CN111711197B - Second-order cone operation control method for alternating current and direct current power distribution network containing power electronic transformer - Google Patents

Second-order cone operation control method for alternating current and direct current power distribution network containing power electronic transformer Download PDF

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CN111711197B
CN111711197B CN202010686754.2A CN202010686754A CN111711197B CN 111711197 B CN111711197 B CN 111711197B CN 202010686754 A CN202010686754 A CN 202010686754A CN 111711197 B CN111711197 B CN 111711197B
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power
pet
distribution network
operation control
port
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CN111711197A (en
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穆云飞
张涛
肖迁
贾宏杰
余晓丹
蒲天骄
王晓辉
袁晓东
李强
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Tianjin University
China Electric Power Research Institute Co Ltd CEPRI
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Tianjin University
China Electric Power Research Institute Co Ltd CEPRI
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/02—Circuit arrangements for ac mains or ac distribution networks using a single network for simultaneous distribution of power at different frequencies; using a single network for simultaneous distribution of ac power and of dc power
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin

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Abstract

The invention discloses a method for controlling the operation of a second-order cone of an alternating current and direct current power distribution network containing a power electronic transformer, which comprises the following steps: constructing a multi-period operation control model of the PET-containing AC/DC hybrid power distribution network; the injection power of different ports of the PET is controlled by utilizing the flexible regulation and control capability of the PET, so that the mutual coordination of the power among the different ports is realized, and the exchange requirement of power balance among an AC sub-network and a DC sub-network is met; and performing convex relaxation on the multi-period operation control model of the AC/DC hybrid power distribution network by adopting second-order cone programming and linear approximation, and improving the solving efficiency of the multi-period operation control problem of the AC/DC hybrid power distribution network containing PET. The invention effectively reduces the system loss and improves the system operation economy; the original nonlinear model is subjected to convex relaxation by adopting second-order cone relaxation and linear approximation, so that the PET-containing AC/DC distribution network second-order cone operation control model is provided, the accuracy is high, and the solving efficiency is improved.

Description

Second-order cone operation control method for alternating current and direct current power distribution network containing power electronic transformer
Technical Field
The invention relates to the field of operation scheduling modeling of an alternating-current and direct-current power distribution network, in particular to a method for controlling operation of a second-order cone of the alternating-current and direct-current power distribution network with a power electronic transformer.
Background
The development of renewable energy technology provides new challenges and higher requirements for flexible access and effective regulation of power systems. The AC/DC hybrid Power distribution network with a Power Electronic Transformer (PET) as a core can realize flexible interconnection among different voltage and frequency Power grids, can realize flexible grid connection of a distributed Power supply at multiple voltage levels, is beneficial to plug and play and consumption of renewable energy sources, and is widely concerned by related scholars and engineering circles. Meanwhile, due to the characteristics of access of a large number of power electronic flexible devices, alternating current-direct current hybrid connection, three-phase load asymmetry, strong coupling of active power and reactive power and the like, the problems of establishment, analysis, solution and the like of an optimization model of the system face a lot of challenges.
1) In the aspect of optimized operation, each port is equivalent to a Voltage Source Converter (VSC), a PET equivalent model is established, loss characteristics of the PET Converter are further considered, and therefore a multi-port PET steady-state model is established. 2) In the field of electric energy interconnection, a PET (positron emission tomography) with an intermediate direct current link isolates a power distribution network into a plurality of alternating current subnets and direct current subnets with mutually independent voltage and frequency, and the control strategy of each PET port needs to be comprehensively considered during operation so as to meet the power exchange requirements of the PET and the subnets. Aiming at the problem, a multi-port PET operation strategy optimization combination method based on generalized droop control is provided, switching of different operation modes of multi-port PET is achieved through optimization and adjustment of a droop coefficient of a PET port, and the method can well adapt to renewable energy source fluctuation. 3) Aiming at the problem of operation scheduling of an alternating current-direct current hybrid power distribution network constructed based on an electric energy internet core device PET, a multi-period optimization model is a massive high-dimensional complex nonlinear programming problem based on power flow, the solving difficulty is high, and the solving efficiency can be greatly improved by linearizing an original optimization model. At the present stage, a second-order cone relaxation technology is adopted, so that second-order cone day-ahead optimal scheduling modeling of the alternating-current and direct-current power distribution network can be realized, and an analysis basis is provided for establishing a second-order cone operation scheduling model of the alternating-current and direct-current hybrid power distribution network.
