阅读说明：本技术 基于增广节点导纳矩阵的交直流混合配电网谐波分析方法 (Harmonic analysis method for AC/DC hybrid power distribution network based on augmented node admittance matrix ) 是由 程昆 夏杨红 韦巍 于 2021-06-04 设计创作，主要内容包括：本发明提出一种基于增广节点导纳矩阵的交直流混合配电网谐波分析方法,所述方法主要是建立交直流互联变流器的拓扑结构以及控制器的状态方程,整合得到系统的状态方程,从而利用控制理论的输入输出关系得到互联变流器的广义二端口导纳矩阵再在互联变流器的广义二端口网络矩阵的基础上,建立系统各元件适当模型,按照基尔霍夫电压和电流定律联系起母线电压和电流并分别形成直流和交流子系统的节点导纳矩阵,最终形成交直流混合配电网的增广节点导纳矩阵并结合模态分析法进行交直流配电网的电能质量分析。本发明方法能够有效解决交直流互联网络的谐波分析问题并识别出谐波在交直流混合配电网中的具体传递路径。(The invention provides an AC/DC hybrid power distribution network harmonic analysis method based on an augmented node admittance matrix, which mainly comprises the steps of establishing a topological structure of an AC/DC interconnected converter and a state equation of a controller, integrating to obtain a state equation of a system, obtaining a generalized two-port admittance matrix of the interconnected converter by utilizing an input-output relation of a control theory, establishing a proper model of each element of the system on the basis of the generalized two-port network matrix of the interconnected converter, linking bus voltage and current according to kirchhoff voltage and a current law, respectively forming node admittance matrixes of DC and AC subsystems, finally forming the augmented node admittance matrix of the AC/DC hybrid power distribution network, and combining a modal analysis method to carry out electric energy quality analysis on the AC/DC power distribution network. The method can effectively solve the problem of harmonic analysis of the AC-DC interconnected network and identify the specific transmission path of the harmonic in the AC-DC hybrid power distribution network.)

1. A harmonic analysis method of an alternating current-direct current hybrid power distribution network based on an augmented node admittance matrix is characterized by comprising the following steps:

under a two-phase static coordinate system, a proportional resonant controller is adopted to control an interconnected converter in an AC/DC hybrid power distribution network, state equations of the interconnected converter and the proportional resonant controller are respectively established, a general state equation is finally obtained through integration, then a generalized two-port admittance matrix of the interconnected converter is obtained through the input-output relation of a control theory, and the generalized two-port admittance matrix is converted into a three-phase coordinate system:

wherein Δ i_ac,BPCRepresenting filter inductance L at alternating current side of interconnected converter under three-phase coordinate system_fSmall signal of current above, Δ i_dc,BPCRepresenting the small signal of the direct-current side current, Deltav, in a three-phase coordinate system_ac,BPCRepresenting the small signal, Deltav, of the AC side voltage in a three-phase coordinate system_dc,BPCAnd the direct-current side voltage small signal under a three-phase coordinate system is shown.

y_ijAnd expressing corresponding equivalent admittance in the generalized two-port model of the interconnected converter, and obtaining the equivalent admittance through a transfer function matrix of a total state equation solving system.

Respectively establishing node admittance matrixes of the direct-current power distribution network and the alternating-current power distribution network, and combining the generalized two-port admittance matrixes of the interconnected converters converted to the three-phase coordinate system to form an augmented node admittance matrix of the alternating-current and direct-current hybrid power distribution network:

wherein Y is_acNode admittance matrix, Y, representing an AC subnetwork_dcA node admittance matrix representing the dc sub-network. Δ i_ac,kDenotes the kthSmall current signal, Δ i, of individual AC subnetwork nodes_dc,kIndicating a small current signal, Δ v, at the kth DC-subnetwork node_ac,kVoltage small signal, Δ i, representing the kth ac subnetwork node_dc,kAnd the voltage small signal of the kth direct current sub-network node is represented, and n and m are the number of the nodes of the alternating current sub-network and the direct current sub-network respectively.

And carrying out harmonic analysis by using the augmentation node admittance matrix of the AC/DC hybrid power distribution network.

