Method for analyzing transient stability of tracking-constructing network type series-parallel system by considering influence of power coupling and current amplitude limiting

Abstract

The invention relates to a tracking-networking type hybrid system transient stability analysis method considering the influence of power coupling and current amplitude limiting, and belongs to the field of grid-connected control technology and system stability analysis. The method comprises the following steps: establishing a tracking-constructing network type converter hybrid system transient analysis model considering current amplitude limiting, introducing a global sensitivity analysis method, quantifying the contribution rate of each variable to the system response variance under the action of multi-parameter coupling, and realizing sensitivity identification of key parameters; based on a power angle characteristic curve and an expansion phase diagram theory, performing qualitative and quantitative analysis on transient response characteristics of the GFM converter in the whole fault process, and revealing a dynamic mechanism of the GFM converter; on the basis of an equal area rule, reasonable approximation is carried out on a damping effect, transient stability calculation is carried out on an established switching system, and a limit cut-off angle of the GFM under the influence of damping and power coupling is obtained through derivation. The method has accuracy and effectiveness under the conditions of different parameter settings and different faults.

Description

TECHNICAL FIELD

[0001] The application relates to a method for analyzing transient stability of a grid-forming and grid-following hybrid system considering the influence of power coupling and current limiting, and belongs to the technical field of grid-connected control and system stability analysis. BACKGROUND

[0002] With the increasing penetration of power electronic devices such as new energy generation and energy storage devices in the power grid, a large number of grid-connected converters are connected to the power system, which has profoundly changed the dynamic characteristics and stability mechanism of the power grid. In the traditional AC power grid dominated by synchronous generators, the transient instability of the system is mainly caused by the large inertia of the rotor motion equation and the dynamic characteristics of the excitation winding. However, grid-connected converters lack physical rotors, and their synchronization behavior with the grid is no longer dependent on mechanical rotating parts, but is completely determined by the control strategy. According to the different synchronization mechanisms, grid-connected converters are mainly divided into grid-following (GFL) and grid-forming (GFM) types. GFL converters usually track the phase of the grid voltage with the help of a phase-locked loop and generate a reference voltage signal accordingly, exhibiting current source characteristics. GFM converters, on the other hand, actively regulate the output power to maintain the stability of the system frequency and voltage, exhibiting voltage source characteristics. Therefore, the traditional stability theory based on synchronous generators is no longer applicable to the new type of power system dominated by power electronic devices, and it is necessary to consider the dynamic interaction mechanism between different types of power sources.

[0003] The control characteristics of GFL and GFM are in contrast: GFL is good at power tracking but needs strong grid support and is prone to instability under weak grid conditions; GFM can autonomously build voltage and frequency, enhancing system stability. Therefore, in the face of the complex transient interaction mechanism caused by the hybrid connection of the two, research needs to start from single-machine grid connection and multi-machine homogeneous system and gradually deepen to the stability analysis of heterogeneous hybrid systems.

[0004] The transient stability of single-type converters (GFL or GFM) under grid fault conditions has been systematically studied. He Hongli et al. analyzed the system operating trajectory under different fault clearance times for GFM converters with current limiting, and proposed an adaptive limiting strategy to optimize the limit clearance time. Ebrahim Rokrok et al. explored the influence of saturated current angle on GFM stability and proposed an optimal angle design method. Fu Xikun et al. established a GFM reduced-order model considering power coupling and current limiting, revealed the influence of power coupling on the potential energy distribution of the system and the weakening effect of current limiting on damping characteristics based on the energy function method, and studied the coupling relationship between the active and reactive rings inside the GFM controller, which is fundamentally different from the power coupling between different converter types. Zhang Jingyi et al. introduced the influence of damping and reactive rings based on the traditional equal-area rule and proposed an iterative equal-area method to evaluate the transient stability margin of the system, but did not consider the influence of current limiting and the calculation is relatively complex.

[0005] Compared with single-machine systems, the research on multi-machine homogeneous hybrid systems is still insufficient. Yi Xiang et al. constructed the transient interaction model of parallel GFL converter system, revealed the transient coupling mechanism based on the equal-area criterion, and quantitatively analyzed the influence of current injection phase angle on the synchronous stability. Wu Feng et al. considered the current-limiting mode switching process for GFM parallel system, proposed a transient synchronous stability analysis model, and established a system stability domain analysis method based on the theory of flow stability.

[0006] For heterogeneous hybrid systems, Zong Haoxiang et al. proposed a frequency-domain analysis method from the perspective of synchronization, revealing the interaction instability mechanism of GFL and GFM grid-connected systems, but not quantifying the influence of key parameters. Li Yang et al. proposed a sensitivity analysis method based on the equivalent impedance criterion, which can identify the dominant parameters, but does not consider the interaction between parameters. Traditional sensitivity analysis methods usually analyze parameters in isolation, which is difficult to effectively quantify the coupling between parameters, and the modeling complexity is high. Therefore, it is necessary to propose a new method that can consider the interaction between parameters to accurately evaluate the comprehensive influence on system stability. Wang Guanqi et al. established a mathematical model of GFL-GFM hybrid system, analyzed the existence condition of steady-state equilibrium point after system disturbance, and proposed key indicators to evaluate system stability and strength, but did not involve in-depth analysis of the transient process mechanism. Shen Chao et al. based on the transient coupling model of GFL and GFM, discussed the influence of different current phase angles on the transient stability margin of virtual synchronous machine (VSG), but did not consider the effect of current limiting. Chen Zhenyi considered the limiting element of GFM in modeling, established the active transient model of the system, but did not quantitatively analyze the influence of reactive power and damping.

[0007] Although some progress has been made in the study of the influence of current limiting on the transient characteristics of converters, the research on heterogeneous hybrid systems composed of GFL and GFM is still limited, especially lacking comprehensive consideration of the influence of current limiting and damping of GFM converters. SUMMARY

[0008] The technical problem solved by the present application is to provide a transient stability analysis method for homogeneous-heterogeneous hybrid systems considering the influence of power coupling and current limiting, which is a method for constructing a transient stability analysis method for homogeneous-heterogeneous hybrid systems considering the influence of power coupling and damping effect, for evaluating the transient stability of heterogeneous hybrid systems considering the influence of power coupling and damping effect. The present application has accuracy and effectiveness in different parameter settings and different fault conditions in the constructed hybrid system.

[0009] The technical solution of the present application is a transient stability analysis method for homogeneous-heterogeneous hybrid systems considering the influence of power coupling and current limiting, which comprises:

[0010] Step1, a GFL-GFM hybrid system transient analysis model considering current limiting is established, and a global sensitivity analysis method is introduced to quantify the contribution rate of each variable to the system response variance under the coupling of multiple parameters, and to realize the sensitivity identification of key parameters;

[0011] Step2, based on the power angle characteristic curve and the extended phase diagram theory, the transient response characteristics of GFM converter in the whole process of fault are qualitatively and quantitatively analyzed, and the dynamic mechanism is revealed;

[0012] Step3, further, based on the equal-area rule, the damping effect is reasonably approximated, and the transient stability calculation of the switching system is carried out, and the limit removal angle of GFM considering the coupling effect of damping and power is derived.

[0013] Further, the Step1 comprises:

[0014] Step1.1, the topology structure of the hybrid system; the hybrid system is a power electronic system of GFL and GFM converter mixed networking, which has the characteristics of GFL converter tracking power grid and transmitting power and the advantages of GFM converter supporting voltage and providing inertia, and both the converters are configured with filter inductance and filter capacitance; the GFL converter is connected to the power grid through inductance and grid impedance, and the GFM converter is connected through inductance and resistance; the hybrid system monitors the output current and node voltage of the GFL and GFM converters, outputs PWM signals through the respective control modules to drive the converters, and realizes the electrical interaction between the hybrid system and the power grid.

[0015] Step1.2, the control architecture of the grid-connected parallel converter is constructed; the output phase angle of the phase-locked loop (PLL) is shown in formula (1):

[0016] θ PLL =∫[ω0+(K p +K i ∫)U GFL_q ]dt (1)

[0017] Wherein, K p and K i are proportional and integral gains; ω0=100π rad / s is the rated angular frequency; θ pll is the output angle of the PLL; U GFL-q is the q-axis component of the GFL voltage; t represents time;

[0018] Taking the grid voltage V g as the common reference system, then

[0019] δ GFL =∫(K p U GFL_q +K i ∫UGFL_q dt)dt (2)

[0020] where K p and K i are proportional and integral gains, respectively; δ GFL is the phase angle difference of GFL converter with respect to the common reference frame; U GFL-q is the q-axis component of GFL voltage; t represents time;

[0021] Step 1.4, construct and construct the parallel converter control architecture; the active control loop can be represented as shown in equation (3):

[0022]

[0023] where J is the virtual inertia; ω0=100π rad / s is the rated angular frequency; P m and P e are the active power reference value and the output active power, respectively; D is the damping coefficient; δ GFM is the phase angle difference between the virtual synchronous machine and the power grid; ω GFM is the angular velocity of the GFM converter; t represents time;

[0024] The mathematical equation of the reactive power control loop is:

[0025]

