CN109991481B - Three-phase unbalance measurement method based on sequence components and measurement values - Google Patents

Three-phase unbalance measurement method based on sequence components and measurement values Download PDF

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CN109991481B
CN109991481B CN201910191539.2A CN201910191539A CN109991481B CN 109991481 B CN109991481 B CN 109991481B CN 201910191539 A CN201910191539 A CN 201910191539A CN 109991481 B CN109991481 B CN 109991481B
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sequence component
sequence
current
voltage
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CN109991481A (en
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郝思鹏
刘思亦
蔡欣灵
张仰飞
刘海涛
陈光宇
张小莲
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Nanjing Institute of Technology
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    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
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Abstract

The invention relates to a three-phase unbalance measurement method based on sequence components and measurement values, which comprises the steps of firstly, carrying out phase sequence decomposition on three-phase electric quantity by using a symmetric component method to obtain the magnitude relation between the sequence components and the phasors; secondly, defining a measurement mode of three-phase balance rate and unbalance rate of the sequence component containing the zero sequence component, wherein the specific mode is as follows: the proportion of the three-phase positive sequence component in the total amount is used for measuring the three-phase balance rate, and the proportion of the part except the positive sequence component in the total amount is used for measuring the three-phase unbalance rate; and finally, calculating according to the measurement value to obtain the three-phase imbalance rate. When the measured value is any one group of a line voltage value without zero sequence component, a line current value without zero sequence component, a phase voltage value with zero sequence component and a phase current value with zero sequence component, a measurement result can be obtained.

Description

Three-phase unbalance measurement method based on sequence components and measurement values
Technical Field
The invention belongs to the technical field of power quality analysis, and particularly relates to a three-phase unbalance measurement method based on sequence components and measurement values.
Background
The problem of unbalanced three phases is increasingly prominent due to high-power single-phase load, roof photovoltaic distributed power access and the like. The three-phase imbalance of the power system causes the efficiency of the motor to be reduced, the line loss is increased, and the like, and the precision of a measuring instrument and a metering instrument is also influenced. Accurate three-phase unbalance measurement is the basis of analysis and treatment, and the existing three-phase unbalance measurement has many forms and a certain difference, thereby bringing troubles to engineering application.
Three-phase balanced system voltages, currents contain only positive sequence components, and therefore three-phase imbalances are generally measured by the sequence components. The International Electrotechnical Commission (IEC) proposes that the three-phase imbalance rate is represented by the ratio of the effective fundamental wave values of the negative sequence component and the positive sequence component, and the zero sequence component is ignored in the form, so that the three-phase imbalance is particularly serious in a four-wire system containing the zero sequence component in the engineering. The three-phase unbalance rate is expressed by the percentage of the square root mean value of the negative sequence fundamental wave component or the zero sequence fundamental wave component and the positive sequence fundamental wave component of voltage and current in the national standard 'electric energy quality-three-phase voltage unbalance', the two concepts of the negative sequence three-phase unbalance rate and the zero sequence three-phase unbalance rate are formed by the regulation, the unified three-phase unbalance rate cannot be formed, the use has limitation, the unbalance rate parameters are not distributed between 0 and 1, namely the unbalance rate possibly exceeds 100%, and the explanation in the engineering is difficult.
The existing instrument mainly measures the effective values of three-phase voltage, current and other physical quantities, and the phasor required by phase sequence decomposition is difficult to obtain. For ease of engineering calculations, the Institute of Electrical and Electronics Engineers (IEEE) defines the phase voltage imbalance ratio (PVUR) based on the effective value; the american Electrical Manufacturers Association (NEMA) and the International Large grid committee (International country on Large Electric Systems, CIGRE) define the line voltage imbalance ratio (LVUR). Other associations or power companies also provide practical measurement modes of three-phase voltage and current imbalance rates based on measured values. The measurement mode based on the measurement value is relatively simple to calculate, but the measurement mode lacks the corresponding relation with the sequence component measurement mode, the result is sometimes different greatly among different measurement modes, and the accuracy and the reliability of the measurement mode are questioned to some extent.
Disclosure of Invention
The invention aims to provide a three-phase unbalance measurement method based on sequence components and measurement values, which unifies the description of balance rate and unbalance rate under the condition of zero sequence component and zero sequence component-free.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a three-phase unbalance measurement method based on sequence components and measurement values is characterized in that: the method comprises the following steps:
step 1, carrying out phase sequence decomposition on three-phase electric quantity by using a symmetric component method to obtain a magnitude relation between a sequence component and a phasor;
step 2, defining a measurement mode of the three-phase balance rate and the unbalance rate of the sequence component containing the zero-sequence component, wherein the specific mode is as follows: the proportion of the three-phase positive sequence component in the total amount is used for measuring the three-phase balance rate, and the proportion of the part except the positive sequence component in the total amount is used for measuring the three-phase unbalance rate;
and 3, calculating according to the measured values to obtain the three-phase imbalance rate.
The measured value in the step 3 is any one group of a line voltage value without a zero-sequence component, a line current value without a zero-sequence component, a phase voltage value with a zero-sequence component and a phase current value with a zero-sequence component.
