A method and system for stability analysis of a double-ended flexible DC system

Abstract

The application discloses a kind of double-ended flexible DC system stability analysis method and system, the method includes: establishing single-converter-ideal DC source system, and determining dominant mode;Based on double-ended flexible DC system, the transfer function of DC side state variable is determined;According to the dominant mode, the transfer function is simplified, and the reduced order model is obtained;Based on the reduced order model, the analytical condition of system small disturbance stability is determined, and the stability of double-ended flexible DC system is analyzed using the analytical condition.The application simplifies the model of general double-ended flexible DC system by model reduction, reveals the stability mechanism of the DC side of the system, provides the analytical condition of small disturbance stability of the DC side state variable of flexible DC transmission system, which is conducive to fully utilizing the transmission capacity of double-ended flexible DC system and improving the frequency stability of the system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electric power, and particularly relates to a double-ended flexible DC system stability analysis method and system. BACKGROUND

[0002] With the increasing popularity of new energy power generation, long-distance large-scale power transmission through high voltage direct current (HVDC) has become the mainstream power transmission mode of modern power grids. The wide application of voltage source converters (VSCs), especially the emerging modular multilevel converters (MMCs), enables high voltage direct current transmission systems to operate more flexibly, but also introduces some new stability problems.

[0003] Among them, the existing technology is mainly focused on the influence of grid-connected converters on the stability of the alternating current system. For example, the phase-locked loop (PLL) cannot accurately track the phase of the point of common coupling (PCC), which may worsen the stability of the entire system; the voltage control loop with improper parameters may cause low-frequency resonance on the alternating current side. However, the existing technology does not provide relevant analysis methods for the instability mechanism and stability conditions of the direct current side, and cannot prevent the instability of the direct current side frequency of the flexible DC system in advance, thereby affecting the power transmission capacity of the flexible DC system and failing to ensure the safe and stable operation of the system. SUMMARY

[0004] The purpose of the present application is to provide a double-ended flexible DC system stability analysis method and system to solve the problem that the existing technology lacks stability analysis of the direct current side of the flexible DC system, thereby affecting the power transmission capacity of the system and bringing safety hazards to the operation of the system.

[0005] To achieve the above purpose, the present application provides a double-ended flexible DC system stability analysis method, comprising:

[0006] establishing a single-converter-ideal DC source system and determining a dominant mode;

[0007] determining the transfer function of the direct current side state variable based on the double-ended flexible DC system;

[0008] simplifying the transfer function according to the dominant mode to obtain a reduced order model;

[0009] Based on the reduced order model, an analytic condition of small signal stability of the system is determined, and the stability of the double-terminal flexible HVDC system is analyzed by using the analytic condition.

[0010] Further, the establishment of the single-converter-ideal DC source system and the determination of the dominant mode comprise:

[0011]

[0012] where R and L are the equivalent resistance and inductance of the DC side respectively; C is the equivalent capacitance; g0 is the equivalent conductance of the converter to the DC side; R and L are the resistance and inductance of the DC line respectively; R and L are the equivalent resistance and inductance of each bridge arm respectively; P is the active power of the AC input of the converter; u is the voltage on C; subscript 0 is the steady-state value; C is the capacitance of each sub-module; and N is the number of sub-modules of each bridge arm. dc and L dc are the equivalent resistance and inductance of the DC side respectively; C M is the equivalent capacitance; g0 is the equivalent conductance of the converter to the DC side; R l and L l are the resistance and inductance of the DC line respectively; R arm and L arm are the equivalent resistance and inductance of each bridge arm respectively; P c is the active power of the AC input of the converter; u c is the voltage on C M ; subscript 0 is the steady-state value; C sm is the capacitance of each sub-module; and N is the number of sub-modules of each bridge arm.

