CN109755942B - Tidal current expanding method and device based on optimization method - Google Patents

Tidal current expanding method and device based on optimization method Download PDF

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CN109755942B
CN109755942B CN201711064949.8A CN201711064949A CN109755942B CN 109755942 B CN109755942 B CN 109755942B CN 201711064949 A CN201711064949 A CN 201711064949A CN 109755942 B CN109755942 B CN 109755942B
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CN109755942A (en
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巨云涛
金铭鑫
黄依静
王安琪
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China Agricultural University
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Abstract

The invention discloses a tide expansion method and a tide expansion device based on an optimization method, wherein the method comprises the following steps: establishing a relaxed bus voltage limit equation according to a limit formula; establishing a power flow optimization problem with a local voltage controller through an optimization formula; establishing an optimization model of a zero injection bus, an optimization model of a PV bus and an optimization model of a PQ bus through a constraint equation; and solving the optimization model of the zero injection bus, the optimization model of the PV bus and the optimization model of the PQ bus through the IPM of the constant black plug matrix to obtain an integer tap position, and performing functional test under the conditions of three-phase balance and unbalance. The method can improve the convergence of the nonlinear sensitivity method under the heavy load condition, is suitable for detecting and relaxing the infeasible voltage limitation under the heavy load condition, and ensures the solvability of the power flow.

Description

Tidal current expanding method and device based on optimization method
Technical Field
The invention relates to the technical field of power system expanded power flow, in particular to an expanded power flow method and device based on an optimization method.
Background
The local voltage controllers are addressed by a sensitivity-based approach in the related art that applies a constant impedance matrix to derive a nonlinear sensitivity matrix for the local voltage controllers. Due to the fact that the nonlinearity of the power flow is serious under the heavy load condition, the distributed network power flow which is based on the sensitivity method and corresponds to the local voltage controller needs more iteration times under the heavy load condition.
The nonlinear sensitivity matrix of the voltage control distributed generator can also be derived based on loop analysis, which proves that the nonlinear sensitivity method has better convergence than the linear sensitivity method, however, under heavy load, the nonlinear sensitivity method may have poor convergence, and particularly after the position of the tap switch is adjusted under heavy load, the bus voltage may still exceed the voltage limit, which is needed to be solved urgently.
Disclosure of Invention
The present invention is directed to solving, at least to some extent, one of the technical problems in the related art.
Therefore, an object of the present invention is to provide an optimization-based method for expanding power flow, which can improve the convergence of the nonlinear sensitivity method under a heavy load condition, and is suitable for detecting and relaxing the infeasible voltage limitation under the heavy load condition.
Another objective of the present invention is to provide an expanded power flow device based on the optimization method.
In order to achieve the above object, an embodiment of the present invention provides an expanded trend method based on an optimization method, including the following steps: establishing a relaxed bus voltage limit equation according to a limit formula; establishing a power flow optimization problem with a local voltage controller through an optimization formula; establishing an optimization model of a zero injection bus, an optimization model of a PV bus and an optimization model of a PQ bus through a constraint equation; and solving the optimization model of the zero injection bus, the optimization model of the PV bus and the optimization model of the PQ bus through an IPM (Intelligent Power Module) of a constant blackplug matrix to obtain an integer tap position, and performing functional test under the conditions of three-phase balance and unbalance.
According to the power flow expanding method based on the optimization method, the IPM of the constant blackplug matrix is used for solving the optimization model of the zero injection bus, the optimization model of the PV bus and the optimization model of the PQ bus, so that the integer tap position is obtained, the function test is carried out under the conditions of three-phase balance and unbalance, the purpose of power flow expanding based on the optimization method is achieved, the problem that the non-linearity problem of distributed network power flow of a local voltage controller is solved based on a sensitive method under the heavy load condition, the problem that the limitation of the non-feasible voltage is detected and relaxed under the heavy load condition is solved, the convergence of the non-linear sensitivity method under the heavy load condition is improved, and the method is suitable for detecting and relaxing the limitation of the non-feasible voltage under the heavy load condition.
In addition, the expanded trend method based on the optimization method according to the above embodiment of the present invention may further have the following additional technical features:
further, in one embodiment of the present invention, the bus voltage limit equation is established by a limit formula, the limit formula being:
Figure BDA0001455562240000021
wherein the content of the first and second substances,
Figure BDA0001455562240000022
the lower limit of the square of the bus voltage,
Figure BDA0001455562240000023
for the upper limit of the square of the bus voltage, l and U represent non-negative relaxation variables, UreAnd UimRespectively a real part and an imaginary part of a bus voltage complex variable; guIs the upper limit of the function, g is the mapping, glFor the lower limit of the function,
Figure BDA0001455562240000024
is the bus voltage squared.
