A multi-stage restoration method for a flexible interconnected distribution system based on multi-terminal SOP

Abstract

A multi-stage restoration method for a flexible interconnected distribution system based on multi-terminal SOP, comprising: obtaining the location, number, and normal line topology information of the faulty line in the interconnected distribution network; calculating the information of the nodes and lines that lose power supply after fault isolation according to the faulty line information to determine the scope of the power outage area; obtaining the output data of renewable energy such as wind turbines and photovoltaic in the interconnected distribution network, the corresponding data of the load of all nodes in the required time period, the positions of all tie switches and sectionalizing switches, and the impedance of the corresponding lines; setting the positions and capacities of each port of distributed generation (DG), capacitor banks, and multi-terminal soft switches (SOP) to establish an equipment model; establishing a multi-stage mixed integer programming model for the flexible interconnected distribution system with multi-terminal SOP; solving the objective function of the interconnected power grid restoration process through a solver to formulate a multi-stage restoration strategy for the flexible interconnected distribution system with multi-terminal SOP, and determining the action conditions of each switch and the output status of each device in each stage.

Description

Technical Field

[0001] The present invention proposes a multi-stage restoration method for an interconnected distribution system. Background Art

[0002] With the widespread access of distributed power sources, energy storage, etc., and the large-scale application of technologies such as demand-side response, the traditional distribution network has been transformed into a new type of intelligent distribution network system. Under the new mode, the distribution network will actively optimize the control of distributed generators (DGs), energy storage, demand response resources, reactive power compensation devices, line topologies, and various intelligent devices to form an operation mode of the active distribution network.

[0003] In the active distribution network, the interconnected power grid is a common form. The interconnected power grid is formed by connecting several independent power networks through tie lines or other connection devices, which can improve the power supply reliability and fault recovery ability of each sub-network, and at the same time can improve the power flow of the power grid, change the voltage and reactive power distribution, and improve the power quality of the power grid. The traditional interconnected power grid mainly connects lines or sub-networks into an integrated power grid through tie lines and tie switches. This connected power grid has a certain self-healing ability after a fault, and can change the opening and closing states of each line through network reconfiguration, so that each power grid node that may be restored after a fault gradually returns to the normal operating state.

[0004] The intelligent soft switch (Soft Open Point, SOP) usually refers to the dual-terminal SOP, which can continuously adjust the active and reactive power of the power grid, control the power flow of the power grid, and reduce the network loss in the fault recovery of the distribution network. The SOP can replace the tie line and the tie switch to realize the flexible interconnection between distribution networks, not only effectively improving the restoration effect, but also avoiding problems such as power supply interruption and loop closing impact caused by the switching operation of conventional switches.

[0005] For a large-scale distribution network, if better restoration effects are to be achieved and the flexible interconnection requirements in the multi-line power supply scenario are to be met, the multi-terminal SOP that can further realize the flexible interconnection of multiple feeders on the basis of the conventional dual-terminal soft switch will become an important development direction. When a fault occurs, since the DC bus has the function of isolating the fault current, the multi-terminal SOP can effectively prevent the fault current from crossing between the feeders it connects; during the power supply restoration process, the multi-terminal SOP can not only act as an interconnection switch between sub-networks, but also act as an energy hub to realize the energy support between multiple sub-networks, provide effective voltage support for the fault side, thereby expanding the power supply restoration range and enhancing the resilience of the power grid system. In addition, the multi-terminal SOP also has greater potential than the dual-terminal SOP in improving power quality, coping with the uncertainty of renewable energy, and three-phase imbalance. In summary, it is necessary to introduce a multi-terminal SOP in the flexible interconnected distribution network and formulate a more detailed and effective multi-stage restoration plan. Summary of the Invention

[0006] The present invention aims to overcome the above-mentioned disadvantages of the prior art and provides a multi-stage restoration method for a flexible interconnected distribution system based on multi-terminal SOP.

[0007] In the context of an active distribution network, the fault restoration process is different from that of a traditional power grid. It is necessary to consider not only the reconstruction problems involving tie switches and sectionalizing switches, traditional reactive power compensation devices, but also actively controllable devices such as distributed power sources including renewable energy and new power electronic devices including SOP. In order to give play to the role of these devices in post-fault restoration and solve various problems brought about by the introduction of these devices, the present invention contemplates a multi-stage restoration method for a flexible interconnected distribution system based on multi-terminal SOP.

[0008] To achieve the above object, the technical solution of the present invention is as follows:

[0009] A multi-stage restoration method for a flexible interconnected distribution system based on multi-terminal SOP, characterized in that the method comprises the following steps:

[0010] S1: Obtain the location, number, etc. of the faulty line in the interconnected distribution network and the line topology information in the normal operating state, and transfer to step S2;

[0011] S2: Calculate the information of the nodes and lines that lose power supply after fault isolation according to the faulty line information, determine the scope of the power outage area, and transfer to step S3;

[0012] S3: Obtain the output data of renewable energy such as wind turbines and photovoltaic in the interconnected distribution network, the corresponding data of the load of all nodes at the required time period, the positions of all tie switches and sectionalizing switches, and the impedance of the corresponding lines, and transfer to step S4;