[0013] Further, the determination of the transfer function of the DC side state variable comprises the determination of the transfer function of the equivalent complex impedance of the DC side:

[0014]

[0015] where Δu dc is the DC voltage variation; Δi dc is the DC current variation; R M = 2R arm / 3; L M = 2L arm / 3; the upper and lower subscripts V represent the relevant electrical quantities of the control voltage side; U s is the AC side power voltage amplitude; and are the proportional and integral gains of the constant DC voltage controller of the control voltage side respectively; and σ I is the time constant of the inner loop current controller.

[0016] Further, the reduced order model is:

[0017]

[0018] where F(s) is the binomial expression of the reduced order model, and a0, a1 and a2 are binomial coefficients.

[0019] Further, the determining, based on the reduced-order model, of an analytical condition for small signal stability of the system comprises:

[0020]

[0021]

[0022] wherein P c cr is the critical power transfer of the HVDC system; u dcn is the rated DC voltage; M min is the required minimum stability margin; is the upper bound of the proportional gain of the DC voltage controller at the voltage side.

[0023] The application also provides a two-terminal flexible DC system stability analysis system, comprising:

[0024] a dominant mode determining unit configured to establish a single-converter-ideal DC source system and determine a dominant mode;

[0025] a transfer function determining unit configured to determine, based on the two-terminal flexible DC system, a transfer function of a DC side state variable;

[0026] a reduced-order model generating unit configured to simplify the transfer function according to the dominant mode to obtain a reduced-order model;

[0027] a stability analysis unit configured to determine, based on the reduced-order model, an analytical condition for small signal stability of the system, and analyze the stability of the two-terminal flexible DC system by using the analytical condition.

[0028] Further, the dominant mode determining unit is configured to establish a single-converter-ideal DC source system and determine a dominant mode, comprising:

[0029]

[0030] wherein R dc and L dc are the equivalent resistance and inductance of the DC side respectively; C M is the equivalent capacitance; g0 is the equivalent conductance of the converter to the DC side; R l and L l are the resistance and inductance of the DC line respectively; R arm and L arm are the equivalent resistance and inductance of each bridge arm respectively; P c is the active power of the AC input of the converter; u c is the voltage on C M ; subscript 0 is the steady-state value; C sm is the capacitance of each sub-module; and N is the number of sub-modules of each bridge arm.

[0031] Further, the transfer function determination unit is configured to determine a transfer function of the equivalent complex impedance of the DC side:

[0032]

[0033] where Δu dc is a DC voltage variation; Δi dc is a DC current variation; R M = 2R arm / 3; L M = 2L arm / 3; the upper and lower indices V represent the relevant electrical quantities of the control voltage side; U s is an AC side power supply voltage amplitude; and are a proportional gain and an integral gain of the constant DC voltage controller of the control voltage side, respectively; σ I is a time constant of the inner loop current controller.

[0034] Further, the reduced order model is:

[0035]

[0036] where F(s) is a binomial expression of the reduced order model, and a0, a1, a2 are binomial coefficients.

[0037] Further, the stability analysis unit is configured to determine an analytical condition for small disturbance stability of the system based on the reduced order model, including:

[0038]

[0039]

[0040] where P c cr is a critical transmission power of the HVDC system; u dcn is a rated DC voltage; M min is a required minimum stability margin; is an upper bound of the proportional gain of the constant DC voltage controller of the control voltage side.

[0041] Compared with the prior art, the application has the beneficial effects that:

[0042] The application discloses a double-ended flexible DC system stability analysis method and system, and the method comprises the following steps: establishing a single-converter-ideal DC source system and determining a dominant mode; determining a transfer function of a DC side state variable based on a double-ended flexible DC system; simplifying the transfer function according to the dominant mode to obtain a reduced-order model; determining an analytical condition of system small disturbance stability based on the reduced-order model, and analyzing the stability of the double-ended flexible DC system by using the analytical condition.

