An analytical method for the impact of reactive power droop control on the stability of VSG under large disturbances

Abstract

The present invention relates to the field of electric power technology, and specifically discloses a method for analyzing the influence of reactive power droop control on the large-disturbance stability of VSG. The method is based on a basic control structure of a typical amplitude-phase controlled VSG scheme based on a second-order SG model implemented in a dq coordinate system. The control structure includes a distributed power supply, a three-phase voltage source inverter, a filter inductor, an AC bus, a power control loop, a virtual impedance control loop, a current control loop, and a PWM module. The method also provides an impedance large-disturbance stability boundary under a balance point condition during a voltage drop period when reactive power droop is considered, thereby broadening the impedance large-disturbance stability boundary of the system. Reactive power droop control helps to improve the large-disturbance stability of the system.

Description

Technical Field

[0001] The present invention relates to the field of electric power technology, and in particular to a method for analyzing the influence of reactive power droop control on the stability of VSG with large disturbances. Background Art

[0002] A virtual synchronous generator (VSG) uses a designed power control loop to control the grid-connected converter as a voltage source, providing inertia, frequency, and voltage regulation support for the grid. Using the Thevenin equivalent circuit method, the grid-connected VSG system can be simplified as a voltage source with a series-controlled output impedance. Output impedance plays a significant role in power response characteristics and system stability. By designing a virtual impedance, the output impedance of the VSG can be reshaped to optimize its dynamic response and stability.

[0003] Traditionally, the design of grid-connected converter output impedance is based on a stability analysis of small disturbances. Even when the impact of large disturbances (such as short-circuit faults and line trips) on the output impedance is considered, the reactive power control loop is often neglected. Consequently, little research has been conducted on the impact of reactive power droop control on the stability of VSGs subjected to large disturbances during voltage dips. In practical applications, when reactive power droop control is employed, the rapid response of the reactive power loop during voltage dips causes changes in the virtual internal potential, which in turn affects the system's stability. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for analyzing the influence of reactive power droop control on the large disturbance stability of VSG, so as to improve the large disturbance stability of the system.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for analyzing the impact of reactive power droop control on the stability of VSGs subjected to large disturbances is proposed. The method is based on the basic control structure of a typical amplitude-phase controlled VSG scheme based on a second-order SG model implemented in a dq coordinate system. The control structure includes a distributed power supply, a three-phase voltage source inverter, a filter inductor, an AC bus, a power control loop, a virtual impedance control loop, a current control loop, and a PWM module.

[0007] The active power loop of VSG can be given by the following formula:

[0008]

[0009] Where: M is the moment of inertia, P ref is the active power instruction, P is the output active power, k p is the active droop coefficient, D is the damping coefficient, and ω is the output frequency;

[0010] The reactive power loop can be expressed as:

[0011]

[0012] Where: Q ref is the reactive power instruction, E ref is the internal reference voltage, E is the virtual internal potential, Q is the output reactive power, k Q is the reactive power droop coefficient;

[0013] The reactive power droop control link can be expressed by the following expression:

[0014] E=E ref -(QQ ref ) / k Q

[0015] The calculation formula for reactive power output is:

[0016]

[0017] Where U is the grid voltage, E is the virtual internal potential, Z is the output impedance, θ is the output impedance angle, and δ is the power angle;

[0018] The calculation formula for active power output is:

[0019]

[0020] Preferably, the virtual internal potential at the initial moment is E0, the corresponding reactive output is Q0, and E0 satisfies the following equation:

[0021]

[0022] make

[0023]

[0024] Solving the equation yields:

[0025]

[0026] Q0=Q ref +k Q (E ref -E0).

[0027] Preferably, the calculation process of the virtual internal potential and the output reactive power after the voltage drops is as follows:

[0028]

[0029] Where U sag is the fault grid voltage, E1 is the virtual internal potential after the voltage drops;

[0030] make

[0031]

[0032] , solving the equation we can get the grid voltage drop after:

[0033]

[0034] Q1=Q ref +k Q (E ref -E1).

