Method for constructing unified power flow model of AC / DC hybrid distribution network

Abstract

A method for constructing a unified power flow model of an AC-DC hybrid distribution network belongs to the technical field of AC-DC hybrid distribution networks. The purpose of the present invention is an important prerequisite and basis for the steady-state operation analysis of the AC-DC hybrid distribution network, the design of corresponding operation modes and control methods, as well as the configuration and setting of relevant relay protection devices. It is a method for constructing a unified power flow model of an AC-DC hybrid distribution network that can converge quickly and stably for AC-DC hybrid distribution networks with different control strategies and different topological structures. The process of the present invention is as follows: a steady-state model of a power electronic converter, a unified power flow model of an AC-DC hybrid distribution network based on a node-branch matrix, power flow calculation of the AC-DC distribution network, determining whether the power constraint is satisfied. If not, the data is updated and recalculated. If satisfied, the program ends. The unified power flow model of the AC-DC hybrid distribution network of the present invention has a fast calculation speed, high calculation efficiency, strong applicability, and good application effect.

Description

Technical Field

[0001] The present invention belongs to the technical field of AC-DC hybrid distribution networks. Background Art

[0002] In recent years, with the rapid development of the economic society, the urban scale has been continuously expanding, the electricity load has been increasing year by year, and users' requirements for power supply reliability and power supply quality have been continuously improving. Under the background of "dual carbon", the grid connection penetration rate of renewable energy has been continuously increasing, and new loads such as electric vehicles have been continuously connected to the distribution network. The existing AC distribution network faces problems such as insufficient power supply capacity, line saturation, and multiple power conversion links. At the same time, due to the open-loop operation limitation of the traditional AC distribution network, it is impossible to quickly track and respond to the output of distributed renewable energy and the changes of new loads, nor can it continuously and accurately adjust the power flow, making the deviation of system voltage and equipment load rate become an increasingly prominent problem in the operation and management of the distribution network, bringing many challenges to the optimal configuration, operation control, power quality, safety, and stability of the distribution network. With the rapid development of power electronic conversion technology, DC networking technology has rapidly emerged, effectively streamlining the power conversion links for distributed renewable energy generation and new load access to the distribution network, improving the controllability, flexibility, and stability of the distribution network containing distributed power sources, electric vehicles, etc., as well as the power supply quality and reliability of the system, and thus becoming an important direction for the development of urban distribution networks.

[0003] Power flow calculation of the power system is an important means to calculate the node voltages, phase angles, and line power distributions in the power system according to the parameters of each component and the network structure given in the system, and is the basis for work such as power system operation analysis, planning, reliability assessment, optimal dispatching, and protection configuration. Existing models and methods for power flow calculation of AC-DC hybrid distribution networks have limited adaptability to the network topology structure and cannot fully adapt to urban AC-DC hybrid distribution networks with certain characteristic topologies in different application scenarios. Summary of the Invention

[0004] The purpose of the present invention is a crucial prerequisite and foundation for the steady-state operation analysis of AC-DC hybrid distribution networks, the design of corresponding operation modes and control methods, as well as the configuration and setting of relevant relay protection devices, and a method for constructing a unified power flow model of AC-DC hybrid distribution networks that can converge quickly and stably for AC-DC hybrid distribution networks with different control strategies and different topological structures.

[0005] The process of the present invention is as follows:

[0006] S1. Establish a steady-state model of the power electronic converter

[0007] S1.1. Establish a steady-state model of the VSC converter

[0008] According to the PWM principle, the relationship between the AC-side voltage and the DC-side voltage is:

[0009]

[0010] Where: μ represents the DC voltage utilization rate, and M is the pulse width modulation ratio. Then the relationship between the AC voltage reference value and the DC voltage reference value is:

[0011]

[0012] Combining Equation (1) and Equation (2) can obtain the following relationship:

[0013] V n = MV k (3)

[0014] Where: η c is the converter efficiency. Then the power relationship on both sides of the converter is:

[0015] P nk = P d / η c (4)

[0016] Under master-slave control, the reactive power on the AC side of the VSC is determined by the power factor angle of the converter:

[0017]

[0018] During droop control, when the VSC is in the inverter state, the reactive power is expressed as:

[0019] Q nk = (V max - V n ) / λ (6)

[0020] λ = (V max - V min ) / Q max (7)

[0021] Where: V max represents the upper limit of the converter voltage, V min represents the lower limit of the voltage, λ represents the reactive power droop gain of the converter, and Q max represents the upper limit of the reactive power supported by the converter;

[0022] S1.2. Establish the steady-state model of the DC / DC converter

[0023] Find the nodes 1, 2, 3, 4,..., h connected to the m node, and obtain the branch power using the voltage of the kth iteration as follows:

[0024] Where: R mx represents the branch resistance; PM Denote the load carried by the m node;

[0025] The currents flowing through the n and m branches are expressed as:

[0026]

[0027] Combined with the voltage at the m point and the parameters of the DC / DC converter, the duty cycle and equivalent parameters of the converter at the (k + 1)-th iteration are obtained.