[0043] The application simplifies the model of the general double-ended flexible DC system through model reduction, reveals the stability mechanism of the DC side of the system, gives the analytical condition of small disturbance stability of the DC side state variable of the flexible DC transmission system, and is favorable for fully utilizing the power transmission capacity of the double-ended flexible DC system and improving the frequency stability of the system. BRIEF DESCRIPTION OF DRAWINGS

[0044] In order to more clearly illustrate the technical solutions of the application, the following will briefly introduce the drawings needed to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0045] Figure 1 is a flowchart of a double-ended flexible DC system stability analysis method provided by an embodiment of the application;

[0046] Figure 2 is a DC side equivalent circuit schematic diagram of a grid-connected MMC provided by an embodiment of the application;

[0047] Figure 3 is a transfer function block diagram of a DC side state variable of a double-ended flexible DC system provided by an embodiment of the application;

[0048] Figure 4 is a dynamic response process of a DC current when the power transmission suddenly changes, provided by an embodiment of the application;

[0049] Figure 5 is an influence of a proportional gain of a constant DC voltage controller on critical power transmission, provided by an embodiment of the application;

[0050] Figure 6 is a structural schematic diagram of a double-ended flexible DC system stability analysis system provided by an embodiment of the application. DETAILED DESCRIPTION

[0051] With reference to the drawings and embodiments of the present application, the technical solutions in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only a part of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present application.

[0052] It should be understood that the step numbers used herein are only for the convenience of description, and are not limited to the execution sequence of the steps.

[0053] It should be understood that the terms used in the present application are only for the purpose of describing specific embodiments and are not intended to limit the present application. As used in the present application and the appended claims, unless otherwise clear from the context, the singular forms "a", "an" and "the" are intended to include the plural forms.

[0054] The terms "comprise" and "include" indicate the presence of the described features, integers, steps, operations, elements, and / or components, but do not exclude one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0055] The term "and / or" means any combination of one or more of the associated listed items and all possible combinations, and includes these combinations.

[0056] Referring to Figure 1 , an embodiment of the present application provides a double-ended flexible DC system stability analysis method. As shown in Figure 1 , the double-ended flexible DC system stability analysis method comprises steps S10 to S40. Each step is as follows:

[0057] S10, a single converter-ideal DC source system is established, and a dominant mode is determined.

[0058] In this step, a single converter-ideal DC source system needs to be established first. Referring to Figure 2 , Figure 2 is a schematic diagram of the DC side equivalent circuit of the grid-connected modular multilevel converter (MMC). The transfer function of the single converter-ideal DC source system (excluding the controller dynamics) is:

[0059]

[0060] In the formula, R dc and L dc are the equivalent resistance and inductance of the DC side respectively; C M is the equivalent capacitance; g0 is the equivalent conductance of the converter to the DC side; R l and Ll These are the resistance and inductance of a DC line, respectively; R arm and L arm These are the equivalent resistance and inductance of each bridge arm, respectively; P c The active power input to the converter is measured in AC; u c C M Voltage on; subscript 0 is the steady-state value; C sm The capacitance of each submodule; N is the number of submodules per bridge arm.

[0061] The dynamic characteristics of the grid-connected MMC controller can be described by equation (2). According to equation (2), the poles of the transfer function are all located in the right half-plane, and the constant power controller will not jeopardize the stability of the DC side. Therefore, the overall system stability is determined only by equation (1).

[0062]

[0063] In the formula, and These are the proportional and integral gains of a constant power controller, respectively; σ I is the time constant of the inner loop current controller.

[0064] According to equation (1), the oscillation frequency of the dominant mode can be obtained as:

[0065]

[0066] S20. Based on the dual-ended flexible DC system, determine the transfer function of the DC side state variables.

[0067] In this step, we first establish a model of a two-terminal flexible DC system, and then derive the transfer function of the DC side state variables of the system.

[0068] Specifically, a system model of the voltage-controlled MMC2 is established, and its transfer function is:

[0069]

[0070] Where, Δu dc Δi represents the change in DC voltage. dc R represents the change in direct current. M =2R arm / 3;L M =2L arm / 3; the superscript and subscript V represent electrical quantities related to the control voltage side; U s This refers to the amplitude of the AC power supply voltage. and These are the proportional and integral gains of the constant voltage controller on the voltage control side, respectively.

