A Subsynchronous Modal Energy Analysis Method for Power Systems

Abstract

The present invention discloses a subsynchronous modal energy analysis method for a power system in the field of subsynchronous oscillation analysis research of a power system, comprising: firstly, establishing a Hamiltonian model of a power system for a given power system; then, based on the established Hamiltonian model, deriving the subsynchronous modal energy structure of the given power system; finally, obtaining the determination principle of the cause of subsynchronous oscillation of the power system through the properties of each energy item in the subsynchronous modal energy structure. The subsynchronous modal energy analysis method of the present invention is widely applicable to the analysis and research of subsynchronous oscillation problems of power systems, can reveal the physical mechanism of subsynchronous oscillation energy interaction, explain the causes of subsynchronous oscillation phenomena of power systems under different mechanisms, and can observe the process of development and propagation of subsynchronous oscillations.

Description

Technical Field

[0001] The invention belongs to the research field of subsynchronous oscillation analysis of power systems, and specifically relates to a subsynchronous modal energy analysis method for power systems. Background Art

[0002] As the proportion of new energy and power electronic equipment in the power system continues to expand, the objects involved in the subsynchronous oscillation problem of the power system are becoming increasingly complex.

[0003] Due to the interaction between the DC transmission system and the turbine generator shaft system, the Square Buttle DC transmission project in the United States experienced subsynchronous oscillations caused by the torsion interaction of the shaft system during the commissioning. Due to the interaction between the wind farm and the series compensation of the power system, the Texas wind farm in the United States and the Guyuan doubly fed wind farm in Hebei, China have also experienced subsynchronous oscillations, causing a large number of wind turbines to be disconnected from the grid. The Hami direct-drive wind farm in Xinjiang also interacted with the weak power grid connected to it, resulting in the disconnection of multiple thermal power units 300km away. Due to the interaction between complex power electronic equipment, during the commissioning of the Nanhui Flexible Direct Current Project, the Nan'ao Flexible Direct Current Project, and the Xiamen Flexible Direct Current Project in China, subsynchronous oscillations of 20Hz to 30Hz also occurred between the doubly fed wind farm and the flexible direct current converter station, affecting the steady-state operation of the system. In addition, there are hidden dangers of subsynchronous oscillations between photovoltaic power generation and weak power grids, between DC transmission and weak power grids, and between direct-drive wind farms and DC transmission.

[0004] Traditional subsynchronous oscillation research methods are mainly carried out from the time domain and frequency domain perspectives, including time domain simulation method, eigenvalue analysis method, impedance analysis method, frequency scanning method, etc. However, these methods cannot reveal the physical mechanism of subsynchronous oscillation energy interaction in power systems, and it is difficult to gain insight into the development and propagation process of subsynchronous oscillations. Summary of the invention

[0005] In view of the deficiencies of the prior art, an object of the present invention is to provide a subsynchronous modal energy analysis method for a power system to solve the problems raised in the above background technology.

[0006] The purpose of the present invention can be achieved through the following technical solutions:

[0007] A subsynchronous modal energy analysis method for a power system, comprising:

[0008] Firstly, a Hamiltonian system model is established for a given power system;

[0009] Then, based on the established Hamiltonian model, the subsynchronous modal energy structure of a given power system is derived;

[0010] Finally, the determination principle of the cause of subsynchronous oscillation of power system is obtained through the properties of each energy item in the subsynchronous mode energy structure.

[0011] Preferably, the power system Hamiltonian model is as follows:

[0012]

[0013] In the formula, x 1 is the power system energy variable; u 1 Input variables for power system ports; y 1 J is the output variable of the power system port; 1 (x 1 ) is the internal structure matrix of the power system, which is an antisymmetric matrix, namely J 1 (x 1 )=-J 1 T (x); R 1 (x 1 ) is the damping matrix of the power system, which is a semi-positive definite matrix, that is, R 1 (x 1 )=R T 1 (x 1 )≥0; H 1 (x 1 ) is the total energy stored in the power system, i.e., the energy function; g 1 (x 1 ) is the power system port structure matrix.