Further, in an embodiment of the present invention, the trend optimization problem is established by the following optimization formula:
min∑(u+v)
Figure BDA0001455562240000025
wherein t is the position of the transformer tap, tminAnd tmaxThe minimum value limit and the maximum value limit of the transformer tap position are respectively, h is mapping, v is a non-negative relaxation variable, and s.t. is a constraint condition.
Further, in an embodiment of the present invention, the establishing an optimization model of a zero injection bus, an optimization model of a PV bus, and an optimization model of a PQ bus further includes:
for the zero injection bus, the first constraint equation h is expressed as a pair of linear equations:
Figure BDA0001455562240000026
wherein, IreAnd IimRespectively the real and imaginary part of the injected current, YzeroFor the admittance row corresponding to the zero injection bus, U is the complex bus voltage,
Figure BDA0001455562240000027
and
Figure BDA0001455562240000028
the real and imaginary parts of the equation, respectively.
For the PV bus, a second constraint equation h is expressed in pairs as:
Figure BDA0001455562240000031
wherein the content of the first and second substances,
Figure BDA0001455562240000032
for the voltage control target of the PV bus, the subscript PV is the corresponding vector or matrix row of the PV bus, diag is the diagonal matrix, the conjugate of the complex variable, SreIn order to inject the real part of the complex power,
Figure BDA0001455562240000033
is the real part of the equation, YPVFor admittance rows corresponding to PQ bus-bars, UPVIs the PV bus voltage, U is the complex bus voltage,
Figure BDA0001455562240000034
is the real part of the PV bus voltage squared,
Figure BDA0001455562240000035
the imaginary part of the PV bus voltage squared.
For the PQ bus, the third constraint equation h is expressed in pairs as:
Figure BDA0001455562240000036
wherein S isreAnd SimRespectively, the fact that complex power is injectedThe partial and imaginary parts are each a function of,
Figure BDA0001455562240000037
and
Figure BDA0001455562240000038
real and imaginary parts of the equation, diag is the diagonal matrix, conjugate of complex variable, subscript PQ is the corresponding vector or matrix row of PQ bus, UPQIs PQ bus voltage, YPQU is the complex bus voltage for the admittance row corresponding to the PQ bus.
Further, in one embodiment of the present invention, the integer tap positions are obtained by rounding the fractional values of the tap positions.
In order to achieve the above object, an embodiment of another aspect of the present invention provides an expanded power flow device based on an optimization method, including: the limiting equation establishing module is used for establishing a relaxed bus voltage limiting equation according to a limiting formula; the optimization problem establishing module is used for establishing a power flow optimization problem with a local voltage controller through an optimization formula; the optimization model establishing module is used for establishing an optimization model of the zero injection bus, an optimization model of the PV bus and an optimization model of the PQ bus through a constraint equation; and the power flow expansion module is used for solving the optimization model of the zero injection bus, the optimization model of the PV bus and the optimization model of the PQ bus through IPM of the constant black plug matrix to obtain an integer tap position, and performing functional test under three-phase balance and unbalance conditions.
According to the expanded power flow device based on the optimization method, the IPM of the constant blackplug matrix is used for solving the optimization model of the zero injection bus, the optimization model of the PV bus and the optimization model of the PQ bus, so that the integer tap position is obtained, the function test is carried out under the conditions of three-phase balance and unbalance, the purpose of expanding the power flow based on the optimization method is achieved, the problem that the distributed network power flow of a local voltage controller is non-linear under the heavy load condition based on a sensitive method and the problem that the infeasible voltage limitation is detected and relaxed under the heavy load condition are solved, the convergence of the non-linear sensitivity method under the heavy load condition is improved, and the expanded power flow device is suitable for detecting and relaxing the infeasible voltage limitation under the heavy load condition.
In addition, the expanded power flow device based on the optimization method according to the above embodiment of the present invention may further have the following additional technical features:
further, in one embodiment of the present invention, the restriction equation in the restriction equation establishing module is:
Figure BDA0001455562240000041
wherein the content of the first and second substances,
Figure BDA0001455562240000049
the lower limit of the square of the bus voltage,
Figure BDA0001455562240000042
for the upper limit of the square of the bus voltage, l and U are respectively non-negative relaxation variables, UreAnd UimReal and imaginary parts, g, of complex variables of the bus voltage, respectivelyuIs the upper limit of the function, g is the mapping, glFor the lower limit of the function,
Figure BDA0001455562240000043
is the bus voltage squared.
