Islanding microgrid modeling and order reduction method based on direct truncation and routh approximation

Abstract

A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation includes: 1) acquiring and preprocessing data from the islanded microgrid; 2) partitioning the islanded microgrid and performing small-signal modeling on each partition; 3) constructing a candidate order set, selecting the lowest candidate order as the initial target order, and assembling the small-signal model to obtain a high-order model; 4) extracting channels from the high-order model to generate a transfer function, and determining the numerator and denominator of the transfer function based on the target order; 5) directly truncating the numerator of the transfer function and using the Routh approximation method to reduce the order of the transfer function to obtain a low-order model; 6) determining whether the low-order model meets stability and consistency indices. If yes, the final reduced-order model of the islanded microgrid is obtained; otherwise, the next target order is selected, and the process returns to step 4). This invention stably and controllably reduces a high-order islanded microgrid model to a low-order fast model.

Description

Technical Field

[0001] This invention relates to the field of brain disease treatment technology, specifically to a method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation. Background Technology

[0002] With the growth of global energy demand and increasingly stringent environmental constraints, power systems are rapidly evolving towards a high proportion of renewable energy. The installed capacity of renewable energy continues to climb, and large-scale grid connection of renewable energy and rapid expansion of distributed energy have become the norm. Against this backdrop, microgrids (including AC / DC hybrid topologies and converter-dominated power electronic interfaces), capable of locally aggregating multiple sources, storage, and loads and possessing independent operating capabilities, are gradually becoming an important power grid carrier. However, the low inertia and strong coupling characteristics of power electronics significantly amplify the uncertainty of small-signal dynamics, making the system more prone to oscillations, low damping, or even instability under small disturbances. Therefore, incorporating small-disturbance stability constraints into operational optimization (Energy Management System (EMS) / Optimal Power Flow (OPF)) and control tuning has become an essential engineering requirement. Existing technologies for small-signal modeling and order reduction in microgrids mainly include: mechanism-based integrated linearization modeling (including loops, networks, loads, and energy storage physical components such as droop control, phase-locked loops (PLLs), virtual synchronous machines (VSMs), and voltage-oriented control (VOCs)); and various model order reduction methods, such as modal truncation, singular perturbation, Kron equivalence, coherent clustering / regional equivalence, balance truncation and Hankel norm approximation, Krylov / Padé moment matching and the Passive Reduced-Order Interconnect Macromodeling Algorithm (PRIMA), consistency transformation, and energy functions. These methods have been widely applied in conventional power systems or single-AC microgrids, but when used in high-order hybrid AC / DC coupling models of isolated microgrids, they generally suffer from the following problems and shortcomings:

[0003] First, there are issues with high dimensionality, computational heaviness, and difficulty in online application. Models involving multiple inverters, multiple direct current (DC) nodes, and multiple line couplings often result in high-order differential-algebraic equations (DAE) / state-space models (often reaching tens of orders). When used for EMS / OPF simultaneous stability assessment or online sensitivity evaluation, the solution time and memory overhead are large, making it difficult to meet real-time requirements. Second, numerical order reduction methods such as balanced truncation and Krylov generally optimize energy or interpolation errors, but do not necessarily explicitly guarantee Hurwitz stability and passive / positive real physical properties. When used in non-minimum phase, strongly coupled power electronic systems, they may result in analytical stability after order reduction but physical distortion. Furthermore, the strong coupling of AC / DC subnetworks through power / voltage / current equations leads to large spans and high ill-formation in the coefficients of high-order characteristic polynomials after algebraic elimination. This makes some numerical order reduction methods sensitive to coefficient scale, and the fitting results drift significantly with operating conditions (operating point, voltage level, load power factor). Finally, some methods require solving reachability / controllability-observability Gramian equations, solving large-scale Lyapunov equations, or constructing high-dimensional projection subspaces, which are complex to implement and highly dependent on toolchains; they are also difficult to maintain in field environments where parameters change frequently.

[0004] The aforementioned problems arise because the high-order models of isolated microgrids encompass multiple time scales of power electronic controllers (measurement filtering, outer loop droop, inner loop current / voltage, power loop) and the electromagnetic-electrical dynamics of AC networks and DC buses / lines. Multi-loop interactions and algebraic interconnections result in clustered eigenvalues ​​and parameter sensitivity. Simultaneously, changes in operating points cause the linearized model to drift between different operating conditions, requiring the order reduction method to be concise, repeatable, stable, and consistent across both the frequency and time domains. Existing technologies often encounter the following difficulties in addressing these issues: first, how to explicitly guarantee stability and retain dominant pole damping and natural frequencies during order reduction; second, how to simultaneously satisfy the constraints of frequency domain amplitude and phase and time domain indices without increasing implementation complexity; and third, how to quickly embed the order reduction results into online optimization and stability assessment processes, avoiding real-time bottlenecks caused by massive matrix operations. Therefore, there is an urgent need for an order reduction modeling method that operates at the transfer function level, has short computational links, controllable stability, and is suitable for online applications, providing an efficient and reliable low-order equivalent model for small-disturbance stability constraints, parameter tuning, and scheduling optimization of microgrids. Summary of the Invention

[0005] The purpose of this invention is to provide a method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation, comprising the following steps:

[0006] 1) Obtain network internal parameter data, control and measurement parameter data, and steady-state operating point data of the isolated microgrid.

[0007] 2) Preprocess the acquired data to obtain preprocessed data.

[0008] 3) Divide the isolated microgrid into partitions, and based on the preprocessed data, perform small-signal modeling for each partition to obtain the small-signal model for each partition.

[0009] 4) Construct a candidate order set, select the lowest candidate order from the candidate order set as the initial target order, and assemble the small signal model of each partition to obtain the high-order model of the islanded microgrid.

[0010] 5) Extract channels from the high-order model of the islanded microgrid, generate the transfer function, and determine the numerator and denominator of the transfer function based on the target order.

[0011] 6) The numerator of the transfer function is directly truncated, and the denominator of the transfer function is processed by the Routh approximation order reduction method to obtain a low-order model of an islanded microgrid for online small-signal stability determination.

[0012] 7) Determine whether the low-order model of the islanded microgrid meets the stability and consistency indicators. If yes, the final reduced-order model of the islanded microgrid is obtained. If not, select the next candidate order from the candidate order set from low to high as the target order and return to step 5.

[0013] Furthermore, the network internal parameter data includes the network topology.

[0014] The network topology of the isolated microgrid includes a DC terminal, an AC terminal, and an IC terminal.

[0015] The DC terminal includes a DC-side bus, m converters, m DC-side loads, and m-1 DC-side lines, where m is a positive integer.

[0016] The DC side line includes a resistor R1 and an inductor L1.