[0071] Please see Figure 3 ,Figure 3 The transfer function block diagram of the state variable of the DC side of the flexible HVDC system. According to (2), the constant power controller does not endanger the stability of the DC side, and therefore, the characteristic equation that determines the stability of the system can be expressed as:

[0072] F(s) = 1 + (sC M + g0)(sL dc + R dc + Z(s)) (5)

[0073] S30, simplifying the transfer function according to the dominant mode to obtain a reduced order model.

[0074] In this step, the transfer function is simplified near the dominant frequency to obtain a reduced order model.

[0075] According to formula (3), the transfer function is simplified near the dominant frequency, as shown in formula (6):

[0076]

[0077] Combining formulas (4), (5), and (6), we have:

[0078]

[0079] Since the equivalent inductance of the DC side has the following relationship:

[0080]

[0081] Further, formula (7) can be simplified as:

[0082]

[0083] S40, based on the reduced order model, determining the analytical condition for small disturbance stability of the system, and using the analytical condition to analyze the stability of the double-ended flexible HVDC system.

[0084] In this step, if the system is small disturbance stable, the coefficients a0, a1, and a2 in formula (9) all need to be greater than 0, and in general cases, a0 and a2 are both greater than 0. Therefore, combining formulas (9) and (1), the HVDC system transmission power needs to satisfy the following conditions:

[0085]

[0086] Where, P c cr is the critical transmission power of the HVDC system; u dcn is the rated DC voltage.

[0087] The stability margin M is defined according to the relative distance between the current operating state and the critical state:

[0088]

[0089] From equation (11), the minimum stability margin is achieved when Therefore, when the minimum stability margin required by the system is M min , the proportional gain of the DC voltage controller on the voltage source side needs to satisfy:

[0090]

[0091] where is the upper bound of the proportional gain of the DC voltage controller on the voltage source side.

[0092] In one embodiment, to help understand, the dynamic response of the DC current when the transmitted power is suddenly changed is also provided, as shown in Figure 4 . The relevant parameters of the test system are shown in Table 1 below:

[0093] Table 1

[0094]

[0095]

[0096] From Figure 4 , it can be seen that when the equivalent inductance L dc on the DC side increases, the system damping gradually decreases, and when L dc = 0.3 H, the system is stable; when L dc = 0.5 H, the system is unstable. Specifically, if the actual transmitted power exceeds the critical transmitted power, the system damping will become negative, resulting in divergent oscillation, as shown in Figure 4 . At the same time, it is also verified that increasing the equivalent inductance L dc on the DC side will lead to a decrease in the oscillation frequency.

[0097] Further, please refer to Figure 5 , Figure 5 for the influence of the proportional gain of the DC voltage controller on the critical transmitted power. It can be seen that as the proportional gain of the controller increases, the critical transmitted power P c cr presents a downward trend, and the results obtained by the reduced-order model are very close to those obtained by the full-order model. Therefore, to ensure sufficient stability margin and fully utilize the transmission capacity of the HVDC system, needs to be less than the recommended upper limit.

[0098] In summary, the embodiment of the present application proposes a small disturbance stability analysis method for the DC side of a two-terminal flexible HVDC system, greatly simplifies the model of a general two-terminal HVDC system through model reduction, and reveals the stability mechanism of the DC side of the system. The method provides an analytical condition for the small disturbance stability of the DC side state variable of the flexible HVDC transmission system, which is conducive to fully utilizing the transmission capacity of the HVDC system and improving the frequency stability of the system.

[0099] Referring to Figure 6 The embodiment of the present application also provides a two-terminal flexible HVDC system stability analysis system, comprising:

[0100] A dominant mode determination unit 01 is configured to establish a single converter-ideal DC source system and determine a dominant mode.

[0101] A transfer function determination unit 02 is configured to determine a transfer function of a DC side state variable based on a two-terminal flexible HVDC system.

[0102] A reduced-order model generation unit 03 is configured to simplify the transfer function according to the dominant mode to obtain a reduced-order model.