Further, in an embodiment of the present invention, the optimization formula in the optimization problem establishing module is:
min∑(u+v)
Figure BDA0001455562240000044
wherein t is the position of the transformer tap, tminAnd tmaxThe minimum value limit and the maximum value limit of the transformer tap position are respectively, h is mapping, v is a non-negative relaxation variable, and s.t. is a constraint condition.
Further, in an embodiment of the present invention, the optimization model building module further includes:
for the zero injection bus, the first constraint equation h is expressed as a pair of linear equations:
Figure BDA0001455562240000045
wherein, IreAnd IimRespectively the real and imaginary part of the injected current, YzeroFor the admittance row corresponding to the zero injection bus, U is the complex bus voltage,
Figure BDA0001455562240000046
and
Figure BDA0001455562240000047
the real and imaginary parts of the equation, respectively.
For the PV bus, a second constraint equation h is expressed in pairs as:
Figure BDA0001455562240000048
wherein the content of the first and second substances,
Figure BDA0001455562240000051
for the voltage control target of the PV bus, the subscript PV is the corresponding vector or matrix row of the PV bus, diag is the diagonal matrix, the conjugate of the complex variable, SreIn order to inject the real part of the complex power,
Figure BDA0001455562240000052
is the real part of the equation, YPVFor admittance rows corresponding to PV bus-bars, UPVIs the PV bus voltage, U is the complex bus voltage,
Figure BDA0001455562240000053
is the real part of the PV bus voltage squared,
Figure BDA0001455562240000054
the imaginary part of the PV bus voltage squared.
For the PQ bus, the third constraint equation h is expressed in pairs as:
Figure BDA0001455562240000055
wherein S isreAnd SimRespectively the real and imaginary parts of the injected complex power,
Figure BDA0001455562240000056
and
Figure BDA0001455562240000057
real and imaginary parts of the equation, diag is the diagonal matrix, conjugate of complex variable, subscript PQ is the corresponding vector or matrix row of PQ bus, UPQIs PQ bus voltage, YPQU is the complex bus voltage for the admittance column corresponding to the PQ bus voltage.
Further, in one embodiment of the present invention, the integer tap positions are obtained by rounding the fractional values of the tap positions.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The foregoing and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of an extended power flow method based on an optimization method according to an embodiment of the invention;
fig. 2 is a schematic structural diagram of an extended power flow device based on an optimization method according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.
The expanded power flow method and the device based on the optimization method according to the embodiment of the invention are described below with reference to the accompanying drawings, and first, the expanded power flow method based on the optimization method according to the embodiment of the invention will be described with reference to the accompanying drawings.
Fig. 1 is a flow chart of an extended trend method based on an optimization method according to an embodiment of the present invention.
As shown in fig. 1, the extended power flow method based on the optimization method includes the following steps:
in step S101, a relaxed bus voltage limit equation is established according to a limit formula.
Further, in one embodiment of the present invention, the bus voltage limit equation is established by a limit formula, the limit formula being:
Figure BDA0001455562240000061
wherein the content of the first and second substances,
Figure BDA0001455562240000062
the lower limit of the square of the bus voltage,
Figure BDA0001455562240000063
upper limit of the square of the bus voltage, l and U being non-negative relaxation variables, UreAnd UimReal and imaginary parts, g, of complex variables of the bus voltage, respectivelyuIs the upper limit of the function, g is the mapping, glFor the lower limit of the function,
Figure BDA0001455562240000064
is the square of the bus voltage.
In step S102, a power flow optimization problem with local voltage controllers is established by an optimization formula.
Further, in an embodiment of the present invention, the power flow optimization problem is established by the following optimization formula:
min∑(u+v)
Figure BDA0001455562240000065
wherein t is the position of the transformer tap, tminAnd tmaxThe method comprises the steps of respectively limiting the minimum value and the maximum value of a transformer tap position, h is mapping, v is a non-negative relaxation variable, and s.t. is a constraint condition.
In step S103, an optimization model of the zero injection bus, an optimization model of the PV bus, and an optimization model of the PQ bus are established by the constraint equations.