[0017] The AC terminal includes an AC-side bus, n-1 AC-side lines, n inverters, AC-side load I, and n-1 AC-side load II, where n is a positive integer.

[0018] The AC side circuit includes a resistor R2 and an inductor L2.

[0019] The IC terminal includes a bidirectional converter.

[0020] One end of the AC side busbar is connected to the power grid, and the other end is connected to the bidirectional converter.

[0021] The AC-side busbar has n AC-side nodes.

[0022] An AC-side line is provided between two adjacent AC-side nodes.

[0023] An inverter is connected in parallel to each AC-side node.

[0024] AC-side load I is connected in parallel to the AC-side node closest to the power grid, and AC-side load II is connected in parallel to the other AC-side nodes.

[0025] One end of the DC-side bus is connected to the bidirectional converter.

[0026] The DC-side busbar has m DC-side nodes.

[0027] A DC-side line is provided between two adjacent DC-side nodes.

[0028] Each DC-side node is connected in parallel with one converter and one DC-side load.

[0029] The control and measurement parameter data include power measurement low-pass cutoff frequency, inverter droop, DC / DC droop, and IC synthesis droop.

[0030] The steady-state operating point data includes the initial values ​​of inverter voltage and current, steady-state operating point of power angle frequency, initial values ​​of converter voltage and current, initial values ​​of line and load current, and IC switching power.

[0031] Furthermore, the preprocessing includes dp coordinate synchronization, filtering, and drooping pre-mapping.

[0032] The data after dp coordinate synchronization is shown below:

[0033] (1)

[0034] (2)

[0035] In the formula, Indicates the inverter index. Indicates the first The local frequency of each inverter. This represents the defined network frequency. Indicates time. Represents a time variable. Indicates the first The frequency difference of the inverters. Indicates the first An inverter in time The angle of attack.

[0036] The filtered data is shown below:

[0037] (3)

[0038] (4)

[0039] In the formula, s represents the Laplace operator. , These represent the active power and reactive power measured instantaneously, respectively. This indicates the cutoff frequency of the measured low-pass filter. This represents the active power after filtering. This represents the reactive power after filtering.

[0040] The data after the drooping pre-mapping is shown below:

[0041] (5)

[0042] (6)

[0043] (7)

[0044] In the formula, This indicates the frequency reference value of the AC-side droop loop output. This indicates the rated frequency of the AC side bus. This represents the active power-frequency droop factor. This indicates the steady-state setpoint of the active power on the AC side. This indicates the reference voltage value output by the AC side drooping loop. This indicates the rated voltage of the AC side bus. This represents the reactive power-voltage droop coefficient. This indicates the steady-state setpoint of the reactive power on the AC side. This indicates the voltage reference value output by the DC / DC droop loop. This indicates the rated voltage of the DC side bus. This represents the power-DC voltage droop factor. This represents the active power after filtering on the DC side. This indicates the steady-state setpoint of the active power on the DC side. This indicates the reference value of active power on the IC side. This indicates the steady-state power exchange setpoint on the IC side. This represents the DC voltage-power droop factor. This indicates the actual voltage of the DC-side bus. This indicates the actual voltage of the DC-side bus. This represents the frequency-power droop factor. This represents the active power after filtering on the AC side. This represents the reactive power after filtering on the AC side.

[0045] Furthermore, the islanded microgrid is divided into AC-side partitions, DC-side partitions, and IC-side partitions.

[0046] Furthermore, the small-signal model of the AC-side partition is as follows:

[0047] (8)

[0048] (9)

[0049] (10)

[0050] In the formula, This represents the derivative vector of the AC side line current. This represents the AC-side line self-dynamic matrix. This indicates the small-signal deviation of the AC side line current. , These represent the AC-side line voltage-current coupling matrix and the AC-side line frequency interference matrix, respectively. This indicates the small-signal deviation of the AC side bus voltage. This represents the small signal deviation of the network frequency. This represents the derivative vector of the load current on the AC side. This represents the load parameter matrix on the AC side. This indicates the small-signal deviation of the load current on the AC side. , These represent the admittance matrix of the AC-side load to the AC-side bus voltage and the frequency interference matrix of the AC-side load, respectively. This indicates the small-signal deviation of the AC side bus voltage. This represents the small-signal deviation of the AC-side bus voltage in the dq coordinate system. , These represent the coordinate phase transformation matrix and the phase angle perturbation matrix, respectively. This indicates the small signal deviation of the inverter output voltage. This indicates the small-signal deviation of the AC side power angle.

[0051] The small-signal model of the DC-side partition is shown below:

[0052] (11)

[0053] (12)

[0054] (13)

[0055] In the formula, This represents the derivative vector of the DC-side line current. This represents the self-dynamic matrix of a DC line. This indicates the small-signal deviation of the DC-side line current. This represents the voltage and current admittance matrix. This indicates the small-signal deviation of the DC-side line voltage. This represents the derivative vector of the DC-side load current. The differential admittance matrix represents the static resistive load. This indicates the small-signal deviation of the DC-side bus voltage. This represents the derivative vector of the converter output voltage. This represents a self-dynamic matrix. This indicates the small-signal deviation of the converter output voltage. This represents the coupling matrix from the equivalent injected current to the port voltage. This indicates the small-signal deviation of the converter input current.

[0056] The small-signal model of the IC-side partition is shown below:

[0057] (14)

[0058] (15)

[0059] In the formula, This indicates a small signal deviation in the IC-side communication power. This represents the DC voltage-power droop factor. This indicates the small-signal deviation of the DC terminal voltage. This represents the frequency-power droop factor. This represents the small-signal deviation of the frequency in a microgrid system. This represents the small-signal deviation of the d-axis component of the AC input current. This represents the steady-state operating value of the AC terminal voltage. This indicates the small signal deviation in communication power. This represents the steady-state operating value of the communication power. This indicates the small-signal deviation of the AC terminal voltage. This represents the small-signal deviation of the q-axis component of the AC input current. This indicates the small signal deviation of the reactive power input at the AC terminal.

[0060] Furthermore, the small signal deviation is as follows:

[0061] (16)

[0062] In the formula, This represents the small-signal deviation variable. This represents the actual measured value. This represents the steady-state operating value.

[0063] Furthermore, the high-order model of the islanded microgrid is shown below:

[0064] (17)

[0065] In the formula, The vector representing the derivatives of the state variables. , , , These represent the state matrix, input matrix, output matrix, and direct transmission matrix, respectively. This represents the state variable vector of a microgrid system. This represents the input vector. This represents the output vector.

[0066] Furthermore, the transfer function is as follows:

[0067] (18)

[0068] In the formula, This represents the transfer function. This represents the Laplace operator. Represents the identity matrix. , , , Representing the state matrix and input matrix respectively The column vector and output matrix corresponding to the selected input. The row vector and direct transfer matrix corresponding to the selected output The element that corresponds to the selected input-output.

