A method for calculating power flow in distribution networks that takes into account the SOP voltage-loss relationship

Abstract

This invention provides a distribution network power flow calculation method considering the voltage-loss relationship of the State of Power (SOP), where the SOP consists of two back-to-back converters. The method includes: establishing a basic model for optimal distribution network power flow scheduling; employing an optimization method using convex relaxation techniques to model the power, voltage, and topology change constraints of the distribution network as a mixed-integer second-order cone model; and establishing an AC power flow model for the converters. Using this distribution network power flow calculation method, the power flow distribution under the actual operating constraints of the distribution network can be solved to minimize generation costs and network losses.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of power distribution network power flow calculation, and particularly relates to a power distribution network power flow calculation method considering the voltage-loss relationship of intelligent soft open points (SOP). BACKGROUND

[0002] Intelligent soft open points (SOP) realize the decoupling of alternating current networks through back-to-back converters, and can flexibly control power flow, thereby providing a new means for the operation and dispatching of power distribution networks.

[0003] The prior art mainly adopts a simplified active loss model, such as a constant loss or a fixed proportion with current / injection power, to model the intelligent soft open points in the dispatching optimization problem of power distribution networks. Such modeling method can completely linearize the operation constraints of the intelligent soft open points, but ignores the influence of alternating current-dc voltage on the loss, and is not suitable for situations where the influence of voltage on the loss needs to be accurately considered.

[0004] In addition, there is no unified method for modeling the intelligent soft open points in optimization problems. SUMMARY

[0005] To solve the above problems, the application provides a power distribution network power flow calculation method considering the voltage-loss relationship of intelligent soft open points. For the power, voltage and topology change constraints of the power distribution network, a convex relaxation technique is used to model a mixed integer second-order cone model. For the intelligent soft open points, an alternating current power flow model is used.

[0006] The application is implemented by the following technical solutions:

[0007] A power distribution network power flow calculation method considering the voltage-loss relationship of SOP, wherein the SOP is composed of two back-to-back converters; the method comprises:

[0008] A basic model of power distribution network power flow optimization dispatching is established, and a convex relaxation technique is used to model the power, voltage and topology change constraints of the power distribution network as a mixed integer second-order cone model. An alternating current power flow model of the converter is established.

[0009] Further,

[0010] The alternating current power flow model is linearized and optimized by using a quadratic approximation method.

[0011] Further,

[0012] A basic model of power distribution network power flow optimization dispatching is established, including

[0013] S11 establishes a target function:

[0014] The sum of the network loss and the generation cost is minimized as the optimization objective, and the expression is

[0015] Min (1)

[0016] wherein and are decision variables;

[0017] In equation (1): represents the number of nodes in the distribution network; is the branch current between node and node ; is the branch resistance between node and node ; is the number of power sources in the distribution network; represents the quadratic term fitting coefficient of the generation cost curve; represents the linear term fitting coefficient of the generation cost curve; is the active power injected by the power source into the connected node ;

[0018] S12 determines the constraint conditions:

[0019] 1) Node power balance constraint

[0020] For each node, according to the law of conservation of energy, the total power injected into the node should be zero, that is,

[0021] , (2)

[0022] , (3)

[0023] wherein , , and are decision variables;

[0024] In equations (2) and (3): is the active power injected by the branch into the directly connected node ; is the reactive power injected by the branch into the directly connected node ; is the active power injected by the converter into the directly connected node ; is the reactive power injected by the converter into the directly connected node ; represents the node Number of directly connected nodes; representing the power injection of node Number of directly connected converters; representing the reactive power injection of node to power supply, representing the active load demand of node ; representing the reactive load demand of node ; representing the active load shedding of node ; representing the reactive load shedding of node ;

[0025] For and , the following constraints should be met:

[0026] , (4),

[0027] , (5),

[0028] Equation (4) limits the upper and lower limits of load shedding of load nodes; equation (5) provides that once load shedding occurs, the power factor of the original load node should always remain unchanged;