[0103] A stability analysis unit 04 is configured to determine an analytical condition for the small disturbance stability of the system based on the reduced-order model, and analyze the stability of the two-terminal flexible HVDC system by using the analytical condition.

[0104] In one specific embodiment, the dominant mode determination unit 01 is configured to establish a single converter-ideal DC source system and determine a dominant mode, and comprises:

[0105]

[0106] wherein R dc and L dc are the equivalent resistance and inductance of the DC side respectively; C M is the equivalent capacitance; g0 is the equivalent conductance of the converter to the DC side; R l and L l are the resistance and inductance of the DC line respectively; R arm and L arm are the equivalent resistance and inductance of each bridge arm respectively; P c is the active power of the AC input of the converter; u c is the voltage on C M ; subscript 0 is the steady-state value; C sm is the capacitance of each sub-module; and N is the number of sub-modules of each bridge arm.

[0107] In one specific embodiment, the transfer function determination unit 02 is configured to determine the transfer function of the equivalent complex impedance of the DC side as follows:

[0108]

[0109] where Δu dc is the DC voltage variation; Δi dc is the DC current variation; R M = 2R arm / 3; L M = 2L arm / 3; the upper and lower indices V represent the control voltage side related electrical quantities; U s is the AC side power supply voltage amplitude; and are the proportional and integral gains of the DC voltage controller on the control voltage side respectively; σ I is the time constant of the inner loop current controller.

[0110] In one embodiment, the reduced order model is:

[0111]

[0112] where F(s) is the binomial expression of the reduced order model, and a0, a1, a2 are binomial coefficients.

[0113] In one embodiment, the stability analysis unit 04 is configured to determine an analytical condition for small signal stability of the system based on the reduced order model, including:

[0114]

[0115]

[0116] where P c cr is the critical transmission power of the HVDC system; u dcn is the rated DC voltage; M min is the required minimum stability margin; is the upper bound of the proportional gain of the DC voltage controller on the control voltage side.

[0117] It can be understood that the two-terminal flexible DC system stability analysis system provided in the embodiment is configured to perform the two-terminal flexible DC system stability analysis method provided in the above embodiment, and the effects achieved can refer to the above method embodiment part, and will not be further described here.

[0118] In several embodiments provided in the present application, it should be understood that the disclosed system, device and method can be implemented in other manners. For example, the described device embodiments are merely schematic. For example, the division of the units is only a logical function division. There can be another division manner for the actual implementation, for example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the displayed or discussed mutual couplings or direct couplings or communication connections between different units, or the among different units, can be indirect couplings or communication connections through some interfaces, devices or units, and can be in electrical, mechanical or other forms.

[0119] The units described as separated components can or can not be physically separated, and the components displayed as units can or can not be physical units, i.e., can be located in one place, or can be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purposes of the embodiments.

[0120] In addition, each functional unit in the embodiments of the present application can be integrated in one processing unit, or each unit can exist physically as a separate unit, or two or more units can be integrated in one unit. The above integrated unit can be implemented in the form of hardware, or in the form of hardware plus software function units.

[0121] The integrated unit implemented in the form of software function units can be stored in a computer readable storage medium. The above software function unit stored in a storage medium includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor to execute some steps of the method described in the embodiments of the present application. The above storage medium includes a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various storage media that can store program codes.

[0122] Finally, it should be noted that the above embodiments are merely used to illustrate the technical solutions of the present application, rather than limit them. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements to some technical features, without departing from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A stability analysis method for a dual-ended flexible DC system, characterized in that, include: Establish a single converter-ideal DC source system and determine the dominant mode; Based on a dual-ended flexible DC system, determine the transfer function of the DC side state variables; The transfer function is simplified based on the dominant mode to obtain a reduced-order model. Based on the reduced-order model, the analytical conditions for the system's stability under small disturbances are determined, and the stability of the double-ended flexible DC system is analyzed using these analytical conditions. The establishment of the single converter-ideal DC source system and the determination of the dominant mode include: In the formula, R dc and L dc These are the equivalent resistance and inductance on the DC side, respectively; C M g is the equivalent capacitance; g0 is the equivalent conductance of the converter to the DC side; R l and L l These are the resistance and inductance of a DC line, respectively; R arm and L arm These are the equivalent resistance and inductance of each bridge arm, respectively; P c The active power input to the converter is measured in AC; u c C M Voltage on; subscript 0 is the steady-state value; C sm The capacitance of each submodule; N is the number of submodules per bridge arm.

