Power Impedance Modeling Method and Stability Evaluation Method Based on Virtual Synchronous Control

Abstract

The present invention discloses a power impedance modeling method based on virtual synchronous control, which performs dq impedance modeling for port shore power supply in frequency bands based on virtual synchronous control, including: respectively constructing each small-signal dq model required for dq impedance modeling; according to the constructed small-signal dq models, using different dynamic links for modeling in different frequency bands, where in the low-frequency region, the dynamic links used are the power controller and the voltage controller; in the medium-low frequency region, the dynamic links used are the voltage-current loop and the power loop; in the intermediate frequency region, the dynamic link used is the voltage-current loop; in the high-frequency region, the dynamic links used are the current loop, the sampling low-pass filter, the control delay, and the voltage loop. The present invention can accurately characterize the differences in impedance characteristics of port shore power supply in each frequency band, construct an accurate impedance model based on virtual synchronous control in frequency bands, and effectively realize the small-signal stability assessment of the port shore power supply system.

Description

Technical Field

[0001] The present invention relates to the technical field of port shore power supply, and in particular to a power supply impedance modeling method and a stability evaluation method based on virtual synchronous control. Background Art

[0002] As a traditional mode of transportation, water transport has a great impact on the ecological environment. Diesel generators are used as the power of floating cranes all year round. Oil pollution, oil smoke and noise will have a serious impact on the environment and atmosphere. In addition, when ships are waiting for locks and anchors, they also need to use auxiliary engines to generate electricity to meet the electricity needs of ship duty, life, lighting equipment, etc., and continuously emit toxic and harmful substances such as sulfide, carbon oxides, and PM2.5, which have seriously affected the ecological environment of inland lakes and the economic development of the floating crane industry.

[0003] The ship shore power supply system generally uses a 10kV overhead line as input voltage, and outputs three voltage levels of ship power supply voltage such as 400V / 50Hz, 440V / 60Hz and 6.6kV / 60Hz through transformers and inverters. Figure 1 As shown. In order to enhance inertia and damping, virtual synchronous control has been gradually studied in port shore power supply to simulate the external characteristics of synchronous machines to provide inertia and damping. However, with the access of a large number of power electronic ship loads to the shore power system, the negative damping of the constant power load will weaken the stability margin of the port shore power supply and may cause system oscillation. Therefore, the control interaction between the port shore power supply and the ship PWM rectifier load of the virtual synchronous control needs further study.

[0004] Impedance-based stability analysis can effectively deal with the above problems. Its basic principle is to apply the generalized Nyquist stability criterion (GNC) to the source-to-load impedance ratio of the system, and the key to impedance-based stability analysis lies in impedance modeling. According to different coordinate systems, impedance forms can be divided into the following categories: dq impedance, αβ impedance, polar coordinate impedance sequence and sequence impedance. Among them, dq impedance and sequence impedance are widely studied. After considering frequency coupling, both sequence impedance and dq impedance are two-dimensional matrices, and the stability analysis methods based on sequence impedance and dq impedance are essentially the same. However, in the dq coordinate system, the three-phase balanced converter system is linear and time-invariant, so each link can be directly linearized, and the dq impedance can be derived by Laplace transforming the obtained linear time-invariant model. Therefore, dq impedance modeling is simpler and the impedance model expression is more concise.

[0005] At present, the dq impedance model of the converter is usually established by considering components such as the phase-locked loop (PLL) and DC voltage. Then, according to the control actions among the onshore power supply at the inverter port, the PWM rectifier load, and the power grid, a method for suppressing oscillations is proposed from the perspective of the PWM rectifier, or the control interaction between the onshore power supply at the inverter port and the PWM rectifier load is determined using the measured dq impedance. However, in the existing technology, for the dq impedance model of the onshore power supply at the port, the model differences of the control delay and the sampling filter in the dq coordinate system and the stationary coordinate system are ignored, and due to the multi-time-scale control characteristics of the onshore power supply at the port, the impedance characteristics in each frequency band will also show significant differences. Therefore, the dq impedance model cannot accurately represent the impedance characteristics in each frequency band. Therefore, there is an urgent need to provide a method for impedance modeling of the onshore power supply at the port based on virtual synchronous control, so as to improve the model accuracy and thus improve the reliability of the small-signal stability assessment of the onshore power supply system with virtual synchronous control. Summary of the Invention

[0006] The technical problem to be solved by the present invention is: aiming at the technical problems existing in the prior art, the present invention provides a power impedance modeling method based on virtual synchronous control with a simple implementation method, high modeling efficiency and accuracy, which can accurately represent the differences in the impedance characteristics of each frequency band of the onshore power supply at the port, and a stability assessment method with high evaluation accuracy and reliability, which can efficiently realize the small-signal stability assessment of the onshore power supply system at the port.