[0013] S4: Set the positions and capacities of each port of the distributed power source (DG), capacitor bank, and multi-terminal soft switch (SOP), and establish models of various devices according to the characteristics and parameters of devices such as DG, capacitor, and multi-terminal SOP;

[0014] S5: Based on the device models established in step S4, considering reconstruction and power flow distribution, construct a line power flow model of the interconnected power grid, and perform second-order cone transformation on the power flow model, so as to establish a multi-stage mixed integer programming model of a flexible interconnected distribution system with multi-terminal SOP;

[0015] S6: According to the information in the above steps, solve the objective function of the interconnected power grid restoration process through a solver, formulate a multi-stage restoration strategy for a flexible interconnected distribution system with multi-terminal SOP, and determine the action conditions of each switch and the output status of each device in each stage.

[0016] Further, in the step S2, determining the range of the power outage area includes the following steps:

[0017] S2-1: Establish an objective function with the fewest power outage nodes

[0018]

[0019] In the formula, N I is the number of nodes in the distribution network; χ i is the energized state of node i under the fault isolation state, which is 1 when energized and 0 otherwise.

[0020] S2-2: Solve the objective function according to the radial power flow constraint, and calculate all χ ij for the line ij that is 0 and χ i for the node i that is 0, that is, the power outage nodes and lines are obtained.

[0021]

[0022]

[0023]

[0024]

[0025]

[0026] In the formula, b ij indicates that node i is the parent node of node j; W is the set of all lines; Ψ ij is the virtual power flow through line ij; χ ij is the energized state of line ij under the fault isolation state, which is 1 when energized and 0 otherwise; M is a sufficiently large number.

[0027] Further, in the step S4, establishing the models of various devices includes the following steps:

[0028] S4-1: Establish a capacitor bank model

[0029] Set the first time period after the fault isolation and before the restoration. After that, during the restoration process, since the time is short, the tap positions of the capacitor bank should remain the same at each node after restoration and should not be adjusted with time. The constraint conditions of the capacitor bank during the restoration process are as follows:

[0030]

[0031]

[0032]

[0033]

[0034] In the formula, represents the tap position of the capacitor bank connected to node i at time t; represents the reactive power regulation amount of each tap of the capacitor bank connected to node i; X t,i represents the power supply state of node i at time t, where 1 represents power supply and 0 represents no power supply.

[0035] S4-2: Establish a multi-terminal soft open points (SOP) model

[0036] The multi-terminal SOP can accurately control the active and reactive power flows of the power grid at a low operating cost, achieve the optimal power distribution between the connected ports, and avoid the risks caused by frequent switching operations. The multi-terminal SOP model takes into account power losses, capacity constraints, and power balance. The constraint conditions of the multi-terminal SOP at time t are as follows:

[0037]

[0038]

[0039]

[0040] In the formula, respectively represent the active and reactive powers of port m at time t; represents the active power loss of port m at time t; represents the apparent power limit of port m; A m represents the power loss coefficient of port m; N vsc is the number of ports of the SOP;

[0041] S4-3: Establish a distributed generator (DG) model

[0042] The constraint conditions of the DG model at time t are as follows:

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] In the formula, respectively represent the active and reactive power outputs of the DG at node i at time t; Indicates the energized state of the DG at node \(i\) at time \(t\). If energized, it is 1; otherwise, it is 0. Indicates the ramp rate limit power of the DG at node \(i\) between every two time periods; \(P\) i DG,min and \(P\) i DG,max and are the upper and lower limits of the active and reactive power of the DG at node \(i\), respectively.

[0049] By linearizing the constraints in Equation (18), we can obtain:

[0050]

[0051] Furthermore, in the step S5, the establishment of the multi-stage mixed-integer programming model for the flexible interconnected distribution system includes the following steps:

[0052] S5-1: Establish a line reconfiguration model

[0053] The reconfiguration process of the distribution system with multi-terminal SOPs needs to satisfy the constraints that the line topology is connected, there are no islands, and it does not affect the normal operating area. The corresponding line topology constraints are as follows:

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] In the formula, \(b\) ij,t represents whether node \(i\) is the parent node of node \(j\) at time \(t\). If it is, it is 1; otherwise, it is 0; \(X\) ij,t represents the energized state of the \(ij\) line at time \(t\). If energized, it is 1; otherwise, it is 0.

[0061] In addition, to ensure that the system can meet the radiality constraint without connecting the SOP and can supply power to the line through the SOP when the SOP is connected. The SOP ports are set to be power sources that can provide virtual power flow, and the traditional single-commodity flow (SCF) constraint is added to form the improved virtual power flow constraint.

[0062]

[0063]

[0064]

[0065] In the formula, F ij,t is the virtual power flow of line ij at time t; is the virtual power flow generated by node i with SOP at time t; is the opening state of SOP port m connected to node i. The port is open as 1, otherwise 0.