2. The method for analyzing the harmonic waves of the alternating-current and direct-current hybrid power distribution network based on the augmented node admittance matrix according to claim 1, wherein the input and output quantities of the general state equation are specifically as follows:

Δx＝[Δx_1αβ,Δx_2αβ,Δω,Δi_ac,αβ,Δv_oαβ,Δi_oαβ]^T

Δu＝[Δv_pccαβ,Δv_dc,αβ]^T

wherein, Δ x_1αβ,Δx_2αβRepresenting the intermediate state variables of the proportional resonant controller. Δ v_dc,αβIndicating a dc side voltage small signal. Δ i_ac,αβRepresenting the filter inductance L at the AC side of the interconnected converters_fSmall signal of current above, Δ v_oαβIndicating a small signal of the AC side capacitor voltage, Δ i_oαβIndicating a small signal of the current in the inductor on the side of the interconnected converters near the grid, Deltav_pccαβRepresenting a grid-connected voltage small signal.

3. The method for harmonic analysis of the alternating current-direct current hybrid power distribution network based on the augmented node admittance matrix according to claim 1, wherein the harmonic analysis using the augmented node admittance matrix of the alternating current-direct current hybrid power distribution network specifically comprises:

and decomposing the characteristic value of the augmented node admittance matrix by combining a modal analysis method to obtain a characteristic value diagonal matrix and left and right characteristic vectors, determining the frequency and the nodes of resonance, and determining the influence of different nodes of the alternating-current and direct-current hybrid power distribution network on a certain resonance mode by taking the product of the left and right characteristic vector values corresponding to the certain resonance mode as a resonance participation factor so as to complete the critical harmonic frequency judgment and the harmonic transmission path analysis in the hybrid power distribution network.

Technical Field

The invention relates to an AC/DC hybrid power distribution network harmonic analysis method based on an augmented node admittance matrix, and belongs to the electric energy quality analysis technology in the field of renewable new energy.

Background

The power distribution network is divided into a direct current power distribution network and an alternating current power distribution network, at present, main power generation still comes from alternating current generated by a power plant, most of loads are alternating current loads, meanwhile, with continuous introduction of power electronic equipment, direct current loads are increased day by day, energy loss of direct current power transmission relative to alternating current power transmission is low, the stability problem of alternating current power transmission can not occur, therefore, alternating current and direct current are in a state of coexisting in synchronous development, and the research on the alternating current and direct current hybrid power distribution network also has great practical significance.

On the other hand, harmonic waves generated by unstable natural characteristics of new energy easily cause power switching tubes such as IGBTs in the distributed power supply to be affected by the harmonic waves and cannot work normally. Harmonic resonance can also cause overvoltage of a capacitor, and harmonic waves in an alternating current bus can enable a direct current bus to generate corresponding harmonic voltage, so that the harmonic waves are transmitted to a direct current side from an alternating current side, and the safe and stable operation of a direct current power distribution network is influenced. Therefore, the research on the harmonic problem in the background of the alternating current-direct current hybrid micro-grid has important theoretical research value for the development of modern power production and power technology.

The existing harmonic problem is that a node admittance matrix is established in a pure alternating current power distribution network and a pure direct current power distribution network, further analysis is carried out by utilizing a modal analysis method based on characteristic value decomposition, and contribution of each node participation factor of a resonance mode to resonance is quantitatively analyzed by calculating the node participation factors. However, due to the existence of an alternating current and direct current heterogeneous network in the alternating current and direct current hybrid power distribution network, the original node admittance modeling method is only suitable for a pure direct current or pure alternating current power network, and an augmented node admittance matrix of the alternating current and direct current hybrid power distribution network cannot be directly established, so that the establishment of a compatible alternating current and direct current sub-network augmented node admittance matrix is very critical for the electric energy quality analysis and broadening application to the alternating current and direct current hybrid power distribution network.

The method mainly comprises the steps of establishing a topological structure of an alternating current-direct current interconnected converter and a state equation of a controller, integrating to obtain a state equation of a system, and obtaining an equivalent two-port network matrix of the interconnected converter by utilizing an input-output relation of a control theory. On the basis of establishing a proper model of each element of the system, the bus voltage and the bus current can be connected according to the kirchhoff voltage and current law, the self-admittance and the mutual admittance of the alternating current and direct current system are obtained, and an augmented node admittance matrix of the alternating current and direct current hybrid power distribution network is formed and further modal analysis is carried out by combining a two-port network matrix of the interconnected converters.

The method can effectively expand the application of the augmentation node admittance matrix for constructing the AC/DC hybrid power distribution network to the AC/DC hybrid network. The method for constructing the augmented node admittance matrix is characterized in that a generalized two-port admittance model of an interconnected converter is formed, the augmented node admittance matrix of the whole hybrid power distribution network is deduced by combining a direct current sub-network admittance matrix and an alternating current sub-network admittance matrix, and harmonic analysis is further carried out by combining a modal analysis method.