[0007] To solve the above technical problems, the technical solution proposed by the present invention is:

[0008] A power impedance modeling method based on virtual synchronous control is applied to the onshore power supply at the port. The inverter of the onshore power supply at the port adopts virtual synchronous control. This method performs dq impedance modeling for the onshore power supply at the port in different frequency bands based on virtual synchronous control. The steps include:

[0009] Respectively construct each small-signal dq model required for dq impedance modeling, including the dq model with control delay, the dq model of the sampling low-pass filter, the small-signal model of active and reactive power, the small-signal model of the power controller, and the dq model of the voltage and current loops;

[0010] According to the constructed small-signal dq models, different dynamic links are used for modeling in different frequency bands to achieve dq impedance modeling in different frequency bands. Among them, in the low-frequency region, the dynamic links used are the power controller and the voltage controller; in the mid-low frequency region, the dynamic links used are the voltage and current loops and the power loop; in the mid-frequency region, the dynamic link used is the voltage and current loop; in the high-frequency region, the dynamic links used are the voltage and current loops, the sampling low-pass filter, and the control delay.

[0011] Furthermore, a small-signal model of the control delay in the αβ-axis is established according to the following formula:

[0012]

[0013] where and are the duty cycles on the αβ-axis before the control delay; and are the duty cycles on the αβ-axis after the control delay; T s = 1.5 / f s , and f s is the switching frequency;

[0014] According to the conversion relationship of the transfer function from the stationary coordinate system to the dq coordinate system, the dq model of the control delay is constructed according to the following formula:

[0015]

[0016] where T del is the control delay time, and ω n is the rated angular frequency of the virtual synchronous control.

[0017] Furthermore, the expression of the sampling low-pass filter for the voltage / current signal is:

[0018]

[0019] In the formula: x represents current (i) or voltage (v); T x = 1 / ω xc , and ω xc is the cut-off frequency of the voltage / current signal low-pass filter, are the voltage or current signals on the αβ-axis before and after the low-pass filter respectively;

[0020] According to the expression of the sampling low-pass filter for the voltage / current signal, the dq model of the sampling low-pass filter for the voltage / current signal is obtained as:

[0021]

[0022] where K x represents the dq model of the sampling low-pass filter, x represents current (i) or voltage (v); T x = 1 / ω xc , and ω xc is the cut-off frequency of the voltage / current signal low-pass filter, and ω n is the rated angular frequency of the virtual synchronous control.

[0023] Furthermore, based on the steady-state phase difference δ0 between the output voltage of the onshore power supply at the port and the voltage at the PCC point, the conversion relationship when converting the output voltage of the onshore power supply at the port to the voltage at the PCC point is constructed as follows:

[0024]

[0025] where δ0 = P * / (3U0E0ω n L f ); U0 is the rated voltage at the PCC point; E0 is the rated voltage at the output port of the onshore power supply at the port, E d s 、E q s respectively represent the dq components of the port voltage of the virtual synchronous generator in the system coordinate system, and E d c represents the d-axis component of the port voltage of the virtual synchronous generator in the control coordinate system;

[0026] According to the voltage at the PCC point, a small-signal model of active and reactive power is constructed as follows:

[0027]

[0028] where P and Q respectively represent the instantaneous active power and instantaneous reactive power, ΔP and ΔQ respectively represent the small-signal expressions of the instantaneous active power and instantaneous reactive power, u α 、u β respectively represent the αβ-axis components of the three-phase AC voltage, i α 、i β respectively represent the αβ-axis components of the three-phase AC current, U d0 and U q0 are the dq components of the voltage at the PCC point; I d0 and I q0 are the dq components of the output current; G u 、G i respectively represent Δu d 、Δu q respectively represent the dq small-signal components of the voltage at the PCC point, and Δi d 、Δi q respectively represent the dq small-signal components of the three-phase AC current.

[0029] Furthermore, the small-signal model of the constructed active and reactive power controller is as follows:

[0030]

[0031] where θ is the phase of the VSG, E mis the effective value of the internal potential, Δθ is the small-signal variable of the phase of the VSG, ΔE m is the small-signal variable of the effective value of the internal potential, G m 、G g are intermediate variables, s is the Laplace operator, Δu d 、Δu q are the dq small-signal variables of the port voltage respectively, J is the virtual moment of inertia, D p is the active damping coefficient, K q is.