[0066] S5-2: Establish a multi-stage restoration model

[0067] A single node or multiple nodes connected by non-switchable lines form a line block, simplifying the original interconnected power grid into an interconnected power grid composed of all lines and line blocks with remotely controllable switches at both ends. Since a line can be energized only when there is power supply on one side of the line, the power supply state of the non-switchable line is the same as that of all the nodes connected to it, while the switchable line can transmit power only when at least one of the nodes connected to it was powered in the previous moment. The energized state X ij,t needs to satisfy the following constraints:

[0068]

[0069]

[0070]

[0071] In the formula, W S is the set of interruptible lines; W LOSS is the set of lines in the power outage area determined by fault isolation.

[0072] The constraint of formula (29) can introduce an intermediate variable a ij,t , and linearize it to obtain the following constraints

[0073] a ij,t ≤X t-1,i +X t-1,j (32)

[0074] a ij,t ≥X t-1,i (33)

[0075] a ij,t ≥X t-1,j (34)

[0076] X ij,t ≤a ij,t (35)

[0077] S5-3: Establish a line power flow model

[0078] The Distflow power flow model applicable to radial distribution systems is improved by adding a load switch for controlling load disconnection, and the following Distflow power flow model applicable to this study is obtained. Introduce Perform equivalent transformation and relax the power, current, and voltage constraints so that the active power, reactive power, and line current of the disconnected branch are zero, and there are no constraints on the closed branch.

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086] In the formula, is the square of the voltage at node i at time t; is the square of the current in line ij at time t; U std is the base voltage of the power grid; I max represents the maximum current that the line can pass; P ij,t is the active power transmitted in line ij at time t; Q ij,t is the reactive power transmitted in line ij at time t.

[0087] The transformed power flow constraints are as follows:

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] In the formula, P t,i is the active power difference at node i at time t; Q t,i is the reactive power difference at node i at time t; is the active power generated by the PV at node i at time t; is the reactive power generated by the PV at node i at time t; is the active power generated by the wind turbine at node i at time t; is the reactive power generated by the wind turbine at node i at time t; is the active power of the load demand at node i at time t; is the reactive power of the load demand at node i at time t; L t,i is the opening / closing status of the load switch at node i at time t, 1 for on, otherwise 0; r ij represents the resistance of line ij; x ij represents the reactance of line ij.

[0095] S5-4: Determine the operation mode of the SOP port

[0096] To ensure that the lines that are not connected to the external power grid and are only supported by the SOP port can have a slack node, the nodes connected to the SOP port are set as slack nodes, and the control mode corresponding to the SOP port is V-f control, while the control mode of other SOP ports is P-Q control.

[0097]

[0098]

[0099]

[0100] where f ij,t is another virtual power flow of line ij at time t, indicates whether the node i with SOP is connected to the external power grid at time t, 1 for connected, otherwise 0.

[0101] S5-4: Perform second-order cone transformation on the non-linear part of the power flow model

[0102] To ensure that the domain of variables is a convex set during the solution process, second-order cone relaxation is performed on Equation (48) to obtain

[0103]

[0104] Using Equation (52) can transform the original problem into a mixed-integer second-order cone problem, which is convenient for commercial solvers to solve.

[0105] Furthermore, the objective function of the interconnected power grid restoration process in step S6 is as follows:

[0106] The objective function consists of three parts: the un-restored load considering the importance of the load, the total operation time of switches during the restoration process, and the line losses and SOP losses.

[0107] min: F obj = K re F re + K sw F sw + K loss F loss (53)

[0108]

[0109]

[0110]

[0111] Wherein, D i represents the importance degree of the load at node i; λ ij represents the operation time of the switch at line ij; K re , K sw , K loss respectively represent the weight factors of the load recovery amount, the total switch operation time, the line power loss, and the SOP loss in the objective function.

[0112] The present invention comprehensively considers the data information of the interconnected power grid structure, line impedance, node load, and multi-terminal SOP, DG, wind turbines, photovoltaic and other devices, constructs a flexible interconnected power grid model with a 5-terminal SOP connected subnet, and designs new line topology restrictions based on the new characteristics of the line power flow of the multi-terminal SOP interconnected power grid, which can effectively reflect the roles of various devices in the system during the restoration process, ensure a more flexible power flow distribution in the distribution system during the restoration process, and obtain an optimal restoration strategy aiming to effectively increase the load recovery rate while promoting a greater role of high-penetration renewable energy and distributed power sources in the system during fault restoration, and improving the resilience and reliability of the system. And under the condition of using multi-terminal SOP, the computational complexity does not increase significantly, ensuring a high computational efficiency. The beneficial effects of the present invention are:

[0113] 1. It can give full play to the roles of various devices such as DG, SOP, capacitor banks, and renewable energy in the interconnected power grid during fault restoration.

[0114] 2. It solves the problem of power grid reconstruction with SOP. The present invention designs new line topology restrictions based on the new characteristics of the line power flow of the multi-terminal SOP interconnected power grid to ensure a more flexible power flow distribution in the distribution system during the restoration process to meet a better power supply restoration plan.

[0115] 2. By introducing multi-terminal SOP and a new topology method, it can improve the fault restoration speed and fault restoration ability of the active distribution network, reduce the power loss of the power grid, and improve the resilience and reliability of the system. Description of the Drawings

[0116] Figure 1 is the multi-terminal SOP flexible interconnected power distribution system of the present invention.

[0117] Figure 2 is the power curve of the fan and photovoltaic of the present invention during the recovery time.

