Alternating iteration linearization-based power flow calculation method for alternating current and direct current power grid containing multiple types of power electronic equipment

Abstract

The invention discloses a load flow calculation method for an alternating current and direct current power grid containing multiple types of power electronic equipment based on alternating iteration linearization, which comprises the following steps of: 1) calculating load flow of each module of the power electronic equipment by utilizing an unbalanced linear equation of each module of the power electronic equipment based on basic data of a power system; 2) based on the power flow of each module of the power electronic equipment, calculating the injection power flowing from the power electronic equipment into the alternating current and direct current system; 3) based on the injection power flowing into the AC / DC system from the power electronic equipment, calculating the AC / DC power grid power flow distribution by using an AC / DC system imbalance linear equation; according to the method, the calculation speed is increased by performing linearization processing on the power flow equation of each module.

Description

Technical Field

[0001] The present invention relates to the field of power grid power flow calculation, and specifically to a power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization. Background Technique

[0002] With the continuous expansion of the scale of the power system, the continuous enrichment of the types of power sources and loads, and the continuous complexity of the power grid structure, problems such as unbalanced power flow, line congestion, and voltage over-limit in the system have become increasingly prominent. Due to the characteristics of unrestricted interfaces, fast response speeds, and high conversion efficiencies, power electronic devices have been fully applied in aspects such as new energy grid connection and efficient power transmission. Power electronic devices are mainly applied in high-voltage direct current (HVDC) transmission systems and flexible alternating current transmission systems (FACTS). China has included the application of power electronic devices in the key directions of national development and applied them to the grid connection of new energy sources such as wind and light. As of the end of 2023, there are approximately 43 DC transmission lines (including back-to-back) in the country, with a line length of approximately 55,900 kilometers, and 3 DC back-to-back projects. Voltage source converters (VSCs) are widely used in HVDC transmission. It can independently control active power or reactive power and can reverse the current without changing the voltage polarity. In recent years, the research on AC-DC systems based on VSC-HVDC has been increasing. The flexible alternating current transmission system (FACTS) developed and manufactured based on power electronic technology provides a good technical means to improve the flexibility on the grid side. FACTS includes unified power flow controllers (UPFCs), static synchronous compensators (STATCOMs), static synchronous series compensators (SSSCs), etc., and has multiple functions such as voltage regulation, series compensation, power control, and phase shift. In August 2011, the STATCOM demonstration project at the 500 kV Dongguan substation was completed and put into operation, with a capacity of ±200 Mvar. In 2017, the 500 kV Southern Jiangsu UPFC project was put into operation, and its technology is in the leading position in the field of flexible AC transmission in the world. In December 2018, the STATCOM on the west side of Wujiang substation was completed and put into operation, with a capacity of ±300 Mvar. In December 2018, the world's first SSSC was officially put into operation in Shigezhuang, Tianjin. Since power electronic devices can flexibly control physical quantities in the power system, the adjustment of power electronic devices provides a new option for ensuring the safe operation of the power system.

[0003] Because power electronic devices can flexibly regulate electrical quantities in the power system, new paths are opened up for ensuring the safe operation of the power system by adjusting them. The operation of power electronic devices is complex, and a steady-state model that conforms to their operating characteristics needs to be established. At the same time, due to the addition of power electronic devices, the non-linearity of the system steady-state equations is more significant compared to traditional pure AC systems. This not only increases the difficulty of solving the equations but also prolongs the calculation time. Therefore, it is particularly important to explore methods that can effectively calculate the power flow of power systems containing power electronic devices and improve the calculation efficiency, which will provide a solid foundation for evaluating the operating state of the system and thus provide a basic basis for the optimization and control of the power system.

[0004] However, in the probability modeling and scenario generation of large-scale offshore wind power output, the existing technologies have the following deficiencies:

[0005] (1) For the steady-state power flow calculation of power systems containing power electronic devices, the unified iteration method has good convergence, but there is a problem that as the number of power electronic devices increases, the dimension of the Jacobian matrix increases, and the computational burden of matrix operations increases.

[0006] (2) The alternating iteration method has clear physical meaning and is easy to implement, but there is a problem of low computational efficiency.

[0007] (3) Although some simplified solution methods help to improve the calculation efficiency, their calculation results are always an approximate value, resulting in a certain deviation in the evaluation of the system. Summary of the Invention

[0008] The object of the present invention is to provide a power flow calculation method for AC-DC power grids containing multiple types of power electronic devices based on alternating iteration linearization, including the following steps:

[0009] 1) Obtain the basic data of the power system;

[0010] 2) Based on the voltage data of the AC-DC system, construct the unbalanced equations of each module of the power electronic device and perform linearization to obtain the unbalanced linear equations of each module of the power electronic device;

[0011] 3) Based on the basic data of the power system, calculate the power flow of each module of the power electronic device using the unbalanced linear equations of each module of the power electronic device;

[0012] 4) Based on the power flow of each module of the power electronic device, calculate the injection power flowing from the power electronic device into the AC and DC systems;

[0013] 5) Construct the unbalanced equations of the AC and DC systems and perform linearization to obtain the unbalanced linear equations of the AC and DC systems;

[0014] 6) Calculate the power flow distribution of the AC-DC power grid by using the unbalanced linear equations of the AC-DC system based on the injection power flowing from the power electronic device into the AC and DC systems;

[0015] 7) Repeat steps 2)-6), and judge whether the power flow distributions of the AC-DC power grid in two iterations converge. If so, output the final power flow distribution of the AC-DC power grid; if not, return to step 2) and continue the iteration;

[0016] Furthermore, in step 1), the basic data of the power system includes the topological structure of the power system, the magnitudes and locations of the power sources and loads, the types and quantities of the power electronic devices, and the control parameters of the power electronic devices.

[0017] Furthermore, in step 2), the steps of constructing the unbalanced equations of each module of the power electronic device and performing linearization processing include:

[0018] 2.1) Construct the unbalanced equations of each module of the power electronic device, that is:

[0019]

[0020] In the formula, P c.dc is the active power flowing from the converter station to the DC system; ΔP c.dc is the active power unbalance of the converter station flowing to the DC system; P loss is the active power loss; P c is the active power of node c; ΔP f , ΔQ f are the unbalances of the active power and reactive power output by node f; P cf , Q cf are the active power and reactive power flowing from node f to node c; P fp , Q fp are the active power and reactive power flowing from node f to node p; Q f is the reactive power output by node f; Q p is the reactive power flowing from the converter station to node p; is the reactive power reference value; ΔQ p is the unbalance of the reactive power flowing to node p;

[0021]

[0022] In the formula, V p is the voltage amplitude of node p; is the reference voltage amplitude of node p; ΔV p is the voltage amplitude unbalance of node p; Q sh is the reactive power flowing from node p to the parallel side of GUPFC; is the reactive power reference value flowing from node p to the shunt side of the GUPFC; ΔQ sh is the reactive power imbalance flowing from node p to the shunt side of the GUPFC; P nm is the active power flowing from node n to node m; are the active and reactive powers; ΔP nm , ΔQ nm are the active and reactive power imbalances flowing from node n to node m; PEsh = Re(Vsh·Ish * ) is the real part of the active power flowing from node p to the shunt side of the GUPFC; PEse k = Re(Vse k ·I *nm,k ) is the real part of the active power; the power loss on the DC side P dc = 0; ΔPEx is the real part imbalance of the active power;

[0023]

[0024] In the formula, Q sta , are the reactive power and reference reactive power of the STATCOM; ΔQ sta is the reactive power imbalance of the STATCOM; PEsta = Re(Vsta·Ista * ) is the real part of the active power of the STATCOM; ΔPE is the active power imbalance of the STATCOM;