[0028] (1) Duty cycle

[0029] Buck-type DC / DC converter:

[0030]

[0031] Buck-Boost-type DC / DC converter:

[0032]

[0033] (2) Transformer parameters:

[0034] Buck-type DC / DC converter:

[0035]

[0036] Buck-Boost-type DC / DC converter:

[0037]

[0038] Where: N is the number of sub-modules in the converter model; D is the duty cycle; U D , R D are respectively the forward conduction voltage drop and conduction resistance of the diode; R L is the inductance resistance of the inductor coil; R S is the conduction resistance of the MOSFET; M(D) is the turns ratio of the converter model; R E is the sum of the equivalent resistances in the converter circuit; U E is the voltage drop in the equivalent circuit;

[0039] The admittance of the π-type equivalent branch of the DC / DC converter is expressed as:

[0040]

[0041] Considering the line resistance of the transformer branch and through the star-delta transformation, it can finally be equivalent to a π-type branch, and the admittances of the three branches are:

[0042] Since there is U on the transformer branch EThe voltage drop, so the branch injection current needs to be corrected accordingly, I n 、I m are the node injection currents before and after correction:

[0043]

[0044] S2. Establish a unified power flow model for AC-DC hybrid distribution network based on node-branch matrix

[0045] S2.1 Establish a binary node-branch matrix

[0046] (1) Node type matrix W:

[0047]

[0048] (2) Branch connection matrix H:

[0049]

[0050] (3) Connection line type matrix J:

[0051]

[0052] (4) Judgment matrix T:

[0053]

[0054] (5) Direction matrix L:

[0055]

[0056] In Equation (22): The modeling direction of the DC / DC transformer is related to the position of the line resistance connected to it. The head end of the DC / DC transformer modeling is the side connected to the line resistance;

[0057] S2.2. Establish the branch power flow equations for AC-DC hybrid distribution network

[0058] The branch structure of the AC-DC hybrid distribution network is divided into 9 scenarios:

[0059] (1) Scenario 1: Two AC nodes are connected by an AC line, and its branch power flow equation is:

[0060]

[0061] The binary node-branch matrix form is as follows:

[0062]

[0063] (2) Scenario 2: Two DC nodes are connected by a DC line, and its branch power flow equation is:

[0064]

[0065] The binary node-branch matrix form is as follows:

[0066]

[0067] (3) Scenario 3: The AC node is connected to the DC node via a DC line through a VSC, and its branch power flow equation is:

[0068]

[0069] The binary node-branch matrix form is as follows:

[0070]

[0071] Where: a1 and b1 respectively represent whether the converter is in the rectification state or the inversion state, and the expressions of a1 and b1 are as follows:

[0072]

[0073] (4) Scenario 4: The DC node is connected to the AC node via a DC line through a VSC, and its branch power flow equation is:

[0074]

[0075] The binary node-branch matrix form is as follows:

[0076]

[0077] (5) Scenario 5: The AC node is connected to the DC node via an AC line through a VSC, and its branch power flow equation is:

[0078]

[0079] The binary node-branch matrix form is as follows:

[0080]

[0081] (6) Scenario 6: The DC node is connected to the AC node via an AC line through a VSC, and its branch power flow equation is:

[0082]

[0083] The binary node-branch matrix form is as follows:

[0084]

[0085] (7) Scenario 7: Two AC nodes are connected by a DC line through two VSCs. The branch power flow equation is as follows:

[0086]

[0087] The binary node-branch matrix form is as follows:

[0088]

[0089] Where: a2 and b2 represent whether the converter is in the rectification state or the inversion state. The expressions for a2 and b2 are as follows:

[0090]

[0091] (8) Scenario 8: Two DC nodes with different voltage levels are connected by a DC line through a DC / DC. When the injection power direction is the same as the DC / DC transformer modeling direction, the branch power flow equation is as follows:

[0092] P nm = V n (V n G'2+(V n - V m )G'1) (39)

[0093] The binary node-branch matrix form is as follows:

[0094]

[0095] (9) Scenario 9: Two DC nodes with different voltage levels are connected by a DC line through a DC / DC. When the injection power direction is opposite to the DC / DC transformer modeling direction, the branch power flow equation is as follows:

[0096] P nm = V n (V n G'3+(V n - V m )G'1) (41)

[0097] The binary node-branch matrix form is as follows:

[0098]

[0099] S3. AC-DC distribution network power flow calculation

[0100] S3.1. Establish the objective function. The objective function is that the voltage correction amount should satisfy being less than the set accuracy:

[0101]

[0102] Where: ΔV and Δθ respectively represent the correction amount of the voltage amplitude and the correction amount of the voltage phase angle plus; ||·|| ∞ represents the infinity norm, that is, the maximum value of the absolute value of the voltage correction amount; epilson represents the convergence accuracy;

[0103] S3.2. Establish constraint conditions

[0104] (1) Integer constraint of matrix binary variables:

[0105]

[0106] (2) Branch power balance constraint:

[0107]

[0108] For the constant active power control node with a transformer branch, the active power imbalance needs to add the following formula:

[0109] ΔP = P g -UI (46)

[0110] In formulas (45) and (46): nb represents the total number of nodes in the system; represents the active power injected by the node; represents the calculated active power injected by the node; represents the reactive power injected by the node; represents the calculated reactive power injected by the node; P g represents the active power value of the constant active power control node;

[0111]