Disclosure of Invention

The invention aims to provide an AC/DC hybrid power distribution network harmonic analysis method based on an augmented node admittance matrix, which mainly comprises the steps of establishing a topological structure of an AC/DC interconnected converter and a state equation of a controller, integrating to obtain a state equation of a system, and obtaining an equivalent two-port network matrix of the interconnected converter by utilizing an input-output relation of a control theory. On the basis of establishing a proper model of each element of the system, the bus voltage and the bus current can be connected according to the kirchhoff voltage and current law, the self-admittance and the mutual admittance of the alternating current and direct current system are obtained, and an augmented node admittance matrix of the alternating current and direct current hybrid power distribution network is formed and further modal analysis is carried out by combining a two-port network matrix of the interconnected converters. The method can effectively expand the application of the unified node admittance matrix for constructing the alternating current and direct current hybrid power distribution network to the alternating current and direct current hybrid network. The method for constructing the augmented node admittance matrix is characterized in that a generalized two-port admittance model of an interconnected converter is formed, the augmented node admittance matrix of the whole hybrid power distribution network is derived from the direct current sub-network admittance matrix and the alternating current sub-network admittance matrix, and harmonic analysis is further carried out by combining a modal analysis method.

The specific scheme is as follows:

an AC-DC hybrid power distribution network harmonic wave analysis method based on an augmented node admittance matrix specifically comprises the following steps:

under a two-phase static coordinate system, a proportional resonant controller is adopted to control an interconnected converter in an AC/DC hybrid power distribution network, state equations of the interconnected converter and the proportional resonant controller are respectively established, a general state equation is finally obtained through integration, then a generalized two-port admittance matrix of the interconnected converter is obtained through the input-output relation of a control theory, and the generalized two-port admittance matrix is converted into a three-phase coordinate system:

wherein Δ i_ac,BPCRepresenting filter inductance L at alternating current side of interconnected converter under three-phase coordinate system_fSmall signal of current above, Δ i_dc,BPCRepresenting the small signal of the direct-current side current, Deltav, in a three-phase coordinate system_ac,BPCRepresenting the small signal, Deltav, of the AC side voltage in a three-phase coordinate system_dc,BPCAnd the direct-current side voltage small signal under a three-phase coordinate system is shown.

y_ijAnd expressing corresponding equivalent admittance in the generalized two-port model of the interconnected converter, and obtaining the equivalent admittance through a transfer function matrix of a total state equation solving system.

Respectively establishing node admittance matrixes of the direct-current power distribution network and the alternating-current power distribution network, and combining the generalized two-port admittance matrixes of the interconnected converters converted to the three-phase coordinate system to form an augmented node admittance matrix of the alternating-current and direct-current hybrid power distribution network:

wherein Y is_acNode admittance matrix, Y, representing an AC subnetwork_dcA node admittance matrix representing the dc sub-network. Δ i_ac,kIs shown asSmall current signals, Δ i, of k nodes of the AC subnetwork_dc,kIndicating a small current signal, Δ v, at the kth DC-subnetwork node_ac,kVoltage small signal, Δ i, representing the kth ac subnetwork node_dc,kAnd the voltage small signal of the kth direct current sub-network node is represented, and n and m are the number of the nodes of the alternating current sub-network and the direct current sub-network respectively.

And carrying out harmonic analysis by using the augmentation node admittance matrix of the AC/DC hybrid power distribution network.

Further, the input and output quantities of the general state equation are specifically:

Δx＝[Δx_1αβ,Δx_2αβ,Δω,Δi_ac,αβ,Δv_oαβ,Δi_oαβ]^T

Δu＝[Δv_pccαβ,Δv_dc,αβ]^T

wherein, Δ x_1αβ,Δx_2αβRepresenting the intermediate state variables of the proportional resonant controller. Δ v_dc,αβIndicating a dc side voltage small signal. Δ i_ac,αβRepresenting the filter inductance L at the AC side of the interconnected converters_fSmall signal of current above, Δ v_oαβIndicating a small signal of the AC side capacitor voltage, Δ i_oαβIndicating a small signal of the current in the inductor on the side of the interconnected converters near the grid, Deltav_pccαβRepresenting a grid-connected voltage small signal.