[0029] 2) Branch power balance constraint

[0030] The power passing through the branch between node and node needs to meet the law of conservation of energy, taking the sum of total power flowing out of the branch between node and node as an example, which is written as

[0031] , , (6),

[0032] , , (7),

[0033] In equation (7): is the reactance between node and node ;

[0034] Considering the operating state of the branch between node and node , 0-1 decision variables are introduced: represents the state of the branch between node and the operating state of the branch between node , representing the normal operation of the branch between node and node , representing the disconnection of the branch between node and node ,

[0035] , , (8),

[0036] , , (9),

[0037] wherein, represents a positive real number;

[0038] 3) Branch power flow balance and security constraints

[0039] In the distribution network, the node voltage and the branch current connected to the node need to satisfy the branch power flow balance equation using the second-order cone technique, i.e.

[0040] ,

[0041] , (10),

[0042] wherein, is the decision variable;

[0043] In equation (10), is the voltage of node ; is the voltage of node ;

[0044] At the same time, the power passing through the branch between node and node is related to the voltage and current of node and node , and the relationship is An equivalent replacement is made using equation (11) by using the convex relaxation technique,

[0045] , , (11),

[0046] In addition, in the optimization process using the convex relaxation technique, the voltage of any node cannot be out of limit, i.e.

[0047] (12),

[0048] wherein: Vmaxis the upper limit of the voltage of node ; Vminis the lower limit of the voltage of node ;

[0049] 4) Radiant constraint

[0050] The operation rules of the power distribution network require that the network topology is always in a radiant state, i.e.

[0051] , , (13).

[0052] Further,

[0053] Equations (1) to (13) constitute the mixed integer second-order cone model.

[0054] Further,

[0055] The establishment of the AC power flow model of the converter includes:

[0056] The converter is regarded as a node of the network, and the converter loss is considered, and the converter power balance equation is established as equation (14),

[0057] (14),

[0058] wherein, and are decision variables;

[0059] In equation (14), represents the high-order fitting coefficient of the converter power loss curve; represents the low-order fitting coefficient; represents the constant term; represents a parameter introduced to consider the relationship between the voltage across the converter and the loss.

[0060] Further,

[0061] The exponential function is:

[0062] (15),

[0063] wherein, is a decision variable;

[0064] In equation (15), is the voltage of the AC side grid-connected point; is the voltage phase angle of the AC side. the voltage phase angle of the DC side;

[0065] the relationship between the AC and DC voltages on both sides of the converter satisfies

[0066] (16),

[0067] In equation (16), is the modulation ratio, satisfying the upper limit constraint

[0068] (17),

[0069] The DC side voltage is also limited by the converter itself, so

[0070] (18),

[0071] In equation (18), is the upper limit constraint of the DC voltage of the converter; is the lower limit constraint of the DC voltage of the converter.

[0072] Further,

[0073] For the exponential function of equation (14) , linearization optimization is performed using the following quadratic approximation method:

[0074] Assuming that the variables and have a generalized exponential relationship , where is the exponential term, then The linearized constraint expression is:

[0075] (19),

[0076] where,

[0077] (20),

[0078] In equation (20), is a predefined natural number; is the initialization discrete interval.

[0079] Further,

[0080] Using (19) and (20), take and , and as decision variables;

[0081] Substitute into equation (14) to eliminate the exponential function​ .

[0082] The application adopts convex relaxation technology to model power, voltage and topology change constraints of the power distribution network as a mixed integer second-order cone model, and adopts an alternating current flow model for the intelligent soft switch, so that the calculation result of the final voltage level of the power flow calculation conforms to the actual voltage loss and constraints of the power distribution network. Meanwhile, a quadratic approximation method of the intelligent soft switch alternating current flow model is proposed, so that the overall model of the power flow calculation of the power distribution network can obtain a global optimal solution by using a mature solver.