[0069] Among them, the numerator of the transfer function denominator As shown below:

[0070] (19)

[0071] (20)

[0072] In the formula, Indicates the target order. This represents the set of coefficients corresponding to the denominator. This represents the set of coefficients corresponding to the molecule.

[0073] Furthermore, in step 6), the steps for obtaining the low-order model of the islanded microgrid are as follows:

[0074] 6.1) The transfer function molecule is processed by the direct truncation reduction method to obtain a lower-order molecule, as shown below:

[0075] (twenty one)

[0076] In the formula, This represents the Laplace operator. This indicates lower-order molecules. This indicates the lowest order to be retained. Indicates the target order. This represents the set of coefficients retained after the molecule is truncated.

[0077] 6.2) The Routh approximation method is used to process the denominator of the transfer function. The steps are as follows:

[0078] 6.2.1) Based on the denominator of the transfer function, construct the Routh table as follows:

[0079] (twenty two)

[0080] In the formula, These represent the rows and columns of the Routh table, respectively. In the Routh table, the first... Line number The elements of the column also correspond to polynomials. The coefficient. This represents the set of coefficients corresponding to the denominator of the transfer function. If the elements The preset constant ε is used as a substitute. If the first... If all elements in a row are 0, then start with the first... The elements of the row are used to construct an auxiliary polynomial, and the derivative coefficients of the auxiliary polynomial are used to replace the first polynomial. The elements of a row.

[0081] 6.2.2) Read the first column elements from row h+1-k to row h+1 from the Routh table and assemble them to obtain the reduced-order denominator. As shown below:

[0082] (twenty three)

[0083] In the formula, Indicates a reduced order denominator The corresponding set of coefficients.

[0084] 6.2.3) Based on the original transfer function for low-order molecules Gain corrections are performed to obtain a low-order model of the islanded microgrid.

[0085] The gain correction is as follows:

[0086] (twenty four)

[0087] In the formula, This represents the lower-order molecule after gain correction. This represents the gain factor. This represents the primitive transfer function for the Laplace operator s=0. , Let represent the numerator and denominator of the original transfer function when the Laplace operator s=0, respectively. This represents the uncorrected low-order model when the Laplace operator s=0. , Let represent the lower-order numerator and the reduced-order denominator when the Laplace operator s=0, respectively.

[0088] Furthermore, in the low-order model of an islanded microgrid, the denominator is reduced in order. coefficient If all values ​​are greater than 0, then the low-order model of the islanded microgrid satisfies stability.

[0089] The consistency metrics include the natural angular frequency and damping ratio of the low-order model, as shown below:

[0090] (25)

[0091] In the formula, ω represents the natural angular frequency of the low-order model. The damping ratio is denoted as . Both are reduced-order denominators The coefficient. When and Then the low-order model of the islanded microgrid satisfies consistency, where, This indicates the lower limit of the damping ratio. , These represent the upper and lower limits of the natural angular frequency, respectively.

[0092] The technical effects of this invention are undeniable. Under the premise of ensuring stability, this invention rapidly reduces the high-order AC / DC coupling model to a low-order model, which can be used for online small-signal stability determination, sensitivity analysis, EMS / OPF real-time constraint generation and droop parameter tuning, significantly reducing the amount of computation and preserving the physical interpretability of the control parameters.

[0093] The complete process proposed in this invention, namely "block modeling—channel extraction—direct torque control (DTM) + Routh order reduction—gain matching—consistency verification," stably and controllably reduces a high-order islanded microgrid model to a low-order reduced-order model (ROM) while ensuring the interpretability of the physical mechanism. First, by directly truncating the numerator and matching the DC gain, this invention can still maintain strict consistency with the original model in the low-frequency and steady-state stages after order reduction, thereby ensuring that the amplitude-phase relationship of key observations such as DC voltage and system frequency is not distorted. In conjunction with this, the Routh approximation in the denominator makes the reduced-order denominator naturally satisfy the Hurwitz stability condition, and explicitly maps stability indices such as damping ratio and natural frequency into the order reduction coefficients, thus making the stability "visible, adjustable, and verifiable." Building upon this foundation, by employing a parallel, modular configuration of "AC / DC / interconnector converters" coupled with unified ports, this invention significantly reduces the state dimension and improves simulation efficiency: typical scenarios can be reduced from high-order to low-order, preserving the original low-order dynamic processes while delivering orders-of-magnitude acceleration in time-domain simulation and optimization solutions; simultaneously, modular interface definitions allow topology changes and device additions / removals to be updated locally without rebuilding the overall model, facilitating project expansion and version iteration. Furthermore, the reduced-order parameters correspond one-to-one with second-order equivalent quantities, and with steady-state gain preservation, can be directly used for rapid tuning of controllers such as droop coefficients and filter bandwidth, reducing repeated trial-and-error adjustments and debugging on-site. Meanwhile, thanks to unified coordinates and port quantity outputs (bus voltage, injected current, power exchange, etc.), this low-order model can be seamlessly embedded into scheduling and real-time optimization frameworks such as OPF / Model Predictive Control (MPC), forming a rapid evaluation and decision-making closed loop of "steady-state-dynamic integration." Furthermore, by preserving key zeros / dominant poles during order reduction and matching, this method is more robust to parameter drift and operating point variations, making it suitable for AC / DC hybrid systems with multiple inverters in parallel and DC / DC converters and interconnection converters. It has a small computational load, is simple to implement, and can be deployed as an edge-side digital twin for online monitoring of damping and margin and driving parameter self-tuning.

[0094] This invention achieves a combination of advantages, including efficient simulation and rapid tuning, scalable structure and reusable engineering, as well as quantifiable verification and convenient compliance, while ensuring low-frequency-steady-state consistency and explicit controllable stability. Accordingly, microgrids can balance safety margin and economic operation under high-proportion renewable energy penetration, thereby improving renewable energy absorption capacity, reducing commissioning and maintenance costs, and providing a directly implementable reduced-order modeling and control tuning toolchain for practical engineering. Attached Figure Description

[0095] Figure 1 This is a flowchart of the present invention;

[0096] Figure 2 This is a schematic diagram of the block small signal modeling process of the present invention;

[0097] Figure 3 This is a topology diagram of the modular modeling of AC / DC microgrids in this invention. Detailed Implementation

[0098] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0099] Example 1:

[0100] See Figures 1 to 3 A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation includes the following steps:

[0101] 1) Obtain network internal parameter data, control and measurement parameter data, and steady-state operating point data of the isolated microgrid.

[0102] 2) Preprocess the acquired data to obtain preprocessed data.