[0035] Preferably, in order to ensure the degree of current limiting, the following boundary conditions should be met:

[0036]

[0037] Where: t max is the moment of maximum current, δ0 is the power angle when the active power is commanded, k s I ref is the maximum current that the converter can withstand, k s is the overcurrent coefficient, U is the grid voltage, and ω is the output frequency.

[0038] Preferably, considering that the virtual internal potential is affected by the reactive ring disturbance, the power angle swing equation of the system before the fault is:

[0039]

[0040] The corresponding steady-state point at this time is:

[0041]

[0042] After the voltage drop occurs, the power angle swing equation of the system becomes:

[0043]

[0044] The steady-state point after the voltage drops is: (δ Q,s ,Δω=0), the corresponding maximum critical point is: (π-2θ-δ Q,s ,Δω=0); where:

[0045]

[0046] Preferably, according to the existence constraint of the stable working point, it can be known that:

[0047]

[0048] δ Q,sSubstituting the expression into the above formula, we can further deduce that the boundary conditions that the output impedance needs to meet are:

[0049]

[0050] Preferably, the general expression of the energy function during reactive droop control is:

[0051]

[0052] Preferably, (π-2θ-δ Q,s ,Δω=0) into the above general energy function expression, and the critical energy V can be obtained by simplification. cr The expression is:

[0053]

[0054] The initial conditions are the power angle value and frequency disturbance at the moment when the grid voltage drops, that is, the initial conditions are (δ Q,0 ,Δω Q,0 =0); Substituting it into the expression of the energy function, the initial energy value can be obtained:

[0055]

[0056] Preferably, the initial energy value is substituted into the stability criterion V cr -V(δ Q,0 ,0)>0, it can be obtained that the boundary condition that the output impedance should satisfy to ensure the transient power angle stability of the system is:

[0057]

[0058] The beneficial technical effects of the present application mainly include: the introduction of reactive power droop control broadens the impedance large disturbance stability boundary of the system, and reactive power droop control helps to improve the large disturbance stability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0060] Figure 1 This is a block diagram of a VSG control structure provided by an embodiment of the present application;

[0061] Figure 2 This is a control block diagram of a virtual steady-state synchronous impedance control method provided by an embodiment of the present application;

[0062] Figure 3 1 is a power angle curve diagram of a type I large interference provided in an embodiment of the present application;

[0063] Figure 4 This is an impedance stability boundary diagram of a type I large interference provided by an embodiment of the present application;

[0064] Figure 5 This is a diagram of the impedance large interference stability boundary with a balance point operating condition during a voltage drop provided by an embodiment of the present application. DETAILED DESCRIPTION

[0065] To make the purpose, technical solutions, and advantages of the embodiments of this application more clear, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0066] The flowcharts shown in the accompanying drawings are for illustrative purposes only and do not necessarily include all contents and operations / steps, nor must they be executed in the order described. For example, some operations / steps may be decomposed, combined, or partially merged, so the actual execution order may vary depending on the actual situation.

[0067] In the description of this application, the terms "first / second" are only used to distinguish similar objects and do not represent a specific order for the objects. It can be understood that "first / second" can be interchanged with a specific order or sequence where permitted, so that the embodiments of the present application described here can be implemented in an order other than that illustrated or described here.

[0068] It should be understood that the orientation or positional relationship is based on the orientation or positional relationship shown in the accompanying drawings. These orientation terms are only used to facilitate the description of this application and simplify the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, they should not be understood as limiting this application.

[0069] In existing technologies, the design of grid-connected converter output impedance is based on stability analysis for small disturbances. However, there is little research on the design of output impedance for large disturbances (such as short-circuit faults and line tripping). In reality, large disturbances pose even more severe challenges to system stability, potentially causing serious problems such as inrush current and power imbalance. During large disturbances, the system output impedance must meet different performance constraints. Meeting only small-disturbance stability constraints often cannot guarantee stable system operation under large-disturbance conditions.