[0032] Furthermore, the voltage loop adopts a quasi-proportional resonant controller, and the current loop adopts a proportional control. According to the transformation method of the controller from the αβ axis to the dq axis, the dq models of the current proportional controller and the voltage quasi-proportional resonant controller are constructed as follows:

[0033]

[0034]

[0035] Among them, k pi is the proportional coefficient of the current controller, k pv , k rv are the proportional coefficient and the resonant coefficient respectively, ω r is the low-pass cut-off frequency, ω n is the rated angular frequency of the virtual synchronous control, G ic 、G uc represent the dq models of the current and voltage controllers respectively.

[0036] Furthermore, when using different dynamic links for modeling in different frequency bands, in the low-frequency region, ignoring the control delay and the sampling low-pass filter link of the voltage and current signals, the dq impedance model of the onshore power supply of the port is specifically:

[0037]

[0038] In the formula: Z c and Z l are the dq impedances of the filter capacitor and inductor respectively, Z vsil represents the intermediate variable and the dq impedance model of the onshore power supply of the port in the low-frequency band, G uc represents the dq model of the voltage controller;

[0039] In the mid-low frequency region, ignoring the control delay and the sampling low-pass filter link, the dq impedance model of the onshore power supply of the port is constructed as:

[0040]

[0041] Among them, Zvsiml The dq impedance model of the medium and low frequency bands of the onshore power supply for ports, Zc is the dq impedance model of the filter capacitor, and Z L is the dq impedance model of the filter inductor, and K pwm represents Udc / 2, where Udc is the steady-state voltage of the DC side, and G ic represents the dq model of the current controller;

[0042] In the intermediate frequency region, ignoring the power loop, sampling filter, and control delay, the dq impedance model of the onshore power supply for ports is constructed as:

[0043]

[0044] In the high frequency region, ignoring the power control loop, the dq impedance model of the onshore power supply for ports is constructed as:

[0045]

[0046] Among them, G del is the dq model of the control delay.

[0047] A method for evaluating the mutual stability of power supplies based on virtual synchronous control, the steps include:

[0048] Construct the dq impedance model of the power supply according to the above power impedance modeling method;

[0049] Use the constructed dq impedance model of the onshore power supply for ports, the PWM rectifier model, and the generalized Nyquist stability criterion to evaluate the interaction stability of the system of the onshore power supply for ports and the ship PWM rectifier.

[0050] Furthermore, the evaluation of the interaction stability of the system of the onshore power supply for ports and the ship PWM rectifier includes: respectively calculating the dq impedance ratio Z vsil (s) / Z vsr (s) of the virtual synchronous machine and the load of the ship PWM rectifier at each low frequency band, obtaining the Nyquist curve of the characteristic roots, and using the generalized Nyquist stability criterion for stability analysis. When all the characteristic roots satisfy the generalized Nyquist stability criterion when the system parameters change, the system is determined to be stable.

[0051] Furthermore, it also includes a stability adjustment step, including: increasing the AC voltage ratio and resonance coefficient of the onshore power supply for ports, or reducing the DC side voltage ratio coefficient of the load of the ship PWM rectifier to enhance the stability of the onshore power supply system.

[0052] Compared with the prior art, the advantages of the present invention are:

[0053] 1. Considering the multi - time - scale characteristics of the virtual synchronous machine control of the on - shore power supply in the port, after constructing the small - signal dq model, based on the virtual synchronous control, a frequency - band - divided dq impedance model of the on - shore power supply in the port is constructed. During the dq impedance modeling process, different dynamic links are considered within different frequency bands for modeling, so as to accurately characterize the impedance characteristics of the on - shore power supply in different frequency bands, thereby effectively improving the accuracy of the impedance model of the on - shore power supply in the port.

[0054] 2. By using the dq impedance model of the on - shore power supply in the port constructed based on frequency - band division, combined with the PWM rectifier model and the generalized Nyquist stability criterion, the interactive stability assessment of the system of the on - shore power supply in the port and the ship PWM rectifier is realized. Since the dq impedance model of the on - shore power supply in the port constructed based on frequency - band division can accurately characterize the impedance characteristics of the on - shore power supply in different frequency bands, it can effectively improve the assessment accuracy and reliability of the stability of the on - shore power supply system. Brief Description of the Drawings

[0055] Figure 1 It is a simplified circuit diagram of the 440V / 60Hz on - shore power supply system in the port for this embodiment.

[0056] Figure 2 It is a schematic diagram of the implementation process of the impedance modeling method of the on - shore power supply in the port based on virtual synchronous control for this embodiment.

[0057] Figure 3 It is a schematic diagram of the wide - band dq small - signal model of the on - shore power supply in the port constructed for this embodiment.