[0103] 3) Divide the isolated microgrid into partitions, and based on the preprocessed data, perform small-signal modeling for each partition to obtain the small-signal model for each partition.

[0104] 4) Construct a candidate order set, select the lowest candidate order from the candidate order set as the initial target order, and assemble the small signal model of each partition to obtain the high-order model of the islanded microgrid.

[0105] 5) Extract channels from the high-order model of the islanded microgrid, generate the transfer function, and determine the numerator and denominator of the transfer function based on the target order.

[0106] 6) The numerator of the transfer function is directly truncated, and the denominator of the transfer function is processed by the Routh approximation order reduction method to obtain a low-order model of an islanded microgrid for online small-signal stability determination.

[0107] 7) Determine whether the low-order model of the islanded microgrid meets the stability and consistency indicators. If yes, the final reduced-order model of the islanded microgrid is obtained. If not, select the next candidate order from the candidate order set from low to high as the target order and return to step 5.

[0108] In step 4), a set of candidate orders is given in advance. (e.g., orders 2 to 4), and starting from the lowest order as the initial target order. For each given order k, after obtaining the low-order model by directly truncating the numerator and approximating the denominator with Routh, the stability and consistency with the high-order model are verified using error indices such as Routh condition, natural frequency and damping ratio threshold, Bode amplitude-phase difference, and ISE / ITAE. If all indices are satisfied, the low-order model corresponding to that order is considered the final reduced-order model. If any item is not satisfied, the target order is appropriately increased in the candidate set in ascending order, and the process returns to step 5) to re-execute the order reduction and verification until the lowest target order that meets the requirements under the error and stability constraints is found. Thus, "adjusting the target order" is reflected as a discrete iterative search for integer orders k, rather than arbitrary adjustment, ensuring the determinism and reproducibility of the order reduction process.

[0109] If none of the orders in the candidate order set meet the stability and consistency criteria, then the following steps are executed sequentially: i) Expand the candidate order set and repeat the DTM and Routh order reduction process; ii) Apply the 'preserve and incorporate' rule to any existing non-minimum phases or low-frequency critical zeros and then redo the truncation; iii) While keeping the order reduction denominator unchanged, through... iv) Perform molecular correction on the gain and slope matching of the two parameters at low frequencies; limit the consistency check to the frequency band of engineering interest or use segmented ROM; v) if it is still not satisfied, it is determined that the ROM of this channel is not feasible under the current operating point and threshold setting, and it is recommended to retain the high-order model or appropriately relax the threshold. (Reduced-order models are generally applicable in engineering applications).

[0110] Example 2:

[0111] A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation is described in Example 1. Further, the network internal parameter data includes the network topology.

[0112] The network topology of the isolated microgrid includes a DC terminal, an AC terminal, and an IC terminal.

[0113] The DC terminal includes a DC-side bus, m converters, m DC-side loads, and m-1 DC-side lines, where m is a positive integer.

[0114] The DC side line includes a resistor R1 and an inductor L1.

[0115] The AC terminal includes an AC-side bus, n-1 AC-side lines, n inverters, AC-side load I, and n-1 AC-side load II, where n is a positive integer.

[0116] The AC side circuit includes a resistor R2 and an inductor L2.

[0117] The IC terminal includes a bidirectional converter.

[0118] One end of the AC side busbar is connected to the power grid, and the other end is connected to the bidirectional converter.

[0119] The AC-side busbar has n AC-side nodes.

[0120] An AC-side line is provided between two adjacent AC-side nodes.

[0121] An inverter is connected in parallel to each AC-side node.

[0122] AC-side load I is connected in parallel to the AC-side node closest to the power grid, and AC-side load II is connected in parallel to the other AC-side nodes.

[0123] One end of the DC-side bus is connected to the bidirectional converter.

[0124] The DC-side busbar has m DC-side nodes.

[0125] A DC-side line is provided between two adjacent DC-side nodes.

[0126] Each DC-side node is connected in parallel with one converter and one DC-side load.

[0127] The control and measurement parameter data include power measurement low-pass cutoff frequency, inverter droop, DC / DC droop, and IC synthesis droop.

[0128] The steady-state operating point data includes the initial values ​​of inverter voltage and current, steady-state operating point of power angle frequency, initial values ​​of converter voltage and current, initial values ​​of line and load current, and IC switching power.

[0129] Example 3:

[0130] A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation is provided. The main technical contents are described in any one of Embodiments 1 and 2. Furthermore, the preprocessing includes dp coordinate synchronization, filtering, and droop pre-mapping.

[0131] The data after dp coordinate synchronization is shown below:

[0132] (1)

[0133] (2)

[0134] In the formula, Indicates the inverter index. Indicates the first The local frequency of each inverter. This represents the defined network frequency. Indicates time. Represents a time variable. Indicates the first The frequency difference of the inverters. Indicates the first An inverter in time The angle of attack.

[0135] The filtered data is shown below:

[0136] (3)

[0137] (4)

[0138] In the formula, s represents the Laplace operator. , These represent the active power and reactive power measured instantaneously, respectively. This indicates the cutoff frequency of the measured low-pass filter. This represents the active power after filtering. This represents the reactive power after filtering.

[0139] The data after the drooping pre-mapping is shown below:

[0140] (5)

[0141] (6)

[0142] (7)

[0143] In the formula, This indicates the frequency reference value of the AC-side droop loop output. This indicates the rated frequency of the AC side bus. This represents the active power-frequency droop factor. This indicates the steady-state setpoint of the active power on the AC side. This indicates the reference voltage value output by the AC side drooping loop. This indicates the rated voltage of the AC side bus. This represents the reactive power-voltage droop coefficient. This indicates the steady-state setpoint of the reactive power on the AC side. This indicates the voltage reference value output by the DC / DC droop loop. It indicates the rated voltage of the DC side bus. The subscript "con" emphasizes the converter control terminal and control command reference, and is a command quantity in the control system. This represents the power-DC voltage droop factor. This represents the active power after filtering on the DC side. This indicates the steady-state setpoint of the active power on the DC side. This indicates the reference value of active power on the IC side. This indicates the steady-state power exchange setpoint on the IC side. This represents the DC voltage-power droop factor. This indicates the actual voltage of the DC-side bus. It represents the actual voltage of the DC bus. The subscript dc emphasizes the DC bus terminal and the actual measurement. It is a state variable in the power network. This represents the frequency-power droop factor. This represents the active power after filtering on the AC side. This represents the reactive power after filtering on the AC side.

[0144] Example 4:

[0145] A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation is provided. The main technical contents are described in any one of Examples 1 to 3. Furthermore, the islanded microgrid is divided into AC-side partitions, DC-side partitions, and IC-side partitions.