[0112] In the formula: represents the active power of the AC node power source; represents the active power of the AC node load; represents the active power of the DC node power source; represents the active power of the DC node load; represents the reactive power of the AC node power source; represents the reactive power of the AC node load;

[0113] S3.3. Establish the Jacobian matrix and correction equation

[0114] (1) Master-slave control

[0115] The state space equation of the system under the master-slave control mode is expressed as:

[0116]

[0117] (2) Droop control

[0118] Constrain its power

[0119]

[0120] Wherein: Represents the active power droop gain of the DC power supply; Represents the active power droop gain of the AC power supply; Represents the reactive power droop gain of the AC power supply; V max Represents the maximum voltage; f max Represents the maximum frequency;

[0121] Normalization processing is required for the active power constraint of the AC power supply:

[0122] f = V (50)

[0123] Wherein:

[0124]

[0125] During droop control, the positions of the active power imbalance, reactive power imbalance in the active power of the DC power supply, active power of the AC power supply, reactive power of the AC power supply, and reactive power of the VSC inverter side are modified according to Equations (6), (49) and (50). Different from the master-slave control, droop control requires setting a voltage phase angle reference node, and the voltage phase angle and its corresponding reactive power are 0;

[0126] S3.4 Construct the algorithm flow

[0127] (1) Input network parameters and control types;

[0128] (2) Set the initial voltage value and specify the positive direction of the DC / DC converter;

[0129] (3) Form the nodal admittance matrix of the network from the line parameters and the parameters of the converter;

[0130] (4) Calculate the line transmission power and power imbalance respectively by combining the AC-DC power flow calculation model and the power imbalance equation; (5) Classify the node types and calculate each element of the Jacobian matrix to form the Jacobian matrix;

[0131] (6) If it is master-slave control, find the voltage correction amount from the correction equation to correct the voltage; if it is droop control, correspondingly modify the active power of the AC power supply, reactive power of the AC power supply, active power of the DC power supply and the reactive power injected during VSC inversion, and the corresponding elements of the Jacobian matrix, and find the correction amount from the correction equation to correct the voltage;

[0132] (7) If the correction amount meets the iteration accuracy, proceed to the next judgment; if it does not meet the accuracy requirement, the next iteration is required until the voltage correction amount meets the accuracy requirement.

[0133] (8) Judge whether the power constraint is met. If not, update the data and recalculate. If it is met, the program ends.

[0134] The unified power flow model of the AC-DC hybrid distribution network of the present invention has fast calculation speed, high calculation efficiency, strong applicability, and good application effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0135] Figure 1 is the steady-state model of the VSC converter;

[0136] Figure 2 is the DC-DC equivalent model;

[0137] Figure 3 is the possible connection mode in the AC-DC network;

[0138] Figure 4 is the algorithm flow chart;

[0139] Figure 5 is the schematic diagram of the topological structure of Example 1 in the embodiments;

[0140] Figure 6 is the schematic diagram of the topological structure of Example 2 in the embodiments. DETAILED DESCRIPTION OF THE INVENTION

[0141] The following will Figures 1 to 6 further elaborate on the present invention

[0142] 1 Steady-state model of power electronic converters

[0143] 1.1 Steady-state model of VSC converter

[0144] The voltage source converter (VSC) is a key link connecting the AC-DC hybrid power distribution system. The VSC can reverse the power flow by changing the current direction and can independently control the active and reactive power quickly. The steady-state model of the VSC is as Figure 1 shown.

[0145] Figure 1 In it, V PCC represents the voltage at the point of common coupling (PCC); Z c is the equivalent converter impedance, including the impedance of the components connected between the point of common coupling and the AC node; V n represents the voltage of the nth node; V k represents the voltage of the kth node; P nk and Qnk Indicates the active and reactive power flowing from the AC node to the DC node.

[0146] The steady-state equations of the VSC can be described by Equations (1)-(7). According to the PWM principle, the relationship between the AC-side voltage and the DC-side voltage is as follows:

[0147]

[0148] Where: μ represents the DC voltage utilization rate. In this invention, sinusoidal pulse-width modulation is adopted, and the value of μ is M is the pulse-width modulation ratio.

[0149] Then the relationship between the AC voltage reference value and the DC voltage reference value is as shown in the equation:

[0150]

[0151] Combining Equation (1) and Equation (2) can obtain the following relationship:

[0152] V n = MV k (3)

[0153] Where: η c is the converter efficiency.

[0154] Then the power relationship on both sides of the converter is:

[0155] P nk = P d / η c (4)

[0156] Under master-slave control, the reactive power on the AC side of the VSC can be determined by the power factor angle of the converter :

[0157] During droop control, when the VSC is in the inverter state, the reactive power is proportionally shared through the droop gain. Then the reactive power can be expressed as:

[0158] Q nk = (V max - V n ) / λ (6)

[0159] λ = (V max - V min ) / Q max (7)

[0160] Where: V max represents the upper limit of the converter voltage, V min represents the lower limit of the voltage, λ represents the reactive droop gain of the converter, Qmax Indicates the upper limit of reactive power supported by the converter.

[0161] 1.2 Steady-state model of DC / DC converter

[0162] For the treatment of the DC / DC converter branch, it is similar to the treatment of a two-winding transformer in an AC distribution network, and a π-type equivalent circuit model can be established as Figure 2 shown.