It can be seen that the current research results improve the operation level of the PET-containing AC/DC hybrid power distribution network from different aspects, but the utilization of the coordination effect among PET multiports needs to be further improved; in addition, the droop control power distribution network load power is influenced by voltage amplitude and frequency change, static load characteristic description is required to be adopted and used as nonlinear constraint to increase the non-convexity of the model, and after a strong nonlinear loss characteristic equation introduced by a voltage source converter is considered, the non-convexity of the operation control model is further increased, and efficient solution is difficult. Generally speaking, an optimized control model of the PET-containing alternating current and direct current hybrid power distribution network considering the control strategy of the power electronic transformer is absent in the present stage, and a reasonable convex relaxation method is also absent aiming at the nonlinear model.
Disclosure of Invention
The invention provides a method for controlling the operation of a second-order cone of an alternating current and direct current power distribution network containing a power electronic transformer, which effectively reduces the system loss and improves the system operation economy; the original nonlinear model is subjected to convex relaxation by adopting second-order cone relaxation and linear approximation, so that a PET-containing AC/DC distribution network second-order cone operation control model is provided, the accuracy is better, the solving efficiency is improved, and details are described in the following steps:
a method for controlling the operation of a second-order cone of an AC/DC distribution network with a power electronic transformer comprises the following steps:
constructing a multi-period operation control model of the PET-containing AC/DC hybrid power distribution network;
the injection power of different ports of the PET is controlled by utilizing the flexible regulation and control capability of the PET, so that the mutual coordination of the power among the different ports is realized, and the exchange requirement of power balance among an AC sub-network and a DC sub-network is met;
and performing convex relaxation on the multi-period operation control model of the AC/DC hybrid power distribution network by adopting second-order cone programming and linear approximation, and improving the solving efficiency of the multi-period operation control problem of the AC/DC hybrid power distribution network containing PET.
The method specifically comprises the following steps of performing convex relaxation on the alternating current-direct current hybrid power distribution network multi-period operation control model by adopting second-order cone programming and linear approximation:
carrying out convex relaxation on the power flow equation, linearizing the PET loss characteristic equation, and linearizing the static load characteristic equation.
Further, the performing convex relaxation on the power flow equation specifically includes: and converting the original AC and DC power flow constraint equations into second-order conical forms.
The linearization of the PET loss characteristic equation is specifically as follows:
Figure BDA0002587843800000021
in the formula (I), the compound is shown in the specification,
Figure BDA0002587843800000022
is an initial value of the current amplitude of each port converter bridge arm of the PET at the moment t in the current iteration,
Figure BDA0002587843800000023
the square of the current amplitude of the bridge arm of the converter at each port of the PET at the time t; a is c.i ,b c.i ,c c.i Fitting parameters of the I port active loss of the PET are obtained.
Further, the linearizing the static load characteristic equation specifically includes:
Figure BDA0002587843800000031
Figure BDA0002587843800000032
in the formula (I), the compound is shown in the specification,
Figure BDA0002587843800000033
the initial value of the three-phase voltage amplitude of the node i at the moment t at the current iteration is obtained;
Figure BDA0002587843800000034
the square of the three-phase voltage amplitude of the node i at the moment t is obtained;
Figure BDA0002587843800000035
the initial value of the frequency of the alternating current system at the current iteration at the moment t is shown;
Figure BDA0002587843800000036
load three-phase active power and reactive power of an alternating current node i at the moment t;
Figure BDA0002587843800000037
the node i is rated with active power and reactive power; alpha and beta reflect exponential coefficients of the influence of the node voltage change on the load power; k is a radical of formula pf ,k qf A gain factor representing the effect of system frequency changes on load power; omega 0 Is the ac port idle frequency.
