A transient stability analysis method for power systems containing grid-following and grid-forming converters

Abstract

The present invention discloses a transient stability analysis method for a power system containing grid-following and grid-forming converters, and belongs to the field of transient stability analysis of new energy power generation systems. The method is proposed to address the problem of the lack of analytical models for the system. The specific steps are: constructing a system model in which grid-following and grid-forming converters are connected in parallel to an infinite power grid; establishing a mathematical model of a grid-following three-phase synchronous phase-locked loop; analyzing the transient stability process of the grid-following type; establishing a mathematical model of the grid-forming type virtual power angle and analyzing it with a phase diagram; establishing a mathematical model of the grid-forming type output active power; analyzing the transient stability process of the grid-forming type; establishing a mathematical model of the grid-forming type virtual power angle and analyzing it with a phase diagram; the present invention uses circuit theorems to derive a system mathematical model. Compared with the small signal modeling method, the mathematical model effectively analyzes the dynamic characteristics of the system under large disturbances. The present invention solves the problem in the prior art of the lack of an effective mathematical analytical analysis model for power systems containing grid-following and grid-forming converters.

Description

Technical Field

[0001] The present invention belongs to the field of transient stability analysis of renewable energy power generation systems, and specifically relates to a transient stability modeling and analysis method for a power system containing grid-following and grid-forming converters for renewable energy power systems. The method can intuitively analyze the transient power angle stability characteristics of the power system containing grid-forming and grid-following converters. Background Art

[0002] As the proportion of renewable energy generation (REPR) increases, the operating characteristics of power systems are facing significant changes. However, REPRs are typically connected to the grid through power electronic converters. Because the dynamic characteristics of converters differ from those of synchronous generators (SGs), the dynamic performance of the power system will be different. When the grid is subjected to large disturbances, such as grid voltage sags and transmission line faults, the transient stability of power systems with high REPR penetration levels is considered a new challenge.

[0003] Unlike synchronous generators, the dynamic performance and synchronization mechanism of a converter depend on its control method. Currently, there are two control schemes: current control and voltage control. Current-controlled converters follow the frequency and phase angle of the grid voltage and are also known as grid-following converters. As the number of grid-following converters increases in transmission systems, the strength of the grid voltage decreases. Therefore, since voltage-controlled converters can control both the frequency and voltage at the grid output, voltage-controlled converters are needed to improve the strength of the grid voltage. These voltage-controlled converters are also known as grid-forming converters.

[0004] In the prior art, there is a problem that the transient stability analysis method for power systems containing grid-following and grid-forming converters lacks a mathematical model for analyzing transient power angle stability under large disturbances. Summary of the Invention

[0005] Purpose of the invention: In view of the deficiencies of existing research, the purpose of the present invention is to provide a mathematical model of a power system containing grid-following and grid-forming converters, which can better reflect the nonlinear dynamic process of the power angle during system faults, and solve the problem in the prior art of lack of a mathematical model for analyzing the stability of transient power angle under large disturbances for power systems containing grid-following and grid-forming converters.

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

[0007] To achieve the above objectives, the present invention provides a transient modeling method for a power system including grid-following and grid-forming converters, comprising the following steps:

[0008] Step 1: Construct a system model in which a grid-following converter and a grid-forming converter are connected in parallel to an infinite power grid;

[0009] The system model consists of a grid-following converter and a grid-forming converter, each passing through L GFL , L GFM Connect in parallel to the common coupling point, and then pass through L BUS Connected to the infinite power grid. The grid-connected angle in the grid-following converter control structure is detected by a three-phase synchronous phase-locked loop (PLL). This angle then passes through the current loop to generate the drive signal. The grid-following converter employs a three-loop control strategy: the power loop generates the amplitude and phase commands for the voltage reference, the voltage loop reflects the control objective, and the current loop acts as a limiter. This is then fed into the pulse width modulation generator to generate the converter's drive signal.

[0010] Step 2: Establish the q-axis voltage U output by the three-phase synchronous phase-locked loop of the grid-following converter q Mathematical model of

[0011] The system model in step 1 is converted into a circuit model, where the grid-type converter is converted into a controlled current source model, and the grid-type converter is converted into a controlled voltage source model. Based on the Thevenin circuit theorem, the output voltage U of the grid-type converter is established. PLL ∠θ PLL The vector model of the three-phase synchronous phase-locked loop is obtained, and the mathematical model of the q-axis voltage output by the three-phase synchronous phase-locked loop is obtained; by analogy with the synchronous motor, the difference between the phase angle of the voltage at the output of the grid-type converter and the phase angle of the voltage at the infinite bus terminal is defined as the virtual power angle δ of the grid-type converter. L The difference between the voltage phase angle of the output terminal of the grid-type converter and the voltage phase angle of the infinite bus terminal is defined as the virtual power angle δ of the grid-type converter. D .