[0163] In the present invention, the DC / DC converters take Buck and Buck-Boost type transformers as examples. The DC / DC converter can be divided into two types according to the control method: non-voltage regulation and voltage regulation. When the converter is under non-voltage regulation control, the duty cycle D is constant, and the nodal admittance matrix can be directly established to solve the network power flow; when the converter is under voltage regulation control, the output voltage is constant, the duty cycle D is a variable value, and the parameters of the converter also change accordingly.

[0164] Taking the n and m branches as examples, find the other nodes 1, 2, 3, 4,..., h connected to the m node, and use the voltage of the k-th iteration to obtain the branch power as follows:

[0165]

[0166] In the formula: R mx represents the branch resistance; P M represents the load carried by the m node.

[0167] The current flowing through the n and m branches can be expressed as:

[0168]

[0169] Combined with the voltage at the m point and the parameters of the DC / DC converter, the duty cycle and equivalent parameters of the converter for the (k + 1)-th iteration are obtained as follows:

[0170] (1) Duty cycle

[0171] Buck type DC / DC converter:

[0172]

[0173] Buck-Boost type DC / DC converter:

[0174]

[0175] (2) Transformer parameters:

[0176] Buck type DC / DC converter:

[0177]

[0178] Buck - Boost DC / DC Converter:

[0179]

[0180] Where: N is the number of sub - modules in the converter model; D is the duty cycle; U D , R D are the forward conduction voltage drop and conduction resistance of the diode respectively; R L is the inductance resistance of the inductor coil; R S is the conduction resistance of the MOSFET; M(D) is the turns ratio of the converter model; R E is the sum of the equivalent resistances in the converter circuit; U E is the voltage drop in the equivalent circuit.

[0181] The admittance of the π - type equivalent branch of the DC / DC converter can be expressed as:

[0182]

[0183] Considering the star - delta transformation of the line resistance of the transformer branch, it can ultimately be equivalent to a π - type branch, and the admittances of the three branches are calculated as follows:

[0184]

[0185] Due to the voltage drop of U E on the transformer branch, the injected current into its branch needs to be corrected accordingly. I n , I m are the node injected currents before and after correction:

[0186]

[0187] 2 Unified Power Flow Model of AC - DC Hybrid Distribution Network Based on Node - Branch Matrix

[0188] 2.1 Establishing Binary Node - Branch Matrix

[0189] To uniformly describe the grid structure of the AC - DC hybrid distribution network, a binary node - branch matrix is established:

[0190] (1) Node type matrix W:

[0191]

[0192] (2) Branch connection matrix U:

[0193]

[0194] (3) Connection line type matrix J:

[0195]

[0196] (4) Judgment matrix T:

[0197]

[0198] (5) Direction matrix L:

[0199]

[0200] In formula (22): The modeling direction of the DC / DC transformer is related to the position of the line resistance connected to it. The head end of the DC / DC transformer modeling is the side connected to the line resistance.

[0201] 2.2 Establishment of branch power flow equations for AC-DC hybrid distribution networks

[0202] The branch structure of the AC-DC hybrid distribution network can be divided into 9 cases in total, as Figure 3 shown.

[0203] (1) Scenario 1: Two AC nodes are connected by an AC line, and its branch power flow equation is:

[0204]

[0205] Express formula (23) in the form of a binary node-branch matrix as follows:

[0206]

[0207] (2) Scenario 2: Two DC nodes are connected by a DC line, and its branch power flow equation is:

[0208]

[0209] Express formula (25) in the form of a binary node-branch matrix as follows:

[0210]

[0211] (3) Scenario 3: An AC node is connected to a DC node through a VSC via a DC line, and its branch power flow equation is:

[0212] Express formula (27) in the form of a binary node-branch matrix as follows:

[0213]

[0214] In the formula: a1 and b1 respectively represent whether the converter is in the rectification state or the inversion state.

[0215] The expressions of a1 and b1 are as follows:

[0216]

[0217] (4) Scenario 4: The DC node is connected to the AC node through a DC line via a VSC, and its branch power flow equation is:

[0218] Express Equation (30) in the binary node-branch matrix form as follows:

[0219]

[0220] (5) Scenario 5: The AC node is connected to the DC node through an AC line via a VSC, and its branch power flow equation is:

[0221] Express Equation (32) in the binary node-branch matrix form as follows:

[0222]

[0223] (6) Scenario 6: The DC node is connected to the AC node through an AC line via a VSC, and its branch power flow equation is:

[0224]

[0225] Express Equation (34) in the binary node-branch matrix form as follows:

[0226]

[0227] (7) Scenario 7: Two AC nodes are connected through two VSCs via a DC line, and its branch power flow equation is:

[0228] Express Equation (36) in the binary node-branch matrix form as follows:

[0229]

[0230] In the formula: a2 and b2 represent whether the converter is in the rectification state or the inversion state.