[0118] Figure 3 is the power curve of the load of the present invention during the recovery time.

[0119] Figure 4 is the schematic diagram of the recovery process of the interconnected power grid under the condition of 6-line faults of the present invention.

[0120] Figure 5 is the curve of the change of the load recovery rate of the interconnected power grid under the condition of 6-line faults of the present invention.

[0121] Figure 6 is the curve of the change of the SOP active power of the interconnected power grid under the condition of 6-line faults of the present invention.

[0122] Figure 7 is the curve of the change of the SOP reactive power of the interconnected power grid under the condition of 6-line faults of the present invention.

[0123] Figure 8 is the curve of the change of the DG output of the interconnected power grid under the condition of 6-line faults of the present invention.

[0124] Figure 9 is the schematic diagram of the recovery process of the interconnected power grid under the fault of the equivalent transformer TA of the present invention.

[0125] Figure 10 is the curve of the change of the load recovery rate of the interconnected power grid under the fault of the equivalent transformer TA of the present invention.

[0126] Figure 11 is the curve of the change of the SOP active power of the interconnected power grid under the fault of the equivalent transformer TA of the present invention.

[0127] Figure 12 is the curve of the change of the SOP reactive power of the interconnected power grid under the fault of the equivalent transformer TA of the present invention.

[0128] Figure 13 is the curve of the change of the DG active power of the interconnected power grid under the fault of the equivalent transformer TA of the present invention.

[0129] Figure 14 is the schematic diagram of the interconnected power grid using the tie switch of the present invention.

[0130] Figure 15 is the curve of the change of the load recovery rate during the process of the interconnected power grid under the condition of 6-line faults of the present invention.

[0131] Figure 16 It is the curve of the change in the load recovery rate during the interconnection of power grids under the fault of the equivalent transformer TA of the present invention.

[0132] Figure 17 It is the flowchart of the method of the present invention. Specific implementation method

[0133] The following further describes the present invention in conjunction with the accompanying drawings.

[0134] Refer to Figures 1 to 16 , a multi-stage restoration method for a flexible interconnected distribution system based on multi-terminal SOP, which establishes a new topological structure constraint and multi-stage restoration strategy for a power grid including multi-terminal SOP. The method includes the following steps:

[0135] S1: Obtain the location, number, etc. of the faulty line in the interconnected distribution network and the line topology information in the normal operation state, and transfer to step S2;

[0136] S2: Calculate the information of the nodes and lines that lose power supply after fault isolation according to the faulty line information, determine the scope of the power outage area, and transfer to step S3;

[0137] S3: Obtain the output data of renewable energy such as wind turbines and photovoltaic in the interconnected distribution network, the corresponding data of the load of all nodes in the required time period, the positions of all tie switches and disconnecting switches, and the impedance of the corresponding lines, and transfer to step S4;

[0138] S4: Set the positions and capacities of each port of distributed power sources (DGs), capacitor banks, and multi-terminal soft switches (SOPs). According to the characteristics and parameters of devices such as DGs, capacitors, and multi-terminal SOPs, establish models of various devices;

[0139] S5: Based on the device models established in step S4, considering network reconfiguration and power flow distribution, construct a line power flow model of the interconnected power grid, and perform second-order cone transformation on the power flow model, so as to establish a multi-stage mixed integer programming model for a flexible interconnected distribution system including multi-terminal SOP;

[0140] S6: According to the information in the above steps, solve the objective function of the interconnected power grid restoration process through a solver, formulate a multi-stage restoration strategy for a flexible interconnected distribution system including multi-terminal SOP, and determine the action conditions of each switch and the output status of each device in each stage.

[0141] In step S2, determining the scope of the power outage area includes the following steps:

[0142] S2-1: Establish an objective function with the fewest power outage nodes

[0143]

[0144] In the formula, N I is the number of nodes in the distribution network; χ i is the energized state of node i under the fault isolation state, which is 1 when energized and 0 otherwise.

[0145] S2-2: Solve the objective function according to the radial power flow constraint, and calculate all χ ij for the line ij with a value of 0 and χ i for the node i with a value of 0, that is, the de-energized nodes and lines are obtained.

[0146]

[0147]

[0148]

[0149]

[0150]

[0151] In the formula, b ij indicates that node i is the parent node of node j; W is the set of all lines; Ψ ij is the virtual power flow through line ij; χ ij is the energized state of line ij under the fault isolation state, which is 1 when energized and 0 otherwise; M is a sufficiently large number.

[0152] In the step S4, establishing the models of various devices includes the following steps:

[0153] S4-1: Establish the capacitor bank model

[0154] Set the first time period after the fault isolation and before the restoration. Since the restoration process is short after this, the gear positions of the capacitor banks should remain the same after the nodes are restored and do not change with time. The constraint conditions of the capacitor banks during the restoration process are as follows:

[0155]

[0156]

[0157]

[0158]

[0159] In the formula, represents the gear position of the capacitor bank connected to node i at time t; represents the reactive power regulation amount of each gear of the capacitor bank connected to node i; Xt,i Indicates the power supply status of node i at time t. 1 represents power supply, and 0 represents no power supply.

