Power grid optimal power flow calculation method based on convex relaxation technology and related equipment

Abstract

The embodiment of the invention discloses a power grid optimal power flow calculation method based on a convex relaxation technology and related equipment, first active power flow, first reactive power flow, second active power flow and second reactive power flow can simulate operation of alternating current and direct current power grids including high-voltage direct current power transmission, and through the convex relaxation technology, the optimal power flow of the power grid can be calculated. And a non-convex optimization problem in the power flow is converted into a convex optimization problem which is easy to solve, so that the accuracy and the calculation efficiency of the optimal power flow are ensured by calculating the optimal power flow by using the branch power flow model optimized by the convex relaxation technology, and the analysis requirement of an alternating current and direct current hybrid power grid is met.

Description

[Technical field]

[0001] The present invention relates to the technical field of power system analysis, and in particular to a power grid optimal power flow calculation method based on convex relaxation technology and related equipment. [Background technology]

[0002] In modern power transmission systems, high-voltage direct current (HVDC) technology has become increasingly important because it can effectively connect AC and DC grids in different regions. In particular, HVDC systems using voltage source converters and modular multilevel converters can be configured and operated in a multi-port manner, which is particularly evident in the application of offshore wind farms connected to the grid. The HVDC system enhances system security and provides auxiliary services for the AC transmission system through its active reactive power control capability.

[0003] However, existing HVDC converter station models have limitations when analyzing power flow distribution in AC / DC hybrid power grids. Different converter station technologies have different control characteristics, which requires the use of accurate optimal power flow models to analyze the operation of these systems. Traditional optimal power flow models are mainly used in pure AC power grid power flow calculations, but when it comes to AC / DC hybrid power grids that contain both AC and DC, traditional optimal power flow models cannot meet the analysis needs of AC / DC hybrid power grids. [Summary of the invention]

[0004] In view of this, the present invention provides a power grid optimal power flow calculation method based on convex relaxation technology and related equipment.

[0005] The specific technical scheme of the first embodiment of the present invention is: a method for calculating the optimal power flow of a power grid based on convex relaxation technology, the method comprising: constructing a first active power flow of the transformer from the AC bus to the DC node of the AC / DC hybrid power grid, a first reactive power flow of the transformer from the AC bus to the DC node, a second active power flow of the transformer from the DC node to the AC bus, and a second reactive power flow of the transformer from the DC node to the AC bus according to a first voltage amplitude of the AC bus in the AC / DC hybrid power grid, a first voltage phase angle of the AC bus, a second voltage amplitude on the transformer filter side, and a second voltage phase angle on the transformer filter side; performing convex relaxation on the first active power flow, the first reactive power flow, the second active power flow, and the second reactive power flow to obtain a branch power flow model of the AC / DC hybrid power grid; and using the branch power flow model to obtain the optimal power flow of the AC / DC hybrid power grid.

[0006] Preferably, the convex relaxation of the first active power flow, the first reactive power flow, the second active power flow and the second reactive power flow is performed to obtain the branch power flow model of the AC / DC hybrid power grid, including: constructing a first power flow model of the AC / DC hybrid power grid according to the first active power flow and the first reactive power flow; the first power flow model is a power flow model from the AC bus to the DC node; constructing a second power flow model of the AC / DC hybrid power grid according to the first active power flow, the second active power flow, the equivalent resistance of the transformer and the current flowing through the transformer; the second power flow model is an active power flow A power flow model; a third power flow model of the AC / DC hybrid power grid is constructed according to the first reactive power flow, the second reactive power flow, the equivalent reactance of the transformer and the current flowing through the transformer; the third power flow model is a reactive power flow model; a fourth power flow model is constructed according to the first voltage amplitude, the first active power flow, the first reactive power flow, the equivalent resistance of the transformer and the equivalent reactance of the transformer; the fourth power flow model is a power flow model on the transformer filter side; the first power flow model, the second power flow model, the third power flow model and the fourth power flow model constitute the branch power flow model.

[0007] Preferably, the first power flow model is obtained using the following formula:

[0008]

[0009] in, is the first voltage amplitude, is the current flowing through the transformer, is the first active power flow, is the first reactive power flow, t c is the voltage conversion factor, cie is the line from the AC bus to the DC node of the specific converter, A collection of inverters.

[0010] Preferably, the fourth power flow model is obtained using the following formula:

[0011]

[0012] in, is the second voltage amplitude, is the first voltage amplitude, t c is the voltage conversion factor, r c tf is the equivalent resistance of the transformer, is the first active power flow, is the equivalent reactance of the transformer, is the first reactive power flow, cie is the line from the AC bus to the specific converter of the DC node, A collection of inverters.