[0231] The expressions of a2 and b2 are as follows:

[0232]

[0233] (8) Scenario 8: Two DC nodes with different voltage levels are connected through a DC / DC via a DC line, and when the injection power direction is the same as the DC / DC transformer modeling direction, its branch power flow equation is:

[0234] P nm = V n (V n G'2 + (V n - V m )G'1) (39)

[0235] Express Equation (39) in the form of a binary node - branch matrix as follows:

[0236]

[0237] (9) Scenario 9: When two DC nodes with different voltage levels are connected by a DC line through a DC / DC, and the injection power direction is opposite to the modeling direction of the DC / DC transformer, the branch power flow equation is:

[0238] P nm = V n (V n G'3 + (V n - V m )G'1) (41)

[0239] Express Equation (41) in the form of a binary node - branch matrix as follows:

[0240]

[0241] Power Flow Calculation of AC - DC Distribution Network

[0242] 3.1 Objective Function The objective function is that the correction amount of voltage should satisfy being less than the set accuracy:

[0243]

[0244] Where: ΔV and Δθ represent the correction amount of voltage amplitude and the correction amount of voltage phase angle respectively; ||·|| ∞ represents the infinity norm, that is, taking the maximum value of the absolute value of the voltage correction amount; epilson represents the convergence accuracy.

[0245] 3.2 Constraint Conditions

[0246] (1) Integer constraint of matrix binary variables:

[0247]

[0248] (2) Branch power balance constraint:

[0249]

[0250] Since there is a U on the transformer branch EWhen the voltage drops, the branch current needs to be corrected accordingly. Therefore, for the constant active power control node with a transformer branch, the active power imbalance needs to be added with the following formula:

[0251] ΔP = P g -UI (46)

[0252] In formulas (45) and (46): nb represents the total number of nodes in the system; represents the active power injected into the node; represents the calculated active power injected into the node; represents the reactive power injected into the node; represents the calculated reactive power injected into the node; P g represents the active power value of the constant active power control node.

[0253] In the formula: represents the active power of the AC node power source; represents the active power of the AC node load; represents the active power of the DC node power source; represents the active power of the DC node load; represents the reactive power of the AC node power source; represents the reactive power of the AC node load.

[0254] 3.3 Jacobian Matrix and Correction Equation

[0255] The Jacobian matrix is a matrix formed by arranging first-order partial derivatives in a certain way. Each node involves two imbalances, namely reactive power imbalance and active power imbalance, and these two imbalances correspond to two state variables, namely voltage amplitude and voltage phase angle. Under different control modes, the expression form of its Jacobian matrix is different.

[0256] (1) Master-Slave Control

[0257] In the Jacobian matrix of master-slave control, the balanced node, PQ node, PV node, V node, and P node involve reactive power imbalance and active power imbalance, and the state variables they correspond to are voltage amplitude and voltage phase angle respectively. For the balanced node, both the active power imbalance and the reactive power imbalance are 0, and the corresponding state variables are also 0; for the PV node, V node, and P node, the reactive power imbalance and the corresponding state variables are all 0, and the elements located on the diagonal matrix and with a value of 0 are set to 1. Therefore, the state space equation of the system under the master-slave control mode can be expressed as:

[0258]

[0259] (2) Droop Control

[0260] During droop control, to achieve the proportional sharing of active power of the AC power node, reactive power of the AC power source, active power of the DC power source, and reactive power of the inverter side of the VSC converter, it is necessary to impose constraints on their powers as follows:

[0261]

[0262] In the formula: represents the active power droop gain of the DC power source; represents the active power droop gain of the AC power source; represents the reactive power droop gain of the AC power source; V max represents the maximum voltage; f max represents the maximum frequency.

[0263] Normalization processing is required for the active power constraint of the AC power source:

[0264] f = V (50)

[0265] Among them:

[0266]

[0267] During droop control, the positions of the active power imbalance and reactive power imbalance in the active power of the DC power source, active power of the AC power source, reactive power of the AC power source, and reactive power of the inverter side of the VSC are modified according to equations (6), (49), and (50). Different from the master-slave control, droop control requires setting a voltage phase angle reference node, and the voltage phase angle and its corresponding reactive power are 0.

[0268] 3.4 Algorithm Flow

[0269] The AC-DC power flow calculation process in this paper is as Figure 4 shown below:

[0270] (1) Input network parameters and control types;

[0271] (2) Set the initial voltage value and specify the positive direction of the DC / DC converter;

[0272] (3) Form the nodal admittance matrix of the network from the line parameters and the parameters of the converter;

[0273] (4) Calculate the line transmission power and power imbalance respectively by combining the AC-DC power flow calculation model and the power imbalance equation; (5) Classify the node types and calculate each element of the Jacobian matrix to form the Jacobian matrix;

[0274] (6) If it is master-slave control, the voltage correction amount is obtained from the correction equation to correct the voltage; if it is droop control, the active power of the AC power source, the reactive power of the AC power source, the active power of the DC power source, and the reactive power injected during VSC inversion, as well as the elements of the corresponding Jacobian matrix, are correspondingly modified, and the correction amount is obtained from the correction equation to correct the voltage;

[0275] (7) If the correction amount meets the iteration accuracy, the next judgment is carried out; if the accuracy requirement is not met, the next iteration is required until the voltage correction amount meets the accuracy requirement;

[0276] (8) Judge whether the power constraint is satisfied. If not, update the data and recalculate. If satisfied, the program ends.