The technical scheme provided by the invention has the beneficial effects that:
1. the method analyzes the steady-state model of the multi-port power electronic transformer applicable to the low-voltage AC/DC hybrid power distribution network, considers the loss characteristic of the multi-port power electronic transformer, and provides a model basis for establishing the operation control model of the AC/DC hybrid power distribution network containing the power electronic transformer. The established multi-period operation control model containing the power electronic transformer can effectively reduce the active loss of system operation and improve the economical efficiency of system operation by performing coordinated optimization control on the injection power of the power electronic transformer and the output power of the distributed power supply;
2. the invention solves the problem of convex planning of the operation control model of the AC/DC hybrid power distribution network containing the power electronic transformer, the AC/DC power flow equation is convexly relaxed by adopting a second-order cone relaxation technology, and then the nonlinear loss characteristic equation and the nonlinear static load characteristic equation of the power electronic transformer are linearized by utilizing a successive approximation method, so that the second-order cone operation control model of the AC/DC hybrid power distribution network containing the power electronic transformer is provided.
Drawings
FIG. 1 is a flow chart of a method for controlling the operation of a second order cone of an AC/DC distribution network with a power electronic transformer;
FIG. 2 is a system for testing an AC/DC hybrid power distribution network including an electronic power transformer;
FIG. 3 is a diagram illustrating the results of a day-ahead operational schedule;
wherein, (a) the active power is output for the distributed power supply and the main network; (b) The method is a schematic diagram of the active loss of the system before and after the output and optimization of the energy storage device.
FIG. 4 is a flow chart of the present invention for solving the original nonlinear non-convex problem by transforming it into a second order cone problem.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention are described in further detail below.
The method aims at solving the problems that a PET-containing alternating current and direct current hybrid power distribution network optimization control model considering a power electronic transformer control strategy is lacked at the present stage, and a reasonable convex relaxation method is lacked in the nonlinear model. Referring to fig. 1, the invention provides a method for controlling the operation of a second order cone of an ac/dc distribution network containing a power electronic transformer, which is described in detail in the following:
step 101: constructing a multi-period operation control model of the PET-containing AC/DC hybrid power distribution network so as to exert the flexible regulation and control capability of the power electronic transformer and improve the operation performance of the system;
step 102: the injection power of different ports of the PET is controlled by utilizing the flexible regulation and control capability of the PET, so that the mutual coordination of the power among the different ports is realized, and the exchange requirement of power balance among an AC sub-network and a DC sub-network is met;
step 103: because the constructed multi-period operation control model of the PET-containing AC/DC hybrid power distribution network is a non-convex model, on the basis, the non-convex model is subjected to convex relaxation by adopting a Second-order Cone Programming (SOCP) method and a linear approximation method, so that the solution efficiency of the multi-period operation control problem of the PET-containing AC/DC hybrid power distribution network is improved.
The SOCP method and the linear approximation method are well known to those skilled in the art, and are not described in detail in the embodiments of the present invention.
In concrete implementation, the non-convex model comprises nonlinear power flow equation constraint, nonlinear PET loss characteristic equation constraint, nonlinear static load characteristic constraint and the like, belongs to a non-convex optimization problem, and is difficult to realize quick and efficient solution through an optimization algorithm.
The convex relaxation refers to the fact that the nonlinear constraint equation is converted into a second-order cone constraint form and a linear constraint form, so that the non-convex optimization problem is converted into a convex optimization problem, and the solving efficiency can be greatly improved.
The scheme in the above embodiment is detailed and expanded by combining a specific calculation formula, an example and fig. 2-4, and is described in detail as follows:
step 201: constructing a steady-state model and a droop control strategy of the multi-port power electronic transformer;
wherein, this step 201 includes:
step 2021) constructing a steady-state model of the multi-port power electronic transformer
PET can realize the power interaction between the alternating current-direct current sub-net, coupling alternating current-direct current system, and the active power and the PET active loss of each friendship of operation in-process PET, direct current port injection satisfy the power balance constraint constantly:
Figure BDA0002587843800000051
wherein, M and N respectively represent the number of the PET AC and DC ports.