[0083] Other features and advantages of the present application will be set forth in the following description, and in part will become apparent to those skilled in the art from the description, or can be learned by practice of the present application. The objects and other advantages of the present application can be achieved and obtained by the structure set forth in the description, claims and drawings. BRIEF DESCRIPTION OF DRAWINGS

[0084] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows. Obviously, the drawings in the following description are some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0085] Figure 1 The alternating current equivalent circuit model of the converter in the present application is shown;

[0086] Figure 2 The node power distribution network test system IEEE RBTS BUS6 F4 is shown;

[0087] Figure 3 The branch impedance table 1 of the test system of the embodiment of the present application is shown;

[0088] Figure 4 The converter parameter table 2 of the test system of the embodiment of the present application is shown;

[0089] Figure 5 The distributed power supply parameter table 3 of the test system of the embodiment of the present application is shown;

[0090] Figure 6 The node load table 4 of the test system of the embodiment of the present application is shown;

[0091] Figure 7 The calculation result data table 5 of the test system of the embodiment of the present application according to the power flow calculation model of the present application is shown.

[0092] Figure 1 In:

[0093] vsci representing the converter connected to the node i ;

[0094] representing the node i AC measured real power; representing the node i AC measured reactive power; representing the real power output by the converter connected to the node i ; representing the reactive power output by the converter connected to the node i ; representing the real power output by the converter connected to the node i ; representing the reactive power output by the converter connected to the node i , defaulting to zero; representing the AC measured current of the converter connected to the node i ; representing the equivalent AC side resistance of the converter connected to the node i ; representing the DC current flowing through the DC branch between the node i and the node h ; j representing the equivalent AC side reactance of the converter connected to the node i , j is the imaginary unit; representing the current input to the DC side of the converter connected to the node i ; representing the node i AC measured voltage; representing the equivalent AC voltage of the converter connected to the node i ; representing the equivalent DC voltage of the converter connected to the node i ; representing the DC current flowing through the DC branch between the node i and the node k ; representing the node i equivalent DC resistance of the DC branch between the node and the node ; i representing the equivalent DC resistance of the DC branch between the node k and the node ; i representing the power loss of the converter connected to the node

[0095] AC grid

[0096] DC grid

[0097] national ‘AC’ grid represents the equivalent national AC grid after modeling the DC part of the converter as AC;

[0098] s represents AC and cc represents DC. DETAILED DESCRIPTION

[0099] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0100] It is particularly stated that the symbols involved in the following description, which are not explicitly declared as “decision variables”, all represent given parameters. The decision variable refers to an important attribute that can be freely selected or considered by a decision maker in a certain decision-making process, indicating the scope of the decision, and is also an important variable to be examined by the decision maker when making a decision.

[0101] A power flow calculation method for distribution network considering the relationship between intelligent soft switch (SOP) voltage and loss,

[0102] First, a basic model of power flow optimization scheduling of the distribution network is established. The optimization method of convex relaxation technology is adopted to model the power, voltage and topological change constraints of the distribution network as a mixed integer second-order cone model.

[0103] Secondly, an AC power flow model of the converter is established. The intelligent soft switch (SOP) is composed of two back-to-back converters.

[0104] The specific modeling process is as follows:

[0105] S1, a basic model of power flow optimization scheduling of the distribution network is established.

[0106] S11, the objective function is established.

[0107] The minimum sum of network loss and generation cost is taken as the optimization objective, and the expression is,

[0108] Min (1),

[0109] wherein and are decision variables.

[0110] in equation (1) is the number of nodes in the distribution network; is the branch current between node and node ; is the branch resistance between node and node ; is the number of power sources in the distribution network; is the active power injected by the power source into the directly connected node ;

[0111] 1) Node power balance constraint.

[0112] For each node , according to the law of conservation of energy, the total power injected into the node should be zero, i.e.