[0146] Example 5:

[0147] A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation is described in any one of Examples 1 to 4. Further, the small-signal model of the AC-side partition is as follows:

[0148] (8)

[0149] (9)

[0150] (10)

[0151] In the formula, This represents the derivative vector of the AC side line current. This represents the AC-side line self-dynamic matrix. This indicates the small-signal deviation of the AC side line current. , These represent the AC-side line voltage-current coupling matrix and the AC-side line frequency interference matrix, respectively. This indicates the small-signal deviation of the AC side bus voltage. This represents the small signal deviation of the network frequency. This represents the derivative vector of the load current on the AC side. This represents the load parameter matrix on the AC side. This indicates the small-signal deviation of the load current on the AC side. , These represent the admittance matrix of the AC-side load to the AC-side bus voltage and the frequency interference matrix of the AC-side load, respectively. This indicates the small-signal deviation of the AC side bus voltage. This represents the small-signal deviation of the AC-side bus voltage in the dq coordinate system. , These represent the coordinate phase transformation matrix and the phase angle perturbation matrix, respectively. This indicates the small signal deviation of the inverter output voltage. This indicates the small-signal deviation of the AC side power angle.

[0152] The small-signal model of the DC-side partition is shown below:

[0153] (11)

[0154] (12)

[0155] (13)

[0156] In the formula, This represents the derivative vector of the DC-side line current. This represents the self-dynamic matrix of a DC line. This indicates the small-signal deviation of the DC-side line current. This represents the voltage and current admittance matrix. This indicates the small-signal deviation of the DC-side line voltage. This represents the derivative vector of the DC-side load current. The differential admittance matrix represents the static resistive load. This indicates the small-signal deviation of the DC-side bus voltage. This represents the derivative vector of the converter output voltage. This represents a self-dynamic matrix. This indicates the small-signal deviation of the converter output voltage. This represents the coupling matrix from the equivalent injected current to the port voltage. This indicates the small-signal deviation of the converter input current.

[0157] The small-signal model of the IC-side partition is shown below:

[0158] (14)

[0159] (15)

[0160] In the formula, This indicates a small signal deviation in the IC-side communication power. This represents the DC voltage-power droop factor. This indicates the small-signal deviation of the DC terminal voltage. This represents the frequency-power droop factor. This represents the small-signal deviation of the frequency in a microgrid system. This represents the small-signal deviation of the d-axis component of the AC input current. This represents the steady-state operating value of the AC terminal voltage. This indicates the small signal deviation in communication power. This represents the steady-state operating value of the communication power. This indicates the small-signal deviation of the AC terminal voltage. This represents the small-signal deviation of the q-axis component of the AC input current. This indicates the small signal deviation of the reactive power input at the AC terminal.

[0161] Example 6:

[0162] A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation is described in any one of Examples 1 to 5. Further, the small-signal deviation is as follows:

[0163] (16)

[0164] In the formula, This represents the small-signal deviation variable. This represents the actual measured value. This represents the steady-state operating value.

[0165] Example 7:

[0166] A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation is described in any one of Examples 1 to 6. Further, the high-order model of the islanded microgrid is shown below:

[0167] (17)

[0168] In the formula, The vector representing the derivatives of the state variables. , , , These represent the state matrix, input matrix, output matrix, and direct transmission matrix, respectively. This represents the state variable vector of a microgrid system. This represents the input vector. This represents the output vector.

[0169] Example 8:

[0170] A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation is described in any one of Examples 1 to 7. Further, the transfer function is as follows:

[0171] (18)

[0172] In the formula, This represents the transfer function. This represents the Laplace operator. Represents the identity matrix. , , , Representing the state matrix and input matrix respectively The column vector and output matrix corresponding to the selected input. The row vector and direct transfer matrix corresponding to the selected output The element that corresponds to the selected input-output.

[0173] Among them, the numerator of the transfer function denominator As shown below:

[0174] (19)

[0175] (20)

[0176] In the formula, Indicates the target order. This represents the set of coefficients corresponding to the denominator. This represents the set of coefficients corresponding to the molecule.

[0177] Example 9:

[0178] A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation is provided. The main technical details are described in any one of Examples 1 to 8. Further, in step 6), the steps for obtaining the low-order model of the islanded microgrid are as follows:

[0179] 6.1) The transfer function molecule is processed by the direct truncation reduction method to obtain a lower-order molecule, as shown below:

[0180] (twenty one)

[0181] In the formula, This represents the Laplace operator. This indicates lower-order molecules. This indicates the lowest order to be retained. Indicates the target order. This represents the set of coefficients retained after the molecule is truncated.

[0182] 6.2) The Routh approximation method is used to process the denominator of the transfer function. The steps are as follows:

[0183] 6.2.1) Based on the denominator of the transfer function, construct the Routh table as follows:

[0184] (twenty two)

[0185] In the formula, These represent the rows and columns of the Routh table, respectively. In the Routh table, the first... Line number The elements of the column also correspond to polynomials. The coefficient. This represents the set of coefficients corresponding to the denominator of the transfer function. If the elements The preset constant ε is used as a substitute. If the first... If all elements in a row are 0, then start with the first... The elements of the row are used to construct an auxiliary polynomial, and the derivative coefficients of the auxiliary polynomial are used to replace the first polynomial. The elements of a row.

[0186] 6.2.2) Read the first column elements from row h+1-k to row h+1 from the Routh table and assemble them to obtain the reduced-order denominator. As shown below:

[0187] (twenty three)

[0188] In the formula, Indicates a reduced order denominator The corresponding set of coefficients.

[0189] 6.2.3) Based on the original transfer function for low-order molecules Gain corrections are performed to obtain a low-order model of the islanded microgrid.

[0190] The gain correction is as follows:

[0191] (twenty four)

[0192] In the formula, This represents the lower-order molecule after gain correction. This represents the gain factor. This represents the primitive transfer function for the Laplace operator s=0. , Let represent the numerator and denominator of the original transfer function when the Laplace operator s=0, respectively. This represents the uncorrected low-order model when the Laplace operator s=0. , Let represent the lower-order numerator and the reduced-order denominator when the Laplace operator s=0, respectively.

[0193] Example 10:

[0194] A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation is presented, with the main technical contents described in any one of Examples 1 to 9. Further, when the denominator of the reduced order model of the islanded microgrid... coefficient If all values ​​are greater than 0, then the low-order model of the islanded microgrid satisfies stability.

[0195] The consistency metrics include the natural angular frequency and damping ratio of the low-order model, as shown below:

[0196] (25)

[0197] In the formula, ω represents the natural angular frequency of the low-order model. The damping ratio is denoted as . Both are reduced-order denominators The coefficient. When and Then the low-order model of the islanded microgrid satisfies consistency, where, This indicates the lower limit of the damping ratio. , These represent the upper and lower limits of the natural angular frequency, respectively.