[0026] where K is the integral constant of the voltage loop; U GFM is the voltage of the GFM converter; t is time; Q m and Q e are the reference reactive power and the output reactive power, respectively; D q is the droop coefficient of the reactive power loop; U0 is the reference voltage;

[0027] The logic of the current limiting element being put into or out of operation is shown in equation (5):

[0028]

[0029] where I lim is the maximum allowable amplitude of the current injected by the converter into the power grid; I mag =sqrt(i dref 2 +i qref 2 ), sqrt is square root; φ IGFM is the angle between the output current of the GFM converter and the d-axis during the limiting period, which is determined by the limiting strategy; i dref and i qref are the d-axis and q-axis current reference values output by the voltage loop controlled by the reactive loop; i′qref and i' dref are the current-limited d-axis and q-axis current references;

[0030] Step 1.5, an output power model of the GFM converter in normal operation is established; the output power model of the GFM converter in normal operation is shown in formula (6):

[0031]

[0032] wherein, Z Mg is the coupling impedance of Z GFM and Z g , Z Mg ∠φ Mg = Z GFM + Z g = R Mg +jX Mg , R Mg = Z Mg cosφ Mg ; X Mg = Z Mg sinφ Mg ; ∠φ Mg represents the impedance angle of the coupling impedance Z Mg , Z GFM and Z g are the respective line impedances, Z GFM and Z g are the line impedance of the GFM and the equivalent line impedance of the power grid respectively; φ g = arctan(X g / R g ) is the impedance angle of Z g , P e and Q e are the active power and the reactive power output by the GFM converter in normal operation respectively, X g and R g are the equivalent reactance and the equivalent resistance of the power grid respectively; φ GFL is the impedance angle of Z GFL ; φ Mg is the impedance angle of Z Mg ; δ GFM is the phase angle difference between the virtual synchronous machine and the power grid; I GFL is the effective value of the GFM converter output current; V g is the amplitude of the power grid voltage, and Z GFL is the line impedance;

[0033] Step 1.6, an end voltage model of the converter after triggering current limiting is established; the end voltage model of the converter after triggering current limiting is shown in formula (7) and formula (8):

[0034]

[0035] wherein U GFL is the voltage of the GFL converter; φ GFL = δ GFL + φ IGFL , φ IGFL is the phase angle of the GFL converter output current; φ GFM = δ GFM + φ IGFM ; Z Lg = (Z GFL + Z g ) = Z Lg ∠ φ Lg , Z GFL is the line impedance; φ Lg is the impedance angle of Z Lg ;

[0036] The q-axis component of the GFL converter terminal voltage is shown in equation (9):

[0037]

[0038] Step 1.7, the output power model of the GFM converter in current limiting operation is established; equation (9) is substituted into equation (2), and the output power model of the GFM converter in current limiting operation is obtained in combination with equation (2), as shown in equation (10):

[0039]

[0040] wherein R Mg = Z Mg cos φ Mg ; X Mg = Z Mg sin φ Mg ; P e ' and Q e ' are the active power and the reactive power of the output of the GFM converter in current limiting operation, respectively;

[0041] Step 1.8, the sensitivity model of the key parameters to the system response is established; the sensitivity model of the key parameters to the system response is shown in equation (11):

[0042]

[0043] wherein ITAE_ δ GFM is the error performance index; t0 is the fault occurrence time; t c is the fault clearance time; δ0 is the power angle in steady state operation;

[0044] Further, the Step2 comprises: according to the direction of the power angle first swing when the hybrid system is disturbed, dividing into deceleration type instability and acceleration type instability; respectively performing qualitative analysis on the transient stability of the GFM-GFL hybrid system considering current limiting; using the extended phase theory, obtaining a two-dimensional phase plane containing the coupling state variable by iterative solving the coupling state variable of the GFM and the GFL converter, allowing the grid voltage to drop by 0.5 times, and the fault to last for 0.1s, and quantitatively analyzing the influence of key parameters on the transient stability of the hybrid system.

[0045] Further, the Step2 comprises:

[0046] Step2.1, performing qualitative analysis on the transient stability of the GFM-GFL hybrid system considering current limiting in the deceleration type instability state;

[0047] Step2.2, performing qualitative analysis on the transient stability of the GFM-GFL hybrid system considering current limiting in the acceleration type instability state;

[0048] Step2.3, quantitatively analyzing the influence of key parameters on the transient stability of the hybrid system using the extended phase theory;

[0049] Further, the Step2.1 comprises:

[0050] Step2.1.1, drawing the P-δ curve of the hybrid system from formula (6) and formula (10), and setting the voltage amplitude drop to 0.8 times the rated voltage;

[0051] Step2.1.2, when the grid voltage is temporarily lowered, δ GFM From the initial steady state point (set as point a) to the transient working point (set as point b), at this time, P e >P m According to formula (3), δ GFM will be decelerated;

[0052] Step2.1.3, when the fault is removed within a short time, set the fault removal point as point c, then remove the fault at point c, the current limiting exits in time, the operating point jumps from point c to a new transient working point (set as point d), at this time, P e <P m , δ GFM accelerates along the non-limiting curve, and finally returns to the stable operating point a of the voltage source mode;

[0053] Step2.1.4, when the removal of the fault occurs in a longer time, the system has stabilized at a certain position close to the rated power (set as c' point), at which point the fault is removed, the operating point jumps to a new transient operating point (set as d' point) on the rated limit curve, the current limit cannot be exited in time, and the operating point runs along the rated limit curve to the intersection point of the rated power and the rated limit curve (set as e' point), at this time, the system is locked in the current source mode, the operating point changes significantly, and it is out of synchronization with the power grid, which is a pathological steady-state operating point;

[0054] Further, Step2.2 includes the following specific steps:

[0055] Step2.2.1, draw the P-δ curve of the hybrid system from formula (6) and formula (10), and set the voltage amplitude drop to 0.5 times the rated voltage;

[0056] Step2.2.2, the grid voltage suddenly drops, and δ GFM mutates from the initial steady-state point (set as a point) to the transient operating point (set as b point), at this time, P e <P m , according to formula (3), the power imbalance will cause δ GFM to continuously increase, and then the operating point of the system moves along the limit curve in the direction of increasing δ GFM ;

[0057] Step2.2.3, when the fault is removed in a short time, set the removal point as c point, the operating point jumps from c point to a new transient operating point (set as d point), at this time, P e >P m , when ω GFM <ω0, δ GFM decreases, and then the operating trajectory of the hybrid system runs along the rated limit curve in the direction of decreasing δ GFM , when the hybrid system decelerates to the vicinity of the intersection point of the non-limit curve and the rated limit curve (set as e point), the current limiting is completely exited, the hybrid system returns to normal operation, and the power angle continues to decrease, and finally stabilizes at the initial steady-state point a of the voltage source mode;

[0058] Step2.2.4, when the fault is removed for a longer time, set the fault removal point as c', the operating point jumps to a new transient operating point (set as d' point), δ GFM moves along the blue curve in the direction of increasing δ GFM , and since the current limit cannot be exited in time, the hybrid system finally stabilizes at the steady-state operating point (set as e' point) of the current source mode, at this time, the GFM converter is locked in the current source mode and is out of synchronization with the power grid;

[0059] Further, Step2.3 includes the following specific steps:

[0060] Step 2.3.1, draw the ω-δ phase diagram curve of GFL inverter injecting pure active current during fault;

[0061] Step 2.3.2, when GFL inverter injects pure active current during fault (i.e. φ IGFL = 0), δ IGFM << δ GFM , and since GFM inverter has an inertia link, the angular velocity ω GFM of GFM inverter changes more slowly than the angular velocity ω GFL of GFL inverter, so δ GFM < δ GFL , and thus the active range of φ GFM - φ GFL is [-π / 2, 0]. According to formula (10), the active power coupling term of GFM inverter during fault is I GFL I lim Z g cos(φ GFM - φ GFL - φg), and φ g in the transmission line is approximately equal to π / 2, so the active range of coupling phase angle is [-3π / 2, -π / 2], and the value of coupling term is negative; the reactive power coupling term is I GFL I lim Z g sin(φ GFM - φ GFL + φg), and the active range of coupling phase angle is [0, -π / 2], and the value of coupling term is positive;

[0062] Step 2.3.3, draw the ω-δ phase diagram curve of GFL inverter injecting pure reactive current during fault;

[0063] Step 2.3.4, when GFL inverter injects pure reactive current during fault (i.e. φ IGFL = -π / 2), δ GFL ≈ 0, so the active range of φ GFM - φ GFL is [π / 2, π]. The active range of active power coupling phase angle (φ GFM - φ GFL - φ g ) of GFM inverter during fault is [0, π / 2], and the value of coupling term is positive. The active range of reactive power coupling phase angle (φ GFM - φ GFL + φg) is [π / 2, 3π / 2], and the value of coupling term is negative;

[0064] Step 2.3.5, when φIGFL =0, I GFL When P increases, e ′ will decrease and Q e ′ will increase; φ IGFL =-π / 2, I GFL When P increases, e ′ will increase, Q e ′ decrease; P e Decreasing ′ will increase the acceleration area, P e Increasing the value will reduce the acceleration area; furthermore, although the reactive power loop command is overridden during a fault, modulation calculation will not stop, therefore, Q will remain unchanged during the fault. e The larger the value of ′, the more likely it is to affect Q. ref The larger the deviation, the better. dref (The d-axis voltage reference value of the voltage loop output controlled by the reactive power loop) and u d u qref (The q-axis voltage reference value of the voltage loop output controlled by the reactive power loop) and u q The difference is getting larger and larger. As can be seen from the control logic of the voltage loop, i dref i qref The larger the amplitude, the greater the current will be when the voltage recovers, resulting in a current greater than I. lim The more difficult it is to release the current limit, the worse the system's transient stability becomes. Conversely, the same applies.

