A safety and stability assessment method applicable to AC / DC hybrid power systems

Abstract

This invention provides a safety and stability assessment method applicable to AC / DC hybrid power systems, comprising the following steps: S1, obtaining the port impedance models of each device and network in the AC / DC hybrid power system; S2, calculating the total system admittance matrix based on the port impedance models; S3, obtaining the closed-loop poles based on the total system admittance matrix, wherein the closed-loop poles are the poles of any element in the AC / DC hybrid power system; S4, applying a disturbance to a device in the AC / DC hybrid power system, and calculating the participation factors of the device and its parameters with respect to a certain closed-loop pole; S5, performing a safety and stability assessment on the device based on the participation factors. This method represents DC devices, AC devices, and interface converters using port impedance models, achieving a unified theory for calculating the participation factors of these three types of devices and their parameters, and then performing a safety and stability assessment using the participation factors.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power system analysis, and particularly relates to a safety and stability evaluation method suitable for an AC-DC hybrid power system. BACKGROUND

[0002] With the development of renewable energy and power electronic technology, the new energy network architecture system characterized by a high proportion of new energy determines that power electronic equipment will be applied on a large scale in the power system, and the power system tends to be power electronic. In the traditional power system dominated by synchronous generators, the huge rotor part of the synchronous generator plays a significant role. When the power system is disturbed, the rotor absorbs and releases energy to maintain the energy balance within the system. However, with the high power electronicization of the power system, the network structure and characteristics of the power system have changed greatly, which seriously threatens the safe and stable operation of the new generation of power system. After the large-scale replacement of power electronic equipment for mechanical and electrical energy conversion equipment represented by synchronous generators, the power system has undergone a qualitative change in the physical layer, which is reflected in the reduction of the rotor physical entity, resulting in a significant decrease in the stored kinetic energy and leading to a decrease in the system's ability to resist disturbances. Therefore, the stability analysis and instability principle analysis of the new power system are of great significance to the safe and stable operation of the power system.

[0003] With the large-scale access of power electronic equipment to the power system, the architecture of the power grid is also gradually changing. In the actual power system, on the one hand, AC equipment is still the main form of power load in the current power grid, and the operation and control technology of AC power grid has become mature; on the other hand, a large number of electric vehicles, DC lighting and other DC power equipment are gradually popularized and popularized, and the demand for DC power supply technology is increasing. Therefore, the complex AC-DC hybrid power system structure in which AC and DC sources and AC and DC loads coexist will become the main architecture of the future power system. Among them, the interface converter, as a key device in the AC-DC hybrid power system, plays an important role in connecting the AC bus and the DC bus of the system, and the dynamic characteristics of the AC system and the DC system are coupled with each other, which makes the modeling and stability analysis of the AC-DC hybrid power system more complex.

[0004] Therefore, it is urgent to provide a method for safety and stability evaluation of an AC-DC hybrid power system. SUMMARY

[0005] Technical problems solved

[0006] In view of the above-mentioned defects of the prior art, the present application provides a safety and stability evaluation method suitable for an AC-DC hybrid power system, which represents a DC device, an AC device and an interface converter by a port impedance model, thereby realizing a unified theory of participation factor calculation of the three types of devices and device parameters, and then performing safety and stability evaluation on the AC-DC hybrid power system through participation factor calculation.

[0007] Technical scheme

[0008] To achieve the above object, the present application is implemented by the following technical scheme:

[0009] The present application provides a safety and stability evaluation method suitable for an AC-DC hybrid power system, comprising the following steps:

[0010] S1, obtaining a port impedance model of each device and network in the AC-DC hybrid power system;

[0011] S2, calculating a full-system admittance matrix based on the port impedance model;

[0012] S3, obtaining a closed-loop pole based on the full-system admittance matrix, the closed-loop pole being a pole of any element of the AC-DC hybrid power system;

[0013] S4, applying a disturbance to a device of the AC-DC hybrid power system, and calculating a participation factor of the device and device parameter for a certain closed-loop pole;

[0014] S5, performing safety and stability evaluation on the device based on the participation factor.