[0058] Figure 4 It is a schematic diagram of the simplified dq small - signal model of the on - shore power supply in the port constructed for this embodiment in the middle frequency band.

[0059] Figure 5 It is a schematic diagram of the measurement verification result of the frequency - band - divided dq impedance model of the on - shore power supply in the port constructed by the present invention in a specific application embodiment. Detailed Embodiment

[0060] The following further describes the present invention in conjunction with the drawings in the specification and specific preferred embodiments, but does not limit the protection scope of the present invention thereby.

[0061] This embodiment is applied to a 440V / 60Hz on - shore power supply system in the port. As Figure 1 shown, that is, the ship on - shore power supply system uses a 10kV overhead line as the input voltage, and outputs a 440V / 60Hz - level ship power supply voltage through devices such as transformers and frequency converters. Figure 1 In the upper part off , R f and C f are respectively the AC-side filter inductor, resistor, and capacitor on the inverter side of the onshore power supply at the port; e a , e b and e c are the output voltages of the onshore power supply for the port supplying onshore power; i a , i b and i c are the inductor currents of the onshore power supply for the port supplying onshore power; u ab and u bc are the voltages at the PCC point; U dc1 is the DC-side voltage of the ship's PWM rectifier; i a1 , i b1 and i c1 are the inductor currents of the PWM rectifier; L f1 , R f1 and C d are the filter inductor, parasitic resistor, and DC-side capacitor of the PWM rectifier.

[0062] As Figure 2 shown, in this embodiment, for the impedance modeling method of the onshore power supply at the port based on virtual synchronous control, the inverter of the onshore power supply at the port adopts virtual synchronous control. This method performs dq impedance modeling for the onshore power supply at the port in different frequency bands based on virtual synchronous control. The steps include:

[0063] S01. Respectively construct each small-signal dq model required for dq impedance modeling, including the dq model of the control delay, the dq model of the sampling low-pass filter, the small-signal model of the active and reactive power, the small-signal model of the power controller, and the dq model of the voltage and current loops;

[0064] S02. According to the constructed small-signal dq models, use different dynamic links for modeling in different frequency bands to achieve dq impedance modeling in different frequency bands. Among them, in the low-frequency region, the dynamic links used are the power controller and the voltage controller; in the mid-low-frequency region, the dynamic links used are the voltage and current loops and the power loop; in the mid-frequency region, the dynamic link used is the voltage and current loop; in the high-frequency region, the dynamic links used are the voltage and current loops, the sampling low-pass filter, and the control delay.

[0065] In this embodiment, first establish the small-signal model of the control delay in the αβ axis according to the following formula:

[0066]

[0067] Where and are the duty cycles on the αβ axis before the control delay; and Control the duty cycle on the αβ axis after the control delay; T s = 1.5 / f s , f s is the switching frequency;

[0068] Then, according to the conversion relationship of the transfer function from the stationary coordinate system to the dq coordinate system, the dq model of the control delay is constructed as follows:

[0069]

[0070] where, G del is the dq model of the control delay, T del is the control delay time, ω n is the rated angular frequency of the virtual synchronous control.

[0071] In this embodiment, the expression of the sampling low-pass filter for the voltage / current signal is:

[0072]

[0073] where, x represents current (i) or voltage (v); T x = 1 / ω xc , ω xc is the cut-off frequency of the low-pass filter for the voltage or current signal, are the voltage or current signals on the αβ axis before and after the low-pass filter respectively.

[0074] According to the expression of the sampling low-pass filter for the voltage / current signal, the dq model of the sampling low-pass filter for the voltage / current signal is:

[0075]

[0076] where, K x represents the dq model of the sampling low-pass filter, x represents current (i) or voltage (v); T x = 1 / ω xc , ω xc is the cut-off frequency of the low-pass filter for the voltage or current signal, ω n is the rated angular frequency of the virtual synchronous control.

[0077] In this embodiment, based on the fact that there is a steady-state phase difference δ0 between the output voltage of the onshore power supply and the voltage at the PCC point, the conversion relationship when converting the output voltage of the onshore power supply to the voltage at the PCC point is constructed as:

[0078]

[0079] where, δ0 = P * / (3U0E0ω n Lf ); U0 is the rated voltage of the PCC point; E0 is the rated voltage of the output port of the onshore power supply at the port.

[0080] When voltage disturbances in the dq axes are injected into the ports of the onshore power supply at the port, its output voltage can be expressed as follows:

[0081]

[0082] Where E d s and E q s respectively represent the dq components of the port voltage of the virtual synchronous machine in the system coordinate system, and E d c represents the d-axis component of the port voltage of the virtual synchronous machine in the control coordinate system. Δe d s and Δe q s respectively represent the dq small-signal variables of the port voltage of the virtual synchronous machine in the system coordinate system. Δe d c represents the d-axis small-signal variable of the port voltage of the virtual synchronous machine in the control coordinate system, and Δθ represents the small-signal variable of the phase of the virtual synchronous machine.