The magnitude relation between the sequence component and the phasor in the step 1 is a characteristic relation that the square sum of the effective values of the three-phase electric quantity is three times of the square sum of the effective values of the sequence component, and the specific calculation process is as follows:
when the current value is taken as a calculation parameter, the calculation flow is as follows:
Figure GDA0002078686370000021
Figure GDA0002078686370000022
Figure GDA0002078686370000023
let the A-phase positive sequence current be I1Angle 0 DEG, negative sequence current of
Figure GDA0002078686370000024
Zero sequence current of
Figure GDA0002078686370000025
Then the current phasor has a relationship with the magnitude of the sequence phasor:
Figure GDA0002078686370000026
Figure GDA0002078686370000027
Figure GDA0002078686370000028
in the formula (I), the compound is shown in the specification,
Figure GDA0002078686370000029
is the phasor of the three-phase current,
Figure GDA00020786863700000210
positive, negative and zero sequence current components;
the simplified relationship between the magnitude of the sequence component and the phasor is as follows:
Figure GDA00020786863700000211
the magnitude relation between the sequence component and the phasor in the step 1 is a characteristic relation that the square sum of the effective values of the three-phase electric quantity is three times of the square sum of the effective values of the sequence component, and the specific calculation process is as follows:
when the voltage value is taken as a calculation parameter, the calculation process is as follows:
Figure GDA00020786863700000212
Figure GDA0002078686370000031
Figure GDA0002078686370000032
let the A-phase positive sequence voltage be U1Angle 0 DEG, negative sequence current of
Figure GDA0002078686370000033
Zero sequence current of
Figure GDA0002078686370000034
The voltage phasor is related to the magnitude of the sequence component by:
Figure GDA0002078686370000035
Figure GDA0002078686370000036
Figure GDA0002078686370000037
in the formula (I), the compound is shown in the specification,
Figure GDA0002078686370000038
is the phasor of the three-phase voltage,
Figure GDA0002078686370000039
positive, negative and zero sequence voltage components;
the simplified relationship between the magnitude of the sequence component and the phasor is as follows:
Figure GDA00020786863700000310
the specific calculation process of the step 3 is as follows: when the measured value is a line current value without zero sequence component, the measured line current forms a closed triangle, and for the line current, the positive sequence component of the AB line is set as I1Angle 0 DEG, negative sequence component of
Figure GDA00020786863700000320
Because there is no zero sequence component, the relationship between the sequence component and the phasor is as follows:
Figure GDA00020786863700000311
Figure GDA00020786863700000312
Figure GDA00020786863700000313
wherein, IAB、IBC、ICAAre respectively the effective value of the current of the three-phase line, I1、I2The magnitudes of the positive and negative sequence components of the AB line current,
Figure GDA00020786863700000314
the included angle between the positive sequence component and the negative sequence component of the AB line current is formed;
simplifying the calculation, we can get:
Figure GDA00020786863700000315
Figure GDA00020786863700000316
in the formula (I), the compound is shown in the specification,
Figure GDA00020786863700000317
in general I1>I2Can find out I1、I2；
Figure GDA00020786863700000318
Figure GDA00020786863700000319
According to the measurement form of the sequence component balance rate and the unbalance rate, the sequence component is substituted to obtain a corresponding expression of the line electric flow measurement:
Figure GDA0002078686370000041
Figure GDA0002078686370000042
in the formula, epsilonbIs the three-phase equilibrium ratio, epsilonubThe three-phase imbalance ratio is obtained.
The specific calculation process of the step 3 is as follows: when the measured value is a line voltage value without zero sequence component, the measured line voltage forms a closed triangle, and for the line voltage, the positive sequence component of the AB line is set as U1Angle 0 DEG, negative sequence component of
Figure GDA0002078686370000043
Because there is no zero sequence component, the relationship between the sequence component and the phasor is as follows:
Figure GDA0002078686370000044
Figure GDA0002078686370000045
Figure GDA0002078686370000046
wherein, UAB、UBC、UCAAre respectively the effective value of three-phase line voltage, U1、U2The magnitudes of the positive sequence component and the negative sequence component of the AB line voltage,
Figure GDA0002078686370000047
the included angle between the positive sequence component and the negative sequence component of the AB line voltage is shown;
simplifying the calculation, we can get:
Figure GDA0002078686370000048
Figure GDA0002078686370000049
in the formula (I), the compound is shown in the specification,
Figure GDA00020786863700000410
usually U1>U2Can find U1，U2；
Figure GDA00020786863700000411
Figure GDA00020786863700000412
According to the measurement form of the sequence component balance rate and the unbalance rate, the sequence component is introduced to obtain a corresponding expression of the line voltage measurement:
Figure GDA00020786863700000413
Figure GDA00020786863700000414
in the formula, epsilonbIs the three-phase equilibrium ratio, epsilonubThe three-phase imbalance ratio is obtained.