[0065] Step 2.3.6: Perform a quantitative analysis of the power response characteristics at the moment of operation mode transition shown in Step 2.1 and Step 2.2; at the instant of voltage recovery, u d It will increase as the voltage recovers, u dref with u d The gap continues to narrow, and similarly, i dref Start decreasing until i dref lim Limiting is disabled when the fault lasts for too long and the voltage drops significantly. dref with u d The difference will increase accordingly, and the time for the limit exit will be delayed.

[0066] Furthermore, Step 3 includes:

[0067] Step 3.1: At the short-term fault clearing time, draw different φ values. IGFM Take the corresponding P-δ curve and determine the acceleration area and deceleration area;

[0068] Step 3.2: Use the ω-δ obtained in Step 2.3 GFM The curve is calculated by taking D times (DΔω) of the vertical axis and δ. GFM ​The area surrounding the damping power is used to quantify the damping energy consumed during the current limiting process. Combining equations (3) and (10), we can obtain:

[0069]

[0070] Among them, V k V represents the system's kinetic energy, specifically the increase in the system's kinetic energy during the fault occurrence. p V represents the work done by the unbalanced power after the fault is cleared. REF It means that δ c S is a constant representing the potential energy reference value at the stable equilibrium point. D1 δ is the transient damping area; c The work angle at the stable equilibrium point; δ f It is the power angle corresponding to the system's angular velocity returning to the rated angular velocity after the fault is cleared; Δω is the angular velocity deviation;

[0071] Step 3.3: When the grid voltage drops to 0.5 times the rated voltage, the current I during the fault period... GFL =130A(φ IGFL The limiting cut-off angle is obtained by using the improved equal area method considering power coupling under the condition that = 0).

[0072] This invention provides a transient stability analysis system for a grid-connected hybrid system that considers the effects of power coupling and current limiting. The system includes a module for executing the transient stability analysis system for the grid-connected hybrid system that considers the effects of power coupling and current limiting.

[0073] The present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements a transient stability analysis method for a grid-type hybrid system that considers the effects of power coupling and current limiting.

[0074] The present invention provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a transient stability analysis method for a grid-type hybrid system considering the effects of power coupling and current limiting.

[0075] This invention provides a computer program product, including a computer program that, when executed by a processor, implements a transient stability analysis method for a grid-type hybrid system considering the effects of power coupling and current limiting.

[0076] The beneficial effects of this invention are:

[0077] 1. The application clarifies the system operating point trajectory change mechanism of GFM converter when deceleration type instability and acceleration type instability occur during fault through the power angle characteristic curve; it is found that when the fault duration is long, the current limiting cannot be exited, which eventually leads to the GFM converter locking in the current source mode, forming a pathological stability, changing the original steady state operating point, and leading to loss of synchronization with other units in the system;

[0078] 2. Based on the derived transient analysis model considering current limiting and power coupling, the variation law of GFM converter output power during voltage drop and voltage recovery is clarified; when φ IGFL = 0, with the increase of I GFL , Pe' decreases, and Qe' increases, compared with φ IGFL = -π / 2, the power angle fluctuation will be larger, and the voltage drop will be more serious; when φ IGFL = -π / 2, with the increase of I GFL , Pe' increases, and Pe' decreases, the system stability is enhanced; at the moment of fault removal, according to the power angle range at the moment of removal, Pe and Qe' will appear sudden increase or sudden decrease;

[0079] 3. Based on the improved equal area rule considering power coupling and damping effect, it is proved that the equal area rule considering the damping effect on the regulation of transient process can more accurately evaluate the system stability; reducing the value of φ IGFM within a certain range is beneficial to the system stability, and increasing the value of φ IGFM will accelerate the GFM converter locking in the current source mode. BRIEF DESCRIPTION OF DRAWINGS

[0080] Figure 1 The mixed system topology in the application;

[0081] Figure 2 The GFL converter control system diagram in the application;

[0082] Figure 3 The GFM converter control system diagram in the application;

[0083] Figure 4 The equivalent circuit diagram of the mixed system in the application; Figure 4 (a) is the equivalent circuit diagram of the system before triggering current limiting in the application; Figure 4 (b) is the equivalent circuit diagram of the system after triggering current limiting in the application;

[0084] Figure 5 The transient analysis model of the mixed system considering current limiting in the application;

[0085] Figure 6P-δ curve of deceleration type in the present application;

[0086] Figure 7 P-δ curve of acceleration type in the present application; Figure 7 (a) P-δ curve of acceleration type in the present application when short-time fault is removed; Figure 7 (b) P-δ curve of acceleration type in the present application when long-time fault is removed;

[0087] Figure 8 ω-δ phase plane of GFM converter in the present application; Figure 8 (a) ω-δ phase plane when GFL converter injects pure active current (φ IGFL = 0) during fault in the present application; Figure 8 (b) ω-δ phase plane when GFL converter injects pure reactive current (φ IGFL = -π / 2) during fault in the present application;

[0088] Figure 9 P-δ curve of different φ IGFM in the present application; Figure 9 (a) P-δ curve when φ IGFM = 0 in the present application; Figure 9 (b) P-δ curve when φ IGFM = 0.2 in the present application;

[0089] Figure 10 Simulation waveform of each electrical quantity of GFM when deceleration type instability occurs in the present application; Figure 10 (a) Simulation waveform of each electrical quantity of GFM when deceleration type instability occurs after short-time fault is removed in the present application; Figure 10 (b) Simulation waveform of each electrical quantity of GFM when deceleration type instability occurs after long-time fault is removed in the present application;

[0090] Figure 11 Simulation waveform of each electrical quantity of GFM when acceleration type instability occurs in the present application; Figure 11 (a) Simulation waveform of each electrical quantity of GFM when acceleration type instability occurs after short-time fault is removed in the present application; Figure 11 (b) Simulation waveform of each electrical quantity of GFM when acceleration type instability occurs after long-time fault is removed in the present application;

[0091] Figure 12 Waveform diagram of influence of different φ IGFL on GFM in the present application; Figure 12 (a) Waveform diagram of influence of φ IGFL = 0 on GFM in the present application; Figure 12 (b) Waveform diagram of influence of φ IGFL = π / 2 on GFM in the present application;

[0092] Figure 13 Different I during the fault period in this invention lim The effect on GFM; Figure 13 (a) is I when the fault duration is 0.5s in this invention. lim Comparative graphs showing the effects of 1.3 PU and 1.2 PU on GFM; Figure 13 (b) is I when the fault duration is 0.6s in this invention. lim Comparative graphs showing the effects of 1.3 PU and 1.5 PU on GFM;

[0093] Figure 14 φ in this invention IGFM A comparison chart showing the impact of different values ​​on the system; Figure 14 (a) φ is the fault duration of 0.4s to 0.8s in this invention. IGFM =0.2rad instability and φ IGFM A comparison chart showing stability at 0 rad. Figure 14 (b) φ is the value when the fault duration is 0.4s to 1s in this invention. IGFM =0.1rad instability and φ IGFM A comparison chart showing stability at 0 rad. Detailed Implementation

[0094] Example 1: As Figures 1-14 As shown, a transient stability analysis method for a grid-connected hybrid system considering the effects of power coupling and current limiting is presented. The method includes:

[0095] Step 1: Establish a transient analysis model of the GFL-GFM hybrid system considering current limiting, and introduce a global sensitivity analysis method to quantify the contribution rate of each variable to the system response variance under the multi-parameter coupling effect, so as to realize the sensitivity identification of key parameters.

[0096] Furthermore, Step 1 includes:

[0097] Step 1.1, Topology of the Hybrid System: The hybrid system is a power electronic system that combines GFL and GFM converters in a mixed network. It combines the grid tracking and power transmission characteristics of GFL converters with the voltage support and inertia provision advantages of GFM converters. Both converters are equipped with filter inductors and filter capacitors. Figure 1 This is a topology diagram of a hybrid system; the GFL converter is connected to the grid via an inductor and grid impedance, and the GFM converter forms a branch via an inductor and resistor; the system monitors the output current and node voltage of the GFL and GFM converters, and drives the converters by outputting PWM signals through their respective control modules, thereby realizing the electrical interaction between the hybrid system and the grid.