[0012] Step 3: Analyze the transient stability process of the grid-following converter;

[0013] The system initially operates at the equilibrium point. When a grid fault occurs, the system operating point suddenly changes. When the grid-following converter operates stably, Under the action of L After first decreasing, then oscillating for several cycles near the new equilibrium point, and finally stabilizing at the new equilibrium point; when the grid-following converter loses stability, the virtual power angle δ L Continue to decrease.

[0014] Step 4: Establish a second-order mathematical model of the virtual power angle of the grid-following converter and analyze it using the phase diagram method;

[0015] After establishing its dynamic mathematical model by combining the three-phase synchronous phase-locked loop control block diagram, the virtual power angle δ of the grid-following converter is L The mathematical model of the q-axis voltage output by the three-phase synchronous phase-locked loop obtained in step 2 is combined with the line impedance model considering the frequency characteristics to solve the virtual power angle δ used by the system to analyze the stability of large-disturbance power angle synchronization. LThe second-order dynamic mathematical model of .

[0016] Step 5: Establish a mathematical model of the active power output of the grid-connected converter;

[0017] Based on the system equivalent mathematical model obtained in step 2, the Thevenin circuit theorem is applied to establish a mathematical model of the electromagnetic power output by the grid-type converter.

[0018] Step 6: Analyze the transient stability process of the grid-type converter;

[0019] The system initially operates at the equilibrium point. When a grid fault occurs, the system operating point suddenly changes. When the grid-connected converter operates stably, Under the action of D After the process of increasing first, oscillating around the new equilibrium point for several cycles, and finally stabilizing at the new equilibrium point; when the grid-type converter loses stability, the virtual power angle δ D Continue to increase.

[0020] Step 7: Establish a second-order mathematical model of the virtual power angle of the grid-type converter and analyze it using the phase diagram method;

[0021] After establishing its dynamic mathematical model by combining the power loop control block diagram of the grid-type converter, the virtual power angle δ D The expression is combined with the mathematical model of the output electromagnetic power of the grid-type converter obtained in step 5 to solve the virtual power angle δ used by the system to analyze the large disturbance power angle synchronization stability. D The second-order dynamic mathematical model of .

[0022] Furthermore, the power system in step 1 includes an infinite grid-side voltage vector E∠θ0, a filter inductor L f1 ,L f2 , line impedance L GFM ,L GFL and L BUS φ0 is the phase difference between the grid-type converter terminal voltage and output current. In the steady state, θ PLL will be equal to θ GFL .

[0023] Furthermore, in step 2, I∠φ0+θ PLL Indicates the output current of the grid-following converter, U PLL ∠θ PLL It is the voltage amplitude and phase angle detected by the three-phase synchronous phase-locked loop. Output voltage U PLL ∠θ PLL The vector model can be expressed as:

[0024] U PLL ∠θ PLL =jI∠(φ0+θGFL )X g +K1V∠θ GFM +K2E∠θ0 (14)

[0025] Wherein, θGFM and θGFL represent the phase angles at the output of the grid-forming and grid-following converters, respectively; I∠φ0+θPLL represents the current phasor at the output of the grid-following converter; V∠θGFM represents the voltage phasor at the output of the grid-forming converter; E∠θ0 represents the infinite grid-side voltage vector; XGFM, XGFL, and XBUS are circuit reactances; K1 and K2 represent proportionality coefficients, and K1 = XBUS / (XBUS+XGFM), K2 = XGFM / (XBUS+XGFM); Xg represents the circuit impedance, and Xg = XGFL+(XBUS / / XGFM); where K1 = X BUS / (X BUS +X GFM ),K2=X GFM / (X BUS +X GFM ) and X g =X GFL +(X BUS / / X GFM ).

[0026] The mathematical model of the q-axis voltage output by the three-phase synchronous phase-locked loop can be expressed as:

[0027] U q =i d X g -K2Esin(θ GFL -θ0)+K1Vsin(θ GFM -θ GFL ) (15)

[0028] Wherein, id+jiq=I∠φ0, id and iq represent the d-axis and q-axis components of I∠φ0, respectively, θGFM and θGFL represent the phase angles at the output of the grid-forming and grid-following converters, respectively, V∠θGFM represents the voltage phasor at the output of the grid-forming converter, E∠θ0 represents the infinite grid-side voltage vector, XGFM, XGFL, and XBUS are circuit reactances, K1 and K2 represent proportionality coefficients, and K1=XBUS / (XBUS+XGFM), K2=XGFM / (XBUS+XGFM), Xg represents the circuit impedance, and Xg=XGFL+(XBUS / / XGFM); wherein, i d +ji q =I∠φ0.