[0015] Further, the port impedance model is divided into a first-order impedance matrix of a DC device, a second-order impedance matrix of an AC device and a third-order impedance matrix of an interface converter according to different access modes of the device, and is respectively as follows:

[0016] Z DC (s)=[Z dc (s)]

[0017]

[0018]

[0019] Wherein, Z DC (s) represents a port impedance matrix of a DC device, and its element Z dc (s) is a DC port impedance transfer function; Z AC (s) represents a port impedance matrix of an AC device, and its element Z dd (s), Z dq (s), Zqd (s), Z qq (s) are d-axis, q-axis impedance transfer functions respectively; Z IC (s) represents the port impedance matrix of the interface converter, whose elements are Z dd (s), Z dq (s), Z ddc (s), Z qd (s), Z qq (s), Z qdc (s), Z dcd (s), Z dcq (s), Z dc (s) are d-axis, q-axis and DC port impedance transfer functions respectively, and the impedance model of all devices is written as a diagonal matrix, as shown in the following formula:

[0020] Z app (s) = diag(Z AC-1 ,…,Z AC-M ,Z IC ,Z DC-1 ,…,Z DC-N )

[0021] Wherein, M and N represent the number of devices in the alternating current system and the direct current system respectively.

[0022] Further, the port impedance model is divided into alternating current network and direct current network according to the typical structure of the alternating current-direct current hybrid power system, and the alternating current network and the direct current network are connected with alternating current devices and alternating current ports of the interface converter and direct current devices and direct current ports of the interface converter respectively, as shown in the following formula:

[0023] Z net (s) = diag(Z AC-net ,Z DC-net ).

[0024] Further, the whole system admittance matrix is:

[0025] Y sys (s) = [Z app (s) + Z net (s)] -1 .

[0026] Further, the calculation method of the participation factor of the device for a certain closed loop pole includes:

[0027] When a disturbance is applied to the port impedance of the device, the change value of the port impedance is approximately proportional to the port impedance, as shown in the following formula:

[0028] ΔZ k (λ) = εZ k (λ)

[0029] Where ε represents the perturbation ratio, the subscript k represents any device, and λ represents the closed-loop pole.

[0030] The participation factor of the device with respect to the closed-loop pole is calculated as follows:

[0031]

[0032] Among them, Res λ G represents the residue matrix of the complex function G at the closed-loop pole λ. Z represents the admittance of the k-th device in the total system admittance matrix. λ (k) represents the impedance of the k-th device corresponding to the closed-loop pole λ, <·,·> represents the Frobenius inner product operation of two complex matrices, the superscript * represents the transpose and conjugate of the matrix, and ‖·‖ represents the Frobenius norm of the matrix.

[0033] Furthermore, the perturbation applied to the port impedance of the device is achieved by applying a small perturbation to the power reference value of the port device.

[0034] Furthermore, the method for calculating the participation factor of the device parameters with respect to a certain closed-loop pole includes:

[0035] A small perturbation is applied to the device parameters of the device, and the rate of change of the port impedance is measured and calculated as shown in the following formula:

[0036]

[0037] Where ρ represents the equipment parameter, and the subscript Δ represents the impedance value after parameter disturbance;

[0038] The participation factor of the device parameters with respect to a certain closed-loop pole is calculated as follows:

[0039]

[0040] Beneficial effects

[0041] This invention provides a safety and stability assessment method applicable to AC / DC hybrid power systems. This method improves upon existing impedance models by separately measuring the port impedance models of equipment and the network, calculating the overall system admittance matrix and the closed-loop poles of the system. By measuring the port impedance values ​​of equipment and the rate of change of port impedance with respect to equipment parameters, and combining this with the overall system admittance matrix, the participation factors of macroscopic equipment and specific equipment parameters are calculated. This method represents DC equipment, AC equipment, and interface converters using port impedance models, thus achieving a unified theory for calculating the participation factors of these three types of equipment and their parameters. Compared to state-space model methods, the method provided by this invention does not require obtaining the specific structure of the system, and compared to impedance model methods, it can obtain the participation factors of internal equipment parameters. Attached Figure Description

[0042] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0043] Figure 1 This is a schematic diagram illustrating the steps of a safety and stability assessment method for AC / DC hybrid power systems provided in an embodiment of the present invention.

[0044] Figure 2 This is a topology diagram of a 28-node AC / DC hybrid power system provided in an embodiment of the present invention.

[0045] Figure 3 This is a schematic diagram of a device impedance model and a network impedance model provided in an embodiment of the present invention.

[0046] Figure 4 This is a schematic diagram illustrating the calculation of the admittance matrix of the entire system according to an embodiment of the present invention.

[0047] Figure 5 This is a bar chart showing the normalization of the closed-loop pole participation factor for all devices provided in an embodiment of the present invention.