The specific calculation process of the step 3 is as follows: when the measured value is a phase current value containing a zero-sequence component, for delta/Y0The phase current of the high-voltage side three phases is respectively set as
Figure GDA00020786863700000415
Low side phase current of
Figure GDA00020786863700000416
Low side neutral current of
Figure GDA00020786863700000417
Let the positive sequence component of the low-voltage side a-phase current be I1Angle 0 DEG, negative sequence component of
Figure GDA00020786863700000418
Zero sequence component of
Figure GDA00020786863700000419
The voltages of each phase are:
Figure GDA0002078686370000051
Figure GDA0002078686370000052
Figure GDA0002078686370000053
wherein, I1、I2、I0The amplitudes of the positive sequence component, the negative sequence component and the zero sequence component of the low-voltage side a-phase current,
Figure GDA0002078686370000054
the included angle of the positive sequence component and the negative sequence component of the low-voltage side a-phase current,
Figure GDA0002078686370000055
is low voltage side a phase electricityThe included angle between the flow positive sequence component and the zero sequence component;
since the delta/Y0 connection distribution high voltage side and the low voltage side are provided with zero sequence paths, the primary side phase current and the secondary side phase current can be considered to keep the same phase; the transformer transformation ratio is set as k, and the simplified calculation shows that the primary side line current is as follows:
Figure GDA0002078686370000056
Figure GDA0002078686370000057
Figure GDA0002078686370000058
the size relationship is as follows:
Figure GDA0002078686370000059
Figure GDA00020786863700000510
Figure GDA00020786863700000511
wherein, IA、IB、ICThe three-phase current effective values are respectively,
then there are:
Figure GDA00020786863700000512
Figure GDA00020786863700000513
in the formula (I), the compound is shown in the specification,
Figure GDA00020786863700000514
if I1>I2If the positive and negative sequence components are related to the effective value:
Figure GDA00020786863700000515
Figure GDA00020786863700000516
due to the fact that
Figure GDA00020786863700000517
The phase current three-phase balance rate and the unbalance rate described by the measured values are respectively as follows:
Figure GDA00020786863700000518
Figure GDA00020786863700000519
in the formula, epsilonbIs the three-phase equilibrium ratio, epsilonubThe three-phase imbalance ratio is obtained.
The specific calculation process of the step 3 is as follows: when the measured value is a phase voltage value containing a zero-sequence component, the line voltage end point is also the relation characteristic of the phase voltage end point, and the positive-sequence component of the A phase is set as U1Angle 0 DEG, negative sequence component of
Figure GDA0002078686370000061
Zero sequence component of
Figure GDA0002078686370000062
The phase voltages are:
Figure GDA0002078686370000063
Figure GDA0002078686370000064
Figure GDA0002078686370000065
wherein the content of the first and second substances,
Figure GDA0002078686370000066
are respectively three-phase voltage, U1、U2、U0Is the amplitude of the positive sequence component, the negative sequence component and the zero sequence component of the phase voltage of the phase A,
Figure GDA00020786863700000620
is the included angle between the positive sequence component and the negative sequence component of the phase A voltage,
Figure GDA0002078686370000068
the included angle between the positive sequence component and the zero sequence component of the phase voltage of the phase A is set;
considering that the terminal of the line voltage is also the terminal characteristic of the phase voltage, according to the relation between the phase voltage and the line voltage, the relation of effective values is as follows:
Figure GDA0002078686370000069
Figure GDA00020786863700000610
Figure GDA00020786863700000611
wherein, UAB、UBC、UCAThree-phase line voltage effective values respectively;
the simplified calculation can result in:
Figure GDA00020786863700000612
Figure GDA00020786863700000613
in the formula (I), the compound is shown in the specification,
Figure GDA00020786863700000614
if U is1>U2If the positive and negative sequence components are related to the effective value:
Figure GDA00020786863700000615
Figure GDA00020786863700000616
due to the fact that
Figure GDA00020786863700000617
The phase voltage three-phase balance rate and the unbalance rate described by the measured values are respectively as follows:
Figure GDA00020786863700000618
Figure GDA00020786863700000619
in the formula, epsilonbIs the three-phase equilibrium ratio, epsilonubThe three-phase imbalance ratio is obtained.
The three-phase unbalance measurement method based on the sequence components and the measurement values has the following beneficial effects: firstly, decomposing three-phase phasors into three groups of symmetrical sequence components with different group sequences according to a symmetrical component method to obtain the magnitude relation between the three-phase phasors and the sequence components; and measuring the three-phase balance rate according to the proportion of the three-phase positive sequence component in the total amount, wherein the part except the positive sequence component is used for measuring the three-phase unbalance rate, and obtaining a three-phase unbalance measurement form based on the sequence component. Therefore, the description of the balance rate and the unbalance rate under the condition of containing zero sequence components and not containing zero sequence components is the same, the parameter is between 0 and 1, a three-phase unbalance rate measurement form containing each sequence component is constructed, the influence of each sequence component on the balance rate and the unbalance rate is accurately reflected, and the problem that the influence of the zero sequence component cannot be reflected by the original sequence component measurement form is solved.
Secondly, aiming at the line voltage and line current without the zero sequence component, the phase voltage with the zero sequence component and the phase voltage with the zero sequence component, the problem of obtaining the magnitude of the sequence component based on the measured value is solved, and the measured value corresponding to the sequence component is constructed to express the three-phase balance rate and the unbalance rate, so that the three-phase balance rate and the unbalance rate have uniqueness, and the confusion caused by multiple measuring modes of the original measured value and non-uniform results is solved.