Figure BDA0002587843800000052
The active power output by the PET alternating current port at the moment t is represented;
Figure BDA0002587843800000053
outputting active power for a direct current port of the PET at the time t; superscript m, n = {1,2, … } represents the corresponding PET AC and DC port numbers;
Figure BDA0002587843800000054
is the active loss of the multiport PET at the moment t. PET is composed of a large number of power electronic devices, and its power loss during operation is not negligible and must be considered, where the power loss of PET includes: the loss model of each port of PET can be obtained through curve fitting, and the loss model can be specifically expressed as a quadratic function of bridge arm current of the port converter.
Figure BDA0002587843800000055
Wherein the content of the first and second substances,
Figure BDA0002587843800000056
the I port of the PET has active loss at the time t; a is c.i ,b c.i ,c c.i Fitting parameters of active loss of an i port of the PET;
Figure BDA0002587843800000057
for each port converter bridge armThe magnitude of the flow. And total active power loss of PET
Figure BDA0002587843800000058
Expressed as active loss of each AC port of PET
Figure BDA0002587843800000059
And active loss of each direct current port of PET
Figure BDA00025878438000000510
The sum is shown in formula (3). Wherein the content of the first and second substances,
Figure BDA00025878438000000511
a three-phase system is shown.
Figure BDA00025878438000000512
The steady-state model of the multi-port power electronic transformer considering the PET loss characteristics is summarized in the formulas (1) to (3), and the method can be suitable for a three-phase asymmetric alternating current-direct current hybrid power distribution network and can be used for optimizing and analyzing the three-phase asymmetric alternating current-direct current hybrid power distribution network.
Step 2022) droop control strategy for multi-port power electronic transformer
The control strategy of each port of the PET specifically includes: a constant voltage control strategy, a constant power control strategy, a droop control strategy, etc., for a PET having multiple ports, in order to achieve a balanced constraint on the power injected into the PET, the following two methods are generally adopted:
1) A master-slave control mode, namely one port of the PET adopts constant voltage control to ensure that the voltage of the port is constant, the other ports adopt constant power control to inject a set power value, and the constant voltage control port can automatically adjust the power value injected by the port according to the magnitude of unbalanced power, thereby realizing the power balance of the multi-port PET;
2) In view of the above, the PET ports of the present invention adopt a droop control method, in which active power injected into all ac ports of the PET is adjusted according to an active/frequency droop curve, reactive power injected into ac ports is adjusted according to a reactive/voltage droop curve, and active power injected into dc ports of the PET is adjusted according to an active/voltage droop curve, so as to satisfy the constraint shown in the following formula (4).
The multi-port PET droop control strategy meets the constraint shown in the formula (4), the PET alternating current port meets the P/omega and Q/U droop characteristic equation constraint, and the direct current port meets the P/U droop characteristic equation constraint.
Figure BDA0002587843800000061
Wherein the content of the first and second substances,
Figure BDA0002587843800000062
active power and reactive power output by each phase at the moment t of the PET alternating current port;
Figure BDA0002587843800000063
all are droop slopes; omega 0 ,
Figure BDA0002587843800000064
Respectively the no-load frequency and the voltage amplitude of the alternating current port; omega t ,
Figure BDA0002587843800000065
Actual frequency and voltage amplitude at time t respectively; omega max ,ω min Respectively an upper limit and a lower limit of the allowable frequency; u shape ac.max ,U ac.min Respectively an upper limit and a lower limit of a voltage amplitude; p ac.max ,Q ac.max The PET alternating current port allows the maximum value of active power and reactive power to be output.
Figure BDA0002587843800000066
Is the real output at the moment t of the direct current port,
Figure BDA0002587843800000067
is the droop slope;
Figure BDA0002587843800000068
is the no-load voltage amplitude;
Figure BDA0002587843800000069
the voltage amplitude at the t moment is a PET direct current port; u shape dc.max ,U dc.min The port voltage amplitude is the upper and lower limits; p dc.max And outputting the maximum value of the active power for the direct current port of the PET.
Formula (4) describes a constraint equation which is satisfied by the active power, the reactive power and the voltage amplitude output by the port when the PET low-voltage alternating current port and the direct current port adopt droop control, and a power flow calculation model when the multiport PET is applied to the optimization analysis of the alternating current-direct current hybrid power distribution network is formed by combining the PET steady-state models in the formulas (1) to (3).