[0025]

[0026] In the formula, ΔPEse is the active power imbalance of the SSSC; PEse = Re(Vsssc·Isssc * ) is the real part of the active power of the SSSC;

[0027] 2.2) Simplify the imbalance equations of each module of the power electronic device to obtain:

[0028]

[0029] Among them, the vector F VSC = [ΔP c.dc , ΔP f , ΔQ f , ΔQ p T , the vector F GUPFC = [ΔV p / ΔQsh, ΔP nm , ΔQ nm , ΔPEx] T , the vector F STATCOM = [ΔV​p / ΔQsh, ΔPEsta] T , vector F SSSC = [ΔP nm / ΔQ nm , ΔPEsta] T ; x VSC , x GUPFC , x STATCOM and x SSSC represent the bus voltage of the power electronic device, i.e., and f VSC , f GUPFC , f STATCOM , f SSSC are multivariate functions of x VSC , x GUPFC , x STATCOM and x SSSC ;

[0030] 2.3) Using the voltage variables of the AC-DC system as the input variables, linearize the unbalanced equations of each module of the power electronic device to obtain:

[0031]

[0032] In the formula, the superscripts k AIML , k AIML -1 represent the iteration times; represents the linearized variable; represents the unbalance of the linearized variable; the function f PEDs = f VSC , f GUPFC , f STATCOM , f SSSC .

[0033] Furthermore, in step 4), the injection powers flowing from the power electronic device into the AC and DC systems include the injection powers of the VSC converter station, GUPFC, STATCOM, and SSSC, i.e.:

[0034] (P in , Q in ) = h(V PEDs , V AC / DC ) (7)

[0035] In the formula, h(·) is the node power injection expression, V PEDs and V AC / DC are the input variables, P in and Q in are the output variables.

[0036] Furthermore, the injection power of the VSC converter station is as follows:

[0037]

[0038] Wherein, the admittance Z tf = G tf + jB tf , the voltage Voltage

[0039] Furthermore, the injection power of the GUPFC includes the power flowing into the GUPFC from the shunt node, the power flowing from node m k to node n k , and the power flowing from node n k to node m k ;

[0040] Among them, the power flowing into the GUPFC from the shunt node is as follows:

[0041]

[0042] Wherein, the admittance Zsh = Gsh + jBsh, the voltage θsh is the voltage phase angle; Vsh is the voltage amplitude; Gsh, Bsh are the conductance and susceptance; Psh, Qsh are the active and reactive powers flowing into the GUPFC from the shunt node;

[0043] The power flowing from node m k to node n k is as follows:

[0044]

[0045] Wherein, the admittance Zse k = Gse k + jBse k , the voltage Voltage Voltage P mn,k 、Q mn,k are the active and reactive powers flowing from node m k to node n k ;

[0046] The power flowing from node n k to node m k is as follows:

[0047]

[0048] Wherein, P nm,k 、Q nm,k are the active and reactive powers flowing from node n k to node mk Active and reactive power

[0049] Furthermore, the injected power of the STATCOM is as follows:

[0050]

[0051] where the admittance Zsta = Gsta + jBsta, and the voltage Psta and Qsta are the injected active and reactive powers of the STATCOM

[0052] Furthermore, the injected power of the SSSC includes the power flowing from node m to node n and the power flowing from node n to node m;

[0053] Among them, the power flowing from node m to node n is as follows:

[0054]

[0055] where the admittance Zsssc = Gsssc + jBsssc, and the voltage Voltage Voltage

[0056] The power flowing from node n to node m is as follows:

[0057]

[0058] Furthermore, in step 5), the steps of constructing the unbalanced equations of the AC and DC systems and performing linearization processing include:

[0059] 5.1) Construct the power unbalanced equation of bus i in the AC system, that is:

[0060]

[0061] Among them, are the voltages of buses i and j; Y ij is the element in the i-th row and j-th column of the nodal admittance matrix of the AC system; P i and Q i are the active and reactive power injections on bus i respectively; ΔP i and ΔQ i are the active and reactive power unbalances on bus i;

[0062] 5.2) Simplify the power unbalanced equation of bus i in the AC system to obtain:

[0063] F AC = f AC (V AC ) = 0 (16)

[0064] In the formula, vector F AC =[ΔP,ΔQ] T ; V AC is the bus voltage of the AC system; f AC is a function of voltage V AC .

[0065] 5.3) Construct the DC system node unbalance equation, i.e.:

[0066] ΔP dci =P Gi -P Li +P c.dc,i -V dc,i ∑ j V dcj Y dc,ij =0 (17)

[0067] In the formula, V dc,i is the voltage of DC bus i; Y dc.ij is the element in the i-th row and j-th column of the DC system node conductance matrix; P G,i , P L,i are the active power generation and active load power on DC bus i respectively; ΔP dci is the active power unbalance of the DC system node; V dcj is the voltage of node j; P c.dc,i is the active power of DC bus i;

[0068] 5.4) Simplify the DC system node unbalance equation to obtain:

[0069] F DC =f DC (V DC )=0 (18)

[0070] In the formula, vector F DC =[ΔP dc1 ,ΔP dc2 ,ΔP dc3 ,…] T , V DC is the bus voltage of the DC system; f DC is a function of V DC ;

[0071] 5.5) Based on the simplified AC and DC system node unbalance equations, construct the power mismatch equation of the AC-DC system, i.e.:

[0072]

[0073] Among them, f AC / DCis the power mismatch equation for the AC-DC system, P in and Q in are the input variables, and V AC / DC is the variable to be solved for;

[0074] 5.6) At the reference point χ0, perform a Taylor expansion on the power mismatch equation of the AC-DC system, retain the first-order terms and ignore the higher-order terms to obtain the unbalance equations of the AC and DC systems, that is:

[0075]

[0076] Furthermore, the convergence criterion is as follows:

[0077] max|χ (k) -χ (k-1) | < ε AIML (21)

[0078] where χ represents all state variables in the system, including the bus voltages of the AC-DC system and power electronic devices; the superscript (k) represents the k-th iteration; ε AIML is the convergence coefficient.

[0079] The technical effects of the present invention are beyond doubt, and the beneficial effects of the present invention are as follows:

[0080] (1) By analyzing the physical characteristics of various power electronic devices, analyzing the characteristics of their power flow equations, and based on the idea of iterative solution, a power flow calculation iterative solution model for an AC-DC hybrid system containing a large number of power electronic devices is constructed.

[0081] (2) The linearized alternating iteration method (AIM based on Linearization, AIML) is used to calculate the deterministic power flow of the AC-DC system containing power electronic devices. The calculation speed is accelerated by linearizing the power flow equations of each module, and a convergence criterion is adopted to ensure the calculation accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 is a flowchart;

[0083] Figure 2 is a schematic diagram of each iteration of three different algorithms;

[0084] Figure 3 is the equivalent circuit diagram of power electronic devices: (a) VSC converter station; (b) GUPFC (or UPFC); (c) STATCOM; (d) SSSC;

[0085] Figure 4 is the DC power flow bus voltage amplitude in each case: (a) Case 1; (b) Case 2; (c) Case 3;

[0086] Figure 5 The phase angles of the DC power flow bus voltages in each case study: (a) Case study 1; (b) Case study 2; (c) Case study 3. Specific implementation manners

[0087] The present invention will be further described below in conjunction with embodiments, but it should not be understood that the above-mentioned subject matter scope of the present invention is limited to the following embodiments. Without departing from the above-mentioned technical idea of the present invention, various substitutions and modifications made according to common general knowledge and conventional means in the art shall all be included within the protection scope of the present invention.