[0029] Define θ GFM ,θ GFL The phase difference between the phase angle θ0 of the infinite grid voltage is the virtual power angle δ Land δ D .

[0030] δ L =θ GFL -θ0 (16)

[0031] δ D =θ GFM -θ0 (17)

[0032] Furthermore, in step 3 Denotes the virtual power angle δ of the grid-connected converter L The rate of change can be expressed as:

[0033]

[0034] Where, represents the rate of change of the virtual power angle δL of the grid-following converter, Kp and Ki represent the proportional and integral coefficients in the three-phase synchronous phase-locked loop, and Uq represents the q-axis voltage output by the three-phase synchronous phase-locked loop;

[0035] Furthermore, the dynamic mathematical model of the three-phase synchronous phase-locked loop in step 4 can be expressed as:

[0036] θ PLL =∫[ω0+(K p +K i ∫)U q ] (19)

[0037] θ0=∫ω0dt (20)

[0038] Where ω0 is the grid frequency, K p and K i are the proportional and integral parameters of the PI controller respectively.

[0039] The line impedance model of the grid-following converter considering the frequency characteristics can be expressed as:

[0040] X GFL =ω PLL L GFL (twenty one)

[0041]

[0042] where ω PLL is the angular frequency of the three-phase synchronous phase-locked loop.

[0043] The combined equations (15)-(22) can be used to obtain the virtual power angle δ of the grid-following converter for the power system including the grid-forming and grid-following converters: L The second-order dynamic mathematical model of:

[0044]

[0045] Wherein, δL and δD represent the virtual power angles of the grid-following and grid-forming converters, respectively; δL represents the rate of change of the virtual power angle δL of the grid-following converter; ω0 represents the grid frequency; Kp and Ki represent the proportional and integral coefficients in the three-phase synchronous phase-locked loop, respectively; V∠θGFM represents the voltage phasor at the output of the grid-forming converter; E∠θ0 represents the infinite grid-side voltage vector; id and iq represent the d-axis and q-axis components of I∠φ0, respectively; XGFM, XGFL, and XBUS are circuit reactances; LGFL represents the line inductance; K1 and K2 represent proportional coefficients, and K1 = XBUS / (XBUS+XGFM) and K2 = XGFM / (XBUS+XGFM); Xg represents the circuit impedance, and Xg = XGFL+(XBUS / / XGFM);

[0046] Furthermore, in step 5, V∠θ GFM represents the voltage vector at the output of the grid-type converter. Therefore, applying the Thevenin circuit theorem, the mathematical model of the output electromagnetic power of the grid-type converter can be obtained as follows:

[0047]

[0048] Where V∠θGFM represents the voltage phasor at the output of the grid-forming converter, E∠θ0 represents the infinite grid-side voltage vector, XGFM, XGFL, and XBUS are circuit reactances, K1 represents the proportionality coefficient and K1 = XBUS / (XBUS+XGFM), θGFM and θGFL represent the phase angles at the output of the grid-forming and grid-following converters, θ0 is the grid voltage phase angle, and id and iq are the d-axis and q-axis components of the output current of the grid-following converter, respectively. d and i q They are the d-axis and q-axis components of the output current of the grid-following converter respectively.

[0049] Furthermore, in step 6 It can be expressed as:

[0050]

[0051] Where KD represents the proportional coefficient of the active power control loop, ωp represents the cutoff frequency of the low-pass filter in the active power control loop, Pref represents the reference value of the active power control loop output power, and PGFM represents the active power control loop output electromagnetic power.

[0052] Furthermore, the dynamic mathematical model of the power loop in step 7 is shown in equation (25). The combined equations (16), (17), (24) and (25) can be used to obtain the virtual power angle δ of the grid-forming converter for the power system including the grid-following and grid-forming converters: D The second-order dynamic mathematical model of:

[0053]

[0054] Wherein, represents the rate of change of the virtual power angle δD of the grid-forming converter, KD represents the proportional coefficient of the active power control loop, ωp represents the cutoff frequency of the low-pass filter in the active power control loop, Pref represents the reference value of the output power of the active power control loop, V∠θGFM represents the voltage phasor at the output end of the grid-forming converter, E∠θ0 represents the infinite grid-side voltage vector, XGFM, XGFL and XBUS are the circuit reactances, K1 represents the proportional coefficient and K1 = XBUS / (XBUS+XGFM), θGFM and θGFL represent the phase angles of the grid-forming and grid-following converter output ends, respectively, θ0 is the grid voltage phase angle, id and iq are the d-axis and q-axis components of the output current of the grid-following converter, respectively.