[0160] S4-2: Establish a multi-terminal soft open points (SOP) model

[0161] The multi-terminal SOP can accurately control the active and reactive power flows of the power grid at a low operating cost, achieve the optimal power distribution between the connected ports, and avoid the risks caused by frequent switching operations. The multi-terminal SOP model takes into account power losses, capacity constraints, and power balance. The constraint conditions of the multi-terminal SOP at time t are as follows:

[0162]

[0163]

[0164]

[0165] In the formula, respectively represent the active and reactive power of port m at time t; represents the active power loss of port m at time t; represents the apparent power limit of port m; A m represents the power loss coefficient of port m; N vsc is the number of ports of the SOP;

[0166] S4-3: Establish a distributed generator (DG) model

[0167] The constraint conditions of the DG model at time t are as follows:

[0168]

[0169]

[0170]

[0171]

[0172]

[0173] In the formula, respectively represent the active and reactive power outputs of the DG at node i at time t; represents the energized state of the DG at node i at time t. Energized is 1, otherwise 0; represents the ramp rate limit power of the DG at node i between every two time periods; P i DG,min 、P iDG,max , are the upper and lower limits of the active and reactive power of the DG at node i, respectively.

[0174] Linearizing the constraints in Equation (18), we can obtain:

[0175]

[0176] In step S5, the establishment of the multi-stage mixed-integer programming model for the flexible interconnected distribution system includes the following steps:

[0177] S5-1: Establish a line reconfiguration model

[0178] The reconfiguration process of the distribution system with multi-terminal SOPs needs to satisfy the requirements that the line topology is connected, there are no islands, and it does not affect the normal operation area. The corresponding line topology constraints are as follows:

[0179]

[0180]

[0181]

[0182]

[0183]

[0184]

[0185] In the formula, b ij,t represents whether node i is the parent node of node j at time t. If it is, it is 1; otherwise, it is 0; X ij,t represents the energized state of line ij at time t. If it is energized, it is 1; otherwise, it is 0.

[0186] In addition, to ensure that the system can meet the radiality constraints without connecting the SOP and can supply power to the line through the SOP when the SOP is connected. The SOP ports are set as power sources that can provide virtual power flow, and the traditional single-commodity flow (SCF) constraints are added to form the improved virtual power flow constraints.

[0187]

[0188]

[0189]

[0190] In the formula, F ij,t is the virtual power flow of line ij at time t; is the virtual power flow sent by node i with SOP at time t; is the opening state of SOP port m connected to node i. The port is open when it is 1, otherwise it is 0.

[0191] S5-2: Establish a multi-stage restoration model

[0192] In this study, a single node or multiple nodes connected by non-switchable lines form a line block, simplifying the original interconnected power grid into an interconnected power grid composed of all lines and line blocks with remotely controllable switches at both ends. Since a line can be energized only when there is power supply on one side of the line, the power supply state of the non-switchable line is the same as that of all the nodes connected to it, while a switchable line can transmit power only when at least one of the nodes connected to it was powered in the previous moment. The energized state X of the line ij,t The constraints to be satisfied are as follows:

[0193]

[0194]

[0195]

[0196] In the formula, W S is the set of switchable lines; W LOSS is the set of lines in the power outage area determined by fault isolation.

[0197] The constraint in formula (29) can introduce an intermediate variable a ij,t , and linearize it to obtain the following constraints

[0198] a ij,t ≤X t-1,i +X t-1,j (32)

[0199] a ij,t ≥X t-1,i (33)

[0200] a ij,t ≥X t-1,j (34)

[0201] X ij,t ≤a ij,t (35)

[0202] S5-3: Establish a line power flow model

[0203] Improved the Distflow power flow model applicable to radial distribution systems, added load switches for controlling load switching, and obtained the following Distflow power flow model applicable to this study. Introduce Perform equivalent transformation and relax the power, current, and voltage constraints so that the active power, reactive power, and line current of the disconnected branch are zero, and there are no constraints on the closed branches.

[0204]

[0205]

[0206]

[0207]

[0208]

[0209]

[0210]

[0211] In the formula, is the square of the voltage of node i at time t; is the square of the current of line ij at time t; U std is the base voltage of the power grid; I max represents the maximum current that the line can pass; P ij,t is the active power transmitted by line ij at time t; Q ij,t is the reactive power transmitted by line ij at time t.

[0212] The transformed power flow constraints are as follows:

[0213]

[0214]

[0215]

[0216]

[0217]

[0218]

[0219] In the formula, P t,i is the active power difference of node i at time t; Q t,i is the reactive power difference of node i at time t; is the active power generated by the photovoltaic at node i at time t; is the reactive power generated by the photovoltaic at node i at time t; is the active power generated by the wind turbine at node i at time t; is the reactive power generated by the fan at node i at time t; is the active power of the load demand at node i at time t; is the reactive power of the load demand at node i at time t; L t,i is the opening / closing status of the load switch at node i at time t, 1 for on, otherwise 0; r ij represents the resistance of line ij; x ij represents the reactance of line ij.