[0277] 4 Case Study

[0278] To verify the accuracy and effectiveness of the established VSC steady-state model, DC / DC converter model, and AC-DC hybrid distribution network power flow model, the power flow of the AC-DC hybrid distribution network under different control methods is calculated on a computer with Inter(R) Core(TM) i5-7300HQ CPU @ 2.50GHz, 64bit, 16GB RAM, and the power flow calculation results are compared with the PSCAD simulation results.

[0279] 4.1 Case 1: Master-Slave Control Method

[0280] Figure 5 For the topological structure of the 13-node AC-DC hybrid distribution network, the master-slave control method is adopted. The reference value is set as S B = 10 MVA; the efficiency of the VSC converter is 98%, the power factor of the converter is 95%, the modulation ratio of the converter between nodes 2-3 is 0.8, and the modulation ratio of the converter between nodes 8-9 is 0.9; the branch impedance data is shown in Table 1; the node type and load data are shown in Table 2; the 4-5 branch DC-DC transformer is of Buck type with a fixed duty cycle D = 0.97, and the other three transformers are of Buck-Boost type and are all under constant voltage control. The other set parameters are shown in Table 3; the correction error is taken as 0.1. After 3 iterations, the program runs to completion.

[0281] Table 1 Branch Impedance Parameters

[0282]

[0283] Table 2 Node Type and Node Load Parameters

[0284]

[0285] Table 3 DC-DC Converter Parameter Settings

[0286]

[0287] The voltage results of the AC-DC power flow calculation with master-slave control and the PSCAD results are compared as shown in Table 4. According to the data analysis in the table, the average error of the voltage amplitude obtained by the method of the present invention is 0.07% and the average error of the voltage phase angle is 0.02%, indicating the accuracy of the method proposed by the present invention for the power flow calculation of the AC-DC hybrid distribution network under master-slave control.

[0288] Table 4 Voltage Distribution of 13-Node System

[0289]

[0290] 4.2 Example 2: Droop Control Method

[0291] Figure 6 The topological structure of the 10-node AC-DC hybrid distribution network is adopted with the droop control method. The reference values are set as S B = 10 MVA, S vsc = 0.4 MVA, f = 50 Hz; the allowable frequency deviation is 1%, and the allowable voltage deviation is 5%; the efficiency of the VSC converter is 98%, and the power factor of the converter is 95%. Node 1 is the node connected to the upper-level distribution network, and its phase angle is 0°; the branch impedance data is shown in Table 5; the node type and load data are shown in Table 6; the correction error is taken as 0.00001, and the calculation converges after 4 iterations.

[0292] Table 5 Branch Impedance Parameters

[0293]

[0294] Table 6 Node Type and Node Load Parameters

[0295]

[0296] The voltage results of the AC-DC power flow calculation with droop control and the PSCAD results are compared as shown in Table 7. According to the data analysis in the table, the average error of the voltage amplitude obtained by the method of the present invention is 0.007% and the average error of the voltage phase angle is 0.01%, indicating the accuracy of the method proposed by the present invention for the power flow calculation of the AC-DC hybrid distribution network under droop control.

[0297] Table 7 Voltage Distribution of 10-Node System

[0298]

[0299] The symbolic names involved in the present invention:

[0300] V PCC represents the voltage of the point of common coupling (PCC); Z c represents the equivalent impedance of all components and lines between the point of common coupling and the VSC AC-side node; V n represents the voltage of node n; V k represents the voltage of node k; μ represents the DC voltage utilization rate; M represents the pulse width modulation ratio; represents the AC voltage reference value; represents the DC voltage reference value; η c represents the VSC efficiency; P nk represents the active power injected into the VSC AC side; Q nk represents the reactive power injected into the VSC AC side; P d represents the active power output by the VSC DC side; represents the power factor angle of the VSC; V max represents the upper limit of the node voltage; V min represents the lower limit of the node voltage; λ represents the reactive power droop gain of the VSC; Q max represents the upper limit of the reactive power supported by the VSC; D represents the duty ratio of the DC / DC transformer; Z nm represents the AC line impedance; R nm represents the DC line resistance; R mx represents the branch resistance; P M represents the load carried by node m; N represents the number of sub-modules in the DC / DC transformer model; U D represents the forward conduction voltage drop of the diode;

[0301] R D represents the forward conduction resistance of the diode; R L represents the inductance resistance of the inductor coil; R S represents the on-resistance of the MOSFET M(D) represents the turns ratio of the DC / DC transformer; R E represents the equivalent resistance in the DC / DC circuit; U E represents the voltage drop in the equivalent circuit; y lm 、y l0 、y m0 represents the admittance of the π-type equivalent circuit; y1, y2, y3 represent the admittance of the π-type equivalent circuit after star-delta transformation; I' n 、I' m represents the node injection current before correction; I n 、I m represents the node injection current after correction; W node type matrix; H branch connection matrix; J connection line type matrix; T discrimination matrix; L direction matrix; P nmIndicates the active power flowing from node n to node m; Q nm Indicates the reactive power flowing from node n to node m; G nm Indicates the conductance between node n and node m; B nm Indicates the susceptance between node n and node m; θ nm Indicates the phase angle difference between node n and node m;