[0070] Therefore, this application explores the large-interference stability mechanism of VSG from the perspective of impedance optimization, derives the constraints of output impedance under symmetrical voltage drop conditions, and improves the large-interference stability of the VSG system from the perspective of optimizing the design of virtual impedance.

[0071] Figure 1 This is the basic control structure of a typical amplitude-phase controlled VSG scheme based on a second-order SG model implemented in the dq coordinate system. Distributed power sources are connected to the AC bus via a three-phase voltage source inverter. The power control loop generates the amplitude and frequency of the output voltage command. The voltage / virtual impedance control loop simulates the electrical characteristics of the synchronous generator's stator windings. The current control loop uses a PI regulator for precise current tracking and overcurrent protection. Figure 1 In, v abc and i abc They are the three-phase output voltage and output current of VSG, v dq and i dq are the d-axis and q-axis components of the VSG output voltage and output current, respectively, P ref and Q ref where ω represents the active power and reactive power commands, respectively. E represents the virtual internal potential of the VSG, simulating the internal potential of the synchronous generator. ω represents the angular frequency of the virtual internal potential generated by the active power control loop. The control strategy is established in the dq coordinate system. The VSG algorithm generates the reference amplitude and phase of the output voltage. The virtual impedance is used to reshape the output impedance of the VSG. The current control loop improves the system's current control performance and overcurrent protection.

[0072] The active power loop of VSG can be given by the following formula:

[0073]

[0074] Where: M is the moment of inertia, P ref is the active power instruction, P is the output active power, k p is the active droop coefficient, D is the damping coefficient, and ω is the output frequency.

[0075] According to the above formula, the active power control loop of the virtual synchronous generator simulates the droop control and rotor swing equation of the synchronous generator. The former can provide primary frequency regulation function to the power grid, and the latter can provide inertia and damping support.

[0076] Reactive power control uses QE droop to simulate the voltage regulation characteristics of the synchronous generator and generate the amplitude of the virtual internal potential of the VSG.

[0077] The reactive loop can be expressed as:

[0078]

[0079] Where: Qref is the reactive power instruction, E ref is the internal reference voltage, E is the virtual internal potential, Q is the output reactive power, k Q is the reactive power droop coefficient.

[0080] Figure 1 The virtual impedance control in the system adopts the virtual steady-state synchronous impedance (VSSI) control method. The control block diagram of the virtual steady-state synchronous impedance (VSSI) control method is as follows: Figure 2 shown.

[0081] Based on VSSI control, ignoring the delay of the current control loop, the output current is:

[0082]

[0083] Where: Z v 、R v 、X v are virtual impedance, virtual resistance and virtual reactance respectively; θ is the virtual impedance angle; u d and u q are the d and q axis components in the dq coordinate system. Therefore, the dq axis components of the output current can be expressed as:

[0084]

[0085] Where: δ is the power angle, U is the grid voltage.

[0086] By Park inverse transformation, the current of the α-axis can be obtained as:

[0087]

[0088] Taking the derivative of formula (5) we can get

[0089]

[0090] Order α / dt=0, the moment when the current reaches its maximum value

[0091]

[0092] The corresponding maximum current value is:

[0093]

[0094] Assume that the maximum current that the converter can withstand is k s I ref , where k s is the overcurrent coefficient, then the current peak should satisfy the constraint condition: i αmax <k s Iref .

[0095] Furthermore, the impedance constraint condition of electromagnetic transient can be derived as follows:

[0096]

[0097] The rotor swing equation of VSG can be written as:

[0098]

[0099] Where: P ref is the active power command, P is the output active power, D is the damping coefficient, and ω is the output frequency.