[0098] Step1.2, Constructing the control architecture of grid-following parallel converter; Figure 2 The GFL converter control system diagram is shown in FIG. 1, which includes a phase-locked loop (PLL), a current control loop and a PWM module. In the process of analyzing the transient stability, the dynamic of the current inner loop can be ignored, and the transient stability of the GFL converter depends on the response of the PLL. Therefore, the control core is the PLL, which tracks the LCL filter port output voltage v GFL and transforms it into dq0-axis components, taking the q-axis voltage as the input of the PI controller to realize synchronization with the grid. The phase angle of the output of the PLL is shown in equation (1):

[0099] θ PLL =∫[ω0+(K p +K i ∫)U GFL_q ]dt (1)

[0100] wherein K p and K i are proportional and integral gains, ω0=100π rad / s is the rated angular frequency, θ pll is the output angle of the PLL, U GFL-q is the q-axis component of the GFL voltage, and t represents time;

[0101] Taking the grid voltage V g as the common reference frame, we have

[0102] δ GFL =∫(K p U GFL_q +K i ∫U GFL_q dt)dt (2)

[0103] wherein K p and K i are proportional and integral gains, δ GFL is the phase angle difference of the GFL converter relative to the common reference frame, U GFL-q is the q-axis component of the GFL voltage, and t represents time;

[0104] Step1.4, Constructing the control architecture of grid-following parallel converter; Figure 3 The GFM converter control system diagram is shown in FIG. 2, which can be divided into three parts: the active power control loop, the reactive power control loop and the voltage and current inner loop control. In the process of analyzing the transient stability, when the voltage and current inner loop control parameters are designed reasonably, it is considered that the given value of the current inner loop is rapidly tracked by the actual value and remains consistent, so the internal voltage and current control loops are temporarily not considered, and the active control loop can be represented as shown in equation (3):

[0105]

[0106] where J is virtual inertia; ω0=100π rad / s is rated angular frequency; P m and P e are active power reference and output active power, respectively; D is damping coefficient; δ GFM is phase angle difference between virtual synchronous machine and power grid; ω GFM is angular speed of GFM converter; t represents time;

[0107] The mathematical equation of reactive power control loop is:

[0108]

[0109] where K is integral constant of voltage loop; U GFM is voltage of GFM converter; t is time; Q m and Q e are reference reactive power and output reactive power, respectively; D q is droop coefficient of reactive power loop; U0 is reference voltage;

[0110] The logic of current limiting element being put into or out of operation is shown in equation (5):

[0111]

[0112] where I lim is maximum allowable amplitude of current injected into power grid by converter; I mag =sqrt(i dref 2 +i qref 2 ), sqrt is square root; φ IGFM is included angle between output current of GFM converter and d-axis during limiting, which is determined by limiting strategy; i dref and i qref are d-axis and q-axis current reference values output by voltage loop controlled by reactive power loop; i′ qref and i′ dref are d-axis and q-axis current reference values after current limiting;

[0113] During current limiting operation, the original voltage loop output currents i dref and i qref controlled by reactive power loop are forcibly converted into i′ qref and i′ dref by limiting strategy shown in equation (5), at this time, the voltage loop is in a useless state, the control instruction of reactive power loop is covered, and the current inner loop controller tracks the limited current reference value, instead of the output instruction directly output by reactive power loop and modulated by voltage loop;

[0114] Step 1.5, establish the output power model of GFM converter in normal operation; wherein, Figure 4 (a) is the equivalent circuit diagram of the system before triggering current limiting, the output power model of GFM converter in normal operation is shown in formula (6):

[0115]

[0116] Wherein, Z Mg is the coupling impedance of Z GFM and Z g , Z Mg ∠φ Mg = Z GFM + Z g = R Mg +jX Mg , R Mg = Z Mg cosφ Mg ; X Mg = Z Mg sinφ Mg ; ∠φ Mg indicates the impedance angle of coupling impedance Z Mg , Z GFM and Z g are the respective line impedances, Z GFM and Z g are the line impedance of GFM and the equivalent line impedance of the grid respectively; φ g = arctan(X g / R g ) is the impedance angle of Z g , P e and Q e are the active power and reactive power output by GFM converter in normal operation respectively, X g and R g are the equivalent reactance and equivalent resistance of the grid respectively; φ GFL is the impedance angle of Z GFL ; φ Mg is the impedance angle of Z Mg ; δ GFM is the phase angle difference between the virtual synchronous machine and the grid; I GFL is the effective value of GFL converter output current; V g is the grid voltage amplitude, Z GFL is the line impedance;

[0117] Step 1.6, establish the terminal voltage model of the converter after triggering current limiting; Figure 4(b) is the equivalent circuit diagram of the system after triggering current limiting in this invention. The motion equations of the two converters still follow equations (1) and (3) respectively. However, the reactive power loop command of the GFM converter is covered by the current limiting strategy. Therefore, the external characteristics of the GFM converter after triggering current limiting are that of a current source. At this time, the terminal voltage model of the converter after triggering current limiting is shown in equations (7) and (8):

[0118]

[0119] Among them, U GFL The voltage of the GFL converter; φ GFL =δ GFL +φ IGFL , φ IGFL φ is the phase angle of the output current of the GFL converter. GFM =δ GFM +φ IGFM Z Lg =(Z GFL +Z g ) = Z Lg ∠φ Lg Z GFL φ is the line impedance. Lg For Z Lg The impedance angle;

[0120] According to the principle of coordinate transformation, the q-axis component of the terminal voltage of the GFL converter is shown in equation (9):

[0121]

[0122] Step 1.7: Establish the output power model of the GFM converter during current-limited operation; Substitute equation (9) into equation (2) and combine it with equation (8) to obtain the output power model of the GFM converter during current-limited operation, as shown in equation (10):

[0123]

[0124] Among them, R Mg =Z Mg cosφ Mg ;X Mg =Z Mg sinφ Mg ;P e ′ and Q e ′ represents the active power and reactive power output of the GFM converter during current-limited operation, respectively;

[0125] Combining equations (9) and (10), we can obtain Figure 5 The figure shows a transient analysis model of the entire hybrid system during amplitude-limited operation. Figure 5 It can be seen that the GFM converter uses its own I... limand φ GFM The q-axis component U' of the GFL converter machine terminal voltage GFL_q The influence is manifested as the rise and fall of voltage, which is called the GFL converter coupling voltage drop term; and the GFL converter is through I GFL and φ GFL The stability of the GFM converter is affected, which is manifested as the increase and decrease of power, which is called the GFM converter power coupling term.

[0126] Step1.8, a sensitivity model of key parameters to system response is established; the transient analysis model shown in the formula (10) is taken as a target function of the sensitivity analysis of the Sobol method, that is, the calculation output of the transient analysis model is the sample data input of the Sobol method, and the sensitivity model of key parameters to system response is as shown in the formula (11): Figure 5

[0127]

[0128] Where, ITAE_δ GFM is an error performance index; t0 is the fault occurrence time; t c is the fault clearance time; δ0 is the power angle in steady state operation;

[0129] Step2, based on the power angle characteristic curve and the extended phase diagram theory, the transient response characteristics of the GFM converter in the whole process of the fault are qualitatively and quantitatively analyzed, and the dynamic mechanism is revealed;

[0130] Further, the Step2 includes: according to the direction of the power angle first swing when the hybrid system is disturbed, the deceleration type instability and the acceleration type instability are divided; the transient stability of the GFM-GFL hybrid system considering current limiting is qualitatively analyzed; the extended phase diagram theory is adopted, the two-dimensional phase diagram plane containing the coupling state variables is obtained by iterative solving of the coupling state variables of the GFM and the GFL converter, the grid voltage drop is 0.5 times, the fault lasts for 0.1s, and the influence of the key parameters on the transient stability of the hybrid system is quantitatively analyzed.

[0131] Further, the Step2 includes:

[0132] Step2.1, the transient stability of the GFM-GFL hybrid system considering current limiting is qualitatively analyzed under the deceleration type instability state;

[0133] Step2.2, the transient stability of the GFM-GFL hybrid system considering current limiting is qualitatively analyzed under the acceleration type instability state;

[0134] Step2.3, the influence of the key parameters on the transient stability of the hybrid system is quantitatively analyzed by using the extended phase diagram theory; ​

[0135] Furthermore, Step 2.1 includes the following specific steps:

[0136] Step 2.1.1: Plot the P-δ curve of the hybrid system using equations (6) and (10), as follows: Figure 6 The voltage drop is set to 0.8 times the rated voltage, as shown. Figure 6 The deceleration type P-δ curve is shown below;

[0137] Step 2.1.2: When the grid voltage experiences a temporary drop, under the influence of inertia, δ GFM The initial steady-state point (denoted as point a) abruptly changes to the transient operating point (denoted as point b). At this point, P e >P m From equation (3), we can see that δ GFM It will slow down;

[0138] Step 2.1.3: When the fault is cleared within a short period of time, let the fault clearing point be point c. At point c, the fault is cleared, the current limiting is promptly released, and the operating point abruptly changes from point c to a new transient operating point (let's call it point d). At this time, P... e <P m δ GFM It accelerates along the unlimited curve and finally returns to the stable operating point a in voltage source mode;

[0139] Step 2.1.4 When the fault is cleared and the system has been stable at a position close to the rated power for a long period of time (let's call it point c'), the fault is cleared at this point, and the operating point jumps to a new transient operating point on the rated limiting curve (let's call it point d'). The current limiting cannot be cleared in time, and the operating point runs along the rated limiting curve to the intersection of the rated power and the rated limiting curve (let's call it point e'). At this time, the system is locked in the current source mode, the operating point changes significantly, and it loses synchronization with the power grid. This is a pathological steady-state operating point.