[0113] , (2),

[0114] , (3),

[0115] where , , and are decision variables;

[0116] in equations (2) and (3) are: is the active power injected by the branch into the directly connected node ; is the reactive power injected by the branch into the directly connected node ; is the active power injected by the converter into the directly connected node ; is the reactive power injected by the converter into the directly connected node ; represents the number of nodes directly connected to node ; respectively represents the reactive power injected by the power source into the directly connected node , is the active load demand of node ​​​​​​For the reactive power load demand of node ; For the active power load shedding amount of node ; For the reactive power load shedding amount of node .

[0117] For and , the following constraints should be met:

[0118] , (4),

[0119] , (5),

[0120] Equation (4) limits the upper and lower limits of the load node load shedding amount; equation (5) provides that, once load shedding occurs, the power factor of the original load node should always remain unchanged.

[0121] (2) Branch power balance constraint.

[0122] The passing power on the branch between node and node needs to meet the law of conservation of energy, and the sum of the total power flowing out of the branch between node and node is zero, which is written as

[0123] , , (6),

[0124] , , (7),

[0125] In equation (7): is the reactance between node and node ;

[0126] Considering the operating state of the branch between node and node , 0-1 decision variables are introduced: represents the operating state of the branch between node and node , represents the normal operation of the branch between node and node , represents the normal operation of the branch between node and node If the branch between them is broken, then

[0127] , , (8),

[0128] , , (9),

[0129] in, Represents a sufficiently large positive real number, such as .

[0130] (3) Branch power flow balance and safety constraints.

[0131] In a power distribution network, the node voltage and the branch current connected to that node must satisfy the branch power flow balance equation using the second-order cone technique, i.e.

[0132] , , (10),

[0133] in, For decision variables;

[0134] In formula (10): For nodes The voltage; For nodes The voltage;

[0135] Meanwhile, nodes With nodes The power passing through the branch and the injected node With nodes The relationship between voltage and current is as follows By using convex relaxation techniques, equation (11) is used as an equivalent substitution.

[0136] , , (11),

[0137] Furthermore, during the optimization process using convex relaxation techniques, the voltage at any node must not exceed the limit, i.e.

[0138] (12),

[0139] In the formula: For nodes The upper limit of voltage; For nodes The lower limit of the voltage.

[0140] (4) Radiation confinement.

[0141] The operating rules of the distribution network require that the network topology always be in a radial state, that is...

[0142] , , (13).

[0143] In equation (13): This represents any publicly available combination of radiation constraint conditions, such as the loop identification method.

[0144] Thus, equations (1) to (13) constitute the basic second-order cone model for power flow optimization scheduling of the distribution network.

[0145] S2. Establish the converter power flow model.

[0146] The constraint modeling for the converter power involved in equations (2) and (3) is as follows.

[0147] Treat the converter as a node in the network. The active power injected into the AC grid by the converter is The reactive power injected into the AC grid by the converter is The power injected into the DC side by the converter is If the DC side is considered as a special AC network with zero reactance, then the reactive power... Considering that the intelligent soft switch is composed of two back-to-back converters, there is actually no DC grid in the intelligent soft switch. Therefore, we can further assume the DC line resistance... Taking into account the losses of the converter, the power balance equation of the converter is established as shown in equation (14).

[0148] (14),

[0149] in, and These are decision variables.

[0150] In equation (14): The fitting coefficients for higher-order terms of the converter power loss curve; This represents the fitting coefficient for lower-order terms; Represents a constant term; This refers to the parameters introduced to account for the relationship between the voltage across the converter and the losses.

[0151] Exponential function middle,

[0152] (15),

[0153] in, These are decision variables.

[0154] In equation (15): This refers to the voltage at the AC side grid connection point. This refers to the phase angle of the voltage on the AC side; This represents the phase angle of the DC-side voltage.

[0155] When the DC side is considered as a special AC network If the AC side phase angle is selected as the reference phase angle, that is... From this, we can obtain the relationship of the equation on the right side of equation (15).