[0220] S5-4: Determine the operating mode of the SOP port

[0221] To ensure that lines that are not connected to the external power grid and are only supported by the SOP port can have a slack node, the nodes connected to the SOP port are set as slack nodes. The control mode corresponding to the SOP port is V-f control, and the control mode of other SOP ports is P-Q control.

[0222]

[0223]

[0224]

[0225] In the formula, f ij,t is another virtual power flow of line ij at time t, indicates whether node i with SOP is connected to the external power grid at time t, 1 for connected, otherwise 0.

[0226] S5-4: Perform second-order cone transformation on the non-linear part of the power flow model

[0227] To ensure that the domain of variables is a convex set during the solution process, second-order cone relaxation is performed on Equation (48) to obtain

[0228]

[0229] Using Equation (52) can transform the original problem into a mixed-integer second-order cone problem, which is convenient for commercial solvers to solve.

[0230] Furthermore, the objective function of the interconnected power grid restoration process in step S6 is as follows:

[0231] The objective function consists of three parts: the un-restored load considering the importance of the load, the total operation time of switches during the restoration process, and the line power loss and the loss of the SOP.

[0232] min: F obj = K re F re + K sw Fsw +K loss F loss (53)

[0233]

[0234]

[0235]

[0236] wherein, D i represents the importance degree of the load of node i; λ ij represents the operation time of the switch at line ij; K re , K sw , K loss respectively represent the weight factors of the load restoration amount, the total operation time of the switches, the line network loss, and the SOP loss in the objective function.

[0237] To enable those skilled in the art to better understand the present invention, the case study includes the following components:

[0238] I. Case Description and Simulation Result Analysis

[0239] The present invention takes the interconnected power grid system of the 5-terminal SOP connecting the IEEE33-node system and the IEEE69-node system as an example to verify the effectiveness and correctness of the multi-stage restoration software for the multi-terminal SOP flexible interconnected distribution system. The simulation is solved using the toolbox YALMIP under the MATLAB environment and the commercial solver GUROBI. The time considered in the research starts from 9:00 and there are a total of 7 time periods with a time interval of 1.2 minutes.

[0240] The network topology of the multi-terminal SOP flexible interconnected distribution system is as Figure 1 shown. The typical fan and photovoltaic output powers within a day of the flexible interconnected distribution system are as Figure 2 shown, and the active and reactive power conditions of the load are as Figure 3 shown. The system base voltage is 12.66 KV, the base capacity is 1 MVA, the voltage safety range is 0.95 - 1.05 p.u., the capacity of each end of the 5-terminal SOP is 2 MVA, the loss coefficient is 0.02, the remotely controllable tie switches are 101 - 108, and the remotely controllable disconnecting switches are respectively on lines 8, 11, 14, 19, 27, 35, 44, 50, 58, 66, 70, 74, 76, 82, 88, 95, 98. There are a total of 3 distributed power sources (DGs) with a maximum power of 2.8 MW. It is set that it takes 1 time period to provide appropriate voltage from the node connected to the DG to the restoration of power supply to the distributed power source, and the ramp power limit is 0.5 MW / time period. In addition, the system also has 4 photovoltaic power sources and 3 wind power sources, and the specific parameters are shown in Table 1.

[0241] Table 1 Distributed power source, fan, and photovoltaic parameter table

[0242]

[0243] First, verify the effectiveness of the method of the present invention under two typical fault conditions.

[0244] (1) Faults on lines 73, 95, 22, 37, 43, and 58

[0245] The opening and closing conditions of the controllable switches of the lines during the fault recovery process are shown in Table 2, and the corresponding interconnected power grid recovery process is as Figure 4 shown, and the change of the recovery rate is as Figure 5 shown. The active power, reactive power of each port of the SOP, and the change of the active power output of the DG are as Figures 6 - 8 shown. It can be seen that the entire power grid only has 36.78% of the load remaining after fault isolation, and it recovers to 94.88% of the load after 4 time periods, and only the load of node 38 has not been recovered. After recovery, port 2 of the SOP is the main power supply for the power outage area, and other ports supply energy to it through the SOP.

[0246] Table 2 Opening and closing conditions of the controllable switches of the interconnected power grid lines under the condition of 6-line faults

[0247]

[0248] (2) Fault on line 1 (fault at the outlet of the equivalent transformer TA)

[0249] The opening and closing conditions of the controllable switches of the lines during the fault recovery process are shown in Table 3, and the corresponding interconnected power grid recovery process is as Figure 9 shown, and the change of the recovery rate is as Figure 10 shown. The active and reactive powers of each port of the SOP, and the change of the active power output of the DG are as Figures 11 - 13 shown. It can be seen that the entire power grid has 49.42% of the load remaining after fault isolation, and it recovers 100% of the load after 4 time periods, and the power supply is completely restored. During the recovery process, 3 SOP ports at the 69-node sub-network supply power to the power outage area, and 2 ports at the 33-node sub-network supply power to the SOP.

[0250] Table 3 Opening and closing conditions of the controllable switches of the interconnected power grid lines under the fault of the equivalent transformer TA

[0251]

[0252] To verify the effectiveness of the method of the present invention, a comparative study is carried out with two other modes:

[0253] Mode 1: Adopt the discrete IEEE 33-node model and IEEE 69-node model, that is, the model where there is no energy flow between the two subnets.