Further, in an embodiment of the present invention, the establishing an optimization model of a zero injection bus, an optimization model of a PV bus, and an optimization model of a PQ bus further includes:
for a zero injection bus, the first constraint equation h is expressed as a pair of linear equations:
Figure BDA0001455562240000066
wherein, IreAnd IimRespectively the real and imaginary part of the injected current, YzeroFor the admittance row corresponding to the zero injection bus, U is the complex bus voltage,
Figure BDA0001455562240000071
and
Figure BDA0001455562240000072
the real and imaginary parts of the equation, respectively.
For the PV bus, the second constraint equation h is expressed in pairs as:
Figure BDA0001455562240000073
wherein the content of the first and second substances,
Figure BDA0001455562240000074
is a voltage control target of the PV bus; subscript PV is the corresponding vector or matrix row of the PV bus, diag is the diagonal matrix, conjugate of the complex variable, SreIn order to inject the real part of the complex power,
Figure BDA0001455562240000075
is the real part Y of the equationPVFor admittance rows corresponding to PV bus-bars, UPVIs the PV bus voltage, U is the complex bus voltage,
Figure BDA0001455562240000076
is the real part of the PV bus voltage squared,
Figure BDA0001455562240000077
the imaginary part of the PV bus voltage squared.
For the PQ bus, the third constraint equation h is expressed in pairs as:
Figure BDA0001455562240000078
wherein S isreAnd SimRespectively the real and imaginary parts of the injected complex power,
Figure BDA0001455562240000079
and
Figure BDA00014555622400000710
real and imaginary parts of the equation, diag is the diagonal matrix, conjugate of complex variable, subscript PQ is the corresponding vector or matrix row of PQ bus, UPQIs PQ bus voltage, YPQU is the complex bus voltage for the admittance column corresponding to the PQ bus voltage.
In step S104, the optimization model of the zero injection bus, the optimization model of the PV bus, and the optimization model of the PQ bus are solved through IPM of the constant blackplug matrix to obtain integer tap positions, and a functional test is performed under three-phase balanced and unbalanced conditions.
Further, in one embodiment of the present invention, the integer tap positions are obtained by rounding the fractional values of the tap positions.
In a specific embodiment of the present invention, under a three-phase equilibrium condition, the power flow expansion method based on the optimization method proposed in the embodiment of the present invention includes the following steps:
s1: collecting data under light load or heavy load of distributed network power flow of a local voltage controller on the basis of a sensitivity method without considering nonlinearity.
S2: and establishing a relaxed bus voltage limit equation.
Figure BDA0001455562240000081
Wherein the content of the first and second substances,
Figure BDA0001455562240000082
the lower limit of the square of the bus voltage,
Figure BDA0001455562240000083
upper limit of the square of the bus voltage, l and U being non-negative relaxation variables, UreAnd UimReal and imaginary parts, g, of complex variables of the bus voltage, respectivelyuIs the upper limit of the function, g is the mapping, glFor the lower limit of the function,
Figure BDA0001455562240000084
is the square of the bus voltage.
S3: an optimization problem of power flow extension with local voltage controllers is established.
min∑(u+v)
Figure BDA0001455562240000085
Wherein, UreAnd UimRespectively the real part and the imaginary part of a complex variable of the bus voltage, t is the position of a transformer tap, tminAnd tmaxMinimum and maximum limits for transformer tap positions, h is mapping, v is notThe negative relaxation variable, s.t. is the constraint.
S4: and establishing a zero injection bus constraint equation.
Figure BDA0001455562240000086
Wherein, IreAnd IimRespectively the real and imaginary part of the injected current, YzeroFor the admittance row corresponding to the zero injection bus, U is the complex bus voltage,
Figure BDA0001455562240000087
and
Figure BDA0001455562240000088
the real and imaginary parts of the equation, respectively.
S5: and establishing a PV bus constraint equation.
Figure BDA0001455562240000089
Wherein the content of the first and second substances,
Figure BDA00014555622400000810
for the voltage control target of the PV bus, the subscript PV is the corresponding vector or matrix row of the PV bus, diag is the diagonal matrix, the conjugate of the complex variable, SreIs the real part of the injected complex power;
Figure BDA00014555622400000811
is the real part of the equation, YPVFor admittance rows corresponding to PV bus-bars, UPVIs the PV bus voltage, U is the complex bus voltage,
Figure BDA00014555622400000812
is the real part of the PV bus voltage squared,
Figure BDA0001455562240000091
the imaginary part of the PV bus voltage squared.
S6: and establishing a PQ bus constraint equation.