[0140] Furthermore, Step 2.2 includes the following specific steps:

[0141] Step 2.2.1: Plot the P-δ curve of the hybrid system using equations (6) and (10), setting the voltage drop to 0.5 times the rated voltage. Figure 7 The accelerated P-δ curve is shown below;

[0142] Step 2.2.2: When the grid voltage suddenly drops, under the influence of inertia, δ GFM The initial steady-state point (denoted as point a) abruptly changes to the transient operating point (denoted as point b). At this point, P e <P m As can be seen from equation (3), power imbalance will lead to δ GFMwill continue to increase, and then the operating point of the hybrid system moves along the amplitude limiting curve to δ GFM ;

[0143] Step 2.2.3, when the fault is removed in a short time, assuming that the removal point is c, the operating point jumps to a new transient operating point (assuming d), at this time, P e >P m , when ω GFM < ω0, δ GFM decelerates, and then the operating trajectory of the hybrid system will move along the rated amplitude limiting curve to the power angle δ GFM decreases, when the hybrid system decelerates to the vicinity of the intersection point of the non-amplitude limiting curve and the rated amplitude limiting curve (assuming e), the current limiting is completely removed, the hybrid system resumes normal operation, and the power angle continues to decrease and finally stabilizes at the voltage source mode steady-state operating point a;

[0144] Step 2.2.4, when the fault is removed for a long time, assuming that the removal point is c', the operating point jumps to a new transient operating point (assuming d'), δ GFM moves along the rated amplitude limiting curve to δ GFM increases, and since the current limiting cannot be removed in time, the hybrid system finally stabilizes at the current source mode steady-state operating point (assuming e'), at this time, the GFM converter is locked in the current source mode and loses synchronization with the power grid;

[0145] Further, the Step 2.3 specific steps include:

[0146] Step 2.3.1, by iteratively solving the coupling state variables (δ GFM , Δω GFM , δ GFL , ∫U GFL_q ) of the GFM and GFL converters, a two-dimensional phase diagram plane containing the coupling state variables is obtained, and is drawn as shown in Figure 8 (a) ω-δ phase diagram curve obtained when the GFL converter injects pure active current during the fault;

[0147] Step 2.3.2, when the GFL converter inputs pure active current (i.e., φ IGFL = 0), φ IGFM < δ GFM , and since the GFM converter has an inertia link, the angular velocity ω GFM of the GFM converter changes more slowly than the angular velocity ω GFL of the GFL converter, so δ GFM < δ GFL , and therefore φ GFM - φ GFLThe active power coupling term of the GFM converter during a fault is [-π / 2, 0]. From equation (10), the active power coupling term of the GFM converter during a fault is I. GFL I lim Z g cos(φ GFM -φ GFL -φg), and φ in the transmission line g Approximately equal to π / 2, therefore the range of the coupling phase angle is [-3π / 2, -π / 2], with negative values; the reactive power coupling term is I. GFL I lim Z g sin(φ GFM -φ GFL +φg), the range of coupling phase angle is [0, -π / 2], and the coupling term takes a positive value;

[0148] Step 2.3.3, Drawing Figure 8 (b) shows the ω-δ phase diagram curve obtained by injecting pure reactive current into the GFL converter during the fault period.

[0149] Step 2.3.4, During a fault, when the GFL converter injects pure reactive current (i.e., φ) IGFL =-π / 2), δ GFL ≈0, therefore φ GFM -φ GFL The active power coupling phase angle (φ) of the GFM converter during a fault is [π / 2, π]. GFM -φ GFL -φ g The active range of the reactive power coupling term is [0, π / 2], and the coupling term is positive. The reactive power coupling phase angle (φ) is... GFM -φ GFL The range of activity for +φg) is [π / 2, 3π / 2], and the coupling term takes a negative value;

[0150] Step 2.3.5, during the fault period φ IGFL =0, I GFL When P increases, e ′ will decrease and Q e ′ will increase; φ IGFL =-π / 2, I GFL When P increases, e ′ will increase, Q e ′ decrease; P e Decreasing the velocity area will increase P e Increasing the value will reduce the acceleration area; furthermore, although the reactive power loop command is overridden during a fault, modulation calculation will not stop, therefore, Q will remain unchanged during the fault. e The larger the value of ′, the more likely it is to cause problems with Q. ref The larger the deviation, the better. dref(The d-axis voltage reference value of the voltage loop output controlled by the reactive power loop) and u d u qref (The q-axis voltage reference value of the voltage loop output controlled by the reactive power loop) and u q The difference is getting larger and larger. As can be seen from the control logic of the voltage loop, i dref i qref The larger the amplitude, the greater the current will be when the voltage recovers, resulting in a current greater than I. lim The more difficult it is to release the current limit, the worse the system's transient stability becomes. Conversely, the same applies.

[0151] Step 2.3.6: Perform a quantitative analysis of the power response characteristics at the moment of operation mode transition shown in Step 2.1 and Step 2.2; at the instant of voltage recovery, u d It will increase as the voltage recovers, u dref with u d The gap continues to narrow, and similarly, i dref Start decreasing until i dref lim Limiting is disabled when the fault lasts for too long and the voltage drops significantly. dref with u d The difference will increase accordingly, and the time for the limit exit will be delayed.

[0152] Step 3: Further, based on the equal area rule, the damping effect is reasonably approximated, and the transient stability calculation of the established switching system is performed to derive the limiting cut-off angle of GFM considering the influence of damping and power coupling.

[0153] Furthermore, Step 3 includes:

[0154] Step 3.1: At the short-term fault clearing time, draw different φ values. IGFM Take the corresponding P-δ curve and determine the acceleration and deceleration areas, such as... Figure 9 As shown in the figure, the area S1 enclosed by abcd is called the acceleration area. After the fault is cleared at point c, the angular velocity begins to decelerate until it reaches point f, at which point ω=ω0. The area S2 enclosed by defj is called the deceleration area. The relationship between the acceleration area S1 and the deceleration area S2 of the converter is affected by the fault clearing angle δc and the unstable equilibrium point δu of rated limited operation.

[0155] Step 3.2: Use the ω-δ obtained in Step 2.3 GFM The curve is calculated by taking D times (DΔω) of the vertical axis and δ. GFM The damping power area enclosed by the current limiting process is quantitatively characterized by the damping energy consumed, where the damping area corresponding to the accelerating area S1 is S. D1 ​, the damping area corresponding to the deceleration area S2 is S D2 , combining formula (3) and formula (10) can obtain:

[0156]

[0157] Wherein, V k is the kinetic energy of the system, represents the increment of the kinetic energy of the system during the fault occurrence; V p represents the work of unbalanced power after the fault is cleared, V REF is a constant representing the potential reference value of the stable equilibrium point with delta c ; S D1 is the transient damping area; delta c is the power angle of the stable equilibrium point; delta f is the power angle corresponding to the recovery of the system angular velocity to the rated angular velocity after the fault is cleared; and delta omega is the angular velocity deviation.

[0158] Step 3.3, in the working condition that the grid voltage drops to 0.5 times of the rated voltage, the current I GFL =130A (phi IGFL =0) during the fault, the limit removal angle obtained by the improved equal-area method considering power coupling is shown in Table 1.

[0159] Table 1 limit removal angle obtained by different phi IGFM

[0160] IGFM ]]> ​ Without damping The method of the invention Time domain simulation -0.2 0.4636 rad 0.7830 rad 0.9591 rad -0.1 0.4100 rad 0.7000 rad 0.87341 rad 0 0.3561 rad 0.5910 rad 0.7476 rad 0.1 0.3040 rad 0.4980 rad 0.6322 rad 0.2 0.2570 rad 0.4232 rad 0.5490 rad

[0161] The application provides a follow-up network type hybrid system transient stability analysis system considering power coupling and current limiting effect, and the system comprises a module for executing the follow-up network type hybrid system transient stability analysis system considering power coupling and current limiting effect.

[0162] The application provides an electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to realize the follow-up network type hybrid system transient stability analysis method considering power coupling and current limiting effect.

[0163] The application provides a non-transient computer readable storage medium, which stores a computer program, wherein the computer program is executed by a processor to realize the follow-up network type hybrid system transient stability analysis method considering power coupling and current limiting effect.

[0164] The application provides a computer program product comprising a computer program, wherein the computer program is executed by a processor to realize the follow-up network type hybrid system transient stability analysis method considering power coupling and current limiting effect. ​

[0165] As a further aspect of the present invention, it also includes step 4: example analysis and verification. The specific steps of step 4 are as follows:

[0166] Step 4.1: Build a system based on MATLAB / Simulink as follows Figure 1 The same model with the same topology is used for simulation under different parameter settings and different fault conditions.

[0167] Step 4.1.1, the specific settings in the simulation are as follows:

[0168] (1) Main circuit parameters of the fault simulation system: as shown in Table 2.

[0169] Table 2 lists the main parameters.