[0254] Mode 2: Adopt the model where the IEEE 33-node model and the IEEE 69-node model are connected by a tie switch, as Figure 14 shown.

[0255] Mode 3: The sequence restoration scheduling model of the flexible interconnected distribution system based on multi-terminal SOP proposed by the present invention.

[0256] Under the fault conditions of lines 73, 95, 22, 37, 43, and 58, the changes in the load restoration rate during the fault restoration process of the three model schemes are as Figure 15 shown. Under the fault condition of line 1 (fault at the outlet of the equivalent transformer TA), the changes in the load restoration rate during the fault restoration process of the three model schemes are as Figure 16 shown.

[0257] For the three schemes and two fault conditions, the complexity of the multi-stage restoration model of the flexible interconnected distribution system based on multi-terminal SOP and the running time on an Intel(R) Core(TM) i7-8700@3.2GHz computer are shown in Table 4.

[0258] Table 4 Relevant calculation data for the three schemes and two fault conditions

[0259]

[0260] To sum up, the sequence restoration software of the flexible interconnected distribution system based on multi-terminal SOP can effectively reflect the roles of various devices in the system during the restoration process, ensure a more flexible power flow distribution in the distribution system during the restoration process to meet a better power supply restoration plan, can meet the restoration requirements under complex fault conditions, can clearly give the detailed restoration steps in multiple stages after the fault, and under the condition of using multi-terminal SOP, the computational complexity does not increase significantly, the computational efficiency is relatively high, and the prediction time can meet the actual computational requirements.

[0261] In the description of this specification, the schematic expressions of the present invention do not necessarily refer to the same embodiments or examples. Those skilled in the art can combine and combine the different embodiments or examples described in this specification. In addition, the additional content described in the embodiments of this specification is only a list of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms stated in the implementation cases. The protection scope of the present invention also includes equivalent technical means that those skilled in the art can think of according to the inventive concept.

Claims

1. A multi-stage restoration method for a flexible interconnected distribution system based on multi-terminal SOP, characterized in that, it includes the following steps: S1: Obtain the location, number, and normal operating state line topology information of the faulty line in the interconnected distribution network, and transfer to step S2; S2: Calculate the information of the nodes and lines that lose power supply after fault isolation according to the fault line information, determine the scope of the power outage area, and transfer to step S3; The specific determination of the scope of the power outage area includes: S2-1: Set up an objective function with the fewest power outage nodes; where N I is the number of nodes in the distribution network; χ i is the energized state of node i under the fault isolation state, which is 1 when energized and 0 otherwise; S2-2: Solve the objective function according to the radial power flow constraint to calculate all line ij with χ equal to 0 and node i with χ equal to 0, that is, obtain the power-out nodes and lines; ij where χ is 0 and χ i is 0, namely, the power-out nodes and lines are obtained; where b ij indicates that node i is the parent node of node j; W is the set of all lines; Ψ ij is the virtual power flow through line ij; χ ij is the energized state of line ij under fault isolation, which is 1 when energized and 0 otherwise; M is a sufficiently large number; S3: Obtain the renewable energy output data of wind turbines and photovoltaics in the interconnected distribution network, the corresponding data of the loads of all nodes during the required time period, the positions of all tie switches and sectionalizing switches, and the impedance of the corresponding lines, and transfer to step S4; S4: Set the positions and capacities of the distributed power generation (DG), capacitor banks, and each port of the multi-terminal soft switch (SOP). According to the characteristics and parameters of DG, capacitors, and multi-terminal SOP devices, establish models of various devices; S5: Based on the device models established in step S4, considering network reconfiguration and power flow distribution, construct a line power flow model of the interconnected power grid, and perform second-order cone transformation on the power flow model, so as to establish a multi-stage mixed integer programming model for a flexible interconnected distribution system with multi-terminal SOP; S6: According to the information in the above steps, solve the objective function of the interconnected power grid restoration process through a solver, formulate a multi-stage restoration strategy for a flexible interconnected distribution system with multi-terminal SOP, and determine the action conditions of each switch and the output status of each device during each stage; The objective function of the interconnected power grid restoration process is as follows: The model objective function includes three parts: the un-restored load considering the importance of the load, the total action time of the switches during the restoration process, and the network loss of the lines and the loss of SOP; min:F obj =K re F re +K sw F sw +K loss F loss (53) Where, D i represents the importance degree of the load of node i; λ ij represents the action time of the switch at line ij; K re , K sw , K loss respectively represent the weight factors of the load restoration amount, the total action time of the switches, the line power loss, and the SOP loss in the objective function.