2. The stability analysis method for a dual-ended flexible DC system according to claim 1, characterized in that, The transfer function for determining the DC-side state variables includes the transfer function for determining the equivalent complex impedance of the DC side: In the formula, Δu dc Δi represents the change in DC voltage. dc R represents the change in direct current. M =2R arm / 3;L M =2L arm / 3; the superscript and subscript V represent electrical quantities related to the control voltage side; U s This refers to the amplitude of the AC power supply voltage. and These are the proportional and integral gains of the constant DC voltage controller on the control voltage side, respectively; σ I is the time constant of the inner loop current controller.

3. The stability analysis method for a dual-ended flexible DC system according to claim 2, characterized in that, The order reduction model is as follows: In the formula, F(s) is the binomial expression of the reduced-order model, and a0, a1, and a2 are the binomial coefficients.

4. The stability analysis method for a dual-ended flexible DC system according to claim 3, characterized in that, The analytical conditions for determining the stability of the system under small disturbances based on the reduced-order model include: In the formula, P c cr For critical power delivery to HVDC systems; u dcn Rated DC voltage; M min This represents the minimum required stability margin; The upper bound of the proportional gain of the DC voltage controller on the control voltage side.

5. A stability analysis system for a dual-ended flexible DC system, characterized in that, include: The dominant mode determination unit is used to establish a single converter-ideal DC source system and determine the dominant mode; The transfer function determination unit is used to determine the transfer function of the DC side state variables based on a dual-ended flexible DC system. A reduced-order model generation unit is used to simplify the transfer function based on the dominant mode to obtain a reduced-order model; The stability analysis unit is used to determine the analytical conditions for the stability of the system under small disturbances based on the reduced-order model, and to analyze the stability of the double-ended flexible DC system using the analytical conditions. The dominant mode determination unit is used to establish a single converter-ideal DC source system and determine the dominant mode, including: In the formula, R dc and L dc These are the equivalent resistance and inductance on the DC side, respectively; C M g is the equivalent capacitance; g0 is the equivalent conductance of the converter to the DC side; R l and L l These are the resistance and inductance of a DC line, respectively; R arm and L arm These are the equivalent resistance and inductance of each bridge arm, respectively; P c The active power input to the converter is measured in AC; u c C M Voltage on; subscript 0 is the steady-state value; C sm The capacitance of each submodule; N is the number of submodules per bridge arm.

6. The stability analysis system for a dual-ended flexible DC system according to claim 5, characterized in that, The transfer function determining unit is used to determine the transfer function of the equivalent complex impedance on the DC side: In the formula, Δu dc Δi represents the change in DC voltage. dc R represents the change in direct current. M =2R arm / 3;L M =2L arm / 3; the superscript and subscript V represent electrical quantities related to the control voltage side; U s This refers to the amplitude of the AC power supply voltage. and These are the proportional and integral gains of the constant DC voltage controller on the control voltage side, respectively; σ I is the time constant of the inner loop current controller.

7. The stability analysis system for a dual-ended flexible DC system according to claim 6, characterized in that, The order reduction model is as follows: In the formula, F(s) is the binomial expression of the reduced-order model, and a0, a1, and a2 are the binomial coefficients.

8. The stability analysis system for a dual-ended flexible DC system according to claim 7, characterized in that, The stability analysis unit is used to determine the analytical conditions for system stability under small disturbances based on the reduced-order model, including: In the formula, P c cr For critical power delivery to HVDC systems; u dcn Rated DC voltage; M min This represents the minimum required stability margin; The upper bound of the proportional gain of the DC voltage controller on the control voltage side.

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