[0170]

[0171]

[0172] (2) Simulation content:

[0173] To verify the effectiveness and reliability of the proposed transient stability analysis method for a grid-type hybrid system considering power coupling and current limiting effects, the simulation system was configured as follows:

[0174] 1) Set the grid voltage amplitude Vg to drop to 0.8 times the rated voltage at 1.1s. Based on the different fault clearing times, classify the faults into short-time clearing faults and long-time clearing faults. Measure the changes in various electrical quantities of the GFM converter and plot the simulation waveform of deceleration-type instability. 2) Set the grid voltage amplitude Vg to drop to 0.5 times the rated voltage at 1.1s. Based on the different fault clearing times, classify the faults into short-time clearing faults and long-time clearing faults. Measure the changes in various electrical quantities of the GFM converter and plot the simulation waveform of acceleration-type instability.

[0175] 2) The grid voltage amplitude Vg is set to drop to 0.3 times the rated voltage at 1.1s, and the fault is cleared at 1.2s. During the fault, the output current of the GFL converter is 130A, 150A, and 170A respectively, φ IGFL A comparison of the impact of different values ​​on the GFM converter; when the grid voltage amplitude Vg drops to 0.5 times the rated voltage at 1.1s, the GFM converter I... lim Comparison of the effects of different values ​​on the GFM converter;

[0176] 3) Set the grid voltage to drop to 0.5 times the rated voltage, and the current I during the fault period... GFL =130A(φ IGFL Under the condition of φ=0), data were collected at different φ values. IGFM δ GFMThe running value of the GFM is plotted and analyzed;

[0177] Step4.2, Algorithm effectiveness verification:

[0178] The simulation environment is set up to verify the influence of different parameter settings and different fault conditions on system stability. By constructing a hybrid system transient interaction model considering current limiting, the transient model is integrated into the power angle characteristic curve, the extended phase diagram theory and the equal-area rule considering damping, the influence of current limiting, power coupling and damping effect on system transient stability is qualitatively and quantitatively analyzed.

[0179] (1) In the built hybrid system model, the grid voltage amplitude Vg is set to drop to 0.8 times the rated voltage at 1.1s, according to the fault clearing time, the changes of various electrical quantities of GFM converter are as shown in Figure 10 , through the analysis of Figure 10 , the following conclusions are obtained:

[0180] Short-time fault removal, as shown in Figure 8 (a), the same as the qualitative analysis in section 2.1, after the fault occurs, δ GFM decreases, Pe′ increases, ω GFM starts to decelerate, after the fault is removed at 1.3s, the GFM converter exits the limiting in time, δ GFM starts to increase, P e ′ increases slightly, then decreases sharply and then increases to P m , the power angle finally returns to the initial stable point.

[0181] The fault is removed at 6s, the various electrical quantities of GFM converter are as shown in Figure 10 (b). During 4s-6s, the system is stable at c′ point, after the fault is removed, the current limiting cannot exit in time, δ GFM can only decrease again along the rated limiting curve, by observing the curves of δ GFM decrease before and after the fault is removed, it can be found that the curve degree has changed obviously, which verifies that the power angle curve has changed from limiting operation to rated limiting operation. When the operating point jumps from c′ point to d′ point, P e ′ increases suddenly, then decreases, and finally stabilizes at the steady-state operating point e′ of current limiting mode, the system is locked in the current source mode. The above conclusions are completely consistent with the analysis in Step2.1.

[0182] In the built hybrid system model, the grid voltage amplitude Vg is set to drop to 0.5 times the rated voltage at 1.1s, according to the fault clearing time, the changes of various electrical quantities of GFM converter are as shown in Figure 11 , through the analysis of Figure 11 , the following conclusions are obtained:

[0183] Figure 11 (a) is the change process of each electrical quantity of GFM converter when short-time fault is removed. After the fault occurs, δ GFM increases, Pe' decreases, and after the fault is removed at point c, δ GFM decreases, and decreases to Pe' and ω GFM occurs a significant jump, which proves that mode conversion starts, and after the current limiting exits, the operating point returns to the normal operating curve, δ GFM decreases and finally returns to the stable operating point.

[0184] Figure 11 (b) is the change process of each electrical quantity of GFM converter when long-time fault is removed, and the fault is removed at point c', and the operating point jumps to point d' and changes along the rated limiting curve, which is completely consistent with the description in Step 2.1. During the fault, the limiting cannot exit, δ GFM can only always increase along the rated limiting curve and oscillate with a period of 2π, and finally locks to the current source mode stable operating point e'.

[0185] Observing Figure 11 (a) and Figure 11 (b), it is found that the system's ill-conditioned stable point is between 40 degrees and 50 degrees, which is consistent with the ill-conditioned stable point shown in Step 2.1 and Step 2.2 figures (6) and (7), which quantitatively verifies the correctness of the formula (10) derived by the present application.

[0186] (2) In the built hybrid system model, the grid voltage amplitude Vg is set to drop to 0.3 times the rated voltage at 1.1 s, and the fault is removed at 1.2 s, and the GFL converter output current size is 130 A, 150 A, 170 A, respectively, φ IGFL takes different values, and the effects on the GFM converter are shown in Figure 12 , through the analysis of Figure 12 , it can be known that:

[0187] Figure 12 (a) is the change process of the angular velocity, power angle, active power, reactive power and voltage of GFM converter when the GFL injects pure active current during the fault. As the GFL injects pure active current during the fault, Pe' decreases and Qe' increases, and the power support and voltage support decrease, and the increase leads to the increase of the angular velocity and power angle fluctuations during the fault, which worsens the transient stability of the system. At the moment of fault removal, because φ GFM is located at (0, π / 2), P e ' appears a sudden increase, and Q e ' suddenly decreases, which is consistent with the analysis in Step 2.3.

[0188] Figure 12(b) shows the changes in electrical quantities of the GFM converter when the GFL injects pure reactive current during the fault. As the pure reactive current injected by the GFL increases during the fault, the fluctuations in the angular velocity and power angle of the GFM converter during the fault are reduced, the power imbalance of the GFM during the fault is reduced, stronger voltage support is provided, and the transient stability of the system during the fault is enhanced.

[0189] In the established hybrid system model, the grid voltage amplitude Vg is set to drop to 0.5 times the rated voltage at 1.1s. During the fault, the GFM converter I... lim The effects of taking different values ​​on the GFM converter are as follows: Figure 13 As shown, by analyzing Figure 13 Analysis shows that:

[0190] Figure 13 (a) represents a fault duration of 0.5 s, I lim Comparing the graphs of 1.3 PU and 1.2 PU respectively, we can see that I lim The smaller P e The smaller the value of ′, the larger the acceleration area, and under the same conditions, the more likely it is to become unstable; Figure 13 (b) represents a fault duration of 0.6 s, I lim Comparison charts for 1.3 PU and 1.5 PU are provided. lim The larger P is, under the same conditions, because e ′ and P ref The difference decreases, δ GFM The fluctuations also decrease, and the system is more likely to stabilize.

[0191] (3) In the established model, the grid voltage is set to drop to 0.5 times the rated voltage, and the current I during the fault period is... GFL =130A(φ IGFL Under the condition of φ = 0), we obtain different φ IGFM δ GFM The running curve, such as Figure 14 As shown, by analyzing Figure 14 Analysis shows that:

[0192] Figure 14 (a) φ when the fault duration is 0.4s to 0.8s IGFM =0.2rad instability and φ IGFM A comparison chart showing stability at 0 rad. φ IGFM When 0 rad, the CCA calculated in Step 3 is 0.5910 rad. Figure 14 In (a), δ GFMThe coefficient of friction (CCA) begins to decrease after 0.6320 rad and eventually stabilizes. If calculated using the equal-area rule without considering damping, it would be misjudged as instability; the actual CCA is 0.7476 rad. IGFM When = 0.2 rad, the CCA calculated in Section 2.2.2 is 0.4232 rad. Figure 14 (a) δ GFM After reaching 0.6436 rad, it began to increase continuously and eventually locked in the current source mode, with an actual CCA of 0.5490 rad.

[0193] Figure 14 (b) φ when the fault duration is from 0.4s to 1s IGFM = -0.1rad stable and φ IGFM Comparison chart of instability at 0 rad. Figure 14 In (b), φ IGFM When δ = 0 rad, GFM The value was 0.8287 rad during fault clearing, after which the system eventually became unstable and locked into current source mode; φ IGFM When the value is -0.1 rad, the CCA calculated in Section 2.2.2 is 0.7000 rad. Figure 14 In (b), δ GFM The fault clearance was 0.8013 rad, and the system stabilized after the fault was cleared in 1 second.

[0194] In summary, comparing the data calculated in Table 1 demonstrates the conservatism and correctness of the proposed method, and also reveals the significance of φ. IGFM The impact of the selected value on the transient stability of the system.

[0195] The following conclusions can be drawn from the numerical examples:

[0196] 1) Analysis of the two types of instability reveals that, considering current limiting constraints, the operating characteristics of the GFM converter exhibit the following regular changes: First, if the current limiting cannot be exited in time during the current limiting period, the system will be unable to return to its original steady-state operating point and will be locked in a pathological steady-state operating point under current source mode. Second, during a fault, the functional relationship between the active power and the power angle of the GFM converter will dynamically switch between sine and cosine characteristics.