[0013] Preferably, the method further includes: obtaining the converter power loss according to the AC side current of the converter in the AC / DC hybrid power grid and the power loss of the transformer and the converter in the AC / DC hybrid power grid; setting the constraint conditions of the AC / DC hybrid power grid using the converter power loss and a preset power loss threshold; then obtaining the optimal power flow of the AC / DC hybrid power grid using the branch power flow model includes: obtaining the optimal power flow of the AC / DC hybrid power grid using the branch power flow model and the constraint conditions.

[0014] Preferably, obtaining the converter power loss according to the AC side current of the converter in the AC / DC hybrid power grid and the power loss of the transformer and the converter in the AC / DC hybrid power grid includes: obtaining the converter power loss according to the AC side current of the converter in the AC / DC hybrid power grid, the power loss of the transformer in the AC / DC hybrid power grid, the power loss of the switch of the valve and the freewheeling diode in the converter, and the power conduction loss of the valve in the converter.

[0015] Preferably, the converter power loss is obtained using the following formula:

[0016]

[0017] in, is the converter power loss, is the transformer power loss, which includes the no-load power loss of the transformer and the average auxiliary equipment power loss, is the power loss of the switching of the valve and the freewheeling diode in the converter, is the power conduction loss of the valve in the converter, is the AC side current of the converter, cie is the line of the specific converter from the AC bus to the DC node, A collection of inverters.

[0018] The specific technical scheme of the second embodiment of the present invention is: a power grid optimal power flow calculation system based on convex relaxation technology, the system comprising: a power flow acquisition module, a convex relaxation processing module and an optimal power flow output module; the power flow acquisition module is used to construct the first active power flow of the transformer from the AC bus to the DC node of the AC / DC hybrid power grid, the first reactive power flow of the transformer from the AC bus to the DC node, the second active power flow of the transformer from the DC node to the AC bus, and the second reactive power flow of the transformer from the DC node to the AC bus according to the first voltage amplitude of the AC bus in the AC / DC hybrid power grid, the first voltage phase angle of the AC bus, the second voltage amplitude on the transformer filter side and the second voltage phase angle on the transformer filter side; the convex relaxation processing module is used to perform convex relaxation on the first active power flow, the first reactive power flow, the second active power flow and the second reactive power flow to obtain a branch power flow model of the AC / DC hybrid power grid; the optimal power flow output module is used to obtain the optimal power flow of the AC / DC hybrid power grid using the branch power flow model.

[0019] The specific technical solution of the third embodiment of the present invention is: a power grid optimal power flow calculation device based on convex relaxation technology, comprising a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method as described in any one of the first embodiments of the present application.

[0020] The specific technical solution of the fourth embodiment of the present invention is: a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to perform the steps of the method described in any one of the first embodiments of the present application.

[0021] Implementing the embodiments of the present invention will have the following beneficial effects:

[0022] The first active power flow, the first reactive power flow, the second active power flow and the second reactive power flow in the present invention can simulate the operation of AC and DC power grids including high-voltage DC transmission. Through the convex relaxation technology, the non-convex optimization problem in the power flow is converted into a convex optimization problem that is easy to solve. Therefore, the branch power flow model optimized by the convex relaxation technology is used to calculate the optimal power flow, which ensures the accuracy and calculation efficiency of the optimal power flow and meets the analysis requirements of the AC / DC hybrid power grid.

Brief Description of the Drawings

[0023] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0024] Figure 1 It is a flowchart of the steps of a method for calculating the optimal power flow of a power grid based on convex relaxation technology;

[0025] Figure 2 The schematic diagram of converter station model and parameters;

[0026] Figure 3 This is the single line diagram of Case 5-acdc;

[0027] Figure 4 It is a structural diagram of a power grid optimal power flow calculation system based on convex relaxation technology;

[0028] Among them, 201 is a power flow acquisition module; 202 is a convex relaxation processing module; 203 is an optimal power flow output module. [Specific implementation method]

[0029] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0030] The terms "first", "second", etc. in the specification, claims and drawings of this application are used to distinguish different objects, rather than to describe a specific order. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or modules is not limited to the listed steps or modules, but optionally includes steps or modules that are not listed, or optionally includes other steps or modules that are inherent to these processes, methods, products or devices.

[0031] Reference to "embodiments" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0032] First, the terms, indexes and sets used in AC / DC optimal power flow calculation are defined, as shown in Table 1:

[0033]

[0034] Table 1 Definitions of AC / DC optimal power flow terms, indices and sets

[0035] See also Figure 1 , is a flowchart of a method for calculating the optimal power flow of a power grid based on convex relaxation technology in the first embodiment of the present application, which ensures the accuracy and calculation efficiency of the optimal power flow. The method includes:

[0036] Step 101: according to a first voltage amplitude of an AC bus in an AC / DC hybrid power grid The first voltage phase angle θ of the AC bus i , the second voltage amplitude on the transformer filter side and the second voltage phase angle on the transformer filter side Constructing the first active power flow of the transformer from the AC bus to the DC node of the AC / DC hybrid power grid The first reactive power flow of the transformer from the AC bus to the DC node The second active power flow of the transformer from the DC node to the AC bus Second reactive power flow of the transformer from the DC node to the AC bus

[0037] Step 102: performing convex relaxation on the first active power flow, the first reactive power flow, the second active power flow, and the second reactive power flow to obtain a branch power flow model of the AC / DC hybrid power grid;

[0038] Step 103: Utilize the branch power flow model to obtain the optimal power flow of the AC / DC hybrid power grid.