[0014] Preferably, the total energy H stored in the power system 1 (x 1 ) is described by the energy function of formula (2):

[0015]

[0016] Then the power system energy variable in equation (2) is expressed as the form of the base frequency quantity superimposed on the sub-synchronous quantity, as shown in (3):

[0017]

[0018] In the formula, the subscript 0 represents the fundamental frequency of the corresponding variable, and Δ represents the subsynchronous component of the corresponding variable;

[0019] The subsynchronous modal energy stored in the power system is defined as shown in equation (4):

[0020]

[0021] Preferably, the input quantity and energy variable of the Hamiltonian model of the power system are expressed in the form of a fundamental frequency quantity superimposed on a subsynchronous quantity, as shown in formula (5):

[0022]

[0023] Preferably, the energy variable is expressed in the form of a fundamental frequency quantity superimposed on a secondary synchronization quantity, as shown in formula (6):

[0024]

[0025] Preferably, the rate of change of the subsynchronous modal energy stored in the power system is as shown in formula (7):

[0026]

[0027] The subsynchronous modal energy structure of the power system is shown in formula (8):

[0028] W port =W SSO +W diss +W state (8)

[0029] in,

[0030]

[0031] Preferably, in the formula (8), W port is the subsynchronous modal energy of the port flowing into the power system, which is converted into the following three types of energy: W SSO , W state , W diss .

[0032] Preferably, the subsynchronous oscillation inducement of the power system is W state , W state When it is positive, it provides positive damping for the power system; otherwise, it provides negative damping for the power system.

[0033] Beneficial effects of the present invention:

[0034] 1. The subsynchronous modal energy analysis method of the present invention is widely applicable to the analysis and research of subsynchronous oscillation problems in power systems. It can reveal the physical mechanism of subsynchronous oscillation energy interaction, explain the causes of subsynchronous oscillation phenomena in power systems under different mechanisms, and observe the development and propagation process of subsynchronous oscillations. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0036] Figure 1is a flow chart of the subsynchronous modal energy analysis method of the present invention;

[0037] Figure 2 It is a schematic diagram of a double-fed wind power grid-connected system case in the present invention. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] See also Figure 1 As shown, the present invention proposes a subsynchronous modal energy analysis method for an electric power system. First, the scenario and parameters of the electric power system are obtained. Then, its Hamiltonian model is established according to the scenario and parameters of the electric power system. Based on the established Hamiltonian model, the subsynchronous modal energy structure of the given electric power system is derived. Finally, a principle for determining the cause of subsynchronous oscillation of the electric power system based on the properties of each energy item in the subsynchronous modal energy structure is given.

[0040] Figure 2 The figure shows the structure diagram of the doubly-fed wind power grid-connected system, which is a specific scenario for studying the subsynchronous oscillation problem of the power system. d and i q It represents the dq axis component of the total output current of the generator side and the grid side, i ds ,i qs ,i dr ,i qr are the dq axis components of the stator current and rotor current of the doubly fed wind turbine, i dg ,i qg are the dq axis components of the grid-side current of the double-fed wind turbine, X C is the capacitive reactance of the series compensation capacitor, X T is the equivalent reactance of the transformer, R L is the line resistance, X L is the line reactance.

[0041] The method includes:

[0042] Step 1: Establish a Hamiltonian model for a given power system;

[0043] The Hamiltonian model of the doubly fed wind turbine used is established as follows:

[0044]

[0045] In the formula, x 1 is the energy variable of the doubly-fed wind turbine; u 1Input variable for the double-fed wind turbine port; y 1 is the output variable of the double-fed wind turbine port, J 1 (x 1 ) is the inline structure matrix of the doubly fed wind turbine model, which is an antisymmetric matrix, namely, J 1 (x 1 )=-J 1 T (x); R 1 (x 1 ) is the damping matrix of the doubly fed wind turbine model, which is a semi-positive definite matrix, that is, H 1 (x 1 ) is the total energy stored in the doubly fed wind turbine, i.e., the energy function; g 1 (x 1 ) is the port structure matrix of the doubly fed wind turbine.

[0046] The total energy stored in the double-fed wind turbine H 1 (x 1 ) is described by the following energy function:

[0047]

[0048] in,

[0049] x 1 =[ψ ds ψ qs ψ dr ψ qr Jω r L g i dg L g i qg Cu dc ] T ,

[0050] u 1 =[u ds u qs T m ] T ,

[0051]

[0052]

[0053]

[0054]