Drawings
FIG. 1 is a diagram showing the delta/Y of a three-phase imbalance measurement method based on sequence components and measurement values according to the present invention0And connecting the transformer.
Fig. 2 is a diagram of the relationship between the current phasors at the high-voltage side and the low-voltage side of the transformer based on the three-phase unbalance measurement method of the sequence component and the measurement value.
Detailed Description
The invention is further described below with reference to the drawings and specific preferred embodiments.
A three-phase unbalance measurement method based on sequence components and measurement values is characterized in that: the method comprises the following steps:
step 1, carrying out phase sequence decomposition on three-phase electric quantity by using a symmetric component method to obtain a magnitude relation between a sequence component and a phasor;
step 2, defining a measurement mode of the three-phase balance rate and the unbalance rate of the sequence component containing the zero-sequence component, wherein the specific mode is as follows: the proportion of the three-phase positive sequence component in the total amount is used for measuring the three-phase balance rate, and the proportion of the part except the positive sequence component in the total amount is used for measuring the three-phase unbalance rate;
and 3, calculating according to the measured values to obtain the three-phase imbalance rate.
Further, in step 1, the magnitude relation between the sequence component and the phasor is a characteristic relation that the square sum of the effective values of the three-phase electric quantities is three times the square sum of the effective values of the sequence component, and the specific calculation process is as follows:
when the current value is taken as a calculation parameter, the calculation flow is as follows:
Figure GDA0002078686370000071
Figure GDA0002078686370000072
Figure GDA0002078686370000073
let the A-phase positive sequence current be I1Angle 0 DEG, negative sequence current of
Figure GDA0002078686370000081
Zero sequence current of
Figure GDA0002078686370000082
Then the current phasor has a relationship with the magnitude of the sequence phasor:
Figure GDA0002078686370000083
Figure GDA0002078686370000084
Figure GDA0002078686370000085
in the formula (I), the compound is shown in the specification,
Figure GDA0002078686370000086
is the phasor of the three-phase current,
Figure GDA0002078686370000087
positive, negative and zero sequence current components;
the simplified relationship between the magnitude of the sequence component and the phasor is as follows:
Figure GDA0002078686370000088
when the current value is taken as a calculation parameter, in the step 2, the three-phase balance rate is defined by the square sum of the effective values of the three-phase positive sequence components in the total square sum percentage:
Figure GDA0002078686370000089
defining the three-phase equilibrium ratio as:
Figure GDA00020786863700000810
further, when the voltage value is taken as a calculation parameter, the magnitude relation between the sequence component and the phasor in the step 1 is a characteristic relation that the square sum of the effective values of the three-phase electric quantity is three times the square sum of the effective values of the sequence component, and the specific calculation process is as follows:
Figure GDA00020786863700000811
Figure GDA00020786863700000812
Figure GDA00020786863700000813
let the A-phase positive sequence voltage be U1Angle 0 DEG, negative sequence current of
Figure GDA00020786863700000814
Zero sequence current of
Figure GDA00020786863700000815
The voltage phasor is related to the magnitude of the sequence component by:
Figure GDA00020786863700000816
Figure GDA00020786863700000817
Figure GDA00020786863700000818
in the formula (I), the compound is shown in the specification,
Figure GDA0002078686370000091
is the phasor of the three-phase voltage,
Figure GDA0002078686370000092
positive, negative and zero sequence voltage components;
the simplified relationship between the magnitude of the sequence component and the phasor is as follows:
Figure GDA0002078686370000093
at this time, in step 2, the three-phase equilibrium ratio is defined as follows by using the square sum of the effective values of the three-phase positive sequence components in the sum of the squares of the total quantity:
Figure GDA0002078686370000094
defining the three-phase unbalance rate as:
Figure GDA0002078686370000095
when the measured value is a line current value without zero-sequence component, the positive-sequence and negative-sequence components are calculated and obtained by utilizing the characteristic that the three-phase current effective values form a closed triangle aiming at the current without zero-sequence component, and at the moment, the specific calculation process of the step 3 is as follows:
since the measured line current forms a closed triangle, for the line current, the positive sequence component of the AB line is set as I1Angle 0 DEG, negative sequence component of
Figure GDA0002078686370000096
Because there is no zero sequence component, the relationship between the sequence component and the phasor is as follows:
Figure GDA0002078686370000097
Figure GDA0002078686370000098
Figure GDA0002078686370000099
wherein, IAB、IBC、ICAAre respectively the effective value of the current of the three-phase line, I1、I2The magnitudes of the positive and negative sequence components of the AB line current,
Figure GDA00020786863700000910
the included angle between the positive sequence component and the negative sequence component of the AB line current is formed;
simplifying the calculation, we can get:
Figure GDA00020786863700000911
Figure GDA00020786863700000912
in the formula (I), the compound is shown in the specification,
Figure GDA00020786863700000913
in general I1>I2Can find out I1、I2；
Figure GDA00020786863700000914
Figure GDA00020786863700000915
According to the measurement form of the sequence component balance rate and the unbalance rate, the sequence component is substituted to obtain a corresponding expression of the line electric flow measurement:
Figure GDA00020786863700000916
Figure GDA00020786863700000917
in the formula, epsilonbIs the three-phase equilibrium ratio, epsilonubThe three-phase imbalance ratio is obtained.