[0088] Embodiment 1:

[0089] See Figures 1 to 5 , a power flow calculation method for AC-DC power grids containing multiple types of power electronic devices based on alternating iterative linearization, comprising the following steps:

[0090] 1) Obtain the basic data of the power system;

[0091] 2) Based on the voltage data of the AC-DC system, construct the unbalanced equations of each module of the power electronic device and perform linearization processing to obtain the unbalanced linear equations of each module of the power electronic device;

[0092] 3) Based on the basic data of the power system, calculate the power flow of each module of the power electronic device by using the unbalanced linear equations of each module of the power electronic device;

[0093] 4) Based on the power flow of each module of the power electronic device, calculate the injection power flowing from the power electronic device into the AC and DC systems;

[0094] 5) Construct the unbalanced equations of the AC and DC systems and perform linearization processing to obtain the unbalanced linear equations of the AC and DC systems;

[0095] 6) Based on the injection power flowing from the power electronic device into the AC and DC systems, calculate the power flow distribution of the AC-DC power grid by using the unbalanced linear equations of the AC and DC systems;

[0096] 7) Repeat steps 2)-6), and determine whether the power flow distributions of the AC-DC power grid in two iterations converge. If so, output the final power flow distribution of the AC-DC power grid. If not, return to step 2) and continue the iteration;

[0097] In step 1), the basic data of the power system includes the topological structure of the power system, the magnitudes and locations of the power sources and loads, the types and quantities of the power electronic devices, and the control parameters of the power electronic devices.

[0098] In step 2), the steps of constructing the unbalanced equations of each module of the power electronic device and performing linearization processing include:

[0099] 2.1) Construct the unbalanced equations for each module of the power electronic device, i.e.:

[0100]

[0101] In the formula, P c.dc is the active power flowing from the converter station to the DC system; ΔP c.dc is the unbalance of the active power flowing from the converter station to the DC system; P loss is the active power loss; P c is the active power of node c; ΔP f , ΔQ f are the unbalances of the active power and reactive power output by node f; P cf , Q cf are the active power and reactive power flowing from node f to node c; P fp , Q fp are the active power and reactive power flowing from node f to node p; Q f is the reactive power output by node f; Q p is the reactive power flowing from the converter station to node p; is the reactive power reference value; ΔQ p is the unbalance of the reactive power flowing to node p;

[0102]

[0103] In the formula, V p is the voltage amplitude of node p; is the reference voltage amplitude of node p; ΔV p is the unbalance of the voltage amplitude of node p; Q sh is the reactive power flowing from node p to the parallel side of GUPFC; is the reactive power reference value flowing from node p to the parallel side of GUPFC; ΔQ sh is the unbalance of the reactive power flowing from node p to the parallel side of GUPFC; P nm is the active power flowing from node n to node m; are the active and reactive powers; ΔP nm , ΔQ nm are the unbalances of the active and reactive powers flowing from node n to node m; PEsh = Re(Vsh·Ish * ) is the real part of the active power flowing from node p to the parallel side of GUPFC; PEse k = Re(Vse k ·I *nm,k ) is the real part of the active power; the power loss P dc on the DC side = 0; ΔPEx is the unbalance of the real part of the active power;

[0104]

[0105] Wherein, Q sta and are the reactive power and reference reactive power of the STATCOM; ΔQ sta is the reactive power imbalance of the STATCOM; PEsta = Re(Vsta·Ista * ) is the real part of the active power of the STATCOM; ΔPE is the active power imbalance of the STATCOM;

[0106]

[0107] Wherein, ΔPEse is the active power imbalance of the SSSC; PEse = Re(Vsssc·Isssc * ) is the real part of the active power of the SSSC;

[0108] 2.2) Simplify the imbalance equations of each module of the power electronic device to obtain:

[0109]

[0110] Wherein, the vector F VSC = [ΔP c.dc , ΔP f , ΔQ f , ΔQ p T , the vector F GUPFC = [ΔV p / ΔQsh, ΔP nm , ΔQ nm , ΔPEx] T , the vector F STATCOM = [ΔV p / ΔQsh, ΔPEsta] T , the vector F SSSC = [ΔP nm / ΔQ nm , ΔPEsta] T ; x VSC , x GUPFC , x STATCOM and x SSSC represent the bus voltages of the power electronic device, that is and f VSC , f GUPFC , f STATCOM , f SSSC are functions of x VSC , x GUPFC , x STATCOM and x​SSSC Multivariate function;

[0111] 2.3) Using the voltage variables of the AC-DC system as the input quantity, linearize the unbalanced equations of each module of the power electronic device to obtain:

[0112]

[0113] In the formula, the superscript k AIML , k AIML -1 represents the iteration number; represents the linearized variable; represents the unbalance of the linearized variable; the function f PEDs = f VSC , f GUPFC , f STATCOM , f SSSC .

[0114] In step 4), the injection power flowing from the power electronic device into the AC and DC systems includes the injection power of the VSC converter station, the injection power of the GUPFC (Generalized Unified Power Flow Controller), the injection power of the STATCOM, and the injection power of the SSSC, that is:

[0115] (P in , Q in ) = h(V PEDs , V AC / DC ) (7)

[0116] In the formula, h(·) is the node power injection expression, V PEDs and V AC / DC are the input variables, P in and Q in are the output variables.

[0117] The injection power of the VSC converter station is as follows:

[0118]

[0119] In the formula, the admittance Z tf = G tf +jB tf , the voltage voltage

[0120] The injection power of the GUPFC includes the power flowing from the shunt node into the GUPFC, the power flowing from node m k to node n k , the power flowing from node n k to node mk Power;

[0121] Among them, the power flowing into the GUPFC at the parallel node is as follows:

[0122]

[0123] Among them, the admittance Zsh = Gsh + jBsh, voltage θsh is the voltage phase angle; Vsh is the voltage amplitude; Gsh, Bsh are conductance and susceptance; Psh, Qsh are the active and reactive powers flowing into the GUPFC at the parallel node;

[0124] Node m k Flowing to node n k The power is as follows:

[0125]

[0126] In the formula, the admittance Zse k = Gse k + jBse k voltage Voltage Voltage P mn,k 、Q mn,k are the active and reactive powers flowing from node m k to node n k ;

[0127] Node n k Flowing to node m k The power is as follows:

[0128]

[0129] In the formula, P nm,k 、Q nm,k are the active and reactive powers flowing from node n k to node m k ;

[0130] The injected power of the STATCOM is as follows:

[0131]

[0132] In the formula, the admittance Zsta = Gsta + jBsta, voltage Psta, Qsta are the injected active and reactive powers of the STATCOM.