[0055] Beneficial effects of the present invention:

[0056] 1. The transient stability modeling and analysis method for a power system containing grid-following and grid-forming converters proposed in the present invention solves the problem in the prior art of the lack of an effective mathematical analytical model for power systems containing grid-following and grid-forming converters. Based on the established mathematical model, the power angle stability characteristics of the system during transient processes can be quantitatively analyzed through phase diagram simulation methods.

[0057] 2. The mathematical modeling method of the power system containing grid-following and grid-forming converters proposed in the present invention can better reflect the nonlinear dynamic process of the grid-forming and grid-following converter power systems during large disturbances compared with the traditional small signal modeling method. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a structural diagram of a power system including grid-following type and grid-forming type converters applicable to the present invention;

[0059] Figure 2 This is a simplified circuit diagram of a power system including grid-following and grid-forming converters proposed in the present invention;

[0060] Figure 3 It is a schematic diagram of the three-phase synchronous phase-locked loop control structure;

[0061] Figure 4 This is a schematic diagram of the power loop control structure of the grid-type converter;

[0062] Figure 5 The output voltage-phase angle curve diagram of the grid-following converter and the corresponding phase diagram simulation waveform diagram in the power system containing grid-following converter and grid-forming converter proposed by the present invention;

[0063] Figure 6The output power-phase angle curve diagram of the grid-forming converter and the corresponding phase diagram simulation waveform diagram in the power system containing the grid-following and grid-forming converters proposed by the present invention; DETAILED DESCRIPTION

[0064] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to the accompanying drawings in the embodiments of the present invention.

[0065] The present invention proposes a transient stability analysis method for a power system containing grid-following type and grid-forming type converters, which is applicable to power systems containing grid-forming type and grid-following type converters.

[0066] Figure 1 The transient stability analysis method for a power system with grid-following and grid-forming converters is divided into the following seven steps:

[0067] Step 1: Construct a system model in which a grid-following converter and a grid-forming converter are connected in parallel to an infinite power grid;

[0068] Figure 1 This represents a specific power system containing both grid-type and grid-following converters. The system includes a grid-following converter and a grid-type converter. Both converters are connected in parallel to a common coupling point via LGFL and LGFM, respectively, and then to the infinite grid via LBUS. The grid-type converter employs the following control method: a three-phase synchronous phase-locked loop (SPL) is used to detect the grid connection angle within the grid-type converter, which is then passed through the current loop to generate a drive signal. The grid-type converter employs a three-loop control strategy: the power loop generates amplitude and phase commands for the voltage reference value, the voltage loop achieves control, the current loop acts as a limiter, and finally generates the converter drive signal. The power system of this embodiment includes an infinite grid-side voltage vector E∠θ0, filter inductors Lf1 and Lf2, and line impedances LGFM, LGFL, and LBUS. φ0 is the phase difference between the voltage at the grid-following converter terminal and the output current. In steady state, θPLL will be equal to θGFL.

[0069] Step 2: Establish a mathematical model of the q-axis voltage output by the three-phase synchronous phase-locked loop of the grid-following converter;

[0070] Figure 2 The figure shows the equivalent circuit model of the system model in step 1, where the grid-following converter is replaced by a controlled current source model, and the grid-forming converter is equivalent to a controlled voltage source model. I∠φ0+θPLL is the current at the output of the grid-following converter, and UPLL∠θPLL is the voltage amplitude and phase angle detected by the three-phase synchronous phase-locked loop. Applying the Thevenin circuit theorem, the vector model of the voltage UPLL∠θPLL at the output of the grid-following converter is obtained as:

[0071] U PLL ∠θ PLL=jI∠(φ0+θ GFL )X g +K1V∠θ GFM +K2E∠θ0 (27)

[0072] Wherein, θGFM and θGFL represent the phase angles at the output of the grid-forming and grid-following converters, respectively; I∠φ0+θPLL represents the current phasor at the output of the grid-following converter; V∠θGFM represents the voltage phasor at the output of the grid-forming converter; E∠θ0 represents the infinite grid-side voltage vector; XGFM, XGFL, and XBUS are circuit reactances; K1 and K2 represent proportionality coefficients, with K1 = XBUS / (XBUS+XGFM) and K2 = XGFM / (XBUS+XGFM); and Xg represents the circuit impedance, with Xg = XGFL+(XBUS / / XGFM).