[0083] By canceling out the steady-state components E d s and E q s and E d c and cosδ0, sinδ0, and eliminating the second-order disturbance components ΔθΔe d c we can obtain:

[0084]

[0085] Where G tf represents this matrix, which is used as an intermediate variable. E s respectively represent the amplitudes of the port voltages of the virtual synchronous control.

[0086] From we can obtain the small-signal model of active and reactive power as:

[0087]

[0088] Where P and Q respectively represent the instantaneous active power and instantaneous reactive power, and ΔP and ΔQ respectively represent the small-signal expressions of the instantaneous active power and instantaneous reactive power. u α and u βrespectively represent the αβ-axis components of the three-phase AC voltage, i α and i β respectively represent the αβ-axis components of the three-phase AC current, U d0 and U q0 are the dq components of the PCC point voltage; I d0 and I q0 are the dq components of the output current; G u and G i respectively represent and Δu d and Δu q respectively represent the dq small-signal components of the PCC point voltage, Δi d and Δi q respectively represent the dq small-signal components of the three-phase AC current.

[0089] According to Equation and Equation E s =(Q * +D q (U * -U)-Q) / K q s, the small-signal model of the active and reactive power controller constructed is:

[0090]

[0091] where, θ is the phase of the VSG, E m is the effective value of the internal electromotive force, T set , D p , ω n , T e , θ respectively represent the rated torque, reactive power damping coefficient, rated angular frequency, actual torque of the virtual synchronous control, and the phase of the VSG, Δθ is the small-signal variable of the phase of the VSG, G m and G g are intermediate variables, s is the Laplace operator, Δu d and Δu q are respectively the small-signal variables of the port voltage, Q * is the command value of the instantaneous output reactive power Q, E s represents the port voltage amplitude of the virtual synchronous control, P * is the command value of the instantaneous output reactive power P, U * represents the command value of the port voltage amplitude U.

[0092] In this embodiment, the voltage loop specifically adopts a quasi-proportional-resonant controller, and the current loop adopts a proportional control. According to the transformation method of the controller from the αβ axis to the dq axis, the dq models of the current proportional controller and the voltage quasi-proportional-resonant controller constructed are respectively:

[0093]

[0094]

[0095] where k pi is the proportional coefficient of the current controller, k pv , k rv and ω r are the proportional coefficient, resonance coefficient and low-pass cut-off frequency respectively, ω n is the rated angular frequency of the virtual synchronous control, G ic , G uc represent the dq models of the current and voltage controllers respectively.

[0096] Then, according to the above construction of the small-signal dq model, a segmented-band dq impedance model of the port shore power supply with virtual synchronous control is established. Considering the multi-time-scale characteristics of the virtual synchronous machine control of the port shore power supply, different dynamic links are corresponding to different frequency bands, and during the dq impedance modeling process, the main dynamic links are considered for modeling within different frequency bands. Specifically in this embodiment, the main dynamic links in the low-frequency band of 1 - 20 Hz are the power controller and the voltage controller; the main dynamic links in the medium-low frequency band of 20 - 100 Hz are the voltage loop, power loop and current loop; the main dynamic links in the medium-frequency band of 100 - several hundred Hz are the voltage loop and current loop; the main dynamic links in the high-frequency band of several hundred Hz - 2 kHz are the current loop, sampling low-pass filter, control delay and voltage loop. In the above manner, the broadband small-signal model of the port shore power supply based on virtual synchronous control is as Figure 3 shown, where there is a steady-state phase difference δ0 between the output voltage of the port shore power supply and the voltage at the PCC point, and there is a conversion relationship as shown in Equation (5) when the output voltage of the port shore power supply is converted to the voltage at the PCC point.

[0097] Specifically in this embodiment, when using different dynamic links for modeling within different frequency bands, in the low-frequency region, the control delay, sampling low-pass filter link of the voltage and current signals, and the inner current control loop are ignored, as Figure 3 shown. At this time, the inner current loop is equivalent to "1", and in the low-frequency region, the dq impedance model of the port shore power supply is specifically:

[0098]

[0099] In the formula: Z c and Z l are the dq impedances of the filter capacitor and inductor respectively, Z out1 , Z vsil represent the intermediate variable and the low-frequency band dq impedance model of the port shore power supply respectively, G uc , G tf , Gg , G u , G m , G i respectively represent the intermediate variables of the dq model of the voltage controller.