Step 202: constructing an operation control model of an alternating current-direct current hybrid power distribution network containing a power electronic transformer;
wherein the step 202 comprises the steps of:
step 2021) construct the objective function:
the invention establishes an optimization model by taking the minimum active loss as an objective function, and the established objective function is shown as a formula (5).
Figure BDA00025878438000000610
Wherein T is an optimization time interval;
Figure BDA00025878438000000611
the active loss of PET at the moment t is shown in a formula (3);
Figure BDA00025878438000000612
active power loss of the alternating current distribution network;
Figure BDA00025878438000000613
is the active loss of the direct current distribution network.
Step 2022) constructing constraint conditions;
1) Alternating current and direct current power flow constraint:
Figure BDA0002587843800000071
wherein u (j) is a head-end node set which takes j as a tail-end node branch; v (j) is a tail end node set taking j as a head end node branch; the three-phase active power and reactive power of the head end of the branch ij at the time t are expressed as
Figure BDA0002587843800000072
Figure BDA00025878438000000725
Figure BDA0002587843800000073
Three-phase active power and reactive power injected into the node j at the moment t;
Figure BDA0002587843800000074
represents the branch resistance and reactance of a three-phase system;
Figure BDA0002587843800000075
the three-phase current amplitude of the branch ij at the moment t is obtained;
Figure BDA0002587843800000076
is the three-phase voltage amplitude of the node i at the time t,
Figure BDA0002587843800000077
is the three-phase voltage amplitude of the alternating current node j at the moment t,
Figure BDA0002587843800000078
for the reactive power transmitted by the ac branch jk at time t,
Figure BDA0002587843800000079
active power transmitted by the alternating current branch jk at the time t, wherein k is an alternating current node number.
Figure BDA00025878438000000710
Wherein the content of the first and second substances,
Figure BDA00025878438000000711
for the active power at the head end of the dc branch ij,
Figure BDA00025878438000000712
injecting active power for the direct current node j at the time t; r is ij.dc Representing the branch resistance of the direct-current power distribution network;
Figure BDA00025878438000000713
for the current magnitude of the dc branch ij at time t,
Figure BDA00025878438000000714
the voltage amplitude at time t of the dc node i,
Figure BDA00025878438000000715
for the active power transmitted by the dc branch jk at time t,
Figure BDA00025878438000000716
the voltage amplitude of the dc node j at time t.
2) Distributed power supply operation constraint:
when each port of the PET adopts a droop control strategy, the droop control strategy is also adopted for distributed power supplies in the ac and dc power distribution networks to cope with renewable energy source fluctuation, as shown in the following formulas (8) to (10).
Figure BDA00025878438000000717
Figure BDA00025878438000000718
Figure BDA00025878438000000719
Wherein the content of the first and second substances,
Figure BDA00025878438000000720
the active power and the reactive power which are output outwards by the distributed power supply in the low-voltage mating power grid at the time t are represented;
Figure BDA00025878438000000721
the active power output by the distributed power supply of the direct-current power distribution network at the moment t is represented;
Figure BDA00025878438000000722
k dc calculating an expression reference formula (4) for the slope of the droop curve; u shape ac,0 ,U dc,0 The amplitudes of the no-load voltages of the grid-connected points of the AC and DC distributed power supplies are respectively the amplitudes of the no-load voltages of the grid-connected points of the AC and DC distributed power supplies;
Figure BDA00025878438000000726
is the actual voltage amplitude of the grid-connected point.
3) Static load characteristic constraint:
because the low-voltage AC and DC distribution network adopts a droop control mode, and the load is influenced by the voltage and the frequency of the system at the moment, the load is described by adopting an exponential function type static load model, as shown in the following formulas (11) to (13).
Figure BDA0002587843800000081
Figure BDA0002587843800000082
Figure BDA0002587843800000083
Wherein the content of the first and second substances,
Figure BDA0002587843800000084
load three-phase active power and reactive power of an alternating current node i at the moment t;
Figure BDA0002587843800000085
the node i is rated with active power and reactive power;
Figure BDA0002587843800000086
P oj representing the load active power and the rated active power of the direct current node j at the moment t; alpha, beta and gamma reflect exponential coefficients of the influence of the node voltage change on the load power; k is a radical of pf ,k qf A gain factor representing the effect of system frequency variations on load power.