[0073] Separating the imaginary and real parts of equation (27), the mathematical model of the q-axis voltage output by the three-phase synchronous phase-locked loop can be expressed as:

[0074] U q =i d X g -K2Esin(θ GFL -θ0)+K1V sin(θ GFM -θ GFL ) (28)

[0075] Wherein, id+jiq=I∠φ0, id and iq represent the d-axis and q-axis components of I∠φ0, respectively, θGFM and θGFL represent the phase angles at the output of the grid-forming and grid-following converters, respectively, V∠θGFM represents the voltage phasor at the output of the grid-forming converter, E∠θ0 represents the infinite grid-side voltage vector, XGFM, XGFL, and XBUS are circuit reactances, K1 and K2 represent proportionality coefficients, and K1=XBUS / (XBUS+XGFM), K2=XGFM / (XBUS+XGFM), and Xg represents the circuit impedance, and Xg=XGFL+(XBUS / / XGFM).

[0076] The virtual power angle δL of the grid-following converter is the phase angle difference between the voltage at the output of the grid-following converter and the voltage at the infinite bus terminal. The virtual power angle δD of the grid-forming converter is the phase angle difference between the voltage at the output of the grid-forming converter and the voltage at the infinite bus terminal. The relationships are as follows:

[0077] δ L =θ GFL -θ0 (29)

[0078] δ D =θ GFM -θ0 (30)

[0079] Step 3: Analyze the transient stability process of the grid-following converter;

[0080] The three-phase synchronous phase-locked loop control structure is as follows: Figure 3 As shown, based on the dynamic equation of the phase-locked loop, the virtual power angle δ L Rate of change for:

[0081]

[0082] Where, represents the rate of change of the virtual power angle δL of the grid-following converter, Kp and Ki represent the proportional and integral coefficients in the three-phase synchronous phase-locked loop, and Uq represents the q-axis voltage output by the three-phase synchronous phase-locked loop;

[0083] like Figure 5 As shown, when Figure 1 When a grid fault occurs in a power system, the transient process of the grid-following converter is analyzed: the Ub-δL curve of the grid-following converter changes, and the system operating point suddenly changes from point a to point b. Since the condition holds at point b, δL continues to decrease, and the system operating point moves from point b to point c. Although Uq = 0 holds at point c, it still holds, and δL continues to decrease after point c. After point c, since Uq < 0, when it is satisfied, δL begins to increase. After several cycles of oscillation, the operating point finally stabilizes at the post-fault equilibrium point c. If the condition does not hold before the unstable equilibrium point d, δL continues to decrease, and the system eventually becomes transiently unstable. The established system transient model can be used to analyze the transient power angle changes of the grid-following converter under fault conditions.

[0084] Step 4: Establish a second-order mathematical model of the virtual power angle of the grid-following converter and analyze it using the phase diagram method;

[0085] After establishing the dynamic mathematical model of the three-phase synchronous phase-locked loop, the virtual power angle δ of the grid-following converter is L The mathematical model of the q-axis voltage output by the three-phase synchronous phase-locked loop obtained in step 2 is combined with the line impedance model considering the frequency characteristics to obtain the virtual power angle δ used to analyze the large disturbance power angle synchronization stability of the system. L The second-order dynamic mathematical model is:

[0086]

[0087] Wherein, δL and δD represent the virtual power angles of the grid-following and grid-forming converters, respectively; δL represents the rate of change of the virtual power angle δL of the grid-following converter; ω0 represents the grid frequency; Kp and Ki represent the proportional and integral coefficients in the three-phase synchronous phase-locked loop, respectively; V∠θGFM represents the voltage phasor at the output of the grid-forming converter; E∠θ0 represents the infinite grid-side voltage vector; id and iq represent the d-axis and q-axis components of I∠φ0, respectively; XGFM, XGFL, and XBUS are circuit reactances; LGFL represents the line inductance; K1 and K2 represent proportional coefficients, and K1 = XBUS / (XBUS+XGFM) and K2 = XGFM / (XBUS+XGFM); Xg represents the circuit impedance, and Xg = XGFL+(XBUS / / XGFM);

[0088] Phase diagram analysis results and corresponding voltage-power angle curves are shown in Figure 2. Figure 5 As shown in Figure 3, the results verify the accuracy of the mathematical model and can be used to analyze the transient power angle stability process of the grid-following converter in this system.

[0089] Step 5: Establish a mathematical model of the active power output of the grid-connected converter;

[0090] V∠θGFM represents the voltage vector at the output of the grid-type converter. The Thevenin circuit theorem is used to solve the mathematical model of the electromagnetic power output of the grid-type converter:

[0091]

[0092] Where V∠θGFM represents the voltage phasor at the output of the grid-forming converter, E∠θ0 represents the infinite grid-side voltage vector, XGFM, XGFL, and XBUS are the circuit reactances, K1 represents the proportionality coefficient and K1 = XBUS / (XBUS+XGFM), θGFM and θGFL represent the phase angles at the output of the grid-forming and grid-following converters, respectively, θ0 is the grid voltage phase angle, and id and iq are the d-axis and q-axis components of the output current of the grid-following converter, respectively.