[0302] a1 indicates that the VSC is in the rectification state; b1 indicates that the VSC is in the inversion state; sign() represents the sign function; G'1G'2G'3 represents the conductance of the π - type equivalent circuit after star - delta transformation; ΔV represents the correction amount of the voltage amplitude; Δθ represents the correction amount of the voltage phase angle; ||·|| ∞ Represents the infinity norm, that is, takes the maximum value of the absolute value of the voltage correction amount; epilson represents the convergence accuracy; nb represents the total number of nodes in the system; Indicates the active power injected into the node; Indicates the calculated active power injected into the node; Indicates the reactive power injected into the node; Indicates the calculated reactive power injected into the node; P g Indicates the active power of the constant - power node; Indicates the active power of the AC node power source; Indicates the active power of the AC node load; Indicates the active power of the DC node power source; Indicates the active power of the DC node load; Indicates the reactive power of the AC node power source; Indicates the reactive power of the AC node load; ΔP S Indicates the active power unbalance of the slack node; ΔQ S Indicates the reactive power unbalance of the slack node ΔP PQ Indicates the active power unbalance of the PQ node; ΔQ PQ Indicates the reactive power unbalance of the PQ node; ΔP PV Indicates the active power unbalance of the PV node; ΔP V Indicates the reactive power unbalance of the V node; ΔP P Indicates the active power unbalance of the P node; ΔV PQ Indicates the voltage amplitude correction amount of the PQ node; Δθ PQ Indicates the voltage phase angle correction amount of the PQ node; ΔV S Indicates the voltage amplitude correction amount of the slack node; Δθ S Indicates the voltage phase angle correction amount of the slack node; Δθ PV Indicates the voltage phase angle correction amount of the PV node; ΔV V Indicates the voltage amplitude correction amount of the V node; ΔV PIndicates the correction amount of the P-node voltage amplitude; Indicates the active power of the DC power supply; Indicates the active power of the AC power supply; Indicates the reactive power of the AC power supply; V i Indicates the voltage of node i; f i Indicates the frequency of node i; f max Indicates the maximum frequency; Indicates the droop gain of the active power of the DC power supply; Indicates the droop gain of the active power of the AC power supply Indicates the droop gain of the reactive power of the AC power supply; f represents the estimated frequency; V represents the estimated voltage; S B Indicates the capacity reference value; S vsc Indicates the rated capacity of the VSC; Indicates the maximum reactive power that the VSC is allowed to transmit.

Claims

1. A method for constructing a unified power flow model of an AC / DC hybrid distribution network, characterized in that: S1. Establish the steady-state model of the power electronic converter S1.

1. Establish the steady-state model of the VSC converter According to the PWM principle, the relationship between the AC-side voltage and the DC-side voltage is: In the formula: μ represents the DC voltage utilization rate, and M is the pulse width modulation ratio. Then the relationship between the AC voltage reference value and the DC voltage reference value is: Combining Equation (1) and Equation (2) can obtain the following relationship: V n = MV k (3) Where: η c is the converter efficiency, and the power relationship on both sides of the converter is as follows: P nk = P d / η c (4) Under the master-slave control, the reactive power on the AC side of the VSC is determined by the power factor angle of the converter as follows: When under droop control and the VSC is in the inverter state, the reactive power is expressed as: Q nk = (V max - V n ) / λ (6) λ=(V max -V min ) / Q max (7) Where: V max represents the upper limit of the converter voltage, V min represents the lower limit of the voltage, λ represents the reactive droop gain of the converter, Q max represents the upper limit of the reactive power supported by the converter; S1.

2. Establish the steady-state model of the DC / DC converter Find the nodes 1, 2, 3, 4 ……, h connected to the m node, and use the voltage of the k-th iteration to obtain the branch power as follows: Where: R mx represents the branch resistance; P M represents the load carried by the m-th node; The current flowing through the n, m branch is expressed as: Combining the voltage at the m point and the parameters of the DC / DC converter, the duty ratio and equivalent parameters of the converter for the (k + 1)-th iteration are obtained. (1) Duty ratio Buck-type DC / DC converter: Buck-Boost type DC / DC converter: (2) Transformer parameters: Buck-type DC / DC converter: Buck-Boost type DC / DC converter: Where: N is the number of sub-modules in the converter model; D is the duty cycle; U D , R D are respectively the forward conduction voltage drop and conduction resistance of the diode; R L is the inductance resistance of the inductor coil; R S is the conduction resistance of the MOSFET; M(D) is the turns ratio of the converter model; R E is the sum of the equivalent resistances in the converter circuit; U E is the voltage drop in the equivalent circuit; The π-type equivalent branch admittance of the DC / DC converter is expressed as: Considering the star-delta transformation of the line resistance of the transformer branch, it can finally be equivalent to a π-type branch, and the admittances of the three branches are: Due to the voltage drop of U on the transformer branch, the injected current into its branch needs to be corrected accordingly. I E , I n , and I m are the node injected currents before and after correction: S2. Establish a unified power flow model for the AC-DC hybrid distribution network based on the node-branch matrix S2.