[0156] The relationship between the AC and DC voltages on both sides of the converter satisfies

[0157] (16),

[0158] In equation (16): For the modulation ratio, the following upper limit must be satisfied. constraints

[0159] (17),

[0160] The DC-side voltage is also limited by the converter's own conditions, therefore

[0161] (18),

[0162] In formula (18): This represents the upper limit of the DC voltage of the converter; This is the lower limit of the DC voltage of the converter.

[0163] In summary, equations (1) to (18) describe the complete power flow calculation model of the present invention, taking into account the voltage-loss relationship of intelligent soft switching. Among them, equations (14) to (18) are the general power flow models of converters.

[0164] As the most preferred embodiment of the present invention, for the exponential function of equation (14) The following quadratic approximation method can be used for further linearization optimization:

[0165] Hypothetical variables and Having a generalized exponential relationship ,in Let be the exponent. The linearized constraint is expressed as:

[0166] (19),

[0167] in,

[0168] (20),

[0169] In equation (20), For predefined natural numbers, To initialize the discrete interval, its size should be selected according to the actual accuracy requirements, such as... The smaller the value, the higher the accuracy of linearization.

[0170] Using (19) and (20), take and ,Will Treat them as decision variables, and then... Substituting into equation (14) will eliminate the exponential function. Finally, linearized equations (14), (19), and (20) are obtained.

[0171] After the above discussion of the exponential function The linear optimization can be performed on equations (1) to (20) to obtain the global optimal solution. The solution tool is the commercial software package Gurobi.

[0172] Verification of Examples

[0173] To illustrate the effectiveness and advantages of the technical solution of this invention, an IEEE RBTS BUS6 F4 feeder system is used as a case study, such as... Figure 2 As shown in Table 1. The system branch impedances are also shown in Table 1 (see attached table). Figure 3 As shown in the figure.

[0174] The substation has a total of 25 downstream nodes, of which 23 are load nodes (LP). It is assumed that there are identical intelligent soft switches (converter parameters, see Table 2) between nodes 1 to 21 and between nodes 1 to 23. Figure 4 The DC-side nodes are numbered from 10001 to 10004. Nodes 5, 12, 16, 17, and 22 are equipped with distributed generation (DG) units (parameters shown in Table 3). Figure 5 The load requirements for each node in this system are shown in Table 4 (see appendix). Figure 6 ).

[0175] The algorithm was developed using Julia (Ver 1.9.2) language, and the hardware platform was an Intel(R) Core(TM) i9-10885H with 32GB RAM, and the operating system was Windows 11.

[0176] Results Analysis: Using the optimal power flow calculation method for distribution networks that considers the voltage-loss relationship of intelligent soft switching proposed in this patent, the voltage levels of each node are summarized in Table 5 (see Appendix).Figure 7 As can be seen, all voltages comply with voltage constraints. Voltage level refers to the degree of static voltage at each node in the power grid, based on the rated voltage, and can be derived from the node voltages and rated voltages of each node obtained by the power flow calculation method of this invention.