[0039] The first active power flow, the first reactive power flow, the second active power flow and the second reactive power flow in the method can simulate the operation of AC and DC power grids including high-voltage DC transmission. Through the convex relaxation technology, the non-convex optimization problem in the power flow is transformed into a convex optimization problem that is easy to solve. Therefore, the branch power flow model optimized by the convex relaxation technology is used to calculate the optimal power flow, which ensures the accuracy and calculation efficiency of the optimal power flow and meets the analysis requirements of the AC / DC hybrid power grid.

[0040] Specifically, a static AC / DC converter station model in an AC / DC hybrid power grid is constructed. The schematic diagram of the converter station model can be found in Figure 2, where the HVDC converter converts AC voltage into DC voltage. HVDC converter transformers typically have a short-circuit impedance of 10-20% and an X / R ratio of 30 to 40. The characteristics of the transformer are determined by the impedance Defined, or equivalently by the admittance Definition. Since the tap setting of the converter transformer has a significant impact on the voltage control performance of the HVDC station, it is necessary to consider the voltage transformation factor (i.e., tap ratio) t c (V / V), thereby obtaining the first active power flow, the first reactive power flow, the second active power flow and the second reactive power.

[0041] Specifically, the first active power flow, the first reactive power flow, the second active power flow and the second reactive power are obtained by using the following formula:

[0042]

[0043] in, is the first active power flow, is the first reactive power flow, is the second active power flow, is the second reactive power, is the first voltage amplitude of AC bus i, is the second voltage amplitude on the transformer filter side, θ i is the first voltage phase angle of AC bus i, is the second voltage phase angle on the transformer filter side, and cie is the line from the AC side bus i to the specific converter c on the DC side node e. is the conductance of the transformer, is the transformer susceptance, t c is the voltage conversion factor, A collection of inverters.

[0044] In a specific embodiment, the convex relaxation of the first active power flow, the first reactive power flow, the second active power flow and the second reactive power flow is performed to obtain the branch power flow model of the AC / DC hybrid power grid, including: according to the first active power flow and the first reactive power flow Constructing a first power flow model of the AC / DC hybrid power grid; the first power flow model is a power flow model from the AC bus to the DC node; according to the first active power flow The second active power flow Equivalent resistance of transformer and the current flowing through the transformer Construct a second power flow model of the AC / DC hybrid power grid; the second power flow model is an active power flow model; according to the first reactive power flow The second reactive power flow Equivalent reactance of transformer and the current flowing through the transformer Constructing a third power flow model of the AC / DC hybrid power grid; the third power flow model is a reactive power flow model; according to the first voltage amplitude, the first active power flow The first reactive power flow The equivalent resistance of the transformer and the equivalent reactance of the transformer Construct a fourth power flow model; the fourth power flow model is a power flow model on the transformer filter side The first power flow model, the second power flow model, the third power flow model and the fourth power flow model constitute the branch power flow model.

[0045] Specifically, apply variable replacement on the transformer bus: Substituting variables into the first active power flow, the first reactive power flow, the second active power flow and the second reactive power flow for convex relaxation, a branch power flow model of the AC / DC hybrid power grid is obtained.

[0046] In a specific embodiment, the first power flow model is obtained using the following formula:

[0047]

[0048] in, is the first voltage amplitude, is the current flowing through the transformer, is the first active power flow, is the first reactive power flow, t c is the voltage conversion factor, cie is the line from the AC bus to the DC node of the specific converter, A collection of inverters.

[0049] In a specific embodiment, the second power flow model is obtained using the following formula:

[0050]

[0051] in, is the first active power flow, is the second active power flow, is the equivalent resistance of the transformer, is the current flowing through the transformer.

[0052] In a specific embodiment, the third power flow model is obtained using the following formula:

[0053]

[0054] in, is the first reactive power flow, For the second reactive power flow, is the equivalent reactance of the transformer, is the current flowing through the transformer.

[0055] In a specific embodiment, the fourth power flow model is obtained using the following formula:

[0056]

[0057] in, is the second voltage amplitude, is the first voltage amplitude, t c is the voltage conversion factor, is the equivalent resistance of the transformer, is the first active power flow, is the equivalent reactance of the transformer, is the first reactive power flow, cie is the line from the AC bus to the specific converter of the DC node, A collection of inverters.