[0093] Step 6: Analyze the transient stability process of the grid-type converter;

[0094] Figure 4 The figure shows the power loop control block diagram of the grid-type converter. The dynamic mathematical model of the active power loop is:

[0095]

[0096] Where KD represents the proportional coefficient of the active power control loop, ωp represents the cutoff frequency of the low-pass filter in the active power control loop, Pref represents the reference value of the active power control loop output power, and PGFM represents the active power control loop output electromagnetic power.

[0097] like Figure 6As shown, when Figure 1 When a grid fault occurs in the system shown, the transient process of the grid-type converter is analyzed: the PGFM-δD curve of the grid-type converter changes, and the system operating point suddenly changes from point a to point b. Since the condition holds at point b, δD continues to increase, and the system operating point moves from point b to point c. After δD passes point c, it begins to decrease. After the condition is met, δD begins to decrease, and after several cycles of oscillation, the operating point finally stabilizes at the post-fault equilibrium point c. If the condition does not hold before the unstable equilibrium point d, δD continues to increase, and the system eventually becomes transiently unstable. The established system transient model can be used to analyze the transient power angle changes of the grid-type converter under fault conditions.

[0098] Step 7: Establish a second-order mathematical model of the virtual power angle of the grid-type converter and analyze it using the phase diagram method;

[0099] After establishing the dynamic mathematical model of the power loop of the grid-type converter, the virtual power angle δ D The expression is combined with the mathematical model of the output electromagnetic power of the grid-type converter obtained in step 5 to solve the virtual power angle δ used by the system to analyze the large disturbance power angle synchronization stability. D The second-order dynamic mathematical model is:

[0100]

[0101] Wherein, represents the rate of change of the virtual power angle δD of the grid-forming converter, KD represents the proportional coefficient of the active power control loop, ωp represents the cutoff frequency of the low-pass filter in the active power control loop, Pref represents the reference value of the output power of the active power control loop, V∠θGFM represents the voltage phasor at the output end of the grid-forming converter, E∠θ0 represents the infinite grid-side voltage vector, XGFM, XGFL and XBUS are the circuit reactances, K1 represents the proportional coefficient and K1 = XBUS / (XBUS+XGFM), θGFM and θGFL represent the phase angles of the grid-forming and grid-following converter output ends, respectively, θ0 is the grid voltage phase angle, id and iq are the d-axis and q-axis components of the output current of the grid-following converter, respectively.

[0102] Phase diagram analysis results and corresponding power angle curves are shown in Figure 2. Figure 6 As shown in the figure, the results verify the accuracy of the mathematical model and can be used to analyze the transient power angle stability process of the grid-type converter in this system.

[0103] The above description is only part of the specific implementation methods of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solutions and inventive concepts of the present invention, should be covered by the protection scope of the present invention.

Claims

1. A transient stability analysis method for a power system containing grid-following and grid-forming converters, characterized in that: The steps include: Construct a system model of grid-following and grid-forming converters connected in parallel to an infinite power grid; The system model consists of a grid-following converter and a grid-forming converter, each passing through L GFL , L GFM Connect in parallel to the common coupling point, and then pass through L BUS Access to infinite power grid; where L GFM , L GFL and L BUS is the circuit inductance; Establish a mathematical model of a grid-following three-phase synchronous phase-locked loop; The system model is converted into a circuit model, where the grid-type converter is converted into a controlled current source model. Based on the Thevenin circuit theorem, the output voltage U of the grid-type converter is established. PLL ∠θ PLL The vector model of the three-phase synchronous phase-locked loop is obtained, and the mathematical model of the q-axis voltage output by the three-phase synchronous phase-locked loop is obtained; by analogy with the synchronous motor, the difference between the phase angle of the voltage at the output of the grid-type converter and the phase angle of the voltage at the infinite bus terminal is defined as the virtual power angle δ of the grid-type converter. L , where U PLL ∠θ PLL is the voltage amplitude and phase angle detected by the three-phase synchronous phase-locked loop; Analyze the transient stability process of the grid; The system initially operates at the equilibrium point. When a grid fault occurs, the system operating point suddenly changes. When the grid-following converter operates stably, Under the action of L After first decreasing, then oscillating for several cycles near the new equilibrium point, and finally stabilizing at the new equilibrium point; when the grid-following converter loses stability, the virtual power angle δ L Continuously decreasing; Indicates the virtual power angle δ of the grid-following converter L rate of change; Establish a mathematical model of grid-following virtual power angle and analyze it using phase diagram; After establishing its dynamic mathematical model by combining the three-phase synchronous phase-locked loop control block diagram, the virtual power angle δ of the grid-following converter is L The mathematical model of the output q-axis voltage of the three-phase synchronous phase-locked loop and the line impedance model considering the frequency characteristics are combined to solve the virtual power angle δ used by the system to analyze the stability of the large-disturbance power angle synchronization. L The second-order dynamic mathematical model of Establish a mathematical model for grid-forming active power output; The system model is equivalent to a circuit model, and the grid-type converter is equivalent to a controlled voltage source model. The Thevenin circuit theorem is applied to establish a mathematical model of the output electromagnetic power of the grid-type converter. The difference between the voltage phase angle at the output terminal of the grid-type converter and the voltage phase angle at the infinite bus terminal is defined as the virtual power angle δ of the grid-type converter. D ; Analyze the transient stability process of network type; The system initially operates at the equilibrium point. When a grid fault occurs, the system operating point suddenly changes. When the grid-connected converter operates stably, Under the action of D After the process of increasing first, oscillating around the new equilibrium point for several cycles, and finally stabilizing at the new equilibrium point; when the grid-type converter loses stability, the virtual power angle δ D Continued increase; Denotes the virtual power angle δ of the grid-connected converter L rate of change; Establish a mathematical model of network-type virtual power angle and analyze it using phase diagram; After establishing its dynamic mathematical model by combining the power loop control block diagram of the grid-type converter, the virtual power angle δ D The expression is combined with the obtained mathematical model of the output electromagnetic power of the grid-type converter to solve the virtual power angle δ used by the system to analyze the large disturbance power angle synchronization stability. D The second-order dynamic mathematical model of .