1. Establish the binary node-branch matrix (1) Node type matrix W: (2) Branch connection matrix H: (3) Connection line type matrix J: (4) Judgment matrix T: (5) Direction matrix L: In Equation (22): The modeling direction of the DC / DC transformer is related to the position of the line resistance connected to it. The head end of the DC / DC transformer modeling is the side connected to the line resistance; S2.

2. Establish the branch power flow equation for the AC-DC hybrid distribution network The branch structure of the AC-DC hybrid distribution network is divided into 9 scenarios: (1) Scenario 1: Two AC nodes are connected by an AC line, and its branch power flow equation is: The binary node-branch matrix form is as follows: (2) Scenario 2: Two DC nodes are connected by a DC line, and its branch power flow equation is: The binary node-branch matrix form is as follows: (3) Scenario 3: The AC node is connected to the DC node through a VSC via a DC line, and its branch power flow equation is: The binary node-branch matrix form is as follows: In the formula: a1 and b1 respectively represent whether the converter is in the rectifier state or the inverter state, and the expressions of a1 and b1 are as follows: (4) Scenario 4: The DC node is connected to the AC node through a VSC via a DC line, and its branch power flow equation is: The binary node-branch matrix form is as follows: (5) Scenario 5: The AC node is connected to the DC node through a VSC via an AC line, and its branch power flow equation is: The binary node-branch matrix form is as follows: (6) Scenario 6: The DC node is connected to the AC node through a VSC via an AC line, and its branch power flow equation is: The binary node-branch matrix form is as follows: (7) Scenario 7: Two AC nodes are connected through two VSCs via a DC line, and its branch power flow equation is: The binary node-branch matrix form is as follows: Where: a2 and b2 indicate whether the converter is in the rectification state or the inversion state, and the expressions of a2 and b2 are as follows: (8) Scenario 8: When two DC nodes with different voltage levels are connected by a DC line through a DC / DC, and the injection power direction is the same as the modeling direction of the DC / DC transformer, the branch power flow equation is: P nm = V n (V n G'2+(V n - V m )G’1) (39) The binary node-branch matrix form is as follows: (9) Scenario 9: When two DC nodes with different voltage levels are connected by a DC line through a DC / DC, and the injection power direction is opposite to the modeling direction of the DC / DC transformer, the branch power flow equation is: P nm = V n (V n G'3 + (V n - V m )G’1) (41) The binary node-branch matrix form is as follows: S3. AC-DC distribution network power flow calculation S3.

1. Establish the objective function The objective function is that the correction amount of the voltage should satisfy being less than the set accuracy: Where: ΔV and Δθ respectively represent the correction amount of the voltage amplitude and the correction amount of the voltage phase angle added; ||·|| ∞ represents the infinity norm, that is, taking the maximum value of the absolute value of the voltage correction amount; epilson represents the convergence accuracy; S3.

2. Establish the constraint conditions (1) Integer constraint of matrix binary variables: (2) Branch power balance constraint: For the constant active power control node with a transformer branch, the active power imbalance also needs to add the following formula: ΔP = P g -UI (46) In Equation (45) and Equation (46): nb represents the total number of nodes in the system; represents the active power injected by the node; represents the calculated active power injected by the node; represents the reactive power injected by the node; represents the calculated reactive power injected by the node; P g represents the active power value of the constant active power control node; Wherein: represents the active power of the AC node power source; represents the active power of the AC node load; represents the active power of the DC node power source; represents the active power of the DC node load; represents the reactive power of the AC node power source; represents the reactive power of the AC node load; S3.

3. Establish the Jacobian matrix and the correction equation (1) Master-slave control The state space equation of the system under the master-slave control mode is expressed as: (2) Droop control Constrain its power In the formula: represents the active power droop gain of the DC power supply; represents the active power droop gain of the AC power supply; represents the reactive power droop gain of the AC power supply; V max represents the maximum voltage; f max represents the maximum frequency; The active power constraint of the AC power supply needs to be normalized: f = V(50) Where: During droop control, the positions of the active power imbalance, reactive power imbalance, active power of the DC power supply, active power of the AC power supply, reactive power of the AC power supply, and reactive power injected by the VSC inverter side are modified according to Equations (6), (49), and (50). Different from the master-slave control, droop control needs to set a voltage phase angle reference node, and the voltage phase angle and its corresponding reactive power are 0; S3.4 Construct the algorithm flow (1) Input network parameters and control types; (2) Set the initial voltage value and specify the positive direction of the DC / DC converter; (3) Form the node admittance matrix of the network from the line parameters and the parameters of the converter; (4) Calculate the line transmission power and the power imbalance respectively by combining the AC-DC power flow calculation model and the power imbalance equation; (5) Classify the node types and calculate each element of the Jacobian matrix to form the Jacobian matrix; (6) If it is master-slave control, find the voltage correction amount from the correction equation to correct the voltage; if it is droop control, correspondingly modify the active power of the AC power supply, reactive power of the AC power supply, active power of the DC power supply, and reactive power injected during VSC inversion, and the elements of the corresponding Jacobian matrix, and find the correction amount from the correction equation to correct the voltage; (7) If the correction amount meets the iteration accuracy, proceed to the next judgment; if it does not meet the accuracy requirement, the next iteration is required until the voltage correction amount meets the accuracy requirement; (8) Judge whether the power constraint is met. If not, update the data and recalculate. If it is met, the program ends.

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