[0198] Example 11:

[0199] A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation is provided. The main technical contents are described in any one of Examples 1 to 10. Furthermore, the final reduced-order model of the islanded microgrid is used for online small-signal stability determination, sensitivity analysis, real-time EMS / OPF constraint generation, and droop parameter tuning.

[0200] Example 12:

[0201] See Figures 1 to 3 A method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation, the main technical contents of which include:

[0202] In a unified coordinate system, AC, DC, and bidirectional interconnected converter integrated circuits (ICs) are linearized and assembled into a system state-space model. After extracting high-order transfer functions for key channels, a stable low-order equivalent model is constructed using direct numerator truncation and Router recursion. Gain matching maintains low-frequency / steady-state consistency. This method achieves the following functions: rapidly reducing the high-order AC / DC coupling model to a low order while ensuring stability, enabling online small-signal stability assessment, sensitivity analysis, real-time EMS / OPF constraint generation, and droop parameter tuning. This significantly reduces computational load while preserving the physical interpretability of control parameters. The specific technical solution is as follows:

[0203] This method includes the following main modules: system data acquisition and coordinate preprocessing module, block small signal model generation and port combination module, whole-machine channel construction and high-order transfer function extraction module, and fusion order reduction and consistency verification module; specific implementation steps:

[0204] Step 1: System Data Acquisition and Coordinate Preprocessing

[0205] The system collects and standardizes the topology and device parameters (AC lines / loads, DC lines / loads, interconnect converters), control and measurement settings (power measurement low-pass, inverter P–ω / Q–V droop, DC / DC V–P droop, IC synthesis droop), and steady-state operating points of the hybrid AC / DC microgrid. It completes the coordinate transformation from three-phase to power constant dq and establishes a unified rotating reference based on the network frequency, so that small disturbances such as frequency, phase angle, voltage, and current can be expressed in the same coordinate system, providing consistent input data and reference framework for subsequent linearization and port combination.

[0206] Collect and standardize all the data and running points required for small-signal linearization and order reduction, including:

[0207] Network parameter data: network topology, AC-side line / load R / L, DC-side line Rdc / Ldc, and DC-end load, etc.

[0208] Control and measurement parameter data: power measurement low-pass cutoff frequency, inverter droop, DC / DC droop, IC synthesis droop;

[0209] Steady-state operating point data: initial values ​​of inverter voltage and current, steady-state operating point of power angle and frequency, initial values ​​of DC converter voltage and current, initial values ​​of line and load current, and IC switching power.

[0210] All measurements are interpolated to a uniform sampling rate fs using a synchronous time scale t. Zero-phase FIR or first-order filtering is applied to the voltage / current measurements for noise reduction, resulting in... The Park transformation is used to synchronize the measurements to the DQ coordinate system, and a unified reference or weighted average is selected to define the network frequency. The phase angle and frequency of each inverter satisfy:

[0211] (1)

[0212] (2)

[0213] in, Let m be the local frequency of the m-th inverter. Its power angle. Measurement of low-pass filter and control input generation:

[0214] (3)

[0215] in, and As the measurement input for the AC-side droop loop and the DC / DC droop loop after low-pass filtering.

[0216] Subsequently, this invention designs and normalizes control settings and synthesizes droop control pre-mapping:

[0217] (4)

[0218] (5)

[0219] (6)

[0220] Since most instabilities in the inverter and converter control loops originate from the slow dynamics of the power controller, while the fast dynamics of the inner-loop controller are ignored, it is assumed that each inverter output can ideally track a reference value determined by the droop-based power controller using local measurements. The steady-state quantities can then be solved for or directly given. Small signals are in the following form:

[0221] (7)

[0222] Furthermore, by unifying the dimensions and data structure, the electrical quantities and control parameters measured or given on-site can be standardized into inputs for subsequent small-signal modeling and order reduction processing.

[0223] Step 2: Hybrid AC / DC Block Small Signal Modeling and Port Combination

[0224] The electrical equations for AC zone (inverter outer loop droop, line and load under common dq), DC zone (DC / DC V-P droop and measurement low-pass, DC line / load equations), and IC zone (synthetic droop) are analyzed separately. and The mapping is performed as power exchange and converted to AC / DC port current injection. Small perturbation linearization is then applied to form their respective state and port equations:

[0225] 1) AC side (AC lines, load, inverter)

[0226] (8)

[0227] (9)

[0228] (10)

[0229] in, This is the AC line self-dynamic matrix, which is related to the line RL parameters collected in the previous step; The line voltage and current coupling matrix is ​​then mapped to the port via the line bus correlation matrix; The line frequency interference matrix is ​​obtained by transforming the phasor equations to a common coordinate system. The load RL parameter matrix; This is the admittance matrix of the load to the bus voltage; To and Isotype load interference matrix; This is the coordinate phase transformation matrix; This is the phase angle perturbation matrix. The AC voltage / current port quantities and bus quantities are further correlated via the AC line-bus correlation matrix. Perform topological coupling.

[0230] 2) DC side (DC lines, loads, converters)

[0231] (11)

[0232] (12)

[0233] (13)

[0234] in, This is the self-dynamic matrix of the DC line, which is related to the line RL parameters collected in the previous step; Here are the voltage and current admittance matrices; The differential admittance matrix of the static resistive load; To measure the low-pass cutoff frequency and droop coefficient Matrix-dependent self-dynamic matrices; This is the coupling matrix for the equivalent injected current to the port voltage. The DC line bus is represented by the correlation matrix. Perform topological coupling.

[0235] 3) IC side (port current injection)

[0236] (14)

[0237] (15)

[0238] in The current injected into the DC terminal can be determined by reactive power droop or power distribution strategies, and the current injected into the DC terminal is obtained by linearizing the power balance P=VI. Then, by using the line bus correlation matrix and the port relationships of power / voltage / current, the three models are spliced ​​together to obtain a unified state-space form for the entire system.

[0239] (16)

[0240] Among them, the state variable x is a set of small-signal linearized column vectors of AC side power angle, frequency, voltage and current, and DC side voltage and current, which can be directly used for subsequent transfer function construction and order reduction.

[0241] Step 3: Overall Channel Construction and High-Order Transfer Function Extraction

[0242] Select a single-input single-output channel based on operational and control concerns (e.g., input is a handshake power perturbation). The output is the DC bus voltage deviation. Or network frequency deviation The corresponding B columns and C rows are extracted from the overall state space to construct the SISO model. The transfer function is calculated and organized into numerator / denominator polynomial coefficients. This higher-order transfer function is the direct object for subsequent order reduction, stability and performance constraint generation.