[0133] The injected power of the SSSC includes the power flowing from node m to node n and the power flowing from node n to node m;

[0134] Among them, the power flowing from node m to node n is as follows:

[0135]

[0136] Among them, the admittance Zsssc = Gsssc + jBsssc, voltage Voltage Voltage

[0137] The power flowing from node n to node m is as follows:

[0138]

[0139] In step 5), the steps of constructing the unbalanced equations of the AC and DC systems and performing linearization processing include:

[0140] 5.1) Construct the power unbalanced equation of bus i in the AC system, that is:

[0141]

[0142] Among them, is the voltage of buses i and j; Y ij is the element in the i-th row and j-th column of the node admittance matrix of the AC system; P i and Q i are the active and reactive power injections on bus i respectively; ΔP i and ΔQ i are the active and reactive power unbalances on bus i;

[0143] 5.2) Simplify the power unbalanced equation of bus i in the AC system to obtain:

[0144] F AC = f AC (V AC ) = 0 (16)

[0145] In the formula, the vector F AC = [ΔP, ΔQ] T ; V AC is the bus voltage of the AC system; f AC is a function of the voltage V AC ;

[0146] 5.3) Construct the node unbalanced equation of the DC system, that is:

[0147] ΔP dci = P Gi - P Li + P c.dc,i - V dc,i ∑ j Vdcj Y dc,ij = 0 (17)

[0148] In the formula, V dc,i is the voltage of DC bus i; Y dc.ij is the element at the i-th row and j-th column in the node conductance matrix of the DC system; P G,i , P L,i are the active power generation and active load power on DC bus i respectively; ΔP dci is the active power imbalance of the DC system node; V dcj is the voltage of node j; P c.dc,i is the active power of DC bus i;

[0149] 5.4) Simplify the node imbalance equation of the DC system to obtain:

[0150] F DC = f DC (V DC ) = 0 (18)

[0151] In the formula, vector F DC = [ΔP dc1 , ΔP dc2 , ΔP dc3 ,…] T , V DC is the bus voltage of the DC system; f DC is a function of V DC ;

[0152] 5.5) Based on the simplified AC and DC system node imbalance equations, construct the power mismatch equation of the AC-DC system, that is:

[0153]

[0154] where, f AC / DC is the power mismatch equation of the AC-DC system, P in and Q in are input variables, and V AC / DC is the variable to be solved;

[0155] 5.6) At the reference point χ0, perform Taylor expansion on the power mismatch equation of the AC-DC system, retain the first-order term and ignore the higher-order terms to obtain the imbalance equations of the AC and DC systems, that is:

[0156]

[0157] The convergence criterion is as follows:

[0158] max|χ (k) - χ (k-1) | < εAIML (21)

[0159] Among them, χ represents all state variables in the system, including the bus voltages of AC / DC systems and power electronic devices; the superscript (k) represents the k-th iteration; ε AIML is the convergence coefficient.

[0160] Example 2:

[0161] A power flow calculation method for an AC / DC power grid with multiple types of power electronic devices based on alternating iterative linearization, comprising the following steps:

[0162] 1) Obtain the basic data of the power system;

[0163] 2) Based on the voltage data of the AC / DC system, construct the unbalanced equations of each module of the power electronic device and perform linearization to obtain the unbalanced linear equations of each module of the power electronic device;

[0164] 3) Based on the basic data of the power system, calculate the power flow of each module of the power electronic device using the unbalanced linear equations of each module of the power electronic device;

[0165] 4) Based on the power flow of each module of the power electronic device, calculate the injection power flowing from the power electronic device into the AC and DC systems;

[0166] 5) Construct the unbalanced equations of the AC and DC systems and perform linearization to obtain the unbalanced linear equations of the AC and DC systems;

[0167] 6) Based on the injection power flowing from the power electronic device into the AC and DC systems, calculate the power flow distribution of the AC / DC power grid using the unbalanced linear equations of the AC and DC systems;

[0168] 7) Repeat steps 2)-6), and determine whether the power flow distribution of the AC / DC power grid converges in two iterations. If so, output the final power flow distribution of the AC / DC power grid. If not, return to step 2) and continue the iteration;

[0169] Example 3:

[0170] A power flow calculation method for an AC / DC power grid with multiple types of power electronic devices based on alternating iterative linearization, the technical content is the same as that of Example 2. Further, in step 1), the basic data of the power system includes the topological structure of the power system, the magnitude and location of the source and load, the type and quantity of power electronic devices, and the control parameters of the power electronic devices.

[0171] Example 4:

[0172] A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization, the technical content is the same as any one of Embodiments 2-3. Further, in step 2), the steps of constructing the unbalanced equations of each module of the power electronic device and performing linearization processing include:

[0173] 2.1) Construct the unbalanced equations of each module of the power electronic device, that is:

[0174]

[0175] In the formula, P c.dc is the active power flowing from the converter station to the DC system; ΔP c.dc is the unbalance of the active power flowing from the converter station to the DC system; P loss is the active power loss; P c is the active power of node c; ΔP f , ΔQ f are the unbalances of the active power and reactive power output by node f; P cf , Q cf are the active power and reactive power flowing from node f to node c; P fp , Q fp are the active power and reactive power flowing from node f to node p; Q f is the reactive power output by node f; Q p is the reactive power flowing from the converter station to node p; is the reactive power reference value; ΔQ p is the unbalance of the reactive power flowing to node p;

[0176]

[0177] In the formula, V p is the voltage amplitude of node p; is the reference voltage amplitude of node p; ΔV p is the unbalance of the voltage amplitude of node p; Q sh is the reactive power flowing from node p to the shunt side of GUPFC; is the reactive power reference value flowing from node p to the shunt side of GUPFC; ΔQ sh is the unbalance of the reactive power flowing from node p to the shunt side of GUPFC; P nm is the active power flowing from node n to node m; are the active and reactive powers; ΔP nm , ΔQ nm are the unbalances of the active and reactive powers flowing from node n to node m; PEsh = Re(Vsh·Ish * ) is the real part of the active power flowing from node p to the shunt side of GUPFC; PEsek = Re(Vse k ·I *nm,k ) is the real part of the active power; the power loss P dc = 0; ΔPEx is the imbalance of the real part of the active power;

[0178]

[0179] In the formula, Q sta , are the reactive power and reference reactive power of the STATCOM; ΔQ sta is the reactive power imbalance of the STATCOM; PEsta = Re(Vsta·Ista * ) is the real part of the active power of the STATCOM; ΔPE is the active power imbalance of the STATCOM;

[0180]

[0181] In the formula, ΔPEse is the active power imbalance of the SSSC; PEse = Re(Vsssc·Isssc * ) is the real part of the active power of the SSSC;

[0182] 2.2) Simplify the imbalance equations of each module of the power electronic device to obtain:

[0183]

[0184] Among them, the vector F VSC = [ΔP c.dc , ΔP f , ΔQ f , ΔQ p T , the vector F GUPFC = [ΔV p / ΔQsh, ΔP nm , ΔQ nm , ΔPEx] T , the vector F STATCOM = [ΔV p / ΔQsh, ΔPEsta] T , the vector F SSSC = [ΔP nm / ΔQ nm , ΔPEsta] T ; x VSC , x GUPFC , x STATCOM and x SSSC represent the bus voltages of the power electronic device, that is and f VSC ​, f GUPFC , f STATCOM , f SSSC is a multivariate function with respect to x VSC , x GUPFC , x STATCOM and x SSSC ;

[0185] 2.3) Using the voltage variables of the AC-DC system as the input quantity, linearize the unbalanced equations of each module of the power electronic device to obtain:

[0186]

[0187] In the formula, the superscript k AIML , k AIML -1 represents the number of iterations; represents the linearized variable; represents the unbalance of the linearized variable; the function f PEDs = f VSC , f GUPFC , f STATCOM , f SSSC .

[0188] Example 5:

[0189] A power flow calculation method for an AC-DC power grid with multiple types of power electronic devices based on alternating iterative linearization, the technical content is the same as any one of Examples 2-4. Further, in step 4), the injection power flowing from the power electronic device into the AC and DC systems includes the injection power of the VSC converter station, the injection power of the GUPFC, the injection power of the STATCOM, and the injection power of the SSSC, that is:

[0190] (P in , Q in ) = h(V PEDs , V AC / DC ) (7)

[0191] In the formula, h(·) is the node power injection expression, V PEDs and V AC / DC are the input variables, P in and Q in are the output variables.