[0055] In the formula, u ds ,u qs, u dr ,uqr are the dq axis components of the stator voltage and rotor voltage of the doubly fed wind turbine, ψ ds ,ψ qs , ψ dr , ψ qr are the dq axis components of the stator flux and rotor flux of the doubly fed wind turbine, ω s ,ω r are the synchronous magnetic field angular velocity and the angular velocity per unit of the doubly fed wind turbine rotor, D is the damping of the doubly fed wind turbine rotor, J is the inertia of the doubly fed wind turbine shaft system, R s ,L s ,R r ,L r They are the stator resistance of the doubly fed wind turbine, the stator equivalent two-phase winding self-inductance in the dq coordinate system, the rotor resistance, and the rotor equivalent two-phase winding self-inductance in the dq coordinate system, L m is the mutual inductance between the stator and rotor coaxial equivalent windings in the dq coordinate system, R g ,L g are the line resistance and inductance of the grid-side converter, s dg ,s dg are the dq axis components of the modulation signal of the grid-side converter of the doubly-fed wind turbine, s dr ,s qr are the dq axis components of the modulation signal of the converter side of the doubly fed wind turbine, C is the DC side capacitance, u dc is the DC capacitor voltage.

[0056] The following Hamiltonian model of the transmission line system with series compensation capacitor is adopted:

[0057]

[0058] In the formula

[0059]

[0060] u 2 =[u ys u xs E By E Bx ] T

[0061]

[0062]

[0063] In the formula, u cx ,u cy are the x and y axis components of the series compensation capacitor voltage, E Bx ,E By are the x and y axis components of the infinite grid bus voltage, uxs ,u ys are the x and y axis components of the fan stator voltage, i x ,i y are the x and y axis components of the line current, respectively, and X ΣL =X T +X L .

[0064] All the energy stored in the transmission line system can be described by the following energy function:

[0065]

[0066] in

[0067]

[0068] Step 2: Based on the established Hamiltonian model, the subsynchronous modal energy structure of the given power system is derived;

[0069] The energy variable of the doubly fed wind turbine in equation (2) is expressed as the form of the fundamental frequency quantity superimposed on the sub-synchronous quantity, that is:

[0070]

[0071] In the formula, x 1s =[ψ ds0 ψ qs0 ψ dr0 ψ qr0 J ωr0 L g i dg0 L g i qg0 Cu dc0 ] T , subscript 0 indicates the fundamental frequency of the corresponding variable; Δx 1 =[Δψ ds Δψ qs Δψ dr Δψ qr JΔω r L g Δi dg L g Δi qg CΔu dc ] T , Δ represents the subsynchronous component of the corresponding variable.

[0072] The subsynchronous modal energy stored in the doubly fed wind turbine is defined as shown in equation (6), which refers to the energy obtained by multiplying the two components of the same mode.

[0073]

[0074] Then, the input quantity and energy variable of the Hamiltonian model of the doubly fed wind turbine in equation (1) are expressed in the form of fundamental frequency quantity superimposed on subsynchronous quantity, that is:

[0075]

[0076] In the formula, u 1s =[u ds0 u qs0 T m0 ] T , Δu 1 =[Δu ds Δu qs ΔT m ] T .

[0077] From formula (5), we can get:

[0078]

[0079] Then, substituting formula (8) into formula (7) yields:

[0080]

[0081] in,

[0082]

[0083]

[0084] For the fundamental frequency contained in the system, the following equation holds true:

[0085]

[0086] Substituting formula (10) into formula (9) yields:

[0087]

[0088] From formula (6), the derivative of the subsynchronous modal energy stored in the doubly fed wind turbine system with respect to the energy variable is:

[0089]

[0090] By multiplying both sides of equation (12) by equation (11), we can obtain the rate of change of the subsynchronous modal energy stored in the doubly fed wind turbine system:

[0091]

[0092] Because J 1s With ΔJ 1 is an antisymmetric matrix, so the following holds:

[0093]

[0094] Substituting formula (14) into formula (13), we can obtain:

[0095]

[0096] By integrating both sides of equation (15) from time 0 to t, the subsynchronous modal energy structure of the doubly fed wind turbine system can be obtained:

[0097] W 1port =W 1SSO +W 1diss +W 1state (16)

[0098] in,

[0099]

[0100] Then the input quantity and energy variable of the Hamiltonian model of the transmission line containing series compensation capacitor are expressed as the form of fundamental frequency quantity superimposed on subsynchronous quantity:

[0101]

[0102] In the formula, x 2s =[u cy0 / X C u cx0 / X C X ΣL i y0 X ΣL i x0 ] T , Δx 2 =[Δu cy / X C Δu cx / X C X ΣL Δi y X ΣL Δi x ] T ;u 2s =[u ys0 u xs0 E By0 E Bx0 ] T , Δu 2 =[Δu ys Δu xs ΔE By ΔE Bx ] T . Wherein, the subscript 0 represents the fundamental frequency of the corresponding variable, and Δ represents the subsynchronous component of the corresponding variable.