[0058] In a specific embodiment, the method further includes: obtaining the power loss of the converter according to the AC side current of the converter in the AC / DC hybrid power grid, and the power loss of the transformer and the converter in the AC / DC hybrid power grid; using the power loss of the converter and a preset power loss threshold to set the constraint conditions of the AC / DC hybrid power grid; then using the branch power flow model to obtain the optimal power flow of the AC / DC hybrid power grid includes: using the branch power flow model and the constraint conditions to obtain the optimal power flow of the AC / DC hybrid power grid. On the basis of obtaining the power loss of the converter, by constraining it, the optimal power flow of the power grid can be achieved. This means that on the premise of ensuring the safe and stable operation of the power grid, the power distribution of the power grid is made more reasonable, thereby improving the operation efficiency of the power grid.

[0059] In a specific embodiment, the power loss of the converter is obtained according to the AC side current of the converter in the AC / DC hybrid power grid and the power loss of the transformer and the converter in the AC / DC hybrid power grid, including: obtaining the power loss of the converter according to the AC side current of the converter in the AC / DC hybrid power grid, the power loss of the transformer in the AC / DC hybrid power grid, the power loss of the switch of the valve and the freewheeling diode in the converter, and the power conduction loss of the valve in the converter. Considering the switching power loss of the valve and the freewheeling diode and the power conduction loss of the valve, the loss distribution inside the converter can be further refined, thereby more accurately evaluating the performance of the converter.

[0060] In a specific embodiment, the converter power loss is obtained using the following formula:

[0061]

[0062] in, is the converter power loss, is the transformer power loss, which includes the no-load power loss of the transformer and the average auxiliary equipment power loss, is the power loss of the switching of the valve and the freewheeling diode in the converter, is the power conduction loss of the valve in the converter, is the AC side current of the converter, cie is the line of the specific converter from the AC bus to the DC node, A collection of inverters.

[0063] In a specific embodiment, convex relaxation processing may also be performed on the converter power loss, and the converter power loss after the convex relaxation processing may be used to construct constraint conditions.

[0064] Specifically, the power loss of the converter after convex relaxation is obtained using the following formula:

[0065] in,

[0066] Specifically, when constructing a static AC / DC converter station model in an AC / DC hybrid power grid, after setting the default positive direction, some negative DC grid topologies are defined.

[0067]

[0068] in, is the DC grid topology, def is a line from bus e to bus f, and dfe is a line from bus f to bus e.

[0069] Assume that the AC node voltage amplitude is and DC node voltage All are subject to operational restrictions:

[0070]

[0071]

[0072] in, and are the minimum and maximum values ​​of the AC bus voltage, and I and E are the set of AC buses and DC buses, respectively.

[0073] (1) Static DC grid model:

[0074] The general power flow model for a DC branch is defined as in, is the active power flow from DC node e to f on DC link d, is the active power flow in the opposite direction. In a physical system, the resistance is non-negative Therefore, the branch loss is non-negative, that is The power flow constraints are as follows: in, is the DC link power rating.

[0075] 1. Branch power flow model: The power flow on the DC line is defined as:

[0076]

[0077] in, is the power flow from DC node e to f on DC line d, is the power flow in the opposite direction. The corresponding current variable is and in also, is the voltage amplitude of DC node e, p d is the number of poles of the DC line, r d is the resistance of the DC line, is the DC link current rating.

[0078] 2. Bus injection power model: Bus injection power of DC line The calculation formula is:

[0079]

[0080] in, is the voltage at node f, and is the series conductance of the DC line d, is the series impedance of the flow line d, p d is the number of poles of the DC line, is the voltage amplitude of the DC node e.

[0081] (2) Static AC / DC converter station model:

[0082] (a) Transformer model with taps and series impedance

[0083] Please refer to the specific steps of obtaining the first active power flow, the first reactive power flow, the second active power flow and the second reactive power in this application, and will not be repeated here.

[0084] If the transformer does not exist, or if the transformer's equivalent impedance For values ​​close to 0, the equation for lossless components is used:

[0085]

[0086] (b) Parallel susceptance model as a filter

[0087] To filter out harmonics, filters are often used in HVDC converter stations, especially for LCC technology. Shunt capacitors have a susceptance Reactive power of filter for:

[0088]

[0089] The node balance between the filter capacitors, phase reactors and transformer is:

[0090]

[0091] in, is the active power flowing through the phase reactor, is the reactive power flowing through the phase reactor.

[0092] (c) Series phase reactor model

[0093] The inductor part of the filter, the phase reactor impedance is Its admittance form is Since the filter can be represented as a c = 1, so the first active power flow and the first reactive power flow, the second active power flow and the second reactive power can be used to represent lossy and lossless reactors, respectively. The short-circuit impedance of the phase reactor is generally 7.5%, and the ratio of reactance to resistance X / R is 30.