[0192] Example 6:

[0193] A power flow calculation method for an AC-DC power grid with multiple types of power electronic devices based on alternating iterative linearization, the technical content is the same as any one of Examples 2-5. Further, the injection power of the VSC converter station is as follows:

[0194]

[0195] In the formula, the admittance Z tf = G tf + jB tf , the voltage voltage

[0196] Embodiment 7:

[0197] A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization, the technical content is the same as any one of Embodiments 2-6. Further, the injection power of the GUPFC includes the power flowing into the GUPFC from the shunt node, the power flowing from node m k to node n k and the power flowing from node n k to node m k ;

[0198] Among them, the power flowing into the GUPFC from the shunt node is as follows:

[0199]

[0200] Among them, the admittance Zsh = Gsh + jBsh, the voltage θsh is the voltage phase angle; Vsh is the voltage amplitude; Gsh, Bsh are conductance and susceptance; Psh, Qsh are the active and reactive powers flowing into the GUPFC from the shunt node;

[0201] The power flowing from node m k to node n k is as follows:

[0202]

[0203] In the formula, the admittance Zse k = Gse k + jBse k , the voltage voltage voltage P mn,k , Q mn,k are the active and reactive powers flowing from node m k to node n k ;

[0204] The power flowing from node n k to node m k is as follows:

[0205]

[0206] In the formula, P nm,k , Q nm,kFor node n k Flows to node m k Active and reactive power.

[0207] Embodiment 8:

[0208] A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization, the technical content is the same as any one of Embodiments 2-7. Further, the injection power of the STATCOM is as follows:

[0209]

[0210] In the formula, the admittance Zsta = Gsta + jBsta, the voltage Psta and Qsta are the injected active and reactive powers of the STATCOM.

[0211] Embodiment 9:

[0212] A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization, the technical content is the same as any one of Embodiments 2-8. Further, the injection power of the SSSC includes the power flowing from node m to node n and the power flowing from node n to node m;

[0213] Among them, the power flowing from node m to node n is as follows:

[0214]

[0215] Among them, the admittance Zsssc = Gsssc + jBsssc, the voltage Voltage Voltage

[0216] The power flowing from node n to node m is as follows:

[0217]

[0218] Embodiment 10:

[0219] A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization, the technical content is the same as any one of Embodiments 2-9. Further, in step 5), the steps of constructing the unbalanced equations of the AC and DC systems and performing linearization processing include:

[0220] 5.1) Construct the power unbalanced equation of bus i in the AC system, that is:

[0221]

[0222] Among them, Is the voltage of bus i and j; Yij is the element in the \(i\)-th row and \(j\)-th column of the nodal admittance matrix of the AC system; \(P\) i and \(Q\) i are the active and reactive power injections at bus \(i\) respectively; \(\Delta P\) i and \(\Delta Q\) i are the active and reactive power imbalances at bus \(i\);

[0223] 5.2) Simplify the power imbalance equation of bus \(i\) in the AC system to obtain:

[0224] \(F\) AC = \(f\) AC (\(V\) AC ) = 0 (16)

[0225] In the formula, the vector \(F\) AC = [\(\Delta P\), \(\Delta Q\)] T ; \(V\) AC is the bus voltage of the AC system; \(f\) AC is a function of the voltage \(V\) AC ;

[0226] 5.3) Construct the DC system nodal imbalance equation, that is:

[0227] \(\Delta P\) dci = \(P\) Gi - \(P\) Li + \(P\) c.dc,i - \(V\) dc,i \(\sum\) j \(V\) dcj \(Y\) dc,ij = 0 (17)

[0228] In the formula, \(V\) dc,i is the voltage of DC bus \(i\); \(Y\) dc.ij is the element in the \(i\)-th row and \(j\)-th column of the nodal conductance matrix of the DC system; \(P\) G,i , \(P\) L,i are the active power generation and active power load of DC bus \(i\) respectively; \(\Delta P\) dci is the active power imbalance of the DC system node; \(V\) dcj is the voltage of node \(j\); \(P\) c.dc,i is the active power of DC bus \(i\);

[0229] 5.4) Simplify the DC system nodal imbalance equation to obtain:

[0230] \(F\) DC = \(f\) DC (\(V\) DC ) = 0 (18)

[0231] In the formula, the vector \(F\) DC = [\(\Delta P\) dc1 , \(\Delta P\)dc2 , ΔP dc3 , …] T , V DC is the bus voltage of the DC system; f DC is a function of V DC .

[0232] 5.5) Based on the simplified AC-DC system node imbalance equations, construct the power mismatch equation of the AC-DC system, that is:

[0233]

[0234] where f AC / DC is the power mismatch equation of the AC-DC system, P in and Q in are input variables, and V AC / DC is the variable to be solved;

[0235] 5.6) At the reference point χ0, perform Taylor expansion on the power mismatch equation of the AC-DC system, retain the first-order term and ignore the high-order terms, to obtain the imbalance equation of the AC-DC system, that is:

[0236]

[0237] Example 11:

[0238] A power flow calculation method for an AC-DC power grid with multiple types of power electronic devices based on alternating iterative linearization, the technical content is the same as any one of Examples 2-10. Further, the convergence criterion is as follows:

[0239] max|χ (k) - χ (k-1) | < ε AIML (21)

[0240] where χ represents all state variables in the system, including the bus voltages of the AC-DC system and power electronic devices; the superscript (k) represents the k-th iteration; ε AIML is the convergence coefficient.

[0241] Example 12:

[0242] A power flow calculation method for an AC-DC power grid with multiple types of power electronic devices based on alternating iterative linearization, the technical content is the same as any one of Examples 2-11. GUPFC can be replaced by UPFC.

[0243] Example 13:

[0244] A power flow calculation method for an AC-DC power grid with multiple types of power electronic devices based on alternating iterative linearization, the steps are as follows:

[0245] Step S1: Input the basic data of the power system and the control parameters of the power electronic devices, set the initial voltage values of the AC-DC system and the power electronic devices, and start the iterative calculation.

[0246] Step S2: Based on the voltage data of the AC-DC system, construct the unbalanced equations of each module of the power electronic devices, perform linearization on them, and then calculate the power flow.

[0247] Step S3: Based on the voltage data of the AC-DC system and the power electronic devices, calculate the injection power flowing from the power electronic devices into the AC and DC systems.

[0248] Step S4: Based on the injection power flowing from the power electronic devices into the AC and DC systems, construct the unbalanced equations of the AC and DC systems, perform linearization on them, and calculate the power flow distribution.

[0249] Step S5: Determine whether two iterations (the k-th iteration and the (k - 1)-th iteration) satisfy the convergence criterion of the deterministic power flow.

[0250] The characteristics of Step S1 are as follows:

[0251] Input the basic data of the power system and the parameters of the power electronic devices, including the topological structure of the power system, the magnitudes and locations of the sources and loads, the types, quantities, and control parameters of the power electronic devices, etc. Set the initial voltage values of the AC-DC system and the power electronic devices, and start the iterative calculation.

[0252] The characteristics of Step S2 are as follows:

[0253] S21: Basic linearization method

[0254] The equation to be solved is: F(x) = f(x1, x2, x3, …) = 0. F is a multivariate function of x = [x1, x2, x3, …], and x is the state variable, i.e., the bus voltage magnitude V and the phase angle θ.