When the measured value is a line voltage value without zero sequence component, the positive sequence component and the negative sequence component are calculated and obtained by utilizing the characteristic that the three-phase voltage effective value forms a closed triangle aiming at the voltage without zero sequence component, and at the moment, the specific calculation process of the step 3 is as follows:
as the measured line voltage forms a closed triangle, for the line voltage, the positive sequence component of the AB line is set as U1Angle 0 DEG, negative sequence component of
Figure GDA0002078686370000101
Because there is no zero sequence component, the relationship between the sequence component and the phasor is as follows:
Figure GDA0002078686370000102
Figure GDA0002078686370000103
Figure GDA0002078686370000104
wherein, UAB、UBC、UCAAre respectively the effective value of three-phase line voltage, U1、U2The magnitudes of the positive sequence component and the negative sequence component of the AB line voltage,
Figure GDA0002078686370000105
the included angle between the positive sequence component and the negative sequence component of the AB line voltage is shown;
simplifying the calculation, we can get:
Figure GDA0002078686370000106
Figure GDA0002078686370000107
in the formula (I), the compound is shown in the specification,
Figure GDA0002078686370000108
usually U1>U2Can find U1，U2。
Figure GDA0002078686370000109
Figure GDA00020786863700001010
According to the measurement form of the sequence component balance rate and the unbalance rate, the sequence component is introduced to obtain a corresponding measurement expression:
Figure GDA00020786863700001011
Figure GDA00020786863700001012
in the formula, epsilonbIs the three-phase equilibrium ratio, epsilonubThe three-phase imbalance ratio is obtained.
When the measured value is a phase current value containing a zero-sequence component, the magnitude of the sequence component is obtained by using the current relationship between the high-voltage side and the low-voltage side of the transformer aiming at the phase current of the four-wire system containing the zero-sequence component, and at the moment, the specific calculation process of the step 3 is as follows:
for delta/Y0The phase current of the high-voltage side three phases is respectively set as
Figure GDA00020786863700001013
Low side phase current of
Figure GDA00020786863700001014
Low side neutral current of
Figure GDA00020786863700001015
Let the positive sequence component of the low-voltage side a-phase current be I1Angle 0 DEG, negative sequence component of
Figure GDA00020786863700001016
Zero sequence component of
Figure GDA00020786863700001017
The voltages of each phase are:
Figure GDA00020786863700001018
Figure GDA0002078686370000111
Figure GDA0002078686370000112
wherein, I1、I2、I0The amplitudes of the positive sequence component, the negative sequence component and the zero sequence component of the low-voltage side a-phase current,
Figure GDA0002078686370000113
the included angle of the positive sequence component and the negative sequence component of the low-voltage side a-phase current,
Figure GDA00020786863700001119
the included angle between the positive sequence component and the zero sequence component of the low-voltage side phase a current is formed;
since the delta/Y0 connection distribution high voltage side and the low voltage side are provided with zero sequence paths, the primary side phase current and the secondary side phase current can be considered to keep the same phase; the transformer transformation ratio is set as k, and the simplified calculation shows that the primary side line current is as follows:
Figure GDA0002078686370000115
Figure GDA0002078686370000116
Figure GDA0002078686370000117
the size relationship is as follows:
Figure GDA0002078686370000118
Figure GDA0002078686370000119
Figure GDA00020786863700001110
wherein, IA、IB、ICThe three-phase current effective values are respectively,
then there are:
Figure GDA00020786863700001111
Figure GDA00020786863700001112
in the formula (I), the compound is shown in the specification,
Figure GDA00020786863700001113
if I1>I2If the positive and negative sequence components are related to the effective value:
Figure GDA00020786863700001114
Figure GDA00020786863700001115
due to the fact that
Figure GDA00020786863700001116
The phase current three-phase balance rate and the unbalance rate described by the measured values are respectively as follows:
Figure GDA00020786863700001117
Figure GDA00020786863700001118
in the formula, epsilonbIs the three-phase equilibrium ratio, epsilonubThe three-phase imbalance ratio is obtained.