[0094] (d) AC / DC converter model

[0095] The AC side of the converter can inject active power and reactive power into the phase reactor. Therefore, the power exchange between the AC grid and the DC grid can be achieved through and Two variables are represented, both of which are defined at the AC bus of the converter. The power limit of the converter is as follows:

[0096]

[0097] in, and are the maximum and minimum active power on the AC side of the converter, and They are the maximum and minimum limits of reactive power on the AC side of the converter respectively. is the rated apparent power of the converter on the AC side and the maximum power of the converter.

[0098] The converter consumes part of the active power on the DC side The power limits are as follows:

[0099]

[0100] in, and are the maximum and minimum active power on the DC side of the converter respectively.

[0101] The AC side and DC side power of the converter are coupled by the following equation.

[0102]

[0103] Inverter power loss Defined using a parameterized loss model:

[0104]

[0105] in is the no-load loss of the transformer and the average auxiliary equipment loss, is the switching loss of the valve and the freewheeling diode, is the conduction loss of the valve. is the magnitude of the AC side current of the converter. The AC side current is defined as the active and reactive power injection of the converter and the AC side voltage:

[0106]

[0107] in, is the voltage amplitude at the converter AC bus. and They are the minimum and maximum voltage amplitudes at the AC side bus of the converter, respectively. is the rated current of the converter. The DC current of the converter is subject to the following safety limits:

[0108]

[0109] in, is the current amplitude of the converter DC side, and are the minimum and maximum current amplitudes of the converter DC side, is the voltage amplitude of the DC node e.

[0110] In this embodiment, a general representation of a converter station including converter transformers, reactors and harmonics is used. In the implemented AC / DC optimal power flow tool, these converter auxiliary devices are included in a parameterized manner. The MMC type converter uses a large number of insulated gate bipolar transistors (IGBT) connected in series. These switches are turned on or off at a low frequency to approximate a sinusoidal waveform with a step function. This causes less harmonic distortion on the AC voltage, so the harmonics can be omitted. The grid-commutated converter LCC using thyristors as power electronic switches requires large harmonic filters and reactors. In order to accurately simulate the LCC converter, transformers, filters and reactors should not be omitted. For the LCC converter, there is a fixed ratio between active and reactive power, namely:

[0111]

[0112] in, is the variable representing the thyristor firing angle, Respectively represent the minimum / maximum trigger angle, is the apparent power rating of the converter AC side. , the power balance equation of the DC node is:

[0113]

[0114] Among them, P me is the active power on the line me formed by the bus m connected to the bus e, is the active power on the DC line from bus e to f, is the collection of DC loads.

[0115] The power balance equation of the AC node is:

[0116]

[0117] in, is the active power from DC node i to j on AC line l, is the generator set, P g is the active output of generator g, P m is the active power of load m, is the parallel conductance connected to busbar i, I is the collection of AC busbars, is the reactive power from DC node i to j on AC line l, Q g is the reactive power output of generator g, Q m is the reactive power of load m, is the shunt susceptance connected to busbar i.

[0118] In a specific embodiment, a convex relaxation formula is constructed to approximate a non-convex model in an AC / DC converter station model. Specifically, it includes:

[0119] (1) Static DC grid model

[0120] The → symbol is used below to indicate variable substitution. For example New variable Replacement. The following variable replacement is performed below:

[0121] 1) Busbar injection power model

[0122] For the busbar injection power model, after convex relaxation of the product of the voltage amplitudes, a convex model is obtained:

[0123]

[0124] 1) Branching Flow Model

[0125] First, make the following variable substitutions:

[0126] The second-order cone reconstruction method is applied to the following formula:

[0127] and After substitution, we get the convex model:

[0128]

[0129] because and are all non-negative numbers, the formula is a rotated second-order cone that makes the inequality convex by construction. This can be written as a standard second-order cone constraint:

[0130]

[0131] (2) Static AC / DC converter station model

[0132] 1) AC / DC converter model

[0133] The variables in the converter loss model are related to both the magnitude of the AC side current and the square of the AC side current. Two variables are defined here to represent the converter current, is the current amplitude, is the square of the current amplitude:

[0134]

[0135] The convex relaxation of is:

[0136]

[0137] variable and This is related by an inequality defined in the space of W variables:

[0138]

[0139] Finally, considering the voltage amplitude limitation of the converter, the following inequality is obtained:

[0140]

[0141] if The resulting equation is similar to the classical second-order cone branch load relaxation equation, but does not relate the AC and DC voltages. However, if There is an additional relaxation gap. In the optimal case, this error can be ignored, that is,

[0142] In order to derive the convex relaxation model of LCC, based on The limits of each converter are:

[0143]

[0144] Define the lower limit for reactive power with these parameters:

[0145]

[0146] for Right now Therefore, it behaves inductively relative to the AC grid. Convex relaxation The operating mode is simply defined as the maximum or minimum value Can significantly improve compactness.