[0255] The linearization equation of F(x) with respect to φ(x) at φ(x0) can be obtained by retaining the first-order term of its Taylor expansion:

[0256]

[0257] For the linearization variable φ(x), there are three typical forms, and their state variables are as follows:

[0258]

[0259] In Equation (1), The value of can be obtained by the following formula:

[0260]

[0261] According to Equation (3), first calculate and can be determined according to different linearization types in Equation (2) Multiplying the two can conveniently calculate In the following linearization strategy, since the form (V,θ) is simple and has a low computational burden, this form is adopted for calculation.

[0262] It should be noted that linearization is only applied to the nonlinear equations in the Alternating Iterative Method (AIM), without changing its process and convergence criteria. Therefore, it can be proved that the accuracy of using the Alternating Iterative Method based on Linearization (AIML) is consistent with that of AIM. Figure 1 Shows a schematic diagram of three different methods (Unified Iterative Method (UIM), Alternating Iterative Method (AIM), and Alternating Iterative Method based on Linearization (AIML)) for each iteration.

[0263] Figure 1 J in Nx represents the Jacobian matrix (the subscript Nx represents the dimension of the matrix). The larger the Nx of the Jacobian matrix, the greater the computational burden required to solve the unbalanced equation. If the unbalanced equation is solved by inverting the Jacobian matrix J Nx the time complexity of the inverse matrix is Ο(Nx 3 ). The computational complexity of J N is higher than that of the combination of J N1 , J N2 , …, J Nn (N = N1 + N2 + … + Nn), and this becomes more obvious as N increases. As can be seen from Figure 1 when using UIM for each iteration, a Jacobian matrix containing all variables needs to be calculated. For AIM, although the entire system is divided into several modules, in order to meet its convergence criteria, the Jacobian matrix of each module still needs to be calculated repeatedly. Therefore, it is difficult to compare the computational efficiency of AIM and UIM. Although the entire system of AIML is divided into several modules like AIM, each module of AIML only needs to calculate the Jacobian matrix once. Therefore, for each iteration, the computational efficiency ranking of the three methods is obviously: AIML > AIM ≈ UIM.

[0264] S22: Steady-state model of power electronic equipment

[0265] The equivalent circuits of VSC converter stations, GUPFC (or UPFC), STATCOM, and SSSC are as Figure 1 shown. Note that the steady-state model of the VSC converter station considers the losses related to power exchange, while other models, such as GUPFC (or UPFC), SSSC, and STATCOM, ignore these power losses. ConsideringFigure 2 In the positive direction of power, the local regulation and unbalanced equations of power electronic devices are as follows:

[0266] (1) VSC converter station

[0267] The detailed control parameters of the local regulation of the VSC converter station are given in Table 1.

[0268] Table 1 Control parameters and types of VSC converter station

[0269]

[0270] For the power station, due to the AC bus voltage and the complex power S p = P p + jQ p being known, the voltage of the power station and can be calculated by the following formula:

[0271] For the voltage station, the unbalanced equation is:

[0272]

[0273] where P c.dc is known, is the set value.

[0274] (2) GUPFC (or UPFC)

[0275] For the shunt side, GUPFC (or UPFC) can control the magnitude of the AC bus voltage or the injected reactive power Q refsh . For the series side, GUPFC (or UPFC) can control the power flow of the series branch The unbalanced equation of GUPFC is:

[0276]

[0277] where PEsh = Re(Vsh · Ish * ) and PEse k = Re(Vse k · I *nm,k ), and the superscript "*" is the conjugate of the complex number. In addition, the power loss on the DC side is ignored, i.e., P dc ≈ 0.

[0278] (3) STATCOM

[0279] STATCOM can control the magnitude of the AC bus voltage or the injected reactive power Q refsta . The unbalanced equation of the GUPFC is:

[0280]

[0281] where PEsta = Re(Vsta·Ista * ), and P dc ≈ 0.

[0282] (4) SSSC

[0283] The SSSC can control the active power or the reactive power . The unbalanced equation of the SSSC is:

[0284]

[0285] where PEste = Re(Vsssc·Isssc * ), and P dc ≈ 0.

[0286] The unbalanced equations of the power electronic devices represented in Eqs. (4)-(7) can be simplified to:

[0287]

[0288] where F VSC = [ΔP c.dc , ΔP f , ΔQ f , ΔQ p T , F GUPFC = [ΔV p / ΔQsh, ΔP nm , ΔQ nm , ΔPEx] T , F STATCOM = [ΔV p / ΔQsh, ΔPEsta] T , F SSSC = [ΔP nm / ΔQ nm , ΔPEsta] T , x VSC , x GUPFC , x STATCOM and x SSSC represent the bus voltages of the power electronic devices, i.e.: and

[0289] S32: The linearization formulas of each power electronic device

[0290] ​In the alternating iteration method, the voltage variables of the AC-DC system are used as the input variables of Equation (8). Therefore, Equation (8) can be generally expressed as:

[0291] f PEDs (V PEDs |V AC / DC ) = 0 (9)

[0292] Therefore, the V obtained in the (k - 1)-th iteration AIM and the V to be solved in the k-th iteration AC / DC satisfy Equation (9), that is: AIM PEDs

[0293]

[0294] Using the method mentioned in S21 to perform Taylor expansion on Equation (10) at the reference point χ0, and retaining the first-order term and ignoring the higher-order terms, the linearized expression can be obtained:

[0295]

[0296] Therefore, in the AIM, the V obtained in the (k - 1)-th iteration AIML and the V to be solved in the k-th iteration AC / DC satisfy: AIML PEDs

[0297]

[0298] Solving Equation (12) can obtain the voltages of each node of the power electronic device.

[0299] The characteristics of step S3 are as follows:

[0300] (1) VSC converter station

[0301] The injection power of the VSC converter station is:

[0302]

[0303] where Z tf = G tf + jB tf ,

[0304] (2) GUPFC (or UPFC)

[0305] For the shunt side of GUPFC (or UPFC), the power flowing into GUPFC (or UPFC) at the shunt node is:

[0306] ​​​​

[0307] where Zsh = Gsh + jBsh,

[0308] For the shunt side of GUPFC (or UPFC), at node m k the power flowing to node n k is:

[0309]

[0310] where Zse k = Gse k + jBse k ,

[0311] At node n k the power flowing to node m k is:

[0312]

[0313] (3) STATCOM

[0314] For STATOM, the power flowing into STATCOM at node p is:

[0315]

[0316] where Zsta = Gsta + jBsta,

[0317] (3) SSSC

[0318] For SSSC, the power flowing from node m to node n is:

[0319]

[0320] where Zsssc = Gsssc + jBsssc,

[0321] The power flowing from node n to node m is:

[0322]

[0323] Based on Eqs. (13), (14), (15), (16), (17), (18) and (19), the power injected by the power electronic device into the AC and DC system nodes can be expressed as:

[0324] (P in , Q in ) = h(V PEDs , V AC / DC ) (20)

[0325] where h(·) is the expression of the nodal power injection, and V PEDs and V AC / DC are input variables, and P in and Q in are output variables.

[0326] The features of step S4 are as follows:

[0327] S41: Calculate the AC system nodal imbalance equation

[0328] The power imbalance equation of bus i in the AC system is:

[0329]

[0330] where is the voltage of bus i / j; Y ij is the element in the i-th row and j-th column of the AC system nodal admittance matrix; P i and Q i are the active and reactive power injections on bus i (injections from loads, generators, and power electronic devices), respectively. And equation (21) can be simplified to:

[0331] F AC = f AC (V AC ) = 0 (22)

[0332] where F AC = [ΔP, ΔQ] T , and V AC is the bus voltage of the AC system.