[0100] In the medium and low frequency regions, ignoring the control delay and the sampling low-pass filter section, as Figure 4 shown, the dq impedance model of the onshore power supply for ports is constructed as:

[0101]

[0102] Among them, Z out2 represents the intermediate variable, Z vsiml represents the dq impedance model Zc of the onshore power supply for ports in the medium and low frequency bands, Z L is the dq impedance model of the filter inductor, K pwm represents Udc / 2, where Udc is the DC-side steady-state voltage, G uc , G tf , G g , G u , G m , G i are intermediate variables, G uc is the dq model of the voltage controller, G ic represents the dq model of the current controller.

[0103] In the intermediate frequency region, ignoring the power loop, the sampling filter, and the control delay, the dq impedance model of the onshore power supply for ports is constructed as:

[0104]

[0105] Among them, Z out3 represents the intermediate variable, Z vsim represents the dq impedance model of the onshore power supply for ports in the intermediate frequency band, Z L represents the dq impedance model of the filter inductor, K pwm represents Udc / 2, where Udc is the DC-side steady-state voltage, G ic , G uc respectively represent the dq models of the current controller and the voltage controller, and I represents the identity matrix.

[0106] In the high frequency region, ignoring the power control loop, the dq impedance model of the onshore power supply for ports is constructed as:

[0107]

[0108] Among them, Z out4 represents the intermediate variable, Z vsihThe high-frequency dq impedance model of the onshore power supply at the port. Zc is the dq impedance model of the filter capacitor, and Z L is the dq impedance model of the filter inductor. K pwm , K v , K i respectively represent Udc / 2, the dq model of the voltage low-pass filter, and the dq model of the current low-pass filter. Udc is the steady-state voltage on the DC side. G del , G ic , G uc respectively represent the dq models of the control delay, current controller, and voltage controller.

[0109] In this embodiment, the inverter of the onshore power supply at the port adopts virtual synchronous control. The active power loop simulates the inertia and primary frequency regulation characteristics of a synchronous generator, and the reactive power loop simulates the primary voltage regulation characteristics of a synchronous motor to calculate the instantaneous active and reactive powers. The given value of the αβ-axis voltage can be obtained from the voltage amplitude output by the reactive power loop and the phase angle output by the active power loop. The voltage loop adopts a quasi-proportional resonant controller, and the current loop adopts proportional control. Therefore, for the active power controller and reactive power controller of the virtual synchronous control, the detailed electrical part control equations are as follows:

[0110]

[0111] E s =(Q * +D q (U * -U n )-Q) / K q s

[0112]

[0113]

[0114]

[0115]

[0116] Among them, J is the virtual moment of inertia; ω and ω n are respectively the output angular frequency and rated angular frequency of the virtual synchronous control; T * is the given value of the electromagnetic torque; D p is the active damping coefficient; θ is the phase of the VSG; E m is the effective value of the internal electromotive force; Q* is the command value of the instantaneous output reactive power Q; D p is the reactive damping coefficient; K is the inertia coefficient of the reactive power loop; U n is the rated value of the voltage amplitude U; P is the instantaneous active power, and Q is the instantaneous reactive power; e α* is the α-axis voltage reference value obtained from the voltage amplitude output by the reactive power loop, e β * is the β-axis voltage reference value obtained from the phase angle output by the active power loop; k pv , k rv and ω r are the proportional coefficient, the resonance coefficient, and the low-pass cut-off frequency respectively; k pi is the proportional coefficient of the current controller.

[0117] To verify the effectiveness of the present invention, in a specific application embodiment, the sub-band impedance model of the onshore power supply for ports constructed by using the above method is tested, and the measurement results are as Figure 5 shown. From Figure 5 it can be seen that the sub-band impedance model of the onshore power supply for ports is basically completely consistent with the measured values, that is, the accuracy of the sub-band dq impedance model of the onshore power supply for ports constructed by the present invention is verified.

[0118] The method for evaluating the mutual stability of the onshore power supply for ports based on virtual synchronous control in this embodiment includes the following steps:

[0119] Step 1: Construct the dq impedance model of the onshore power supply for ports according to the above power impedance modeling method;

[0120] Step 2: Use the constructed dq impedance model of the onshore power supply for ports, the PWM rectifier model, and the generalized Nyquist stability criterion to evaluate the interaction stability of the system of the onshore power supply for ports and the ship PWM rectifier.