4) And (4) safety operation constraint:
Figure BDA0002587843800000087
Figure BDA0002587843800000088
ω min ≤ω t ≤ω max (16)
Figure BDA0002587843800000089
Figure BDA00025878438000000810
Figure BDA00025878438000000811
Figure BDA00025878438000000812
Figure BDA00025878438000000813
Figure BDA00025878438000000814
Figure BDA00025878438000000815
Figure BDA00025878438000000827
wherein the content of the first and second substances,
Figure BDA00025878438000000816
the phase voltage magnitude at time t for the ac node,
Figure BDA00025878438000000817
represents the upper and lower limits thereof;
Figure BDA00025878438000000818
is the magnitude of the voltage at the dc node,
Figure BDA00025878438000000819
is the upper and lower limit;
Figure BDA00025878438000000820
the upper and lower limits of active power are output for the alternating current distributed power supply,
Figure BDA00025878438000000821
the upper and lower limits of the reactive power;
Figure BDA00025878438000000822
outputting upper and lower limits of active power for the direct-current distributed power supply;
Figure BDA00025878438000000823
upper and lower limits for state of charge when the ESS is running; e SOCj (t) is the charge capacity of the ESS at the moment t;
Figure BDA00025878438000000824
represents the upper and lower limits of the charging and discharging power of the ESS; p storj (t) is the charging and discharging amount of the ESS at the time t;
Figure BDA00025878438000000825
Figure BDA00025878438000000826
outputting upper and lower limits of three-phase active power for the PET alternating current port; p dc.max ,P dc.min And the upper limit and the lower limit of the active power output by the PET direct current port are represented.
In summary, the equations (6) - (13) and (22) are combined with the power flow calculation model equations (1) - (4) of the multiport PET, so that equality constraint conditions in the operation control model of the PET-containing alternating current and direct current hybrid power distribution network established by the invention are formed; equations (14) - (21), (23) - (24) are the inequality constraints of the operation control model. Thus, from the objective function, equation (5); the equation constraints, equations (1) - (4), (6) - (13), (22); the inequality constraint conditions, namely the equations (14) - (21), (23), (24) and the like form the operation control model of the PET-containing alternating current and direct current hybrid power distribution network.
Step 203: convex relaxation of operation control model
Wherein the step 203 comprises:
step 2031) convex relaxation of the tide equation
Introducing variables
Figure BDA0002587843800000091
And substituted into equations (6), (7), and then the branch current equation therein is relaxed. Therefore, the AC-DC power flow equation can be converted into:
Figure BDA0002587843800000092
Figure BDA0002587843800000093
through the deformation, the original AC and DC power flow constraint equation is converted into a second-order cone form, and the second-order cone programming is convex programming and has excellent mathematical properties.
Step 2032) linearization of PET loss characteristic equation
According to the invention, the power flow equation of the alternating-current and direct-current power distribution networks is subjected to second-order cone relaxation, and the square of branch current is introduced as an optimization variable, so that the nonlinear term of the loss equation described by the formula (2) only contains a current first-order term, and the first-order Taylor expansion is carried out as follows.
Figure BDA0002587843800000094
Formula (27) is a linear form, wherein I c,k-1 For the initial amplitude of the PET port current at the kth iteration,
Figure BDA0002587843800000095
representing the current iteration value, I, of the current variable c,k-1 Satisfied after this iteration
Figure BDA0002587843800000096
I c Amplitude of current output for PET port, b c And fitting coefficients of current amplitude first-order terms in the PET loss characteristic equation.
Therefore, based on the method described by equation (27), equation (2) can be converted to the following linear form:
Figure BDA0002587843800000097
in the formula (I), the compound is shown in the specification,
Figure BDA0002587843800000101
for time t PET eachThe initial value of the current amplitude of the bridge arm of the port converter at the current iteration,
Figure BDA0002587843800000102
the square of the current amplitude of each port converter bridge arm of the PET at the moment t.