Figure BDA0001455562240000092
Wherein S isreAnd SimRespectively the real and imaginary parts of the injected complex power,
Figure BDA0001455562240000093
and
Figure BDA0001455562240000094
real and imaginary parts of the equation, diag is the diagonal matrix, conjugate of complex variable, subscript PQ is the corresponding vector or matrix row of PQ bus, UPQIs PQ bus voltage, YPQU is the complex bus voltage for the admittance column corresponding to the PQ bus voltage.
S7: matlab is applied and the optimization problem described above is solved with IPM with constant blackplug matrix.
S8: the method provided by the embodiment of the invention is compared with the iteration times and time required by the sensitivity method and the expanded trend method, and the functionality of the method is verified.
In another specific embodiment of the present invention, under an unbalanced condition, the expanded power flow method based on the optimization method proposed by the embodiment of the present invention includes the following steps:
s1: and establishing a relaxed bus voltage limit equation.
Figure BDA0001455562240000095
Wherein the content of the first and second substances,
Figure BDA0001455562240000096
the lower limit of the square of the bus voltage,
Figure BDA0001455562240000097
for the upper limit of the square of the bus voltage, l and U are non-negative relaxation variables UreAnd UimAre respectively bus voltageReal and imaginary parts of complex variables, guIs the upper limit of the function, g is the mapping, glFor the lower limit of the function,
Figure BDA0001455562240000098
is the square of the bus voltage.
S2: an optimization problem of power flow extension with local voltage controllers is established.
min∑(u+v)
Figure BDA0001455562240000099
Wherein, UreAnd UimRespectively the real part and the imaginary part of a complex variable of the bus voltage, t is the position of a transformer tap, tminAnd tmaxThe method comprises the steps of respectively limiting the minimum value and the maximum value of a transformer tap position, h is mapping, v is a non-negative relaxation variable, and s.t. is a constraint condition.
S3: and establishing a zero injection bus constraint equation.
Figure BDA0001455562240000101
Wherein, IreAnd IimRespectively the real and imaginary part of the injected current, YzeroFor the admittance row corresponding to the zero-injection bus, U represents the complex bus voltage,
Figure BDA0001455562240000102
and
Figure BDA0001455562240000103
the real and imaginary parts of the equation, respectively.
S4: and establishing a PV bus constraint equation.
Figure BDA0001455562240000104
Wherein the content of the first and second substances,
Figure BDA0001455562240000105
for the voltage control target of the PV bus, the subscript PV is the corresponding vector or matrix row of the PV bus, diag is the diagonal matrix, the conjugate of the complex variable, SreIs the real part of the injected complex power;
Figure BDA0001455562240000106
is the real part of the equation, YPVFor admittance rows corresponding to PV bus-bars, UPVIs the PV bus voltage, U is the complex bus voltage,
Figure BDA0001455562240000107
is the real part of the PV bus voltage squared,
Figure BDA0001455562240000108
the imaginary part of the PV bus voltage squared.
S5: and establishing a PQ bus constraint equation.
Figure BDA0001455562240000109
Wherein S isreAnd SimRespectively the real and imaginary parts of the injected complex power,
Figure BDA00014555622400001010
and
Figure BDA00014555622400001011
real and imaginary parts of the equation, diag is the diagonal matrix, conjugate of complex variable, subscript PQ is the corresponding vector or matrix row of PQ bus, UPQIs PQ bus voltage, YPQU is the complex bus voltage for the admittance column corresponding to the PQ bus voltage.
S6: the optimization problem is solved using an IPM with a constant blackplug matrix using Matlab.
S7: according to [ I.Kocar, J.Mahseredjian, U.Karaagac, G.Soykan, and O.Saad, "Multiphase Load-Flow Solution for Large-Scale Distribution Systems Using MANA," IEEE Transactions on Power Delivery, vol.29, No.2, pp.908-915, Apr.2014 ], a step voltage regulator model is known to be represented by a voltage controlled voltage source and a current controlled current source.
S8: IEEE4 bus test feeder data is collected [ W.H.Kersting, Distribution System Modeling and Analysis, Third edition. boca Raton, Florida: CRC Press,2012 ].
S9: comparing the load flow result adjusted by the step voltage regulator with the iteration times of the method provided by the embodiment of the invention, the method provided by the embodiment of the invention has the advantage of less iteration times.
S10: multiplying the C-phase load on the IEEE4 bus by 2 to obtain the infeasible voltage limit of the method of the embodiment of the invention verifies that the method of the embodiment of the invention has the functionality of detecting the infeasible voltage limit and the relaxation capacity.