[0197] 2) Comparing the injection of pure active current and pure reactive current during the fault period, it can be seen that the steady-state operating point of the system is around 0.14 rad, which is consistent with the quantitative analysis in Section 2.3. Figure 8 The steady-state operating point shown is consistent with the results, and the active and reactive power outputs are also completely consistent with those calculated by equation (10), proving the correctness of the model derived in this invention; when injecting pure reactive current, ω GFM It fluctuates around 315.8 rad / s. Figure 12 δ in (a)GFM In the range of 17.2-17.4 degrees, Figure 12 The delta in (b) GFM Varied in the range of 16.8-16.9 degrees; under the same grid voltage drop degree, Figure 12 The U in (a) GFM Dropped to about 105V at the lowest, Figure 12 Figure 12 Dropped to about 112V in (b), further proving that the reactive current injected by the GFL converter during the fault is beneficial to the system stability.

[0198] 3) The setting of the current limiting value I lim has a key impact on the transient stability of the GFM: under the same fault condition, a higher I lim helps to reduce the power difference and power angle fluctuation, and improve the stability of system recovery; while a lower I lim increases the acceleration area, making the system more prone to instability. Therefore, reasonable setting of the current limit is very important to enhance the transient stability of the system. The value of I lim is also subject to restrictions and requirements, and is not the bigger the better. First of all, the current-carrying capacity of power electronic devices must be considered, and secondly, the value cannot be larger than the fault current without current limiting strategy.

[0199] 4) The value of φ IGFM has a significant impact on the transient stability of the system. Under different fault durations, the increase of φ IGFM reduces the CCA of the system, making it more prone to instability; while a proper reduction of φ IGFM helps to improve the stability boundary of the system, making the system that may have been unstable recover in synchronization after the fault is cleared. In addition, due to the influence of damping and other factors in the actual system response, the real CCA is often greater than the theoretical calculated value based on the undamped equal-area criterion, indicating that the actual dynamic characteristics need to be considered comprehensively in stability analysis to accurately evaluate the transient stability behavior of the system.

[0200] In summary, the invention reveals the trajectory mechanism of the accelerating and decelerating instability of the GFM converter during the fault, points out that the current limiting cannot be exited when it is locked in the current source mode, forming a pathological steady state out of synchronization; analyzes the influence law of different power coupling phases on active and reactive power and system stability, showing that reasonable setting of the phase can enhance the stability and suppress the voltage drop; further, through the improved equal-area criterion considering damping, it is verified that the criterion can more accurately evaluate the transient stability, and it is clear that reducing φ IGFM within a certain range helps to delay instability and improve the recovery ability of the system.

[0201] The application provides a kind of considering power coupling and current limiting influence's follow-structure network type hybrid system transient stability analysis method, first, the hybrid system transient interaction model considering current limiting is established, an index of fusion power angle dynamic performance is proposed, which is applied to the global sensitivity analysis of transient interaction model parameters, to realize the identification and sensitivity quantification of key parameters;Then, combined with the power angle characteristic curve, the change trajectory and mechanism of power angle during deceleration type instability and acceleration type instability are qualitatively analyzed, it is found that the system locked in current source mode will be stable at the ill-conditioned stable operating point;Further, the power angle and current related parameters of GFL converter are integrated into the differential equation of GFM converter, the differential equation is discretized by implicit Euler method, and the coupled state variables of GFM and GFL converter are iteratively solved by Newton iteration method, to obtain a two-dimensional phase diagram plane containing coupled state variables, combined with the improved equal-area rule, the influence of system key parameters on the stability of structure network type converter is quantitatively analyzed.

[0202] The specific embodiments of the application are described in detail above with reference to the accompanying drawings, but the application is not limited to the above-described embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the purpose of the application.

Claims

1. A transient stability analysis method for a grid-type hybrid system considering the effects of power coupling and current limiting, characterized in that: The method includes: Step 1: Establish a transient analysis model of the GFL-GFM hybrid system considering current limiting, and introduce a global sensitivity analysis method to quantify the contribution rate of each variable to the response variance of the hybrid system under the multi-parameter coupling effect, so as to realize the sensitivity identification of key parameters. Step 2: Based on the power angle characteristic curve and extended phase diagram theory, the transient response characteristics of the GFM converter during the entire fault process are qualitatively and quantitatively analyzed to reveal its dynamic mechanism. Step 3: Based on the equal area rule, the damping effect is reasonably approximated, and the transient stability calculation of the established switching system is performed to derive the limiting cut-off angle of the GFM converter considering the effects of damping and power coupling.

2. The transient stability analysis method for a grid-type hybrid system considering the effects of power coupling and current limiting as described in claim 1, characterized in that: Step 1 includes: Step 1.1: Construct the topology of the hybrid system; In the hybrid system, both the GFL and GFM converters are equipped with filter inductors and filter capacitors. The GFL converter is connected to the grid through an inductor and grid impedance, while the GFM converter is connected to the grid through an inductor and a resistor to form a branch. The hybrid system monitors the output current and node voltage of the GFL and GFM converters and drives the converters by outputting PWM signals through their respective control modules, thereby realizing the electrical interaction between the hybrid system and the grid. Step 1.2: Construct the control architecture of the grid-connected parallel converter; the output phase angle of the phase-locked loop (PLL) is shown in equation (1): i PLL =∫[ω0+(K p +K i ∫)U GFL_q ]dt (1) Among them, K p and K i These are the proportional and integral gains, respectively; ω0 = 100π rad / s is the rated angular frequency; θ PLL U is the output angle of the phase-locked loop (PLL). GFL-q The voltage q-axis component of the GFL; t represents time; With grid voltage V g If we consider a common frame of reference, then: δ GFL =∫(K p U GFL_q +K i ∫U GFL_q dt)dt (2) Where, δ GFL This represents the phase angle difference of the GFL converter relative to the common reference frame; Step 1.4: Construct the control architecture of the parallel converter; the active power control loop is represented by equation (3): Where J is the virtual inertia; P m and P e These represent the active power reference value and the active power output of the GFM converter during normal operation, respectively; D is the damping coefficient; ω GFM For the angular velocity of the GFM converter; The mathematical equation for the reactive power control loop is: Where K is the voltage loop integral constant; U GFM Q is the voltage of the GFM converter; m and Q e These represent the reference reactive power and output reactive power of the GFM converter during normal operation, respectively; D q U0 is the reactive power loop droop factor; U0 is the reference voltage. The logic for engaging or disengaging the current limiting circuit is shown in equation (5): Among them, I lim It is the maximum permissible amplitude of the converter-injected grid current; I mag =sqrt(i dref 2 +i qref 2 ), sqrt is the square root; φ IGFM The angle between the output current of the GFM converter and the d-axis during the limiting period is determined by the limiting strategy; i dref and i qref These are the d-axis and q-axis current reference values ​​output by the voltage loop controlled by the reactive power loop; i′ qref and i′ dref These are the reference values ​​for the d-axis and q-axis currents after current limiting. Step 1.5: Establish the output power model of the GFM converter during normal operation; the output power model of the GFM converter during normal operation is shown in equation (6): Among them, Z Mg It is Z GFM and Z g The coupling impedance, Z Mg ∠φ Mg =Z GFM +Z g =R Mg +jX Mg R Mg =Z Mg cosφ Mg ;X Mg =Z Mg sinφ Mg ;∠φ Mg Represents the coupling impedance Z Mg The impedance angle, Z GFM and Z g For their respective line impedances, Z GFM and Z g These are the line impedance of the GFM and the equivalent line impedance of the power grid, respectively; φ g =arctan(X) g / R g ) is Z g The impedance angle, X g and R g These are the equivalent reactance and equivalent resistance of the power grid, respectively; φ GFL For Z GFL The impedance angle; φ Mg For Z Mg The impedance angle; δ GFM The phase angle difference between the virtual synchronous machine and the power grid; I GFL V represents the effective value of the output current of the GFL converter. g Z represents the grid voltage amplitude. GFL Line impedance; Step 1.6: Establish the terminal voltage model of the converter after triggering current limiting; the terminal voltage model of the converter after triggering current limiting is shown in equations (7) and (8): Among them, U GFL The voltage of the GFL converter; φ GFL =δ GFL +φ IGFL , φ IGFL φ is the phase angle of the output current of the GFL converter. GFM =δ GFM +φ IGFM Z Lg =(Z GFL +Z g ) = Z Lg ∠φ Lg ;φ Lg For Z Lg The impedance angle; The q-axis component U′ of the GFL converter terminal voltage GFL_q As shown in equation (9): Step 1.7: Establish the output power model of the GFM converter during current-limited operation; Substitute equation (9) into equation (2), and combine equation (2) to obtain the output power model of the GFM converter during current-limited operation, as shown in equation (10): Among them, P e ′ and Q e ′ represents the active power and reactive power output of the GFM converter during current-limited operation, respectively; Step 1.8: Establish the sensitivity model of key parameters to system response; the sensitivity model of key parameters to system response is shown in Equation (11): Among them, ITAE_δ GFM For error performance indicators; t0 is the time of failure occurrence; t c δ0 is the fault clearing time; δ0 is the power angle during steady-state operation.