[0048] Figure 6 The waveform diagram of the power transmission of the interface converter in an AC / DC hybrid power system under different control parameter settings is provided as an embodiment of the present invention. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0050] See Figure 1 An embodiment of the present invention provides a safety and stability assessment method applicable to AC / DC hybrid power systems, comprising the following steps:

[0051] S1. Obtain the port impedance models of various devices and networks in the AC / DC hybrid power system;

[0052] S2. Based on the port impedance model, the admittance matrix of the entire system is calculated;

[0053] S3. Based on the admittance matrix of the entire system, the closed-loop poles are obtained, and the closed-loop poles are the poles of any element of the AC / DC hybrid power system.

[0054] S4. Apply a disturbance to a device in the AC / DC hybrid power system and calculate the participation factor of the device and its parameters with respect to a certain closed-loop pole.

[0055] S5. Conduct a safety and stability assessment of the device based on the participating factors.

[0056] In this embodiment, the AC / DC hybrid power system is considered as follows: Figure 2 As shown, the entire system has a total of 28 buses, including 14 AC buses and 14 DC buses, which are numbered sequentially. AC bus 14 and DC bus 15 are interconnected via an interface converter. In the AC system, buses 1, 2, and 8 are connected to synchronous generators, and buses 3 and 6 are connected to grid-connected inverters. In the DC system, buses 16, 17, 18, 21, and 23 are connected to grid-connected BUCK converters. The interface converters use DC voltage control mode. To verify the participation factor theory, the control parameters of the interface converters are adjusted, decreasing the current inner loop bandwidth and increasing the phase-locked loop and voltage outer loop bandwidths, thereby bringing the system closer to a critical stable state.

[0057] It should be added that participation factor theory is a theory based on the small-signal model of the system, describing the quantitative relationship between system parameters and closed-loop poles that characterize system stability. Analysis results based on participation factors can optimize equipment parameters and improve system stability. Traditional participation factor theories are mostly based on two types of systems: state-space models and nodal admittance matrices. While state-space models can provide precise relationships between variables and closed-loop poles, detailed state-space models are unavailable for large-scale power systems, limiting their widespread application in practical engineering. Nodal admittance matrices can yield participation factors for macroscopic nodal devices, but they are difficult to use for internal device parameters.

[0058] However, in the specific implementation of this invention, the port impedance models of each device and network in the system are first obtained, and the connection method between the impedance models of each device and the network impedance model is as follows: Figure 3 As shown, the AC ports of the AC equipment are connected to the AC network, the DC ports of the DC equipment are connected to the DC network, and the AC and DC ports of the interface converter are connected to the AC and DC networks respectively, forming a closed-loop model of the system. Further merging the port impedance models of the equipment yields the closed-loop characteristics of the system, as shown below. Figure 4 As shown, the expression for the total system admittance matrix can be derived from it. After calculating the total system admittance matrix, the poles of any element are the closed-loop poles of the AC / DC hybrid power system, thus enabling participation factor analysis of the AC / DC hybrid power system. Figure 5 The calculation results of the nodal participation factors for the 28-bus AC / DC hybrid power system in the embodiment are presented. All calculation results have been normalized. The figure shows the participation factors of the five devices in the AC system, the five devices in the DC system, and the interface converter with respect to the closed-loop pole at 29Hz. It can be seen that the normalized participation factor magnitude corresponding to the interface converter is the largest, thus it can be deduced that the interface converter has the greatest influence on this pole. Finally, a perturbation is applied to the control parameters of the interface converter, and the participation factors of the control parameters can be calculated using the rate of change of the interface converter port impedance. The real part of the participation factor for the current inner loop control bandwidth is negative, while the real parts of the participation factors for the phase-locked loop and voltage outer loop control bandwidth are positive, indicating that the control bandwidth of the current inner loop needs to be increased while the control bandwidths of the phase-locked loop and voltage outer loop need to be decreased to improve system stability.