When the measured value is a phase voltage value containing a zero-sequence component, for the phase voltage containing the zero-sequence component, according to the characteristic that the line voltage end point is also the phase voltage end point, the line voltage and the phase voltage magnitude are used to obtain each sequence component, and at this time, the specific calculation process of the step 3 is as follows:
since the line voltage terminal is also the relation characteristic of the phase voltage terminal, the positive sequence component of the A phase is set as U1Angle 0 DEG, negative sequence component of
Figure GDA0002078686370000121
Zero sequence component of
Figure GDA0002078686370000122
The phase voltages are:
Figure GDA0002078686370000123
Figure GDA0002078686370000124
Figure GDA0002078686370000125
wherein the content of the first and second substances,
Figure GDA0002078686370000126
are respectively three-phase voltage, U1、U2、U0Is the amplitude of the positive sequence component, the negative sequence component and the zero sequence component of the phase voltage of the phase A,
Figure GDA0002078686370000127
is the included angle between the positive sequence component and the negative sequence component of the phase A voltage,
Figure GDA0002078686370000128
the included angle between the positive sequence component and the zero sequence component of the phase voltage of the phase A is set;
considering that the terminal of the line voltage is also the terminal characteristic of the phase voltage, according to the relation between the phase voltage and the line voltage, the relation of effective values is as follows:
Figure GDA0002078686370000129
Figure GDA00020786863700001210
Figure GDA00020786863700001211
wherein, UAB、UBC、UCAThree-phase line voltage effective values respectively;
the simplified calculation can result in:
Figure GDA00020786863700001212
Figure GDA00020786863700001213
in the formula (I), the compound is shown in the specification,
Figure GDA00020786863700001214
if U is1>U2If the positive and negative sequence components are related to the effective value:
Figure GDA00020786863700001215
Figure GDA00020786863700001216
due to the fact that
Figure GDA00020786863700001217
The phase voltage three-phase balance rate and the unbalance rate described by the measured values are respectively as follows:
Figure GDA00020786863700001218
Figure GDA00020786863700001219
in the formula, epsilonbIs the three-phase equilibrium ratio, epsilonubThe three-phase imbalance ratio is obtained.
The above calculation process unifies the description of the balance rate and the unbalance rate under the condition of containing zero sequence components and not containing zero sequence components, and the parameters are between 0 and 1, a three-phase unbalance rate measurement form containing each sequence component is constructed, the influence of each sequence component on the balance rate and the unbalance rate is accurately reflected, and the problem that the original sequence component measurement mode cannot reflect the influence of the zero sequence components is solved.
Aiming at line voltage and line current without zero sequence component, phase voltage with zero sequence component and phase voltage with zero sequence component, the problem of obtaining the magnitude of the sequence component based on a measured value is solved, and the measured value corresponding to the sequence component is constructed to express the three-phase balance rate and the unbalance rate, so that the three-phase balance rate and the unbalance rate have uniqueness, and the problems of multiple measuring modes of the original measured value and confusion caused by non-uniform results are solved.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention; it should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (4)

1. A three-phase unbalance measurement method based on sequence components and measurement values is characterized in that: the method comprises the following steps:
step 1, carrying out phase sequence decomposition on the three-phase electric quantity by using a symmetric component method to obtain a characteristic relation that the magnitude relation between a sequence component and a phasor is the square sum of the effective values of the three-phase electric quantity and is three times of the square sum of the effective values of the sequence component, wherein the specific calculation process is as follows:
when the current value is taken as a calculation parameter, the calculation flow is as follows:
Figure FDA0003032984520000011
Figure FDA0003032984520000012
Figure FDA0003032984520000013
let the A-phase positive sequence current be I1Angle 0 DEG, negative sequence current of
Figure FDA0003032984520000014
Zero sequence current of
Figure FDA0003032984520000015
Then the current phasor has a relationship with the magnitude of the sequence phasor:
Figure FDA0003032984520000016
Figure FDA0003032984520000017
Figure FDA0003032984520000018
in the formula (I), the compound is shown in the specification,
Figure FDA0003032984520000019
is the phasor of the three-phase current,
Figure FDA00030329845200000110
positive, negative and zero sequence current components;
the simplified relationship between the magnitude of the sequence component and the phasor is as follows:
Figure FDA00030329845200000111
step 2, defining a measurement mode of the three-phase balance rate and the unbalance rate of the sequence component containing the zero-sequence component, wherein the specific mode is as follows: the proportion of the three-phase positive sequence component in the total amount is used for measuring the three-phase balance rate, and the proportion of the part except the positive sequence component in the total amount is used for measuring the three-phase unbalance rate;
step 3, calculating according to the measured values to obtain the three-phase unbalance rate; when the measured value is a line current value without zero sequence component, the measured line current forms a closed triangle, and for the line current, the positive sequence component of the AB line is set as I1Angle 0 DEG, negative sequence component of
Figure FDA00030329845200000112
Because there is no zero sequence component, the relationship between the sequence component and the phasor is as follows:
Figure FDA00030329845200000113
Figure FDA00030329845200000114
Figure FDA00030329845200000115
wherein, IAB、IBC、ICAAre respectively the effective value of the current of the three-phase line, I1、I2The magnitudes of the positive and negative sequence components of the AB line current,
Figure FDA00030329845200000116
the included angle between the positive sequence component and the negative sequence component of the AB line current is formed;
simplifying the calculation, we can get:
Figure FDA0003032984520000021
Figure FDA0003032984520000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003032984520000023
in general I1>I2Can find out I1，I2；
Figure FDA0003032984520000024
Figure FDA0003032984520000025
According to the measurement form of the sequence component balance rate and the unbalance rate, the sequence component is substituted to obtain a corresponding expression of the line electric flow measurement:
Figure FDA0003032984520000026
Figure FDA0003032984520000027
in the formula, epsilonbIs the three-phase equilibrium ratio, epsilonubThe three-phase imbalance ratio is obtained.