2. A transient stability analysis method for a power system containing grid-following and grid-forming converters according to claim 1, characterized in that: The grid connection angle in the grid-following converter control structure in the system model is detected by a three-phase synchronous phase-locked loop, and then generates a driving signal after passing through a current loop.

3. The transient stability analysis method for a power system containing grid-following and grid-forming converters according to claim 1, characterized in that: The grid-type converter in the system model adopts a three-loop control strategy. The power loop generates the amplitude and phase instructions of the voltage reference value, the voltage loop reflects the control purpose, and the current loop plays a limiting role. Finally, it is fed into the pulse width modulation generator to generate the converter drive signal.

4. A transient stability analysis method for a power system containing grid-following and grid-forming converters according to claim 1, characterized in that: The power system of the system model includes an infinite grid-side voltage vector E∠θ0, a filter inductor L f1 ,L f2 , line impedance L GFM , L GFL and L BUS ; φ0 is the phase difference between the grid-type converter terminal voltage and output current; In the steady state, θ PLL will be equal to θ GFL .

5. The transient stability analysis method for a power system containing grid-following and grid-forming converters according to claim 1, characterized in that: The three-phase synchronous phase-locked loop of the grid-following converter outputs the q-axis voltage U q In the mathematical model of I∠φ0+θ PLL Indicates the output current of the grid-following converter, U PLL ∠θ PLL is the voltage amplitude and phase angle detected by the three-phase synchronous phase-locked loop; the output voltage U PLL ∠θ PLL The vector model can be expressed as: U PLL ∠θ PLL =jI∠(φ0+θ GFL )X g +K1V∠θ GFM +K2E∠θ0 (1) Among them, θ GFM and θ GFL Respectively represent the phase angle of the output terminal of the grid-forming and grid-following converters, I∠φ0+θ PLL Represents the current phasor at the output of the grid-following converter, V∠θ GFM represents the voltage phasor at the output of the grid-type converter, E∠θ0 represents the infinite grid-side voltage vector, X GFM 、X GFL and X BUS is the circuit reactance, K1 and K2 represent the proportional coefficient and K1=X BUS / (X BUS +X GFM ),K2=X GFM / (X BUS +X GFM ), X g represents the circuit impedance and X g =X GFL +(X BUS / / X GFM ); The mathematical model of the q-axis voltage output by the three-phase synchronous phase-locked loop can be expressed as: U q =i d X g -K2Esin(θ GFL -θ0)+K1Vsin(θ GFM -θ GFL ) (2) Among them, i d +ji q =I∠φ0,i d and i q denote the d-axis and q-axis components of I∠φ0, θ GFM and θ GFL Respectively represent the phase angle of the grid-forming and grid-following converter output terminals, V∠θ GFM represents the voltage phasor at the output of the grid-type converter, E∠θ0 represents the infinite grid-side voltage vector, X GFM 、X GFL and X BUS is the circuit reactance, K1 and K2 represent the proportional coefficient and K1=X BUS / (X BUS +X GFM ),K2=X GFM / (X BUS +X GFM ), X g represents the circuit impedance and X g =X GFL +(X BUS / / X GFM ); Define θ GFM ,θ GFL The phase difference between the phase angle θ0 of the infinite grid voltage is the virtual power angle δ L and δ D ; d L =θ GFL -θ0 (3) d D =θ GFM -θ0 (4).