Further, the harmonic analysis by using the augmented node admittance matrix of the alternating current-direct current hybrid power distribution network specifically comprises:

and decomposing the characteristic value of the augmented node admittance matrix by combining a modal analysis method to obtain a characteristic value diagonal matrix and left and right characteristic vectors, determining the frequency and the nodes of resonance, and determining the influence of different nodes of the alternating-current and direct-current hybrid power distribution network on a certain resonance mode by taking the product of the left and right characteristic vector values corresponding to the certain resonance mode as a resonance participation factor so as to complete the critical harmonic frequency judgment and the harmonic transmission path analysis in the hybrid power distribution network.

The invention has the advantages that:

(1) the method unifies the alternating current-direct current heterogeneous network on the node admittance level.

(2) The method can effectively solve the problem of harmonic analysis of the AC-DC interconnected network and identify the specific transmission path of the harmonic in the AC-DC hybrid power distribution network.

Drawings

Fig. 1 is a schematic diagram of an augmented node admittance matrix of an interconnected converter generalized two-port model and system of an alternating-current/direct-current hybrid power distribution network: the method comprises the following steps that a is a topological structure of the AC/DC hybrid power distribution network, b is a corresponding equivalent admittance in a generalized two-port model of the interconnected converters, and c is an augmented node admittance matrix of the AC/DC hybrid power distribution network.

FIG. 2 is a model of an AC/DC hybrid power distribution network including 11 nodes;

FIG. 3 is a graph of modal impedance versus frequency illustrating the output modal analysis;

fig. 4 a, b, c, d are waveforms and spectrum analysis of node 7 when 635Hz harmonic current is injected into nodes 4, 5, 8, 9, respectively.

Detailed Description

The method is described in further detail below with reference to the accompanying drawings:

fig. 1(a) is a topological structure of an ac/dc hybrid power distribution network, a dc side includes a dc distributed power source such as a photovoltaic power source, an energy storage device and a dc load, which are connected to a dc bus through a converter, an ac side includes a distributed power source such as a fan, an energy storage device and an ac load, which are connected to an ac bus through a converter, the dc bus is connected to the ac bus through an ac/dc interconnection converter, first, a state equation modeling is performed on the interconnection converter topological structure and a controller, a three-phase stationary coordinate system is converted to an α, β two-phase stationary coordinate system through Clark conversion, PR control is performed, and calculation of a constant matrix is correspondingly formed, so that a time variable calculation problem caused by Park conversion is avoided, and further calculation is facilitated. Clark transformation is carried out to a two-phase stationary coordinate system, and small signal analysis and integration are carried out as shown in (5).

Wherein, Δ i_ac,αβRepresenting the filter inductance L at the AC side of the interconnected converters_fSmall signal of current above, Δ v_oαβIndicating a small signal of the AC side capacitor voltage, Δ i_oαβIndicating a small signal of the current in the inductor on the side of the interconnected converters near the grid, Deltav_pccαβRepresents a small signal of the voltage of the grid-connected (AC bus), the upper point represents the derivation quantity, and

wherein, C_fRepresenting the AC-side capacitance, L, of the interconnected converters_fRepresenting the filter inductance, L, on the AC side of the interconnected converters_gRepresenting the interconnected converters near the grid side inductance. O denotes a zero matrix.

Matrix forming Proportional Resonant (PR) controllerThe equation of state of (1) is modeled as (6).

Wherein x₁，x₂Representing the intermediate state variables of the controller, omega representing the angular frequency, z, x representing the controller output and input quantities. K_pIs the proportionality coefficient of a proportional resonant controller, K_RAnd s is a pull operator, and is the resonance coefficient of the proportional controller.

Combining a state equation formed by a topological structure of the converter and a controller, wherein the input and output quantities of the total state equation are as follows:

Δx＝[Δx_1αβ,Δx_2αβ,Δω,Δi_ac,αβ,Δv_oαβ,Δi_oαβ]^T

Δu＝[Δv_pccαβ,Δv_dc,αβ]^T

wherein, Δ x_1αβ,Δx_2αβRepresenting intermediate state variables in the alpha, beta two-phase stationary frame introduced by the PR controller. Δ v_dc,αβIndicating a dc side voltage small signal.