[0333] S42: Calculate the DC system nodal imbalance equation

[0334] The imbalance equation in the DC system is:

[0335] ΔP dci = P Gi - P Li + P c.dc,i - V dc,i ∑ j V dcj Y dc,ij = 0 (23)

[0336] where V dc,i is the voltage of DC bus i; Y dc.ij is the element in the i-th row and j-th column of the DC system nodal conductance matrix; P Gdc,i , P Ldc,i are the active power generation and active load power on DC bus i, respectively. And equation (23) can be simplified to:

[0337] F DC = f DC (V DC ) = 0 (24)

[0338] where F DC = [ΔP dc1 , ΔP dc2 , ΔP dc3 , …] T , and V DC represents the bus voltage of the DC system.

[0339] S43: Linearization formula of AC-DC system

[0340] Based on Eqs. (22) and (24), in AIM, the power mismatch equation of the AC-DC system can be generally expressed as:

[0341] f AC / DC (V AC / DC |P in , Q in ) = 0 (25)

[0342] where f AC / DC is the power mismatch equation of the AC-DC system, where P in and Q in are input variables (known quantities), and V AC / DC is the variable to be solved.

[0343] Therefore, the P AIM and Q in obtained by the k in -th iteration calculation and the V AIM to be solved in the k AC / DC -th iteration satisfy:

[0344]

[0345] Performing Taylor expansion of Eq. (26) at the reference point χ0, retaining the first-order term and ignoring the higher-order terms, the linearization expression can be obtained:

[0346]

[0347] Therefore, in AIML, the P AIML and Q in obtained by the k in -th iteration calculation and the V AIML to be solved in the k PEDs -th iteration satisfy:

[0348]

[0349] Solve Equation (28) to obtain the voltages at each node of the AC-DC system.

[0350] The features of step S5 are as follows:

[0351] Continuously iterate to solve Equations (12), (20), and (28), and determine whether two consecutive iterations (the k-th iteration and the (k - 1)-th iteration) satisfy the convergence criterion of the deterministic power flow:

[0352] max|χ (k) -χ (k-1) |<ε AIML (29)

[0353] where χ represents all state variables in the system, including the bus voltages of the AC-DC system and power electronic devices; the superscript (k) represents the k-th iteration; ε AIML is the convergence coefficient of the deterministic power flow. Usually, ε AIML =10 -6 . If the convergence criterion in Equation (29) is not satisfied, repeat steps S2 to S5; otherwise, calculate other required data and give the calculation results.

[0354] From and the condition that ε AIML is an infinitesimal quantity (ε AIML =10 -6 ), it can be known that (that is: ), at this time the linearized variables approximately approach zero: (that is: ). Then substitute into Equations (12) and (28), and it can be deduced that: and This result is approximately consistent with Equations (10) and (26). Therefore, the calculation results of AIML can approximately satisfy the non-linear equations under the AIM framework.

[0355] Example 14:

[0356] Verification of a power flow calculation method for an AC-DC power grid with multiple types of power electronic devices based on alternating iterative linearization is as follows:

[0357] The present invention designs three test cases to verify the performance of the alternating iterative method based on linearization. Only local regulation of power electronic devices is considered in the test cases. The control parameters of the power electronic devices are given in Table 1. The test case parameters are from MATPOWER. The results of UIM, AIM, and AIML are compared through the test cases, and the calculation time of each method is discussed in detail. The convergence accuracy of these three methods is set to 10 -6 .

[0358] Table 1 Parameters of the numerical example of the present invention

[0359]

[0360]

[0361] All tests were conducted using MATLAB 2023a on a computer with an Intel(R) Core(TM) i7-13700K CPU @ 3.40 GHz and 32 GB of 6400 MHz DDR5.

[0362] (1) Power flow calculation results

[0363] At the same convergence accuracy, Figure 4 and Figure 5 the results of AIML in [reference] are very close to those of AIM and UIM, which further proves the feasibility and high accuracy of AIML for DPF.

[0364] (2) Comparison of running times of different algorithms

[0365] Table 2 describes the calculation times and iteration numbers of the three methods. Both AIML and AIM can be divided into three modules: the AC module, the DC module, and the power electronic device module. The power electronic device module includes four parts: GUPFC (or (UPFC)), SSSC, STATCOM, and VSC. The iteration numbers of each module for the k-th iteration using AIM are given in Table 3.

[0366] Table 2 Comparison of operation times and iteration numbers of different methods

[0367]

[0368] Table 3 Iteration numbers of each module using AIM

[0369]

[0370] Note: In this table, " / " indicates no relevant data.

[0371] In the numerical examples of this paper, when using AIML, each module is calculated only once in each iteration. Therefore, the number of iterations of each module is equal to the number of iterations of AIML. According to Tables 2 and 3, it can be found that in Numerical Example 1, not only is the number of iterations of AIM less than that of AIML (4 < 9), but the total number of iterations of each module is also less than that of AIML (except for the VSC module). This results in a slightly longer calculation time for AIML than for AIM. In Numerical Example 2, although the number of iterations of AIM and the total number of iterations of each module (except for the AC module) are smaller than those of AIML, the calculation time of AIML is almost the same as that of AIM. The reason is that the calculation cost of the AC module is always larger than that of other modules, and the number of iterations of AIM in the AC module is more than that of AIML. In Numerical Example 3, the test system is more complex, and the number of iterations of AIM and UIM increases accordingly. The number of iterations required by AIM is less than that of AIML (9 < 10), but the total number of iterations of each module in AIM is mostly larger than that of AIML (except for the DC system). This makes the calculation time of AIML shorter than that of AIM. In addition, in these three numerical examples, the calculation time of UIM is always the longest.

[0372] From the analysis results of the three numerical examples, it can be seen that AIML can effectively handle the deterministic power flow problem of AC-DC systems containing power electronic devices. Compared with other deterministic power flow calculation methods, when the number of iterations of AIML is less than or equal to that of AIM, AIML is significantly superior to UIM and AIM in terms of calculation efficiency. Moreover, as the system scale continues to expand, this advantage becomes more prominent, further highlighting the value of AIML in complex system analysis.

Claims

1. A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization, characterized in that, It includes the following steps: 1) Obtain the basic data of the power system. 2) Based on the voltage data of the AC-DC system, construct the unbalanced equations of each module of the power electronic device, and perform linearization to obtain the unbalanced linear equations of each module of the power electronic device; 3) Based on the basic data of the power system, use the unbalanced linear equations of each module of the power electronic device to calculate the power flow of each module of the power electronic device; 4) Based on the power flow of each module of the power electronic device, calculate the injection power flowing from the power electronic device into the AC and DC systems; 5) Construct the unbalanced equations of the AC and DC systems, and perform linearization to obtain the unbalanced linear equations of the AC and DC systems; 6) Based on the injection power flowing from the power electronic device into the AC and DC systems, use the unbalanced linear equations of the AC and DC systems to calculate the power flow distribution of the AC-DC power grid; 7) Repeat steps 2)-6), and judge whether the power flow distribution of the AC-DC power grid converges in two iterations. If so, output the final power flow distribution of the AC-DC power grid. If not, return to step 2) and continue the iteration.

2. A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization according to claim 1, characterized in that In step 1), the basic data of the power system includes the topological structure of the power system, the magnitude and location of the power sources and loads, the types and quantities of power electronic devices, and the control parameters of the power electronic devices.