[0147] 2) Busbar injection model of phase reactor

[0148]

[0149] Applying substitution, we obtain the busbar injection model in the second-order cone form:

[0150]

[0151] If no reactor is present, or if the value Then the lossless model of the reactor is obtained:

[0152]

[0153]

[0154] 3) Phase Reactor Branch Flow Model

[0155]

[0156] Apply substitution to obtain the branch power flow model in the second-order cone form:

[0157]

[0158] The branch power flow model based on the second-order cone is obtained by applying the variable replacement method. The reactive power of the filter capacitor under the new variables is:

[0159]

[0160] 4) The node power balance between filter capacitors, phase reactors and transformers remains unchanged.

[0161] 5) Transformer busbar injection model:

[0162]

[0163] After variable substitution, the busbar injection model based on the second-order cone is obtained:

[0164]

[0165]

[0166] If the transformer does not exist, or is numerically The lossless model using the transformer is:

[0167]

[0168] 6) Transformer branch power flow model

[0169]

[0170] Application replacement is used to obtain a branch flow model based on a second-order cone. The specific formula of the branch flow model can be found in the steps of performing convex relaxation on the first active power flow, the first reactive power flow, the second active power flow, and the second reactive power flow in this application to obtain the branch flow model of the AC / DC hybrid power grid, which will not be repeated here.

[0171] In a specific embodiment, the constraints of the AC / DC hybrid power grid in this application include constraints of a static DC power grid model, AC / DC converter, phase reactor, filter, and transformer in addition to the constraints set by the converter power loss and the preset power loss threshold, specifically including:

[0172] (1) Static DC grid model constraints:

[0173]

[0174] Among them, in the static DC grid model r d ≈0.

[0175] (2) Constraints of the static AC / DC converter station model

[0176] 1) AC / DC converter:

[0177]

[0178] Assumptions and The power flows and losses of the converter are derived to be linear with respect to the active power variable. When , the line loss may be negative, and this model simplifies The network flow model used at the time.

[0179] 2) Phase reactor

[0180] Assumptions And the small voltage phase angle condition θ≈0 is satisfied. Apply cos(θ)≈1 and sin(θ≈θ) to obtain the power of the phase reactor. The specific constraints are:

[0181]

[0182] The constraints of the final lossless power flow model are:

[0183]

[0184] 3) Filter:

[0185] The node power balance constraint between the phase reactor and the transformer at the filter is:

[0186]

[0187] 4) Transformer constraints:

[0188] Further assumption And using the small angle approximation, the transformer equation becomes:

[0189]

[0190] The constraints of the lossless power flow model are:

[0191] AC / DC OPF Formulation Overview and Properties:

[0192] The AC branch model is assumed to consist of an ideal transformer in series with a π-element, which is able to represent both the lossy line and the lossy transformer. In contrast, the DC line is modeled as a series resistor.

[0193] Compared with AC grid, there are fewer types of DC branch formulations than AC grid formulations. Similar to AC grid, for AC side passive components and DC grid, the bus injection model (BIM) and branch flow model (BFM) of second-order cone programming (SOC) are equivalent.

[0194] In view of the radiation characteristics of the passive components of the converter station, the busbar injection model SOC BIM based on the second-order cone is the most direct convex relaxation, so in this case SOC BIM has the same model properties as the semi-definite programming SDP and the second-order convex programming QC.

[0195] The calculation example of this embodiment uses the "dcline" model of Matpower to verify the feasibility and optimality of the AC and linearization models. Figure 3The case5_acdc example based on the IEEE 5-bus test system is presented. A three-bus DC grid is embedded in the 5-bus AC system using VSC converters. In the case5_lcc example, the VSC HVDC converters are replaced by LCC converters. For the case5_2grids example, two identical case5_acdc grids are connected via an AC branch. The case5_dcgrid consists of an AC bus and a DC grid with four buses, including DC loads. It represents a DC system with only one AC generator feeding the DC grid with DC loads through a converter. All loads are fed by the generator connected to the AC bus. The case5_dc example is used for validation in Matpower and includes an HVDC link between buses 3 and 5 in the IEEE 5-bus test system. The case5_b2bdc example uses a back-to-back HVDC link using an accurate converter model consisting of two converters and an AC bus. The case24_3zones example connects three IEEE 24-bus reliability test systems using a DC grid. The case_39 and case_3120sp_acdc examples represent the IEEE 39-bus test system and the 3210-bus Polish power system with a DC grid, respectively. The case_588_sdet_acdc example is an extension of the 588-bus system. A 7-bus, 8-branch DC grid is embedded in the AC system. Table 2 shows the key properties of the test cases.

[0196]

[0197] Table 2 AC / DC OPF test case attributes

[0198] The optimization objective remains the same as the conventional OPF, i.e., minimizing the generation cost with active power output as the decision variable. The gap between the specific method and the BIM NLP AC / DC (local) optimal solution is calculated as follows:

[0199]

[0200] BIM NLP: bus injection models nonlinearprogramming, node injection power nonlinear model.