In order to construct a two-port network model of the interconnected converters so as to obtain equivalent node admittance, define new input quantity and output quantity by user,

Δy＝[Δi_ac,BPC,αβ,Δi_dc,BPC,αβ]

Δu*＝[Δv_ac,BPC,αβ,Δv_dc,BPC,αβ]

wherein the subscript BPC indicates the direct AC/DC power converter (bi) connected to the interconnected inverter, Δ i_ac,BPC,αβRepresenting the filter inductance L at the AC side of the interconnected converters_fSmall signal of current above, Δ i_dc,BPC,αβIndicating a small signal of the DC side current, Δ v_ac,BPC,αβIndicating a small signal, Δ v, on the AC side_dc,BPC,αβAnd the voltage small signal of the direct current side is represented, and the delta u represents the voltage small signal of the alternating current side and the direct current side of the interconnected converter, and is an output quantity introduced for constructing an amplification node admittance matrix.

And (7) arranging and converting the input and output relations of the control theory into a three-phase coordinate system.

y_ijAnd representing corresponding equivalent admittance in the generalized two-port model of the interconnected converter, wherein the equivalent admittance is obtained by solving a transfer function matrix of a system for the general state equation, and ij is a position index in the transfer function matrix. Δ i_ac,BPCRepresenting filter inductance L at alternating current side of interconnected converter under three-phase coordinate system_fSmall signal of current above, Δ i_dc,BPCRepresenting the small signal of the direct-current side current, Deltav, in a three-phase coordinate system_ac,BPCRepresenting the small signal, Deltav, of the AC side voltage in a three-phase coordinate system_dc,BPCAnd the direct-current side voltage small signal under a three-phase coordinate system is shown.

And combining the node admittance matrixes of the direct current sub-network and the alternating current sub-network system to form an augmented node admittance matrix (8) of the alternating current and direct current hybrid power distribution network.

Wherein Y represents the corresponding equivalent admittance in the generalized two-port model of the interconnected converter, Y_acNode admittance matrix, Y, representing an AC subnetwork_dcA node admittance matrix representing the dc sub-network. Δ i_ac,kIndicating a small current signal, Δ i, at the kth AC subnetwork node_dc,kIndicating a small current signal, Δ v, at the kth DC-subnetwork node_ac,kVoltage small signal, Δ i, representing the kth ac subnetwork node_dc,kAnd the voltage small signal of the kth direct current sub-network node is represented, and n and m are the number of the nodes of the alternating current sub-network and the direct current sub-network respectively.

And then carrying out harmonic analysis on the formed AC/DC distribution network by combining a modal analysis method. And then, taking the product l x t of the left and right characteristic vector values corresponding to a certain resonance mode as a resonance participation factor, wherein l represents the corresponding left characteristic vector, and t represents the corresponding right characteristic vector, namely determining the influence of different nodes of the system on the certain resonance mode so as to finish the critical harmonic frequency judgment and the harmonic transmission path analysis in the hybrid power distribution network.

The invention is further illustrated below with reference to a specific embodiment:

fig. 2 is an ac/dc distribution network system structure including 11 nodes, the system is composed of 6 dc side nodes and 5 ac side nodes, and the specific parameter values of the line are shown in table 1.

TABLE 1 line specific parameter values

And (3) carrying out eigenvalue decomposition on the augmented node admittance matrix Y, wherein Y is LDT to obtain an eigenvalue diagonal matrix and left and right eigenvectors, thereby determining the frequency and the nodes of the resonance, as shown in Table 2.

TABLE 2 Key resonant frequencies, eigenvalues, and Key nodes obtained from analysis of the node admittance matrix

The mode of resonance of the ac/dc hybrid power distribution network system can be observed in fig. 3, and the degree of resonance of the nodes 6, 7, 8, and 9 is significant, which means that the four nodes in the hybrid power distribution network are easily excited to generate observed harmonic resonance, wherein the key resonance frequencies of the different nodes can be obtained from table 2. The node participation factors in the four key modes listed in table 3 correspond to the phenomenon that corresponding key frequency subharmonics are injected into different nodes in fig. 4, and it can be deduced that the main propagation paths of the frequency subharmonics in the hybrid power distribution network are from node 5 to node 7, and on the basis, the positions and parameters of the active filters can be reasonably configured so as to suppress system harmonics. The analysis result of the graph shows that the establishment of the augmented node admittance matrix is beneficial to the harmonic analysis in the alternating current-direct current hybrid power distribution network.

TABLE 3 Key resonance node engagement factors for four Key modes

It should be understood that the above examples are only for clarity of illustration and are not intended to limit the embodiments. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. This need not be, nor should all embodiments be exhaustive. And obvious variations or modifications of the invention may be made without departing from the scope of the invention.