[0100] At the moment of voltage drop, in addition to the impact current, the output power P e It will also decrease, resulting in power imbalance, which will cause the power angle to be corrected according to formula (10). Among them, the power angle may cross the stability boundary and lose stability, which is the electromechanical transient stability problem.

[0101] In order to suppress the inrush current, it is necessary to increase the virtual impedance; and the larger the impedance value, the lower the power angle curve, and the more likely the power angle instability problem will occur. Therefore, this application derives the stable operating area of ​​the output impedance, so that the inrush current is limited to a reasonable range, and the system remains stable during the power angle swing. If there is no such overlapping stable operating area, the system needs to take additional measures to ensure the stable operation of the VSG. For the convenience of analysis, large disturbances are divided into two categories: Category I is that there is still a balance point after the fault; Category II is that there is no balance point after the fault. This application mainly focuses on large disturbances of Category I.

[0102] The analysis process of type I large disturbance is as follows:

[0103] The power angle curve is as follows Figure 3 As shown, the mathematical expression is:

[0104]

[0105] Where U is the grid voltage, E is the VSG output voltage, Z is the output impedance, θ is the output impedance angle, and δ is the power angle.

[0106] Therefore, the swing equation of the power angle is

[0107]

[0108] like Figure 3 As shown in the figure, the power angle curve of the system before the fault is P, (δ0, Δω=0) and (π-2θ-δ0, Δω=0) are two steady-state points; after the fault, the power angle curve of the system drops to P1, at which point the system still has an equilibrium point: (δs ,Δω=0) and (π-2θ-δ s ,Δω=0).

[0109] From (11), the expression of power angle can be obtained as

[0110]

[0111] In order to ensure the existence of the balance point, the power angle needs to meet the following requirements:

[0112]

[0113] Combining equations (13) and (14), the constraints on the output impedance before and after the disturbance are:

[0114]

[0115] Where: U0 is the initial grid voltage, U sag is the fault grid voltage.

[0116] The constraints of electromagnetic transient current limiting are:

[0117]

[0118] Define the energy function during transient response:

[0119]

[0120] This energy function has clear physical meaning and can give a stability evaluation close to the actual stable region.

[0121] The initial point (δ0, Δω=0) and the maximum critical point (π-2θ-δ s ,Δω=0) are substituted into the energy function to obtain the initial energy V0 and critical energy V cr :

[0122]

[0123] According to Lyapunov's theorem, the constraint condition for system stability is V cr -V0>0. Therefore, the impedance constraint condition under the transient power angle stability constraint can be derived as:

[0124]

[0125] According to formulas (15)(16)(19), Figure 4 The range of the system output impedance under large disturbances of type I is shown. When the output impedance of the VSG is reshaped within this stable region, the VSG system can maintain stable operation under large disturbances of type I, and the inrush current is also suppressed.

[0126] The above analysis does not consider the impact of the reactive power control loop. In practical applications, when reactive power droop control is used, voltage sag disturbances occur, and the rapid response of the reactive power loop causes changes in the virtual internal potential, which in turn affects the stability of the system.

[0127] When the reactive power control loop is considered, the system becomes a two-input and two-output system. It is necessary to combine the nonlinear equations of the two control loops to establish a large-signal model, and use the large-signal model to calculate the steady-state operating points before and after the voltage sag fault.

[0128] The reactive power droop control link can be expressed by the following expression:

[0129] E=E ref -(QQ ref ) / k Q (20)

[0130] The calculation formula for reactive power output is:

[0131]

[0132] The calculation formula for active power output is:

[0133]

[0134] Assume that the virtual internal potential at the initial moment is E0, and the corresponding reactive output is Q0. Combining equations (20), (21), and (22), it can be deduced that E0 satisfies the following equation:

[0135]

[0136] make

[0137]

[0138] Solving the equation yields:

[0139]

[0140] Q0=Q ref +k Q (E ref -E0) (25)

[0141] Similarly, the calculation process of the virtual internal potential and output reactive power after the voltage drops is as follows:

[0142] (26)

[0144] make

[0145]

[0146] , solving the equation we can get the grid voltage drop after:

[0147]

[0148] Q1=Q ref +k Q (E ref -E1) (28)

[0149] At this time, in order to ensure the degree of current limiting, the following boundary conditions should be met:

[0150]

[0151] Where: t max The expressions of and δ0 can be found in equations (7) and (13).