2. A three-phase unbalance measurement method based on sequence components and measurement values is characterized in that: the method comprises the following steps:
step 1, carrying out phase sequence decomposition on the three-phase electric quantity by using a symmetric component method to obtain a characteristic relation that the magnitude relation between a sequence component and a phasor is the square sum of the effective values of the three-phase electric quantity and is three times of the square sum of the effective values of the sequence component, wherein the specific calculation process is as follows:
when the voltage value is taken as a calculation parameter, the calculation process is as follows:
Figure FDA0003032984520000028
Figure FDA0003032984520000029
Figure FDA00030329845200000210
let the A-phase positive sequence voltage be U1Angle 0 DEG, negative sequence current of
Figure FDA00030329845200000211
Zero sequence current of
Figure FDA00030329845200000212
The voltage phasor is related to the magnitude of the sequence component by:
Figure FDA00030329845200000213
Figure FDA00030329845200000214
Figure FDA00030329845200000215
in the formula (I), the compound is shown in the specification,
Figure FDA00030329845200000216
is the phasor of the three-phase voltage,
Figure FDA00030329845200000217
positive, negative and zero sequence voltage components;
the simplified relationship between the magnitude of the sequence component and the phasor is as follows:
Figure FDA0003032984520000031
step 2, defining a measurement mode of the three-phase balance rate and the unbalance rate of the sequence component containing the zero-sequence component, wherein the specific mode is as follows: the proportion of the three-phase positive sequence component in the total amount is used for measuring the three-phase balance rate, and the proportion of the part except the positive sequence component in the total amount is used for measuring the three-phase unbalance rate;
and 3, calculating to obtain the three-phase unbalance rate according to the measured value, forming a closed triangle due to the measured line voltage when the measured value is the line voltage value without zero sequence component, and setting the positive sequence component of the AB line as U for the line voltage1Angle 0 DEG, negative sequence component of
Figure FDA0003032984520000032
Because there is no zero sequence component, the relationship between the sequence component and the phasor is as follows:
Figure FDA0003032984520000033
Figure FDA0003032984520000034
Figure FDA0003032984520000035
wherein, UAB、UBC、UCAAre respectively the effective value of three-phase line voltage, U1、U2The magnitudes of the positive sequence component and the negative sequence component of the AB line voltage,
Figure FDA0003032984520000036
the included angle between the positive sequence component and the negative sequence component of the AB line voltage is shown;
simplifying the calculation, we can get:
Figure FDA0003032984520000037
Figure FDA0003032984520000038
in the formula (I), the compound is shown in the specification,
Figure FDA0003032984520000039
usually U1>U2Can find U1，U2；
Figure FDA00030329845200000310
Figure FDA00030329845200000311
According to the measurement form of the sequence component balance rate and the unbalance rate, the sequence component is introduced to obtain a corresponding expression of the line voltage measurement:
Figure FDA00030329845200000312
Figure FDA00030329845200000313
in the formula, epsilonbIs the three-phase equilibrium ratio, epsilonubThe three-phase imbalance ratio is obtained.
3. A three-phase unbalance measurement method based on sequence components and measurement values is characterized in that: the method comprises the following steps:
step 1, carrying out phase sequence decomposition on the three-phase electric quantity by using a symmetric component method to obtain a characteristic relation that the magnitude relation between a sequence component and a phasor is the square sum of the effective values of the three-phase electric quantity and is three times of the square sum of the effective values of the sequence component, wherein the specific calculation process is as follows:
when the current value is taken as a calculation parameter, the calculation flow is as follows:
Figure FDA0003032984520000041
Figure FDA0003032984520000042
Figure FDA0003032984520000043
let the A-phase positive sequence current be I1Angle 0 DEG, negative sequence current of
Figure FDA0003032984520000044
Zero sequence current of
Figure FDA0003032984520000045
Then the current phasor has a relationship with the magnitude of the sequence phasor:
Figure FDA0003032984520000046
Figure FDA0003032984520000047
Figure FDA0003032984520000048
in the formula (I), the compound is shown in the specification,
Figure FDA0003032984520000049
is the phasor of the three-phase current,
Figure FDA00030329845200000410
positive, negative and zero sequence current components;
the simplified relationship between the magnitude of the sequence component and the phasor is as follows:
Figure FDA00030329845200000411
step 2, defining a measurement mode of the three-phase balance rate and the unbalance rate of the sequence component containing the zero-sequence component, wherein the specific mode is as follows: the proportion of the three-phase positive sequence component in the total amount is used for measuring the three-phase balance rate, and the proportion of the part except the positive sequence component in the total amount is used for measuring the three-phase unbalance rate;
and 3, calculating to obtain the three-phase unbalance rate according to the measured value, and when the measured value is a phase current value containing a zero sequence component, regarding delta/Y0The phase current of the high-voltage side three phases is respectively set as
Figure FDA00030329845200000412
Low side phase current of
Figure FDA00030329845200000413
Low side neutral current of
Figure FDA00030329845200000414
Let the positive sequence component of the low-voltage side a-phase current be I1Angle 0 DEG, negative sequence component of
Figure FDA00030329845200000415
Zero sequence component of
Figure FDA00030329845200000416
The current of each phase is:
Figure FDA00030329845200000417
Figure FDA00030329845200000418
Figure FDA00030329845200000419
wherein, I1、I2、I0Is low voltage side a phase electricityThe magnitudes of the positive, negative and zero sequence components of the flow,
Figure FDA00030329845200000420
the included angle of the positive sequence component and the negative sequence component of the low-voltage side a-phase current,
Figure FDA00030329845200000421
the included angle between the positive sequence component and the zero sequence component of the low-voltage side phase a current is formed;
since the delta/Y0 connection distribution high voltage side and the low voltage side are provided with zero sequence paths, the primary side phase current and the secondary side phase current can be considered to keep the same phase; the transformer transformation ratio is set as k, and the simplified calculation shows that the primary side phase current is as follows:
Figure FDA0003032984520000051
Figure FDA0003032984520000052
Figure FDA0003032984520000053
the size relationship is as follows:
Figure FDA0003032984520000054
Figure FDA0003032984520000055
Figure FDA0003032984520000056
wherein, IA、IB、ICRespectively are effective values of three-phase current,
then there are:
Figure FDA0003032984520000057
Figure FDA0003032984520000058
in the formula (I), the compound is shown in the specification,
Figure FDA0003032984520000059
if I1>I2If the positive and negative sequence components are related to the effective value:
Figure FDA00030329845200000510
Figure FDA00030329845200000511
due to the fact that
Figure FDA00030329845200000512
The phase current three-phase balance rate and the unbalance rate described by the measured values are respectively as follows:
Figure FDA00030329845200000513
Figure FDA00030329845200000514
in the formula, epsilonbIs the three-phase equilibrium ratio, epsilonubThe three-phase imbalance ratio is obtained.
4. A three-phase unbalance measurement method based on sequence components and measurement values is characterized in that: the method comprises the following steps:
step 1, carrying out phase sequence decomposition on the three-phase electric quantity by using a symmetric component method to obtain a characteristic relation that the magnitude relation between a sequence component and a phasor is the square sum of the effective values of the three-phase electric quantity and is three times of the square sum of the effective values of the sequence component, wherein the specific calculation process is as follows:
when the voltage value is taken as a calculation parameter, the calculation process is as follows:
Figure FDA00030329845200000515
Figure FDA00030329845200000516
Figure FDA0003032984520000061
let the A-phase positive sequence voltage be U1Angle 0 DEG, negative sequence current of
Figure FDA0003032984520000062
Zero sequence current of
Figure FDA0003032984520000063
The voltage phasor is related to the magnitude of the sequence component by:
Figure FDA0003032984520000064
Figure FDA0003032984520000065
Figure FDA0003032984520000066
in the formula (I), the compound is shown in the specification,
Figure FDA0003032984520000067
is the phasor of the three-phase voltage,
Figure FDA0003032984520000068
positive, negative and zero sequence voltage components;
the simplified relationship between the magnitude of the sequence component and the phasor is as follows:
Figure FDA0003032984520000069
step 2, defining a measurement mode of the three-phase balance rate and the unbalance rate of the sequence component containing the zero-sequence component, wherein the specific mode is as follows: the proportion of the three-phase positive sequence component in the total amount is used for measuring the three-phase balance rate, and the proportion of the part except the positive sequence component in the total amount is used for measuring the three-phase unbalance rate;
and 3, calculating to obtain the three-phase unbalance rate according to the measured value, and setting the positive sequence component of the A phase as U phase due to the relationship characteristic that the line voltage end point is also the phase voltage end point when the measured value is the phase voltage value containing the zero sequence component1Angle 0 DEG, negative sequence component of
Figure FDA00030329845200000610
Zero sequence component of
Figure FDA00030329845200000611
The phase voltages are:
Figure FDA00030329845200000612
Figure FDA00030329845200000613
Figure FDA00030329845200000614
wherein the content of the first and second substances,
Figure FDA00030329845200000615
are respectively three-phase voltage, U1、U2、U0Is the amplitude of the positive sequence component, the negative sequence component and the zero sequence component of the phase voltage of the phase A,
Figure FDA00030329845200000616
is the included angle between the positive sequence component and the negative sequence component of the phase A voltage,
Figure FDA00030329845200000617
the included angle between the positive sequence component and the zero sequence component of the phase voltage of the phase A is set;
considering that the terminal of the line voltage is also the terminal characteristic of the phase voltage, according to the relation between the phase voltage and the line voltage, the relation of effective values is as follows:
Figure FDA00030329845200000618
Figure FDA00030329845200000619
Figure FDA00030329845200000620
wherein, UAB、UBC、UCAThe effective values of the three-phase line voltage are respectively;
the simplified calculation can result in:
Figure FDA0003032984520000071
Figure FDA0003032984520000072
in the formula (I), the compound is shown in the specification,
Figure FDA0003032984520000073
if U is1>U2If the positive and negative sequence components are related to the effective value:
Figure FDA0003032984520000074
Figure FDA0003032984520000075
due to the fact that
Figure FDA0003032984520000076
The phase voltage three-phase balance rate and the unbalance rate described by the measured values are respectively as follows:
Figure FDA0003032984520000077
Figure FDA0003032984520000078
in the formula, epsilonbIs the three-phase equilibrium ratio, epsilonubThe three-phase imbalance ratio is obtained.
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