[0243] In the B matrix of the MIMO system constructed in the previous step, select the column vector corresponding to the target input perturbation. Select the row vector in matrix C that corresponds to the target output. ; take accordingly (For example, DC voltage channel selection) Frequency channel To form a SISO state space, if necessary, a minimal implementation should be performed first to remove uncontrollable and unobservable subspaces. The transfer function should then be computed and standardized.

[0244] (17)

[0245] The numerator and denominator can be written as follows:

[0246] (18)

[0247] (19)

[0248] Where h is the system order, This is the coefficient set required for subsequent order reduction. Confirm the relative order and gain. High frequency limit Record the positions of poles and zeros; record unstable zeros or constraint-sensitive zeros for preservation during order reduction. Save. and The numerical evaluation is provided, which serves as direct input for the construction of the DTM and Routh tables in step four.

[0249] Step 4: Integrate the order reduction method and consistency verification

[0250] For higher-order channels, the numerator is first directly truncated (preserving the lowest order moment to match low-frequency and steady-state characteristics). Then, the target order is extracted from the higher-order denominator recursively according to the Routh table, while maintaining the Hurwitz-stable equivalent denominator. Subsequently, gain matching is used to make the gain consistent as s→0. Finally, the fidelity of low-frequency, steady-state and dominant dynamics is verified by comparing step, bode and integral error (integral of squared error (ISE) / integral of time-weighted absolute error (ITAE) etc.), and the stability and performance indicators are organized into explicit constraints that can be used for operation optimization and parameter tuning.

[0251] The previous step established The transfer function molecule is reduced to a lower order using the Direct Truncation Method (DTM), which emphasizes fitting the low-frequency and steady-state characteristics to the original channel, preserving the lowest k-th order molecular polynomial to obtain the lower-order molecule. :

[0252] (20)

[0253] If there are zeros that need to be retained (such as non-minimum phase zeros), the corresponding factors should be incorporated. Instead of simply cutting it off.

[0254] For the denominator established in the previous step The Routh Approximation Reduction Technique (RART) is adopted for order reduction. First, a Routh table is constructed, with different rows processed according to the following rules:

[0255] (twenty one)

[0256] Calculate using the recursive formula starting from the third row:

[0257] (twenty two)

[0258] when The row is replaced by the smallest constant ε, and when an integer row is 0, the row is replaced by the derivative coefficient of the auxiliary polynomial of that order. Read the first element of row k+1 and assemble it to obtain the new... If the original system is stable, then >0, therefore Hurwitz.

[0259] To ensure consistent steady-state gain as s→0, according to:

[0260] (twenty three)

[0261] Perform a one-time gain correction; if necessary, scale the molecules proportionally as a whole. Then test again. Routh condition ( >0), or conversion (taking a reduced second-order system as an example):

[0262] (twenty four)

[0263] in, The natural angular frequency of the equivalent reduced-order system. The damping ratio of the system is given, and compared with the threshold index: , Secondly, the Bode amplitude / phase difference threshold can be compared with Nyquist to determine the required order of reduction for the project.

Claims

1. A method for modeling and order reduction of an islanded microgrid based on direct truncation and Routh approximation, characterized in that, Includes the following steps: 1) Acquire network internal parameter data, control and measurement parameter data, and steady-state operating point data of the isolated microgrid; 2) Preprocess the acquired data to obtain preprocessed data; 3) Divide the isolated microgrid into zones, and based on the preprocessed data, perform small-signal modeling for each zone to obtain the small-signal model for each zone; 4) Construct a candidate order set, select the lowest candidate order from the candidate order set as the initial target order, and assemble the small signal model of each partition to obtain the high-order model of the islanded microgrid; 5) Extract channels from the high-order model of the islanded microgrid, generate the transfer function, and determine the numerator and denominator of the transfer function based on the target order; 6) The numerator of the transfer function is directly truncated, and the denominator of the transfer function is processed by the Routh approximation order reduction method to obtain a low-order model of the islanded microgrid for online small-signal stability determination. 7) Determine whether the low-order model of the islanded microgrid meets the stability and consistency indicators. If yes, the final reduced-order model of the islanded microgrid is obtained. If not, select the next candidate order from the candidate order set from low to high as the target order and return to step 5.

2. The method of claim 1, wherein, The network internal parameter data includes the network topology; The network topology of the isolated microgrid includes a DC terminal, an AC terminal, and an IC terminal. The DC terminal includes a DC-side bus, m converters, m DC-side loads, and m-1 DC-side lines, where m is a positive integer; The DC side line includes a resistor R1 and an inductor L1; The AC terminal includes an AC-side bus, n-1 AC-side lines, n inverters, AC-side load I, and n-1 AC-side load II, where n is a positive integer; The AC side circuit includes a resistor R2 and an inductor L2; The IC terminal includes a bidirectional converter; One end of the AC side busbar is connected to the power grid, and the other end is connected to the bidirectional converter; The AC-side busbar is provided with n AC-side nodes; An AC-side line is provided between two adjacent AC-side nodes; One inverter is connected in parallel to each AC-side node; AC-side load I is connected in parallel to the AC-side node closest to the power grid, and AC-side load II is connected in parallel to the other AC-side nodes. One end of the DC-side busbar is connected to the bidirectional converter; The DC-side busbar is provided with m DC-side nodes; A DC-side line is provided between two adjacent DC-side nodes; One converter and one DC-side load are connected in parallel to each DC-side node; The control and measurement parameter data include power measurement low-pass cutoff frequency, inverter droop, DC / DC droop, and IC synthesis droop. The steady-state operating point data includes the initial values ​​of inverter voltage and current, steady-state operating point of power angle frequency, initial values ​​of converter voltage and current, initial values ​​of line and load current, and IC switching power.

3. The method of claim 1, wherein the method is characterized by: The preprocessing includes dp coordinate synchronization, filtering, and drooping pre-mapping; The data after dp coordinate synchronization is shown below: （1） （2） wherein represents the inverter index; represents the local frequency of the th inverter; represents the defined network frequency; represents time; represents the time variable; represents the frequency difference of the th inverter; represents the power angle of the th inverter at time ; The filtered data is shown below: （3） （4） In the formula, s represents Laplacian operator; , respectively represent active power and reactive power measured instantaneously; represents the cut-off frequency of the measuring low-pass filter; represents filtered active power; represents filtered reactive power; The data after the drooping pre-mapping is shown below: （5） （6） （7） wherein represents the frequency reference value of the AC-side droop loop output; represents the AC-side bus rated frequency; represents the active-power-frequency droop coefficient; represents the steady-state setpoint of the AC-side active power; represents the voltage reference value of the AC-side droop loop output; represents the AC-side bus rated voltage; represents the reactive-power-voltage droop coefficient; represents the steady-state setpoint of the AC-side reactive power; represents the voltage reference value of the DC / DC droop loop output; represents the DC-side bus rated voltage; represents the power-direct-current-voltage droop coefficient; represents the DC-side filtered active power; represents the steady-state setpoint of the DC-side active power; represents the IC-side active power reference value; represents the IC-side steady-state power exchange setpoint; represents the direct-current-voltage-power droop coefficient; represents the DC-side bus actual voltage; represents the DC-side bus actual voltage; represents the frequency-power droop coefficient; represents the AC-side filtered active power; represents the AC-side filtered reactive power.