3. The transient stability analysis method for a grid-type hybrid system considering the effects of power coupling and current limiting as described in claim 1, characterized in that: Step 2 includes: classifying instability into deceleration-type and acceleration-type based on the direction of the initial swing of the power angle when the hybrid system is disturbed; performing qualitative analysis on the transient stability of the GFM-GFL hybrid system considering current limiting; using extended phase diagram theory, obtaining a two-dimensional phase diagram plane containing coupled state variables by iteratively solving the coupled state variables of the GFM and GFL converters, setting the grid voltage to drop by 0.5 times and the fault duration to 0.1s, and quantitatively analyzing the impact of key parameters on the transient stability of the hybrid system.

4. The transient stability analysis method for a grid-type hybrid system considering the effects of power coupling and current limiting as described in claim 1, characterized in that: The specific steps of Step 2 include: Step 2.1: Under deceleration-type instability, a qualitative analysis of the transient stability of the GFM-GFL hybrid system considering current limiting is performed. Step 2.2: Under accelerated instability, a qualitative analysis of the transient stability of the GFM-GFL hybrid system taking current limiting into account is performed. Step 2.3: Quantitatively analyze the impact of key parameters on the transient stability of the hybrid system using extended phase diagram theory.

5. The transient stability analysis method for a grid-type hybrid system considering the effects of power coupling and current limiting as described in claim 4, characterized in that: Step 2.1 includes: Step 2.1.1: Plot the P-δ curve of the hybrid system, and set the voltage drop to 0.8 times the rated voltage; Step 2.1.2: When the grid voltage experiences a temporary drop, under the influence of inertia, δ GFM From the initial steady-state point a, it abruptly changes to the transient operating point b. At this point, P e >P m δ GFM Deceleration, P m and P e These represent the active power reference value and the active power output of the GFM converter during normal operation, respectively, δ. GFM The phase angle difference between the virtual synchro and the power grid; Step 2.1.3: When the fault is cleared within a short period of time, let the fault clearing point be point c. At point c, the fault is cleared, the current limiting is promptly released, and the operating point abruptly changes from point c to the new transient operating point d. At this time, P... e <P m δ GFM It accelerates along the unlimited curve and finally returns to the initial steady-state point a of the voltage source mode; Step 2.1.4 When the fault is cleared over a long period of time, the hybrid system has stabilized at a certain position close to the rated power. When the fault is cleared at this point, the operating point jumps to a new transient operating point on the rated limiting curve. The current limiting cannot be removed in time, and the operating point runs along the rated limiting curve to the intersection of the rated power and the rated limiting curve. At this time, the hybrid system is locked in the current source mode, the operating point changes significantly, and it loses synchronization with the power grid. It is a pathological steady-state operating point.

6. The transient stability analysis method for a grid-type hybrid system considering the effects of power coupling and current limiting as described in claim 4, characterized in that: Step 2.2 includes: Step 2.2.1: Plot the P-δ curve of the hybrid system, and set the voltage drop to 0.5 times the rated voltage; Step 2.2.2: When the grid voltage suddenly drops, under the influence of inertia, δ GFM From the initial steady-state point, it abruptly changes to the transient operating point. At this point, P e <P m Power imbalance leads to δ GFM It will continue to increase, and then the operating point of the hybrid system will move along the limiting curve towards δ. GFM Move in the direction of increase, P m and P e These represent the active power reference value and the active power output of the GFM converter during normal operation, respectively, δ. GFM The phase angle difference between the virtual synchro and the power grid; Step 2.2.3: When the fault is cleared within a short time, let the clearing point be point c. The operating point jumps from point c to the new transient operating point. At this time, P e >P m When ω GFM When ω < 0, δ GFM After deceleration, the operating trajectory of the hybrid system will follow the rated amplitude limit curve towards the power angle δ. GFM As the hybrid system decelerates and moves to the vicinity of the intersection of the non-limiting curve and the rated limiting curve, the current limiting completely exits, the hybrid system resumes normal operation, the power angle continues to decrease, and finally stabilizes at the initial steady-state point of the voltage source mode. Step 2.2.4: When the fault is cleared after a relatively long period of time, let the fault clearing point be c′, and the running point abruptly changes to the new transient operating point, δ GFM Along the rated limiting curve towards δ GFM As the current limiter moves in the direction of increase, it cannot exit in time. The hybrid system eventually stabilizes at the steady-state operating point of the current source mode. At this time, the GFM converter is locked in the current source mode and loses synchronization with the grid.

7. The transient stability analysis method for a grid-type hybrid system considering the effects of power coupling and current limiting as described in claim 2, characterized in that: Step 2 includes Step 2.3: Quantitatively analyzing the impact of key parameters on the transient stability of the hybrid system using extended phase diagram theory. Step 2.3 includes: Step 2.3.1: Plot the ω-δ obtained by injecting pure active current into the GFL converter during the fault period. GFM Phase diagram curves; Step 2.3.2, During a fault, when the GFL converter receives pure active current, i.e., φ IGFL =0, φ IGFM <<δ GFM Furthermore, due to the presence of an inertial element in the GFM converter, the angular velocity ω of the GFM converter... GFM Angular velocity ω of GFL converter GFL The change is slower, therefore δ GFM <δ GFL Therefore φ GFM -φ GFL The activity range is [-π / 2, 0]; according to equation (10), the active power coupling term of the GFM converter during the fault period is I. GFL I lim Z g cos(φ GFM -φ GFL -φg), and φ in the transmission line g Approximately equal to π / 2, therefore the range of the coupling phase angle is [-3π / 2, -π / 2], with negative values; the reactive power coupling term is I. GFL I lim Z g sin(φ GFM -φ GFL +φg), the coupling phase angle has a range of [0, -π / 2], and the coupling term takes a positive value; Step 2.3.3: Plot the ω-δ obtained by injecting pure reactive current into the GFL converter during the fault period. GFM Phase diagram curves; Step 2.3.4: During a fault, when the GFL converter injects pure reactive current, i.e., φ IGFL =-π / 2, δ GFL ≈0, therefore φ GFM -φ GFL The active power coupling phase angle (φ) of the GFM converter during a fault is [π / 2, π]. GFM -φ GFL -φ g The active range of the reactive power coupling term is [0, π / 2], and the coupling term is positive; the reactive power coupling phase angle (φ) is... GFM -φ GFL The range of activity for +φg) is [π / 2, 3π / 2], and the coupling term takes a negative value; Step 2.3.5, during the fault period φ IGFL =0, I GFL When P increases, e ′ will decrease and Q e ′ will increase; φ IGFL =-π / 2, I GFL When P increases, e Q increases e ′ decrease; P e Decreasing ′ will increase the acceleration area, P e Increasing Q' will reduce the acceleration area; during the fault period e The larger the value of ′, the more likely it is to cause problems with Q. m The larger the deviation, the lower the d-axis voltage reference value u of the voltage loop output controlled by the reactive power loop. dref The d-axis voltage u of the GFL output voltage d The q-axis voltage reference value u of the voltage loop output controlled by the reactive power loop. qref The d-axis voltage u of the GFL output voltage q The difference is getting larger and larger. As can be seen from the control logic of the voltage loop, i dref i qref The larger the amplitude, the greater the current will be when the voltage recovers, resulting in a current greater than I. lim The more difficult it is to remove the current limit, the worse the transient stability of the system becomes; conversely, the same applies. Step 2.3.6: Perform a quantitative analysis of the power response characteristics at the moment of operation mode transition shown in Step 2.1 and Step 2.2; at the instant of voltage recovery, u d It will increase as the voltage recovers, u dref with u d The gap continues to narrow, and similarly, i dref Start decreasing until i dref lim Limiting is disabled when the fault lasts for too long and the voltage drops significantly. dref with u d The difference will increase accordingly, and the time for the limit exit will be delayed.​ 8. The transient stability analysis method for a grid-type hybrid system considering the effects of power coupling and current limiting as described in claim 2, characterized in that: Step 3 includes: Step 3.1: At the short-term fault clearing time, draw different φ values. IGFM Take the corresponding P-δ curve and determine the acceleration area and deceleration area; Step 3.2: Use the ω-δ obtained in Step 2.3 GFM The curve is calculated by taking D times the vertical axis and δ. GFM The area surrounding the damping power is used to quantify the damping energy consumed during the current limiting process. Combining equations (3) and (10), we can obtain: Among them, V k V represents the system's kinetic energy, specifically the increase in the system's kinetic energy during the fault occurrence. p V represents the work done by the unbalanced power after the fault is cleared. REF It means that δ c S is a constant representing the potential energy reference value at the stable equilibrium point. D1 δ is the transient damping area; c The work angle at the stable equilibrium point; δ f It is the power angle corresponding to the system's angular velocity returning to the rated angular velocity after the fault is cleared; Δω is the angular velocity deviation; Step 3.3: When the grid voltage drops to 0.5 times the rated voltage, the current I during the fault period... GFL =130A(φ IGFL Under the condition of =0), the limit cut-off angle is obtained by using the improved equal area method considering power coupling.

9. A transient stability analysis system for a grid-type hybrid system considering the effects of power coupling and current limiting, characterized in that, The system includes a module for performing a transient stability analysis method for a grid-type hybrid system considering the effects of power coupling and current limiting as described in any one of claims 1 to 8.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the transient stability analysis method for a grid-type hybrid system that considers the effects of power coupling and current limiting as described in any one of claims 1 to 8.

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