[0201] objective(BIMNLP): objective function of the node injection power nonlinear model;

[0202] objective(form): objective function of a specific method;

[0203] gap(form): gap ratio.

[0204] Tables 3 and 4 summarize the results of several test cases, including the gap between different formulas and the BIM NLP ac / dc (local) optimal solution. Table 5 shows the calculation time of different formulas.

[0205]

[0206] Table 3 Results of test case 1

[0207]

[0208] Table 4 Results of test case 2

[0209] It can be seen that the semidefinite programming (SDP) formulation is generally tight, but it is more sensitive to numerical issues. For the developed cases, the BIM and BFM results for the second-order cone programming (SOC) are identical in numerical accuracy. For small cases, the QC formulation appears to be identical to the SOC BIM and SOC BFM, while for larger cases the optimality gap is quite large. This suggests the need to develop a wider variety of test cases. Some test cases show significant optimality gaps for QC and SOC relaxations, while others are tight. It is observed that the SOC approximation is numerically accurate under unconstrained conditions (i.e., the power and current of the DC branches and converter stations are not at their limits). As expected from the derivation, when the loss parameters of the converter station are There are certain errors.

[0210] The computation time of different formulations is shown in Table 5. In the analyzed test cases, it is observed that the SOC BFM model is faster than the SOCBIM model and the optimality gap with the SOC BIM model is very close.

[0211]

[0212]

[0213] Table 5 Calculation time of different formulas

[0214] In the specific embodiments, see Figure 4, is a structural schematic diagram of a power grid optimal power flow calculation system based on convex relaxation technology in the second embodiment of the present application, the system comprising: a power flow acquisition module 201, a convex relaxation processing module 202 and an optimal power flow output module 203; the power flow acquisition module 201 is used to construct the first active power flow of the transformer from the AC bus to the DC node of the AC / DC hybrid power grid, the first reactive power flow of the transformer from the AC bus to the DC node, the second active power flow of the transformer from the DC node to the AC bus, and the second reactive power flow of the transformer from the DC node to the AC bus according to the first voltage amplitude of the AC bus, the first voltage phase angle of the AC bus, the second voltage amplitude of the transformer filter side and the second voltage phase angle of the transformer filter side; the convex relaxation processing module 202 is used to perform convex relaxation on the first active power flow, the first reactive power flow, the second active power flow and the second reactive power flow to obtain a branch power flow model of the AC / DC hybrid power grid; the optimal power flow output module 203 is used to obtain the optimal power flow of the AC / DC hybrid power grid using the branch power flow model.

[0215] The first active power flow, the first reactive power flow, the second active power flow and the second reactive power flow in this system can simulate the operation of AC and DC power grids including high-voltage DC transmission. Through the convex relaxation technology, the non-convex optimization problem in the power flow is transformed into a convex optimization problem that is easy to solve. Therefore, the branch power flow model optimized by the convex relaxation technology is used to calculate the optimal power flow, which ensures the accuracy and calculation efficiency of the optimal power flow and meets the analysis requirements of the AC / DC hybrid power grid.

[0216] In a specific embodiment, the third embodiment of the present application provides a power grid optimal power flow calculation device based on convex relaxation technology, including a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, the processor executes the steps of the method as described in any one of the first embodiments of the present application.

[0217] In a specific embodiment, the fourth embodiment of the present application provides a computer-readable storage medium storing a computer program, characterized in that when the computer program is executed by a processor, the processor executes the steps of the method described in any one of the first embodiments of the present application.

[0218] The above embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

[0219] The above description is only a preferred embodiment of the present invention and does not limit the present invention in other forms. Any technician familiar with the profession may use the technical content disclosed above to change or modify it into an equivalent embodiment with equivalent changes and apply it to other fields. However, any simple modification, equivalent change and modification made to the above embodiment based on the technical essence of the present invention without departing from the content of the technical solution of the present invention still falls within the protection scope of the technical solution of the present invention.

Claims

1. A method for calculating optimal power flow of a power grid based on convex relaxation technology, characterized in that: The method comprises: Constructing a first active power flow of the transformer from the AC bus to the DC node, a first reactive power flow of the transformer from the AC bus to the DC node, a second active power flow of the transformer from the DC node to the AC bus, and a second reactive power flow of the transformer from the DC node to the AC bus in the AC / DC hybrid power grid according to a first voltage amplitude of the AC bus, a first voltage phase angle of the AC bus, a second voltage amplitude on the transformer filter side, and a second voltage phase angle on the transformer filter side; Performing convex relaxation on the first active power flow, the first reactive power flow, the second active power flow, and the second reactive power flow to obtain a branch power flow model of the AC / DC hybrid power grid; The branch power flow model is used to obtain the optimal power flow of the AC / DC hybrid power grid.