[0177] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A power distribution network power flow calculation method considering the SOP voltage-loss relationship, characterized in that, the SOP is composed of two back-to-back converter connections; the method comprises: establishing a basic model of power distribution network power flow optimization scheduling, using the optimization method of convex relaxation technology, modeling the power, voltage and topology change constraints of the power distribution network as a mixed integer second-order cone model; establishing a basic model of power distribution network power flow optimization scheduling, including, S11 establishes the objective function: the optimization objective is to minimize the sum of network loss and generation cost, which is expressed as Min (1), wherein and are decision variables; In formula (1): Represents the number of nodes in the power distribution network; For nodes and nodes Branch current between; For nodes and nodes Branch resistance between; This represents the number of power sources in the distribution network. This represents the quadratic fitting coefficient of the curve representing the power generation cost. This represents the coefficient of fit for the linear term of the power generation cost curve; Inject power into the connected nodes The active power; S12 determines the constraint condition: 1) node power balance constraint for each node, according to the law of conservation of energy, the total power injected into the node should be zero, that is , （2）， , （3）， wherein , , and are decision variables; in formula (2) and (3): active power injected into the directly connected nodes of the branch; reactive power injected into the directly connected nodes of the branch; active power injected into the directly connected nodes of the converter; reactive power injected into the directly connected nodes of the converter; number of nodes directly connected to node number of converters directly connected to node reactive power injected into the directly connected nodes of the power supply, active load demand of node reactive load demand of node active load shedding of node reactive load shedding of node ​​​​​​​ For and should be subject to the following constraints: , (4)， , (5)， formula (4) limits the upper and lower limits of load shedding of the load node; formula (5) provides that once load shedding occurs, the power factor of the original load node should always remain unchanged; 2) branch power balance constraint Node and the branch between node The power passing through the branch between node and node is zero, which is written as , , (6)， , , (7)， In formula (7): is the reactance between the node and the node ; Consider the operating state of the branch between node and node , introduce 0-1 decision variable: , which represents the operating state of the branch between node and node , , which represents the normal operation of the branch between node and node , , which represents the disconnection of the branch between node and node , then , , (8)， , , (9)， wherein represents a positive real number; 3) branch power flow balance and safety constraint the node voltage in the power distribution network and the branch current connected to the node need to satisfy the branch power flow balance equation using the second-order cone technology, that is ， , (10)， wherein are decision variables; In formula (10): is the voltage at node ; is the voltage at node ; M is a positive real number; At the same time, the power passing through the branch between the node and the node is related to the voltage and current of the node and the node as and the equivalent replacement of formula (11) is adopted by the convex relaxation technology, , , (11)， In addition, in the process of optimization using convex relaxation technology, the voltage of any node cannot be out of limit, that is (12)， wherein: is an upper limit of the voltage at node is a lower limit of the voltage at node is a lower limit of the voltage at node​ 4) radial constraint The operation rules of the power distribution network require that the network topology structure is always in a radial state, that is , , (13)； establishing an AC power flow model of the converter.

2. The method of claim 1, wherein, for the AC power flow model, a quadratic approximation method is used for linear optimization.

3. The method of claim 1, wherein, formulas (1) to (13) constitute the mixed integer second-order cone model.

4. The power distribution network power flow calculation method of claim 1, wherein, establishing an AC power flow model of the converter comprises: regarding the converter as a node of the network, considering the loss of the converter, establishing a converter power balance equation as formula (14), (14)， wherein and are decision variables; In formula (14): represents the high order term fitting coefficient of the power loss curve of the converter; represents the low order term fitting coefficient; represents the constant term; represents the parameter introduced to consider the relationship between the voltage across the converter and the loss.

5. The power distribution network power flow calculation method of claim 4, wherein, Exponential function In the above equation, (15)， wherein is a decision variable; In formula (15): is the voltage of the AC side grid point; is the voltage phase angle of the AC side; is the voltage phase angle of the DC side; the relationship between the AC and DC voltages on both sides of the converter satisfies (16)， In formula (16): is the modulation ratio, satisfying the following upper limit constraint (17)， the DC side voltage is also limited by the conditions of the converter itself, so (18)， In formula (18): is an upper limit constraint for the DC voltage of the converter; is a lower limit constraint for the DC voltage of the converter.

6. The power distribution network power flow calculation method of claim 5, wherein, The exponential function of equation (14) is linearized by a quadratic approximation method as follows: Assumed variables and with a generalized exponential relationship where is an exponential term, then The linearized constraint is expressed as: (19)， wherein, (20)， In formula (20): is a predefined natural number; is an initialization discrete interval.

7. The power distribution network power flow calculation method of claim 6, wherein, Using (19) and (20), take and , we have as decision variables; Will Substituting into equation (14), the exponential function is eliminated. .

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