Step 2033) static load characteristic equation linearization
The static load characteristic equation of the droop mode AC and DC distribution network is a nonlinear function related to voltage amplitude and frequency, and is shown in formulas (11) to (13), wherein nonlinear exponential terms
Figure BDA0002587843800000103
That is, the exponential coefficient reflecting the influence of node voltage change on the load power in the static load characteristic equation is in the value of U i The first-order taylor expansion at | =1 is as shown in equation (29).
|U i | x ≈1+x(|U i |-1) (29)
Variable | U in formula (29) i I is the square term of the second-order cone branch power flow model, and is compared with I U by referring to an equation (27) i And | performing first-order Taylor expansion, and then connecting the expansion points in a vertical mode (13), so that linear description of the static load characteristic equation of the direct-current distribution network can be obtained, as shown in a formula (30).
Figure BDA0002587843800000104
Wherein the content of the first and second substances,
Figure BDA0002587843800000105
for the load value of the node j of the direct current distribution network at the moment t,
Figure BDA0002587843800000106
is the initial value of the voltage amplitude of the direct current node j at the moment t in the current iteration,
Figure BDA0002587843800000107
the square of the voltage amplitude at the dc node j at time t.
Is worthy ofIt is noted that the static load characteristic equation of the alternating-current distribution network also has a nonlinear term | U i | x ω, the present invention adopts the following approximation.
Figure BDA0002587843800000108
Wherein, ω is k-1 The frequency of the low-voltage alternating current system is initialized at the k-th iteration. To | U i After first-order Taylor expansion is carried out, the equations (11) and (12) of the static load characteristic of the alternating-current distribution network can be finally converted into the following linear forms through connection of the equations (29) and (31):
Figure BDA0002587843800000109
Figure BDA0002587843800000111
in the formula (I), the compound is shown in the specification,
Figure BDA0002587843800000112
the initial value of the three-phase voltage amplitude of the node i at the moment t at the current iteration is obtained;
Figure BDA0002587843800000113
the square of the three-phase voltage amplitude of the node i at the moment t is obtained;
Figure BDA0002587843800000114
the initial value of the alternating current system frequency at the current iteration at the moment t.
Through the processing, the method converts the original nonlinear non-convex problem into the second-order cone problem, the second-order cone programming essentially belongs to the convex programming category, the optimality and the calculation efficiency of the solution are greatly improved, and the efficient solution can be realized by utilizing the existing mature commercial software. The solved algorithm flow chart is shown in fig. 4, and the convergence criterion is that the absolute difference of the variables of the two iterations is less than 0.001.
Compared with the prior art, the invention provides a multi-port power electronic transformer power flow calculation model applicable to a low-voltage alternating current and direct current hybrid power distribution network, which comprises a power balance constraint equation and a droop control constraint equation, on the basis, the multi-period operation control model containing the PET alternating current and direct current hybrid power distribution network is established in consideration of the PET loss characteristic and the static load characteristic, the power output of distributed power supplies in the PET, alternating current and direct current power distribution networks is coordinated, optimized and scheduled, the system loss is effectively reduced, and the system operation economy is improved.
Meanwhile, the original nonlinear constraint condition is subjected to convex relaxation by adopting a second-order cone relaxation method and a linear approximation method, so that a PET-containing AC/DC distribution network second-order cone operation control model is provided, and the objective function of the model is a formula (5); the equation constraints are the equations (1), (3), (4), (8) - (10), (22), (25), (26), (28), (30), (32), (33); the inequality constraints, namely the equations (14) - (21), (23) and (24), have better accuracy and improve the solving efficiency.
The feasibility of the method in the above example is verified by the following specific calculation examples, which are described in detail below:
an example of constructing an alternating current-direct current hybrid power distribution network containing a power electronic transformer is shown in fig. 2, and in the test system, three-port power electronic transformers are respectively connected with a 10kV high-voltage alternating current distribution network (AC-10 kV), a 380V low-voltage alternating current distribution network (AC-380V) and a 750V low-voltage direct current distribution network (dc-750V).