[0059] In this embodiment, the port impedance model is divided into a first-order impedance matrix for DC equipment, a second-order impedance matrix for AC equipment, and a third-order impedance matrix for interface converters, based on different access methods of the devices, as shown in the following equations:

[0060] Z DC (s)=[Z dc (s)]

[0061]

[0062]

[0063] Among them, Z DC (s) represents the port impedance matrix of the DC equipment, and its elements Z dc (s) is the DC port impedance transfer function; Z AC (s) represents the port impedance matrix of the AC equipment, and its elements Z dd (s), Z dq (s), Z qd (s), Z qq (s) represent the impedance transfer functions along the d-axis and q-axis, respectively; Z IC (s) represents the port impedance matrix of the interface converter, whose elements are Z dd (s), Z dq (s), Z ddc (s), Z qd (s), Z qq (s), Z qdc (s), Z dcd (s), Z dcq (s), Z dc (s) represent the impedance transfer functions for the d-axis, q-axis, and DC port, respectively. The impedance models of all devices are written as diagonal matrices, as shown in the following equation:

[0064] Z app (s)=diag(Z AC-1 ,…,Z AC-M Z IC Z DC-1 ,…,Z DC-N )

[0065] Where M and N represent the number of devices in the AC system and DC system, respectively.

[0066] In this embodiment, the port impedance model is divided into an AC network and a DC network according to the typical structure of an AC / DC hybrid power system. The two networks are respectively connected to the AC port of the AC equipment and the DC port of the interface converter, as shown in the following formula:

[0067] Z net (s)=diag(Z AC-net Z DC-net ).

[0068] In this embodiment, the total system admittance matrix is:

[0069] Y sys (s)=[Z app (s)+Z net (s)]-1 .

[0070] In this embodiment, the method for calculating the participation factor of the device for a certain closed-loop pole includes:

[0071] When a disturbance is applied to the port impedance of the device, the change in port impedance is approximately proportional to the port impedance, as shown in the following formula:

[0072] ΔZ k (λ)=εZ k (λ)

[0073] Where ε represents the perturbation ratio, the subscript k represents any device, and λ represents the closed-loop pole.

[0074] The participation factor of the device with respect to the closed-loop pole is calculated as follows:

[0075]

[0076] Among them, Res λ G represents the residue matrix of the complex function G at the closed-loop pole λ. Z represents the admittance of the k-th device in the total system admittance matrix. λ (k) represents the impedance of the k-th device corresponding to the closed-loop pole λ, <·,·> represents the Frobenius inner product operation of two complex matrices, the superscript * represents the transpose and conjugate of the matrix, and ‖·‖ represents the Frobenius norm of the matrix.

[0077] In this embodiment, the perturbation applied to the port impedance of the device is achieved by applying a small perturbation to the power reference value of the port device.

[0078] In this embodiment, the method for calculating the participation factor of the device parameters with respect to a certain closed-loop pole includes:

[0079] A small perturbation is applied to the device parameters of the device, and the rate of change of the port impedance is measured and calculated as shown in the following formula:

[0080]

[0081] Where ρ represents the equipment parameter, and the subscript Δ represents the impedance value after parameter disturbance;

[0082] The participation factor of the device parameters with respect to a certain closed-loop pole is calculated as follows:

[0083]

[0084] Furthermore, in order to verify the correctness of the participation factor theory, Figure 6Simulated time-domain waveforms of active power transmission by the interface converter are presented. Small disturbances were applied to the AC and DC loads at 10s and 12s in the simulation, respectively, to observe the time-domain power waveforms. (a) and (b) show the waveforms at the critical stability of the system under the initial parameters. (c) and (d) show the results of increasing the current inner loop control bandwidth and decreasing the control bandwidth of the phase-locked loop and voltage outer loop according to the calculated participation factor, demonstrating a significant improvement in system stability. (e) and (f) show the simulation results of adjusting the above parameters in reverse, revealing power waveform oscillations and system instability. In summary, this embodiment demonstrates the application method of the theory involved in this invention, and the results verify the correctness of the theory.

[0085] The analytical method proposed in this invention is based on the impedance mathematical model of an AC / DC hybrid power system. With the addition of known information, it enables qualitative to quantitative participation factor analysis of the system under study. When using the impedance participation factor analysis method, the closed-loop mathematical model of the system must first be obtained to determine the system's stability and stability margin based on the closed-loop poles. When the system has a closed-loop pole in the right half-plane or a closed-loop pole near the imaginary axis, this closed-loop pole is identified as the object of analysis for participation factor theory. Secondly, after identifying the closed-loop pole under study, it is necessary to locate the device that has the greatest impact on it. This requires obtaining the port impedance values ​​of all devices in the system. The larger the relative modulus of the calculated result for a device, the greater its influence on the closed-loop pole under study, and the larger its participation factor. Finally, after identifying the key devices affecting the closed-loop pole, it is necessary to further adjust the control parameters, operating parameters, and circuit parameters of the devices to improve system stability. If the change in the device's port impedance after parameter disturbance can be obtained, the participation factor of the parameters with respect to the closed-loop pole can be accurately calculated. If the real part of the participation factor is positive, it indicates that increasing this parameter will shift the closed-loop poles of the system to the right half-plane, thus worsening the system stability. Conversely, if the real part of the participation factor is negative, it indicates that decreasing this parameter will improve the system stability. In summary, the impedance participation factor analysis theory proposed in this invention can provide a quantitative analytical tool for optimizing equipment parameters to improve system stability.