3. A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization according to claim 1, characterized in that In step 2), the steps of constructing the unbalanced equations of each module of the power electronic device and performing linearization include: 2.1) Construct the unbalanced equations of each module of the power electronic device, that is: Where, P c.dc is the active power flowing from the converter station to the DC system; ΔP c.dc is the active power imbalance flowing from the converter station to the DC system; P loss is the active power loss; P c is the active power of node c; ΔP f , ΔQ f are the imbalances of the active power and reactive power output from node f; P cf , Q cf are the active power and reactive power flowing from node f to node c; P fp , Q fp are the active power and reactive power flowing from node f to node p; Q f is the reactive power output from node f; Q p is the reactive power flowing from the converter station to node p; is the reactive power reference value; ΔQ p is the reactive power imbalance flowing to node p; Where, V p is the voltage amplitude of node p; is the reference voltage amplitude of node p; ΔV p is the voltage amplitude unbalance of node p; Q sh is the reactive power flowing from node p to the shunt side of GUPFC; is the reference value of the reactive power flowing from node p to the shunt side of GUPFC; ΔQ sh is the reactive power unbalance flowing from node p to the shunt side of GUPFC; P nm is the active power flowing from node n to node m; is the active and reactive power; ΔP nm , ΔQ nm are the active and reactive power unbalances flowing from node n to node m; PEsh = Re(Vsh·Ish * ) is the real part of the active power flowing from node p to the shunt side of GUPFC; PEse k = Re(Vse k ·I *nm,k ) is the real part of the active power; the power loss P dc = 0; ΔPEx is the real part unbalance of the active power; Where Q sta and are the reactive power and reference reactive power of the STATCOM; ΔQ sta is the reactive power imbalance of the STATCOM; PEsta = Re(Vsta·Ista * ) is the real part of the active power of the STATCOM; ΔPE is the active power imbalance of the STATCOM; where ΔPEse is the active power imbalance of the SSSC; PEse = Re(Vsssc·Isssc * ) is the real part of the active power of the SSSC; 2.2) Simplify the unbalanced equations of each module of the power electronic device to obtain: Among them, vector F VSC = [ΔP c.dc , ΔP f , ΔQ f , ΔQ p T , vector F GUPFC = [ΔV p / ΔQsh, ΔP nm , ΔQ nm , ΔPEx] T , vector F STATCOM = [ΔV p / ΔQsh, ΔPEsta] T , vector F SSSC = [ΔP nm / ΔQ nm , ΔPEsta] T ; x VSC , x GUPFC , x STATCOM and x SSSC represent the bus voltage of the power electronic device, i.e., and f VSC , f GUPFC , f STATCOM , f SSSC are multivariate functions of x VSC , x GUPFC , x STATCOM and x SSSC ;​ 2.3) Using the voltage variables of the AC / DC system as the input variables, linearize the unbalanced equations of each module of the power electronic device to obtain: where the superscript k AIML and k AIML -1 represent the iteration number; represents the linearized variable; represents the imbalance of the linearized variable; the function f PEDs = f VSC , f GUPFC , f STATCOM , f SSSC .

4. A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization according to claim 1, characterized in that In step 4), the injection power flowing from the power electronic device into the AC and DC systems includes the injection power of the VSC converter station, the injection power of the GUPFC, the injection power of the STATCOM, and the injection power of the SSSC, that is: (P in , Q in ) = h(V PEDs , V AC / DC ) In Equation (7), h(·) is the node power injection expression, V PEDs and V AC / DC are input variables, P in and Q in are output variables.

5. A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization, as described in claim 4, wherein The injection power of the VSC converter station is as follows: where the admittance Z tf = G tf + jB tf , the voltage voltage 6. A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization, as claimed in claim 4, wherein The injection power of the GUPFC includes the power flowing into the GUPFC at the shunt node, the power flowing from node m k to node n k , the power flowing from node n k to node m k ; Among them, the power flowing into the GUPFC at the parallel node is as follows: Among them, the admittance Zsh = Gsh + jBsh, and the voltage θsh is the voltage phase angle; Vsh is the voltage amplitude; Gsh and Bsh are conductance and susceptance; Psh and Qsh are the active and reactive powers flowing into the GUPFC at the shunt node; Node m k Flows to node n k The power is as follows: Wherein, the admittance Zse k = Gse k + jBse k , the voltage voltage voltage P mn,k 、Q mn,k are the active and reactive powers flowing from node m k to node n k ; Node n k Flows to node m k The power is as follows: where P nm,k , Q nm,k are the active and reactive powers flowing from node n k to node m k .

7. A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization according to claim 4, characterized in that, The injection power of the STATCOM is as follows: where the admittance \(Z_{sta}=G_{sta}+jB_{sta}\), and the voltage \(P_{sta}\) and \(Q_{sta}\) are the active and reactive powers injected by the STATCOM.

8. A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization according to claim 4, characterized in that, The injection power of the SSSC includes the power flowing from node m to node n and the power flowing from node n to node m; Among them, the power flowing from node m to node n is as follows: Among them, the admittance Zsssc = Gsssc + jBsssc, voltage Voltage Voltage The power flowing from node n to node m is as follows:

9. A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization according to claim 1, characterized in that In step 5), the steps of constructing the unbalanced equations of the AC and DC systems and performing linearization include: 5.1) Construct the power unbalanced equation of bus i in the AC system, that is: wherein, is the voltage of busbars i and j; Y ij is the element in the i-th row and j-th column of the nodal admittance matrix of the AC system; P i and Q i are the active and reactive power injections on busbar i respectively; ΔP i and ΔQ i are the active and reactive power imbalances on busbar i; 5.2) Simplify the power unbalanced equation of bus i in the AC system to obtain: F AC = f AC (V AC ) = 0 (16) Wherein, vector F AC = [ΔP, ΔQ] T ; V AC is the bus voltage of the AC system; f AC is a function of voltage V AC ; 5.3) Construct the node unbalanced equation of the DC system, that is: ΔP dci = P Gi - P Li + P c.dc,i - V dc,i ∑ j V dcj Y dc,ij = 0 (17) Wherein, V dc,i is the voltage of the DC bus i; Y dc.ij is the element at the i-th row and j-th column in the node conductance matrix of the DC system; P G,i , P L,i are respectively the active power generation and the active load power on the DC bus i; ΔP dci is the unbalance of the active power at the nodes of the DC system; V dcj is the voltage of the node j; P c.dc,i is the active power of the DC bus i; 5.4) Simplify the node unbalanced equation of the DC system to obtain: F DC = f DC (V DC ) = 0 (18) where the vector F DC = [ΔP dc1 , ΔP dc2 , ΔP dc3 , …] T , V DC is the bus voltage of the DC system; f DC is a function of V DC . 5.5) Based on the simplified node unbalanced equations of the AC and DC systems, construct the power mismatch equation of the AC-DC system, that is: Among them, f AC / DC is the power mismatch equation of the AC / DC system, P in and Q in are input variables, and V AC / DC is the variable to be solved; 5.6) At the reference point χ0, perform Taylor expansion on the power mismatch equation of the AC-DC system, retain the first-order term and ignore the higher-order terms to obtain the unbalanced equations of the AC and DC systems, that is:

10. A power flow calculation method for AC-DC power grids with multiple types of power electronic devices based on alternating iterative linearization according to claim 1, characterized in that, The convergence criterion is as follows: max|χ (k) -χ (k-1) |<ε AIML (21) where χ represents all state variables in the system, including the bus voltages of AC / DC systems and power electronic devices; the superscript (k) represents the k-th iteration; and ε AIML is the convergence coefficient.

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