state space equation of a single virtual synchronous machine VSG is converted from the rotating coordinate system dq axis to the public coordinate system xy axis, and the state space equation of a single virtual synchronous machine VSG in the public coordinate system xy axis is obtained as follows: In formula (7), ΔU x , ΔU y With ΔI x , ΔI y is the deviation of node voltage and node current in the common coordinate system xy axis, matrix and The expressions are: S2-3: Combining the state space equations of each virtual synchronous machine VSG under the xy axis of the common coordinate system, the overall state space equation of the new power system dominated by the virtual synchronous machine VSG is obtained: In formula (9), the matrix ΔI M and ΔU M The node injection current and node voltage deviation vector matrix of all virtual synchronous machines VSG; matrix A M , B M , C M and D M The expressions are: In formula (10), j is the number of virtual synchronous machines.

4. The novel power system modeling method including virtual synchronous machines according to claim 3 is characterized in that: The step S3 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 and imaginary parts as follows: In formula (11), G ii With B ii Respectively represent the admittance matrix Y of the i-th node ii The real and imaginary parts, U xi , U yi with I xi ,I yi They represent the real and imaginary parts of the voltage and current of the ith node of the common coordinate system xy axis, respectively, i = 1, 2, ..., r, r is the number of nodes in the power network; S3-2: Linearize equation (11) to obtain the linearized equation of the node voltage: In formula (12), ΔU gen , ΔI gen The node voltage and injection current deviation vector matrix of all virtual synchronous machine VSG nodes, ΔU load , ΔI load is the node voltage and injection current deviation vector matrix of all load nodes, matrix Y GG Represents the admittance matrix between the virtual synchronous machine VSG nodes, the matrix Y LL Represents the admittance matrix between load nodes, matrix Y GL With Y LG is the admittance matrix between the virtual synchronous machine VSG node and the load node; S3-3: Combining equations (9) and (12), the state matrix A of the new power system containing virtual synchronous machine VSG is derived as follows:

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