According to the power flow expanding method based on the optimization method provided by the embodiment of the invention, the IPM of the constant blackplug matrix is used for solving the optimization model of the zero injection bus, the optimization model of the PV bus and the optimization model of the PQ bus, so that the integer tap position is obtained, the function test is carried out under the conditions of three-phase balance and unbalance, the purpose of power flow expanding based on the optimization method is realized, the nonlinear problem that the distributed network power flow of a local voltage controller is responded by a sensitive method under the heavy load condition and the problem that the limitation of the infeasible voltage is detected and relaxed under the heavy load condition are solved, the convergence of the nonlinear sensitivity method under the heavy load condition is improved, and the method is suitable for detecting and relaxing the limitation of the infeasible voltage under the heavy load condition.
Next, an extended power flow apparatus based on an optimization method according to an embodiment of the present invention will be described with reference to the drawings.
Fig. 2 is a schematic structural diagram of an extended power flow device based on an optimization method according to an embodiment of the present invention.
As shown in fig. 2, the extended power flow device 10 based on the optimization method includes: a constraint equation building module 100, an optimization problem building module 200, an optimization model building module 300 and a power flow extension module 400.
The constraint equation establishing module 100 is configured to establish a relaxed bus voltage constraint equation according to a constraint equation. The optimization problem establishing module 200 is used for establishing a power flow optimization problem with local voltage controllers through an optimization formula. The optimization model building module 300 is used for building an optimization model of the zero injection bus, an optimization model of the PV bus and an optimization model of the PQ bus through constraint equations. The power flow expansion module 400 is configured to solve the optimization model of the zero injection bus, the optimization model of the PV bus, and the optimization model of the PQ bus through IPM of the constant black plug matrix to obtain an integer tap position, and perform a functional test under three-phase balanced and unbalanced conditions. The device 10 of the embodiment of the invention can improve the convergence of the nonlinear sensitivity method under the heavy load condition, is suitable for detecting and relaxing the infeasible voltage limitation under the heavy load condition, and ensures the solvability of the tide.
Further, in one embodiment of the present invention, the restriction equation in the restriction equation establishing module 100 is:
Figure BDA0001455562240000111
wherein the content of the first and second substances,
Figure BDA0001455562240000112
the lower limit of the square of the bus voltage,
Figure BDA0001455562240000113
for the upper limit of the square of the bus voltage, l and U represent non-negative relaxation variables, UreAnd UimReal and imaginary parts, g, of complex variables of the bus voltage, respectivelyuIs the upper limit of the function, g is the mapping, glFor the lower limit of the function,
Figure BDA0001455562240000114
is the square of the bus voltage.
Further, in an embodiment of the present invention, the optimization formula in the optimization problem establishing module 200 is:
min∑(u+v)
Figure BDA0001455562240000121
wherein t is the position of the transformer tap, tminAnd tmaxThe method comprises the steps of respectively limiting the minimum value and the maximum value of a transformer tap position, h is mapping, v is a non-negative relaxation variable, and s.t. is a constraint condition.
Further, in an embodiment of the present invention, the optimization model building module 300 further includes:
for a zero injection bus, the first constraint equation h is expressed as a pair of linear equations:
Figure BDA0001455562240000122
wherein, IreAnd IimRespectively the real and imaginary part of the injected current, YzeroFor the admittance row corresponding to the zero injection bus, U is the complex bus voltage,
Figure BDA0001455562240000123
and
Figure BDA0001455562240000124
the real and imaginary parts of the equation, respectively.
For the PV bus, the second constraint equation h is expressed in pairs as:
Figure BDA0001455562240000125
wherein the content of the first and second substances,
Figure BDA0001455562240000126
for the voltage control target of the PV bus, the subscript PV is the corresponding vector or matrix row of the PV bus, diag is the diagonal matrix, the conjugate of the complex variable, SreIn order to inject the real part of the complex power,
Figure BDA0001455562240000127
is a squareReal part of the stroke, YPVFor admittance rows corresponding to PV bus-bars, UPVIs the PV bus voltage, U is the complex bus voltage,
Figure BDA0001455562240000128
is the real part of the PV bus voltage squared,
Figure BDA0001455562240000129
the imaginary part of the PV bus voltage squared.