[0152] Taking into account the influence of the virtual internal potential on the reactive ring disturbance, the power angle swing equation of the system before the fault is modified to:

[0153]

[0154] The corresponding steady-state point at this time is:

[0155]

[0156] After the voltage drop occurs, the power angle swing equation of the system becomes:

[0157]

[0158] The steady-state point after the voltage drops is: (δ Q,s ,Δω=0), the corresponding maximum critical point is: (π-2θ-δ Q,s ,Δω=0). Where:

[0159]

[0160] According to the existence constraint of the stable operating point, it can be seen that:

[0161]

[0162] δ Q,s Substituting the expression (33) into the above equation (34), we can further deduce that the boundary conditions that the output impedance needs to meet are:

[0163]

[0164] According to the equation for obtaining the energy function mentioned above, the general expression of the energy function when considering reactive power droop control can be obtained as follows:

[0165]

[0166] Based on this energy function, the impact of reactive power droop control on transient stability is discussed below.

[0167] (π-2θ-δ Q,s ,Δω=0) into the above general energy function expression, and the simplification can be obtained as V cr The expression is:

[0168]

[0169] The initial conditions are the power angle value and frequency disturbance at the moment when the grid voltage drops, that is, the initial conditions are (δ Q,0 ,Δω Q,0 =0). Substituting it into the expression of the energy function, we can get the initial energy value:

[0170]

[0171] Substitute into the stability criterion V cr -V(δ Q,0 ,0)>0, it can be obtained that the boundary condition that the output impedance should satisfy to ensure the transient power angle stability of the system is:

[0172]

[0173] Where: δ Q,0 ,δ Q,s For the mathematical expressions of and E1, please refer to Equations (31), (33), and (27), respectively.

[0174] The impedance large interference stability boundary under the equilibrium point condition during voltage sag with and without considering reactive power droop is plotted together. Figure 5 In, such as Figure 5 As shown in the figure, the dashed line represents the impedance large-disturbance stability boundary without any reactive power control strategy, and the solid line represents the impedance large-disturbance stability boundary with reactive power droop control. Identical colors represent the same constraint. As can be seen from the figure, the impedance stable region without any reactive power control strategy is the purple portion of the figure; while the stable region enclosed by the impedance boundary with reactive power droop control is the rose-red region in the figure, which completely encompasses the purple region. This demonstrates that the introduction of reactive power droop control broadens the system's impedance large-disturbance stability boundary and contributes to improving the system's large-disturbance stability.

[0175] It should be noted that the storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a ROM (Read-Only Memory), a RAM (Random Access Memory), a magnetic disk or an optical disk.

[0176] It will be understood by those skilled in the art that all or some of the steps, systems, and functional modules / units in the methods disclosed above may be implemented as software, firmware, hardware, and appropriate combinations thereof. In a hardware implementation, the division between the functional modules / units mentioned in the above description does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed by several physical components in cooperation. Some or all physical components may be implemented as software executed by a processor, such as a central processing unit, a digital signal processor, or a microprocessor, or may be implemented as hardware, or may be implemented as an integrated circuit, such as an application-specific integrated circuit. Such software may be distributed on a computer-readable storage medium, which may include a computer-readable storage medium (or a non-transitory medium) and a communication medium (or a temporary medium).

[0177] As is well known to those skilled in the art, the term computer-readable storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules or other data). Computer-readable storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store the desired information and can be accessed by a computer. Furthermore, as is well known to those skilled in the art, communication media typically contains computer-readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism, and may include any information delivery media.