6. The transient stability analysis method for a power system containing grid-following and grid-forming converters according to claim 1, characterized in that: described Indicates the virtual power angle δ of the grid-following converter L The rate of change can be expressed as: in, Indicates the virtual power angle δ of the grid-following converter L The rate of change, K p and K i Represents the proportional and integral coefficients in the three-phase synchronous phase-locked loop, U q It represents the q-axis voltage output by the three-phase synchronous phase-locked loop.

7. The transient stability analysis method for a power system containing grid-following and grid-forming converters according to claim 1, characterized in that: The dynamic mathematical model of the three-phase synchronous phase-locked loop in the second-order mathematical model of the virtual power angle of the grid-following converter can be expressed as: i PLL =∫[ω0+(K p +K i ∫)U q ] (6) θ0=∫ω0dt (7) Where ω0 is the grid frequency, K p and K i Respectively represent the proportional and integral coefficients in the three-phase synchronous phase-locked loop; The line impedance model of the grid-following converter considering the frequency characteristics can be expressed as: X GFL =ω PLL L GFL (8) where ω PLL is the angular frequency of the three-phase synchronous phase-locked loop; The combined equations (2)-(9) can be used to obtain the virtual power angle δ of the grid-following converter for the power system including the grid-forming and grid-following converters: L The second-order dynamic mathematical model of: Among them, δ L and δ D They represent the virtual power angles of the grid-following and grid-forming converters respectively, Indicates the virtual power angle δ of the grid-following converter L The rate of change, ω0 represents the grid frequency, K p and K i Respectively represent the proportional and integral coefficients in the three-phase synchronous phase-locked loop, V∠θ GFM represents the voltage phasor at the output of the grid-type converter, E∠θ0 represents the infinite grid-side voltage vector, i d and i q They represent the d-axis and q-axis components of I∠φ0, respectively, and X GFM 、X GFL and X BUS is the circuit reactance, L GFL Represents line inductance, K1 and K2 represent proportional coefficients and K1=X BUS / (X BUS +X GFM ),K2=X GFM / (X BUS +X GFM ), X g represents the circuit impedance and X g =X GFL +(X BUS / / X GFM ).

8. The transient stability analysis method for a power system containing grid-following and grid-forming converters according to claim 1, characterized in that: In the mathematical model of the output electromagnetic power of the grid-type converter, V∠θ GFM represents the voltage vector at the output of the grid-type converter. Therefore, applying the Thevenin circuit theorem, the mathematical model of the output electromagnetic power of the grid-type converter can be obtained as follows: Where V∠θ GFM represents the voltage phasor at the output of the grid-type converter, E∠θ0 represents the infinite grid-side voltage vector, X GFM 、X GFL and X BUS is the circuit reactance, K1 represents the proportional coefficient and K1=X BUS / (X BUS +X GFM ),θ GFM and θ GFL They represent the phase angles of the grid-forming and grid-following converter output terminals, θ0 is the grid voltage phase angle, and i d and i q They are the d-axis and q-axis components of the output current of the grid-following converter respectively.

9. The transient stability analysis method for a power system containing grid-following and grid-forming converters according to claim 1, characterized in that: described It can be expressed as the virtual power angle δ of the grid-type converter D The rate of change can be expressed as: Among them, K D Represents the proportional coefficient of the active control loop, ω p Indicates the cutoff frequency of the low-pass filter in the active control loop, P ref Indicates the reference value of the active control loop output power, P GFM Indicates the output electromagnetic power of the active control loop.

10. The transient stability analysis method for a power system containing grid-following and grid-forming converters according to claim 1, characterized in that: The dynamic mathematical model of the power loop in the second-order mathematical model of the virtual power angle of the grid-type converter is shown in formula (12). Combining formulas (3), (4), (11) and (12) can obtain the virtual power angle δ of the grid-type converter for the power system including the grid-type and grid-type converters: D The second-order dynamic mathematical model of: in, Denotes the virtual power angle δ of the grid-connected converter D The rate of change, K D Represents the proportional coefficient of the active control loop, ω p Indicates the cutoff frequency of the low-pass filter in the active control loop, P ref Indicates the reference value of the active control loop output power, V∠θ GFM represents the voltage phasor at the output of the grid-type converter, E∠θ0 represents the infinite grid-side voltage vector, X GFM 、X GFL and X BUS is the circuit reactance, K1 represents the proportional coefficient and K1=X BUS / (X BUS +X GFM ),θ GFM and θ GFL They represent the phase angles of the grid-forming and grid-following converter output terminals, θ0 is the grid voltage phase angle, and i d and i q They are the d-axis and q-axis components of the output current of the grid-following converter respectively.

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