[0086] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the protection scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for security and stability assessment of an AC / DC hybrid power system, characterized in that, The method comprises the following steps: S1, obtaining port impedance models of each device and network in an AC-DC hybrid power system; S2, calculating a full-system admittance matrix based on the port impedance models; S3, obtaining closed-loop poles based on the full-system admittance matrix, the closed-loop poles being poles of any element of the AC-DC hybrid power system; S4, applying a disturbance to a device of the AC-DC hybrid power system, and calculating a participation factor of the device and device parameters for a certain closed-loop pole; specifically comprising: applying a disturbance to the port impedance of the device, and the change value of the port impedance being approximately proportional to the port impedance, as shown in the following formula: ΔZ k (λ) = εZ k (λ) wherein, ε represents a disturbance ratio, subscript k represents any device, and λ represents the closed-loop pole; calculating the participation factor of the device for the closed-loop pole, as shown in the following formula: where Res λ G represents the residue matrix of the complex function G at the closed-loop pole λ, Yk(λ) represents the admittance of the kth device in the overall system admittance matrix Z k (λ) represents the impedance of the kth device corresponding to the closed-loop pole λ, <·,·> represents the Frobenius inner product operation of two complex matrices, the superscript * represents the transpose conjugate of the matrix, and ||·|| represents the Frobenius norm of the matrix; S5, performing a security and stability evaluation on the device based on the participation factor.

2. The method for security and stability assessment applicable to AC / DC hybrid power system according to claim 1, characterized in that, The port impedance models are divided into a first-order impedance matrix of a DC device, a second-order impedance matrix of an AC device, and a third-order impedance matrix of an interface converter according to different access modes of the device, and are respectively as shown in the following formulas: Z DC (s) = [Z dc (s)] where Z DC (s) represents the port impedance matrix of the AC device, whose elements are Z dc (s) is the AC port impedance transfer function; Z AC (s) represents the port impedance matrix of the AC device, whose elements are Z dd (s), Z dq (s), Z qd (s), Z qq (s) are the impedance transfer functions under d-axis and q-axis respectively; Z IC (s) represents the port impedance matrix of the interface converter, whose elements are Z dd (s), Z dq (s), Z ddc (s), Z qd (s), Z qq (s), Z qdc (s), Z dcd (s), Z dcq (s), Z dc (s) are the impedance transfer functions under d-axis, q-axis and DC port respectively, and the impedance models of all devices are written as a diagonal matrix as follows: Z app (s) = diag(Z AC-1 ,…,Z AC-M ,Z IC ,Z DC-1 ,…,Z DC-N ) wherein, M and N respectively represent the number of devices in the AC system and the DC system.

3. The method for security and stability assessment applicable to AC / DC hybrid power system according to claim 2, characterized in that, The port impedance models are divided into an AC network and a DC network according to a typical structure of the AC-DC hybrid power system, and the two are respectively connected to the AC port of the AC device and the interface converter and the DC port of the DC device and the interface converter, as shown in the following formula: Z net (s) = diag(Z AC-net ,Z DC-net ).

4. The method for security and stability assessment applicable to AC / DC hybrid power system according to claim 3, characterized in that, The full-system admittance matrix is: Y sys (s) = [Z app (s) + Z net (s)] -1 .

5. The method for security and stability assessment applicable to AC / DC hybrid power system according to claim 4, characterized in that, The disturbance applied to the port impedance of the device is realized by applying a small disturbance to the power reference value of the port device.

6. The method for security and stability assessment applicable to AC / DC hybrid power system according to claim 4, characterized in that, The calculation method of the participation factor of the device parameters of the device for a certain closed-loop pole comprises: applying a small disturbance to the device parameters of the device, measuring and calculating the change rate of the port impedance, as shown in the following formula: wherein, ρ represents the device parameters, and subscript Δ represents the impedance value after parameter disturbance; calculating the participation factor of the device parameters of the device for a certain closed-loop pole, as shown in the following formula: 。

Images