[0103] The subsynchronous mode energy stored in the transmission line system is shown in formula (18).

[0104]

[0105] Further, the subsynchronous modal energy structure of the transmission line system containing series compensation capacitors is as follows:

[0106] W 2port =W 2SSO +W 2diss (19)

[0107] in,

[0108]

[0109] Step 3: Provide the determination principle of the cause of subsynchronous oscillation of power system based on the properties of each energy item in the subsynchronous modal energy structure;

[0110] For the subsynchronous modal energy structure of the doubly fed wind turbine system shown in equation (16), W 1port It is the subsynchronous modal energy of the port flowing into the double-fed wind turbine system from the external system, which can be converted into three types of energy: W 1SSO is the subsynchronous modal energy in the doubly fed wind turbine system, which is a conservative term (independent of the integration path); W 1state , W 1diss are the subsynchronous modal energy of the doubly fed wind turbine system and the subsynchronous modal energy of the doubly fed wind turbine resistance and shaft damping dissipation, respectively. These two energies are non-conservative terms, where W 1diss Always positive.

[0111] For the subsynchronous modal energy structure of the transmission line system shown in equation (19), W 2port is the total port subsynchronous modal energy flowing into the transmission line system from the external system, which can be converted into two types of energy: W 2SSO is the subsynchronous mode energy stored in the transmission line system, which is a conservative term; W 2diss is the subsynchronous modal energy dissipated by the line resistance and is a non-conservative term that is always positive.

[0112] For the doubly-fed wind turbine system, due to W 1state They can be positive or negative, providing positive damping when they are positive and negative damping when they are negative. Therefore, it can be considered that the doubly fed wind turbine is the cause of the oscillation.

[0113] For the transmission line system, due to W 2SSO is a conservative term, and W 2diss It is a non-conservative term that is always positive, so there is no possibility of inducing oscillation.

[0114] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0115] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0116] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0117] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0118] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0119] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A subsynchronous modal energy analysis method for power systems, It is characterized in that include: Firstly, for a given power system, a Hamiltonian model of the power system is established; Then, based on the established Hamiltonian model, the subsynchronous modal energy structure of a given power system is derived; Finally, the determination principle of the cause of subsynchronous oscillation of power system is obtained through the properties of each energy item in the subsynchronous mode energy structure. The Hamiltonian model of the power system is as follows: In the formula, x 1 is the power system energy variable; u 1 Input variables for power system ports; y 1 is the power system port output variable; J 1 (x 1 ) is the internal structure matrix of the power system, which is an antisymmetric matrix, namely J 1 (x 1 )=-J 1 T (x 1 );R 1 (x 1 ) is the damping matrix of the power system, which is a semi-positive definite matrix, that is, R 1 (x 1 )=R 1 T (x 1 )≥0; H 1 (x 1 ) is the total energy stored in the power system, i.e., the energy function; g 1 (x 1 ) is the power system port structure matrix; The total energy H stored in the power system 1 (x 1 ) is described by the energy function of formula (2): Then the power system energy variable in equation (2) is expressed as the form of the base frequency quantity superimposed on the sub-synchronous quantity, as shown in (3): In the formula, the subscript s represents the fundamental frequency component of the corresponding variable, and Δ represents the subsynchronous component of the corresponding variable; The subsynchronous modal energy stored in the power system is defined as shown in equation (4): The input quantity and energy variable change of the Hamiltonian model of the power system are in the form of the fundamental frequency quantity superimposed on the sub-synchronous quantity, as shown in formula (5): The subsynchronous component of the energy variable is shown in formula (6): The change rate of the subsynchronous modal energy stored in the power system is shown in formula (7): The subsynchronous modal energy structure of the power system is shown in formula (8): IN port =In SSO +W diss +W state (8) in, In the formula (8), W port is the subsynchronous modal energy of the port flowing into the power system, which is converted into the following three types of energy: W SSO , W state , W diss .

2. According to the subsynchronous modal energy analysis method of a power system according to claim 1, It is characterized in that The cause of subsynchronous oscillation of the power system is W state , W state When it is positive, it provides positive damping for the power system; otherwise, it provides negative damping for the power system.

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