The optimization results of the day-ahead scheduling are shown in fig. 3. Fig. 3 (a) shows the total active power output by the distributed power supply and the active power injected by the main network, and fig. 3 (b) shows the active power output of the energy storage device in the ac and dc power distribution networks and the active loss of the system before and after optimization. It can be seen that the distributed power output and the active power injected by the main grid are substantially consistent with the load curves in the ac and dc power distribution networks to provide active support to the load during operation. And the energy storage device is charged in a load valley period, such as 00-10, 00-17. Meanwhile, compared with the system before optimization, the total loss of the system in each time period after optimization is reduced by 27.2% in the same ratio, and the active loss of the PET is reduced to 300.3kW from 331.9kW before optimization, and is reduced by 9.5%.
In order to verify the solving efficiency of the method in the day-ahead operation scheduling model, cplex is respectively adopted to solve the SOCP problem and fmincon is used to solve the original nonlinear non-convex problem, and the solving results of different optimization models are shown in Table 1. It can be found that the solving time of the original nonlinear non-convex problem is very slow, the day-ahead operation scheduling model is not converged after being operated by an fmincon solver for 3 hours, the second-order cone operation control model provided by the invention is subjected to 10 iterations, and the convergence is realized after the program is operated for 844s, so that the method has great superiority in solving efficiency, and can basically meet the requirement of the day-ahead operation scheduling on the solving time.
TABLE 1 comparison of results of different model solutions
Figure BDA0002587843800000121
In the embodiment of the present invention, except for the specific description of the model of each device, the model of other devices is not limited as long as the device can perform the above functions.
Those skilled in the art will appreciate that the drawings are only schematic illustrations of preferred embodiments, and the above-described embodiments of the present invention are merely provided for description and do not represent the merits of the embodiments.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (1)

1. A method for controlling the operation of a second-order cone of an AC/DC distribution network containing a power electronic transformer is characterized by comprising the following steps:
constructing a multi-period operation control model of the PET-containing AC/DC hybrid power distribution network;
the injection power of different ports of the PET is controlled by utilizing the flexible regulation and control capability of the PET, so that the mutual coordination of the power among the different ports is realized, and the exchange requirement of power balance among an AC sub-network and a DC sub-network is met;
performing convex relaxation on the multi-period operation control model of the AC/DC hybrid power distribution network by adopting second-order cone programming and linear approximation, and improving the solution efficiency of the multi-period operation control problem of the AC/DC hybrid power distribution network containing PET;
the method for carrying out convex relaxation on the multi-period operation control model of the AC/DC hybrid power distribution network by adopting second-order cone programming and linear approximation specifically comprises the following steps:
carrying out convex relaxation on a power flow equation, linearizing a PET loss characteristic equation, and linearizing a static load characteristic equation;
the process of carrying out convex relaxation on the power flow equation specifically comprises the following steps:
converting an original AC/DC power flow constraint equation into a second-order conical form;
the linearizing the PET loss characteristic equation specifically comprises:
Figure FDA0004056434490000011
in the formula (I), the compound is shown in the specification,
Figure FDA0004056434490000012
is an initial value of the current amplitude of each port converter bridge arm of the PET at the moment t in the current iteration,
Figure FDA0004056434490000013
the square of the current amplitude of the bridge arm of the converter at each port of the PET at the time t; a is a c.i ,b c.i ,c c.i Fitting parameters of active loss of an i port of PET;
the linearizing the static load characteristic equation specifically comprises:
Figure FDA0004056434490000014
Figure FDA0004056434490000015
in the formula (I), the compound is shown in the specification,
Figure FDA0004056434490000016
the initial value of the three-phase voltage amplitude of the node i at the moment t at the current iteration is obtained;
Figure FDA0004056434490000017
the square of the three-phase voltage amplitude of the node i at the moment t is obtained;
Figure FDA0004056434490000018
the initial value of the frequency of the alternating current system at the current iteration at the moment t is shown;
Figure FDA0004056434490000019
load three-phase active power and reactive power of an alternating current node i at the moment t;
Figure FDA0004056434490000021
the node i is rated with active power and reactive power; alpha and beta reflect exponential coefficients of the influence of the node voltage change on the load power; k is a radical of pf ,k qf A gain factor representing the effect of system frequency changes on load power; omega 0 For the no-load frequency, omega, of the AC port t Is the actual frequency at time t.
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