[0121] In this embodiment, by using the dq impedance model of the onshore power supply for ports constructed based on sub-bands, a sub-band small-signal dq impedance model of the virtual synchronous machine is established in the dq coordinate system. By using the established sub-band small-signal dq impedance model of the virtual synchronous machine, the PWM rectifier model, and the generalized Nyquist stability criterion, the interaction stability evaluation of the system of the onshore power supply for ports and the ship PWM rectifier is realized. Since the dq impedance model of the onshore power supply for ports constructed based on sub-bands can accurately characterize the impedance characteristics of different frequency bands of the onshore power supply for ports, the evaluation accuracy of the stability of the onshore power supply system can be effectively improved.

[0122] In this embodiment, the above Step 2 specifically includes: calculating the characteristic roots of the dq impedance ratio Z vsil (s) / Z vsr (s) of the virtual synchronous machine and the load of the ship PWM rectifier respectively in each low-frequency band (low frequency, medium-low frequency, medium frequency, and high frequency), obtaining the Nyquist curve of the characteristic roots, and performing stability analysis by using the generalized Nyquist stability criterion. When all the characteristic roots satisfy the generalized Nyquist stability criterion when the system parameters change, the system is determined to be stable.

[0123] In this embodiment, after step 2, there is also a stability adjustment step, including: enhancing the stability of the onshore power supply system for ships by increasing the AC voltage ratio and resonance coefficient of the onshore power supply for ports, or reducing the DC side voltage ratio coefficient of the load of the ship PWM rectifier. Through the frequency-band division dq impedance model of the onshore power supply for ports based on the virtual synchronous control component, it can be analyzed that the AC power, resonance coefficient of the onshore power supply for ports, and the DC side voltage ratio coefficient of the load of the ship PWM rectifier are related to the stability of the onshore power supply system for ships. By increasing the AC voltage ratio and resonance coefficient of the onshore power supply for ports or reducing the DC side voltage ratio coefficient of the load of the ship PWM rectifier, the stability of the onshore power supply system for ships can be enhanced. In a specific application embodiment, the above stability adjustment method is simulated based on MATLAB / Simulink, verifying the effectiveness of the impedance modeling and stability analysis results of the present invention.

[0124] The above are only the preferred embodiments of the present invention and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Therefore, any simple modifications, equivalent changes, and decorations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the scope of the protection of the technical solution of the present invention.

Claims

1. A power impedance modeling method based on virtual synchronous control, which is applied to the onshore power supply of a port. The inverter of the onshore power supply of the port adopts virtual synchronous control, and is characterized in that This method is based on virtual synchronous control to conduct dq impedance modeling for the onshore power supply of the port in different frequency bands, and the steps include: Construct each small-signal dq model required for dq impedance modeling respectively, including the dq model of control delay, the dq model of sampling low-pass filter, the small-signal model of active and reactive power, the small-signal model of power controller, and the dq model of voltage and current loops; According to the constructed small-signal dq models, different dynamic links are used for modeling in different frequency bands to achieve dq impedance modeling in different frequency bands. Among them, in the low-frequency region, the dynamic links used are power controller and voltage controller; in the medium-low frequency region, the dynamic links used are voltage and current loops and power loop; in the medium-frequency region, the dynamic link used is voltage and current loop; in the high-frequency region, the dynamic links used are voltage and current loops, sampling low-pass filter, and control delay; When using different dynamic links for modeling in different frequency bands, in the low-frequency region, the control delay and the sampling low-pass filter link of voltage and current signals are ignored, and the dq impedance model of the onshore power supply of the port is specifically: Where: Z c and Z l are the dq impedances of the filter capacitor and inductor respectively, and Z vsil is the dq impedance model of the low-frequency section of the onshore power supply at the port, and G uc represents the dq model of the voltage controller; In the medium-low frequency region, the control delay and sampling low-pass filter link are ignored, and the dq impedance model of the onshore power supply of the port is constructed as: Among them, Z vsiml represents the dq impedance model of the medium and low frequency band of the onshore power supply at the port, Zc is the dq impedance model of the filter capacitor, and Z L is the dq impedance model of the filter inductor. K pwm represents Udc / 2, where Udc is the steady-state voltage on the DC side, and G ic represents the dq model of the current controller; In the medium-frequency region, the power loop, sampling filter, and control delay are ignored, and the dq impedance model of the onshore power supply of the port is constructed as: In the high-frequency region, the power control loop is ignored, and the dq impedance model of the onshore power supply of the port is constructed as: Among them, G del is the dq model for controlling the delay.

2. The power impedance modeling method based on virtual synchronous control according to claim 1, wherein Establish a small-signal model of control delay under the αβ axis according to the following formula: Among them, and control the duty cycle on the αβ axis before the delay; and control the duty cycle on the αβ axis after the delay; T s = 1.5 / f s where f s is the switching frequency; According to the conversion relationship of transfer function from the stationary coordinate system to the dq coordinate system, the dq model of control delay is constructed.