[0178] For example, the computer-readable storage medium may be an internal storage unit of the electronic device of the aforementioned embodiment, such as a hard disk or memory of the electronic device. The computer-readable storage medium may also be an external storage device of the electronic device, such as a plug-in hard disk, a smart memory card (SMC), a secure digital (SD) card, a flash memory card, etc. equipped on the electronic device.

[0179] The above is merely a detailed description of the present invention to enable those skilled in the art to understand or implement the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined in this application may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but rather should conform to the widest scope consistent with the principles and novel features claimed in this application.

Claims

1. A method for analyzing the impact of reactive power droop control on the stability of VSGs subjected to large disturbances is based on the basic control structure of a typical amplitude-phase controlled VSG scheme based on a second-order SG model implemented in a dq coordinate system. The control structure includes a distributed power supply, a three-phase voltage source inverter, a filter inductor, an AC bus, a power control loop, a virtual impedance control loop, a current control loop, and a PWM module. The method is characterized by: The active power loop of the VSG is given by: Where: M is the moment of inertia, P ref is the active power instruction, P is the output active power, k p is the active droop coefficient, D is the damping coefficient, and ω is the output frequency; The reactive power loop is expressed as: Where: Q ref is the reactive power instruction, E ref is the internal reference voltage, E is the virtual internal potential, Q is the output reactive power, k Q is the reactive power droop coefficient; The reactive power droop control link is expressed by the following expression: E=E ref -(Q-Q ref ) / k Q The calculation formula for reactive power output is: Where U is the grid voltage, E is the virtual internal potential, Z is the output impedance, θ is the output impedance angle, and δ is the power angle; The calculation formula for active power output is: The power angle swing equation of the system before the fault is: E0 is the virtual internal potential at the initial moment; The power angle of the corresponding steady-state point at this time is: After the voltage drops, the power angle swing equation of the system becomes: U sag is the fault grid voltage, E1 is the virtual internal potential after the voltage drops; The steady-state point after the voltage drops is: (δ Q,s ,Δω=0), the corresponding maximum critical point is: (π-2θ-δ Q,s ,Δω=0); where: The maximum critical point after voltage drop (π-2θ-δ Q,s ,Δω=0) is substituted into the general expression of energy function during reactive droop control, and the critical energy V can be obtained by simplification. cr The expression is: The initial conditions are the power angle value and frequency disturbance at the moment when the grid voltage drops, that is, the initial conditions are (δ Q,0 ,Δω Q,0 =0); Substituting the initial conditions into the expression of the energy function, the initial energy value can be obtained: Substitute the initial energy value into the stability criterion V cr -V(δ Q,0 ,0)>0, it can be obtained that the boundary condition that the output impedance should satisfy to ensure the transient power angle stability of the system is:

2. The method according to claim 1, wherein: Assume that the virtual internal potential at the initial moment is E0, the corresponding reactive output is Q0, and E0 satisfies the following equation: make Solving the equation yields: Q0=Q ref +k Q (E ref -E0).

3. The method according to claim 2, wherein: The calculation process of the virtual internal potential and output reactive power after the voltage drops is as follows: Where U sag is the fault grid voltage, E1 is the virtual internal potential after the voltage drops; make Solving the equation, we can get the grid voltage drop after: Q1=Q ref +k Q (E ref -E1)。 4. The method according to claim 3, wherein: In order to ensure the degree of current limiting, the following boundary conditions should be met: Where: t max is the moment of maximum current, δ0 is the power angle when the active power is commanded, k s I ref is the maximum current that the converter can withstand, k s is the overcurrent coefficient, U is the grid voltage, and ω is the output frequency.

5. The method according to claim 1, wherein: According to the existence constraint of the stable operating point, it can be seen that: δ Q,s Substituting the expression into the above formula, we can deduce that the boundary conditions that the output impedance needs to meet are:

6. The method according to claim 5, characterized in that: The general expression of the energy function during reactive droop control is:

Images