2. The method for calculating the optimal power flow of a power grid based on convex relaxation technology according to claim 1, characterized in that: The performing convex relaxation on the first active power flow, the first reactive power flow, the second active power flow and the second reactive power flow to obtain a branch power flow model of the AC / DC hybrid power grid includes: Constructing a first power flow model of the AC / DC hybrid power grid according to the first active power flow and the first reactive power flow; the first power flow model is a power flow model from the AC bus to the DC node; constructing a second power flow model of the AC / DC hybrid power grid according to the first active power flow, the second active power flow, the equivalent resistance of the transformer and the current flowing through the transformer; the second power flow model is an active power flow model; constructing a third power flow model of the AC / DC hybrid power grid according to the first reactive power flow, the second reactive power flow, the equivalent reactance of the transformer and the current flowing through the transformer; the third power flow model is a reactive power flow model; A fourth power flow model is constructed according to the first voltage amplitude, the first active power flow, the first reactive power flow, the equivalent resistance of the transformer and the equivalent reactance of the transformer; the fourth power flow model is the power flow model on the transformer filter side; the first power flow model, the second power flow model, the third power flow model and the fourth power flow model constitute the branch power flow model.

3. The method for calculating the optimal power flow of a power grid based on convex relaxation technology according to claim 2, characterized in that: The first power flow model is obtained using the following formula: in, is the first voltage amplitude, is the current flowing through the transformer, is the first active power flow, is the first reactive power flow, t c is the voltage conversion factor, cie is the line from the AC bus to the DC node of the specific converter, A collection of inverters.

4. The method for calculating the optimal power flow of a power grid based on convex relaxation technology according to claim 2, characterized in that: The fourth power flow model is obtained by using the following formula: in, is the second voltage amplitude, is the first voltage amplitude, t c is the voltage conversion factor, is the equivalent resistance of the transformer, is the first active power flow, is the equivalent reactance of the transformer, is the first reactive power flow, cie is the line from the AC bus to the specific converter of the DC node, A collection of inverters.

5. The method for calculating the optimal power flow of a power grid based on convex relaxation technology according to claim 1, characterized in that: The method further comprises: Obtaining the converter power loss according to the AC side current of the converter in the AC / DC hybrid power grid and the power loss of the transformer and the converter in the AC / DC hybrid power grid; Using the converter power loss and a preset power loss threshold to set the constraint conditions of the AC / DC hybrid power grid; Then the step of using the branch power flow model to obtain the optimal power flow of the AC / DC hybrid power grid includes: The branch power flow model and the constraint conditions are used to obtain the optimal power flow of the AC / DC hybrid power grid.

6. The method for calculating the optimal power flow of a power grid based on convex relaxation technology according to claim 5, characterized in that: The obtaining the converter power loss according to the AC side current of the converter in the AC / DC hybrid power grid and the power loss of the transformer and the converter in the AC / DC hybrid power grid includes: The power loss of the converter is obtained according to the AC side current of the converter in the AC / DC hybrid power grid, the power loss of the transformer in the AC / DC hybrid power grid, the power loss of the switch of the valve and the freewheeling diode in the converter, and the power conduction loss of the valve in the converter.

7. The method for calculating the optimal power flow of a power grid based on convex relaxation technology according to claim 6, characterized in that: The converter power loss is obtained using the following formula: in, is the converter power loss, is the transformer power loss, which includes the no-load power loss of the transformer and the average auxiliary equipment power loss, is the power loss of the switching of the valve and the freewheeling diode in the converter, is the power conduction loss of the valve in the converter, is the AC side current of the converter, cie is the line of the specific converter from the AC bus to the DC node, A collection of inverters.

8. A power grid optimal power flow calculation system based on convex relaxation technology, characterized in that: The system comprises: a power flow acquisition module, a convex relaxation processing module and an optimal power flow output module; The power flow acquisition module is used to construct a first active power flow of the transformer from the AC bus to the DC node, a first reactive power flow of the transformer from the AC bus to the DC node, a second active power flow of the transformer from the DC node to the AC bus, and a second reactive power flow of the transformer from the DC node to the AC bus in the AC-DC hybrid power grid according to a first voltage amplitude of the AC bus, a first voltage phase angle of the AC bus, a second voltage amplitude on the transformer filter side, and a second voltage phase angle on the transformer filter side; The convex relaxation processing module is used to perform convex relaxation on the first active power flow, the first reactive power flow, the second active power flow and the second reactive power flow to obtain a branch power flow model of the AC / DC hybrid power grid; The optimal power flow output module is used to obtain the optimal power flow of the AC / DC hybrid power grid by using the branch power flow model.

9. A power grid optimal power flow calculation device based on convex relaxation technology, comprising a memory and a processor, characterized in that: The memory stores a computer program, and when the computer program is executed by the processor, the processor is caused to perform the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the processor is caused to perform the steps of the method according to any one of claims 1 to 7.

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