3. The power impedance modeling method based on virtual synchronous control according to claim 1, wherein Construct the expression of the sampling low-pass filter for voltage / current signals as: where: x represents current (i) or voltage (v); T x = 1 / ω xc , ω xc is the cut-off frequency of the voltage / current signal low-pass filter, are the voltage or current signals of the αβ axes before and after the low-pass filter respectively; According to the expression of the sampling low-pass filter for voltage / current signals, the dq model of the sampling low-pass filter for voltage / current signals is obtained.

4. The method for power impedance modeling based on virtual synchronous control according to claim 1, characterized in that Based on the existence of a steady-state phase difference δ0 between the output voltage of the onshore power supply of the port and the voltage at the PCC point, construct the conversion relationship formula when converting the output voltage of the onshore power supply of the port to the voltage at the PCC point as: where, δ0 = P * / (3U0E0ω n L f ); U0 is the rated voltage of the PCC point; E0 is the rated voltage of the output port of the onshore power supply at the port, E d s , E q s respectively represent the dq components of the port voltage of the virtual synchronous machine in the system coordinate system, E d c represents the d-axis component of the port voltage of the virtual synchronous machine in the control coordinate system; Construct the small-signal model of active and reactive power according to the voltage at the PCC point as: Among them, P and Q represent instantaneous active power and instantaneous reactive power respectively, ΔP and ΔQ represent the small-signal expressions of instantaneous active power and instantaneous reactive power respectively, and u α and u β represent the αβ-axis components of the three-phase AC voltage respectively, and i α and i β represent the αβ-axis components of the three-phase AC current respectively. U d0 and U q0 are the dq components of the PCC point voltage; I d0 and I q0 are the dq components of the output current; G u and G i represent respectively Δu d and Δu q represent the dq small-signal components of the PCC point voltage respectively, and Δi d and Δi q represent the dq small-signal components of the three-phase AC current respectively.

5. The power impedance modeling method based on virtual synchronous control according to claim 1, characterized in that, Construct the small-signal model of the active and reactive power controller as: where θ is the phase of the VSG, E m is the effective value of the internal potential, Δθ is the small-signal variable of the phase of the VSG, and ΔE m is the small-signal variable of the effective value of the internal potential, G m and G g are intermediate variables, s is the Laplace operator, Δu d and Δu q are the dq small-signal variables of the port voltage respectively, J is the virtual moment of inertia, and D p is the active damping coefficient.

6. The power impedance modeling method based on virtual synchronous control according to any one of claims 1 to 5, characterized in that In the voltage and current loops, the voltage loop adopts a quasi-proportional-resonant controller, and the current loop adopts a proportional control. According to the transformation method of the controller from the αβ axis to the dq axis, the dq models of the current proportional controller and the voltage quasi-proportional-resonant controller are constructed respectively as: where k pi is the proportional coefficient of the current controller, k pv , k rv are the proportional coefficient and the resonant coefficient respectively, ω r is the low-pass cut-off frequency, ω n is the rated angular frequency of the virtual synchronous control, G ic , G uc represent the dq models of the current and voltage controllers respectively.

7. A method for evaluating the mutual stability of power supplies based on virtual synchronous control, characterized in that the steps Include: Construct the dq impedance model of the onshore power supply of the port according to the power supply impedance modeling method described in any one of claims 1 to 6; Use the constructed dq impedance model of the onshore power supply of the port, the PWM rectifier model, and the generalized Nyquist stability criterion to evaluate the interaction stability of the system of the onshore power supply of the port and the ship PWM rectifier.

8. The power supply mutual stability evaluation method based on virtual synchronous control according to claim 7, characterized in that The interaction stability evaluation of the onshore power supply at the port and the ship PWM rectifier system includes: calculating the dq impedance ratio Z vsil (s) / Z vsr (s) of the virtual synchronous machine and the ship PWM rectifier load at each low frequency band, obtaining the Nyquist curve of the characteristic roots, performing stability analysis using the generalized Nyquist stability criterion, and when all characteristic roots satisfy the generalized Nyquist stability criterion when the system parameters change, determining that the system is stable.

9. The method for evaluating the power grid mutual stability based on virtual synchronous control according to claim 7 or 8, characterized in that, It also includes a stability adjustment step, including: enhancing the stability of the onshore power supply system by increasing the AC voltage ratio and resonant coefficient of the onshore power supply of the port, or reducing the DC side voltage ratio coefficient of the load of the ship PWM rectifier.

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