For the PQ bus, the third constraint equation h is expressed in pairs as:
Figure BDA00014555622400001210
wherein S isreAnd SimRespectively the real and imaginary parts of the injected complex power,
Figure BDA00014555622400001211
and
Figure BDA00014555622400001212
real and imaginary parts of the equation, diag is the diagonal matrix, conjugate of complex variable, subscript PQ is the corresponding vector or matrix row of PQ bus, UPQIs PQ bus voltage, YPQU is the complex bus voltage for the admittance column corresponding to the PQ bus voltage.
Further not in one embodiment of the present invention, the integer tap positions are obtained by rounding the fractional values of the tap positions.
It should be noted that the foregoing explanation of the embodiment of the expanded power flow method based on the optimization method is also applicable to the expanded power flow device based on the optimization method of the embodiment, and details are not repeated here.
According to the expanded power flow device based on the optimization method, the optimization model of the zero injection bus, the optimization model of the PV bus and the optimization model of the PQ bus are solved through the IPM of the constant blackplug matrix, so that the integer tap position is obtained, the function test is carried out under the conditions of three-phase balance and unbalance, the purpose of expanding the power flow based on the optimization method is achieved, the nonlinear problem that the distributed network power flow of a local voltage controller is responded by a sensitive method under the heavy load condition and the problem that the limitation of the infeasible voltage is detected and relaxed under the heavy load condition are solved, the convergence of the nonlinear sensitivity method under the heavy load condition is improved, and the expanded power flow device is suitable for detecting and relaxing the limitation of the infeasible voltage under the heavy load condition.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," "circumferential," and the like are used in the orientations and positional relationships indicated in the drawings for convenience in describing the invention and to simplify the description, and are not intended to indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and are therefore not to be considered limiting of the invention.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the present invention, unless otherwise expressly stated or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; they may be directly connected or indirectly connected through intervening media, or they may be connected internally or in any other suitable relationship, unless expressly stated otherwise. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.
In the present invention, unless otherwise expressly stated or limited, the first feature "on" or "under" the second feature may be directly contacting the first and second features or indirectly contacting the first and second features through an intermediate. Also, a first feature "on," "over," and "above" a second feature may be directly or diagonally above the second feature, or may simply indicate that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature may be directly under or obliquely under the first feature, or may simply mean that the first feature is at a lesser elevation than the second feature.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

Claims (4)

1. An extended power flow method, comprising the steps of:
establishing a relaxed bus voltage limit equation according to a limit formula;
establishing a power flow optimization problem with a local voltage controller through an optimization formula;
establishing an optimization model of a zero injection bus, an optimization model of a PV bus and an optimization model of a PQ bus through a constraint equation; and
solving the optimization model of the zero injection bus, the optimization model of the PV bus and the optimization model of the PQ bus through IPM of a constant black plug matrix to obtain an integer tap position, and performing functional test under three-phase balance and unbalance conditions;
establishing the bus voltage limit equation through a limit formula, wherein the limit formula is as follows:
Figure FDA0002938279380000011
wherein the content of the first and second substances,
Figure FDA0002938279380000012
the lower limit of the square of the bus voltage,
Figure FDA0002938279380000013
is the upper limit of the square of the bus voltage, l and U are non-negative relaxation variables, UreAnd UimReal and imaginary parts, g, of complex variables of the bus voltage, respectivelyuIs the upper limit of the function, g is the mapping, glIs the lower limit of the function and,
Figure FDA0002938279380000014
is the bus voltage squared;
establishing the power flow optimization problem through the following optimization formula:
Figure FDA0002938279380000015
wherein t is the position of the transformer tap, tminAnd tmaxRespectively limiting the minimum value and the maximum value of the tap position of the transformer, h is mapping, v is a non-negative relaxation variable, and s.t. is a constraint condition;
the establishing of the optimization model of the zero injection bus, the optimization model of the PV bus and the optimization model of the PQ bus further comprises the following steps:
for the zero injection bus, the first constraint equation h is expressed as a pair of linear equations:
Figure FDA0002938279380000016
wherein, IreAnd IimRespectively the real and imaginary part of the injected current, YzeroFor the admittance row corresponding to the zero injection bus, U is the complex bus voltage,
Figure FDA0002938279380000021
and
Figure FDA0002938279380000022
respectively the real part and the imaginary part of the equation;
for the PV bus, a second constraint equation h is expressed in pairs as:
Figure FDA0002938279380000023
wherein the content of the first and second substances,
Figure FDA0002938279380000024
for the voltage control target of the PV bus, the subscript PV is the corresponding vector or matrix row of the PV bus, diag is the diagonal matrix, the conjugate of the complex variable, SreIn order to inject the real part of the complex power,
Figure FDA0002938279380000025
is the real part of the equation, YPVFor admittance rows corresponding to PV bus-bars, UPVIs PV bus voltage, U is complexThe voltage of the bus-bar is,
Figure FDA0002938279380000026
is the real part of the PV bus voltage,
Figure FDA0002938279380000027
is the imaginary part of the PV bus voltage;
for the PQ bus, the third constraint equation h is expressed in pairs as:
Figure FDA0002938279380000028
wherein S isreAnd SimRespectively the real and imaginary parts of the injected complex power,
Figure FDA0002938279380000029
and
Figure FDA00029382793800000210
real and imaginary parts of the equation, diag is the diagonal matrix, conjugate of complex variable, subscript PQ is the corresponding vector or matrix row of PQ bus, UPQIs PQ bus voltage, YPQU is the complex bus voltage for the admittance row corresponding to the PQ bus.