4. The method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation according to claim 1, characterized in that, The islanded microgrid is divided into AC-side partitions, DC-side partitions, and IC-side partitions.

5. The method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation according to claim 4, characterized in that, The small-signal model of the AC-side partition is shown below: （8） （9） （10） In the formula, The derivative vector of the AC side line current; This represents the AC-side line self-dynamic matrix; This indicates the small-signal deviation of the AC side line current; , These represent the AC-side line voltage-current coupling matrix and the AC-side line frequency interference matrix, respectively. This indicates the small-signal deviation of the AC-side bus voltage; This indicates a small signal deviation in network frequency; The derivative vector of the load current on the AC side; Represents the AC-side load parameter matrix; This indicates the small-signal deviation of the load current on the AC side; , These represent the admittance matrix of the AC-side load to the AC-side bus voltage and the frequency interference matrix of the AC-side load, respectively. This indicates the small-signal deviation of the AC-side bus voltage; This represents the small-signal deviation of the AC-side bus voltage in the dq coordinate system. , These represent the coordinate phase transformation matrix and the phase angle perturbation matrix, respectively. This indicates the small signal deviation of the inverter output voltage; This indicates the small-signal deviation of the AC side power angle; The small-signal model of the DC-side partition is shown below: （11） （12） （13） In the formula, The derivative vector of the DC-side line current; Represents the self-dynamic matrix of a DC line; This indicates the small-signal deviation of the DC-side line current; Represents the voltage and current admittance matrices; This indicates the small-signal deviation of the DC-side line voltage; The derivative vector of the DC-side load current; The differential admittance matrix representing a static resistive load; This indicates the small-signal deviation of the DC-side bus voltage; The derivative vector of the converter output voltage; Represents a self-dynamic matrix; This indicates the small-signal deviation of the converter output voltage; This represents the coupling matrix from the equivalent injected current to the port voltage; This indicates the small-signal deviation of the converter input current; The small-signal model of the IC-side partition is shown below: （14） （15） In the formula, This indicates a small signal deviation in the IC-side communication power. This represents the DC voltage-power droop factor; This indicates the small-signal deviation of the DC terminal voltage; Indicates the frequency-power droop factor; This represents the small-signal deviation of the frequency in a microgrid system. This represents the small-signal deviation of the d-axis component of the AC input current; This represents the steady-state operating value of the AC terminal voltage; This indicates a small signal deviation in communication power; This represents the steady-state operating value of the communication power. This indicates the small-signal deviation of the AC terminal voltage; This represents the small-signal deviation of the q-axis component of the AC input current; This indicates the small signal deviation of the reactive power input at the AC terminal.

6. The method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation according to claim 5, characterized in that, The small signal deviation is as follows: （16） In the formula, Represents the small-signal deviation variable; Indicates the actual measured value; This represents the steady-state operating value.

7. The method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation according to claim 1, characterized in that, The high-order model of the islanded microgrid is shown below: （17） In the formula, The vector representing the derivatives of state variables; , , , These represent the state matrix, input matrix, output matrix, and direct transfer matrix, respectively. Represents the state variable vector of a microgrid system; Represents the input vector; This represents the output vector.

8. The method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation according to claim 1, characterized in that, The transfer function is as follows: （18） In the formula, Represents the transfer function; Represents the Laplace operator; Represents the identity matrix; , , , Representing the state matrix and input matrix respectively The column vector and output matrix corresponding to the selected input. The row vector and direct transfer matrix corresponding to the selected output The element corresponding to the selected input-output; Among them, the numerator of the transfer function denominator As shown below: （19） （20） In the formula, Indicates the order of the objective; This represents the set of coefficients corresponding to the denominator; This represents the set of coefficients corresponding to the molecule.

9. The method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation according to claim 1, characterized in that, In step 6), the steps to obtain the low-order model of the islanded microgrid are as follows: 1) The numerator of the transfer function is processed by the direct truncation reduction method to obtain a lower-order numerator, as shown below: （21） In the formula, Represents the Laplace operator; Indicates lower-order molecules; Indicates the lowest order to retain; Indicates the order of the objective; This represents the set of coefficients retained after molecule truncation. 2) The denominator of the transfer function is processed using the Routh approximation order reduction method, as follows: 2.1) Construct the Routh table based on the denominator of the transfer function, as shown below: （22） In the formula, These represent the rows and columns of the Routh table, respectively. In the Routh table, the first... Line number The elements of the column also correspond to polynomials. The coefficient; This represents the set of coefficients corresponding to the denominator of the transfer function; if the elements , using a preset constant ε as a substitute; if the first If all elements in a row are 0, then start with the first... The elements of the row are used to construct an auxiliary polynomial, and the derivative coefficients of the auxiliary polynomial are used to replace the first polynomial. Row elements; 2.2) Read the first column elements from row h+1-k to row h+1 from the Routh table and assemble them to obtain the reduced-order denominator. As shown below: （23） In the formula, Indicates a reduced order denominator The corresponding set of coefficients; 2.3) Based on the original transfer function, low-order molecules Gain correction is performed to obtain a low-order model of the islanded microgrid; The gain correction is as follows: （24） In the formula, This represents a lower-order molecule after gain correction; Indicates the gain factor; This represents the primitive transfer function for the Laplace operator s=0. , Let represent the numerator and denominator of the original transfer function when the Laplace operator s=0, respectively; This represents the uncorrected low-order model when the Laplace operator s=0. , Let represent the lower-order numerator and the reduced-order denominator when the Laplace operator s=0, respectively.

10. The method for reducing the order of islanded microgrid modeling based on direct truncation and Routh approximation according to claim 9, characterized in that, When the denominator in the low-order model of an islanded microgrid is reduced coefficient If all values ​​are greater than 0, then the low-order model of the islanded microgrid satisfies stability. The consistency metrics include the natural angular frequency and damping ratio of the low-order model, as shown below: （25） In the formula, The natural angular frequency of the low-order model; The damping ratio; Both are reduced-order denominators The coefficient; when and Then the low-order model of the islanded microgrid satisfies consistency, where, Indicates the lower limit of the damping ratio; , These represent the upper and lower limits of the natural angular frequency, respectively.

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