2. A multi-stage restoration method for a flexible interconnected distribution system based on multi-terminal SOP according to claim 1, characterized in that, The specific establishment of models of various devices in step S4 includes: S4-1: Establish a capacitor bank model; Set the first time period before restoration after fault isolation. After that, during the restoration process, since the time is short, the capacitor bank should maintain the same gear after node restoration and will not be adjusted with time; The constraint conditions of the capacitor bank during the restoration process are as follows: In the formula, represents the tap position of the capacitor bank connected to node i at time t; X t,i represents the power supply state of node i at time t, where 1 indicates power supply and 0 indicates no power supply; S4-2: Establish a multi-terminal soft switch (Soft Open Points, SOP) model; The multi-terminal SOP can accurately control the active and reactive power flows of the power grid, achieve the best power distribution between the connected ports, and avoid the risks caused by frequent switching operations; The multi-terminal SOP model takes into account power loss, capacity constraints, and power balance. The constraint conditions of the multi-terminal SOP at time t are as follows: In the formula, respectively represent the active and reactive powers of port m at time t; represents the active power loss of port m at time t; represents the apparent power limit of port m; A m represents the power loss coefficient of port m; N vsc is the number of ports of the SOP; S4-3: Establish a distributed power generation (distributed generator, DG) model; The constraint conditions of the DG model at time t are as follows: In the formula, respectively represent the active and reactive power outputs of the DG at node i at time t; represents the energized state of the DG at node i at time t, where energized is 1 and otherwise 0; represents the ramp limit power of the DG at node i between every two time periods; P i DG,min 、P i DG,max 、 are respectively the upper and lower limits of the active and reactive power of the DG at node i; Linearize the constraints in formula (18) to obtain:

3. A multi-stage restoration method for a flexible interconnected distribution system based on multi-terminal SOP according to claim 1, characterized in that, The establishment of the multi-stage mixed integer programming model for the flexible interconnected distribution system described in step S5 includes the following steps: S5-1: Establish a line reconfiguration model; The reconfiguration process of the distribution system with multi-terminal SOP needs to meet the requirements that the line topology is connected, there are no islands, and the normal operation area is not affected. The corresponding line topology constraints are as follows: where b ij,t represents whether node i is the parent node of node j at time t. If so, it is 1; otherwise, it is 0. X ij,t represents the energization state of line ij at time t. If energized, it is 1; otherwise, it is 0. In addition, to ensure that the system can meet the radiality constraint without connecting the SOP and can supply power to the line through the SOP when the SOP is connected; the SOP port is set as a power source that can provide virtual power flow, and the traditional single-commodity flow (SCF) constraint is added to form an improved virtual power flow constraint; where, F ij,t is the virtual power flow of line ij at time t; is the virtual power flow injected from node i with SOP at time t; is the opening state of SOP port m connected to node i, with the port open being 1 and otherwise 0; S5-2: Establish a multi-stage restoration model; A single node or multiple nodes connected by non-switchable lines form a line block, simplifying the original interconnected power grid into an interconnected power grid composed of all lines and line blocks with remotely controllable switches at both ends; since a line can be energized only when there is power supply on one side of the line, the power supply state of the non-switchable line is the same as that of all the nodes connected to it, while the switchable line can transmit power only when at least one of the nodes connected to it was powered in the previous moment; the energized state X of the line ij,t The constraints to be satisfied are as follows: Where, W S is the set of interruptible lines; W LOSS is the set of lines within the power outage area determined by fault isolation; The constraint of Equation (29) introduces an intermediate variable a ij,t , and linearization is performed to obtain the following constraints a ij,t ≤X t-1,i +X t-1,j (32) a ij,t ≥X t-1,i (33) a ij,t ≥X t-1,j (34) X ij,t ≤ a ij,t (35) S5-3: Establish a line power flow model; The Distflow power flow model applicable to radial distribution systems is improved by adding load switches for controlling load disconnection, resulting in the following Distflow power flow model; the Distflow power flow model introduces Equivalent transformation is carried out, and the power, current, and voltage constraints are relaxed, making the active power, reactive power, and line current of the disconnected branch zero, and there are no constraints on the closed branch; Wherein, is the square of the voltage of node i at time t; is the square of the current of line ij at time t; U std is the base voltage of the power grid; I max represents the maximum current that the line can pass through; P ij,t is the active power transmitted by line ij at time t; Q ij,t is the reactive power transmitted by line ij at time t; The converted power flow constraints are as follows: Wherein, P t,i is the active power difference of node i at time t; Q t,i is the reactive power difference of node i at time t; is the active power generated by the PV at node i at time t; is the reactive power generated by the PV at node i at time t; is the active power generated by the wind turbine at node i at time t; is the reactive power generated by the wind turbine at node i at time t; is the active power of the load demand at node i at time t; is the reactive power of the load demand at node i at time t; L t,i is the opening / closing status of the load switch at node i at time t, 1 for on, otherwise 0; r ij represents the resistance of line ij; x ij represents the reactance of line ij; S5-4: Determine the operation mode of the SOP port; To ensure that the lines that are not connected to the external power grid and only supported by the SOP port can have a balanced node, the nodes connected to the SOP port are set as balanced nodes. The control mode of the corresponding SOP port is V-f control, and the control mode of other SOP ports is P-Q control; where f ij,t is another virtual power flow of line ij at time t, indicates whether node i with SOP is connected to the external power grid at time t. If it is connected, it is 1; otherwise, it is 0. S5-4: Perform second-order cone transformation on the non-linear part of the power flow model; To ensure that the domain of the variables is a convex set during the solution process, second-order cone relaxation is performed on equation (48) to obtain Use equation (52) to transform the original problem into a mixed integer second-order cone problem, which is convenient for commercial solvers to solve.

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