2. The extended power flow method of claim 1, wherein the integer tap positions are obtained by rounding off fractional values of tap positions.
3. An extended power flow device, comprising:
the limiting equation establishing module is used for establishing a relaxed bus voltage limiting equation according to a limiting formula;
the optimization problem establishing module is used for establishing a power flow optimization problem with a local voltage controller through an optimization formula;
the optimization model establishing module is used for establishing an optimization model of the zero injection bus, an optimization model of the PV bus and an optimization model of the PQ bus through a constraint equation; and
the power flow expansion module is used for solving the optimization model of the zero injection bus, the optimization model of the PV bus and the optimization model of the PQ bus through IPM of the constant black plug matrix to obtain an integer tap position and performing function test under the conditions of three-phase balance and unbalance;
the restriction formula in the restriction equation establishing module is as follows:
Figure FDA0002938279380000031
wherein the content of the first and second substances,
Figure FDA0002938279380000032
the lower limit of the square of the bus voltage,
Figure FDA0002938279380000033
for the upper limit of the square of the bus voltage, l and U represent non-negative relaxation variables, UreAnd UimReal and imaginary parts, g, of complex variables of the bus voltage, respectivelyuIs the upper limit of the function, g is the mapping, glFor the lower limit of the function,
Figure FDA0002938279380000034
is the bus voltage squared;
the optimization formula in the optimization problem establishing module is as follows:
Figure FDA0002938279380000035
wherein t is the position of the transformer tap, tminAnd tmaxRespectively limiting the minimum value and the maximum value of the tap position of the transformer, h is mapping, v is a non-negative relaxation variable, and s.t. is a constraint condition;
the optimization model building module further comprises:
for the zero injection bus, the first constraint equation h is expressed as a pair of linear equations:
Figure FDA0002938279380000036
wherein, IreAnd IimRespectively the real and imaginary part of the injected current, YzeroFor the admittance row corresponding to the zero injection bus, U is the complex bus voltage,
Figure FDA0002938279380000037
and
Figure FDA0002938279380000038
respectively the real part and the imaginary part of the equation;
for the PV bus, a second constraint equation h is expressed in pairs as:
Figure FDA0002938279380000039
wherein the content of the first and second substances,
Figure FDA00029382793800000310
for the voltage control target of the PV bus, the subscript PV is the corresponding vector or matrix row of the PV bus, diag is the diagonal matrix, the conjugate of the complex variable, SreIn order to inject the real part of the complex power,
Figure FDA00029382793800000311
is the real part of the equation, YPVFor admittance rows corresponding to PV bus-bars, UPVIs the PV bus voltage, U is the complex bus voltage,
Figure FDA00029382793800000312
is the real part of the PV bus voltage,
Figure FDA00029382793800000313
is the imaginary part of the PV bus voltage;
for the PQ bus, the third constraint equation h is expressed in pairs as:
Figure FDA0002938279380000041
wherein S isreAnd SimRespectively the real and imaginary parts of the injected complex power,
Figure FDA0002938279380000042
and
Figure FDA0002938279380000043
real and imaginary parts of the equation, diag is the diagonal matrix, conjugate of complex variable, subscript PQ is the corresponding vector or matrix row of PQ bus, UPQIs PQ bus voltage, YPQU is the complex bus voltage for the admittance row corresponding to the PQ bus.
4. The extended power flow device of claim 3, wherein the integer tap positions are obtained by rounding off the fractional values of the tap positions.
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