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CN106249068B - A low-frequency measurement method for no-load characteristics of ferromagnetic components - Google Patents

A low-frequency measurement method for no-load characteristics of ferromagnetic components Download PDF

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CN106249068B
CN106249068B CN201610536618.9A CN201610536618A CN106249068B CN 106249068 B CN106249068 B CN 106249068B CN 201610536618 A CN201610536618 A CN 201610536618A CN 106249068 B CN106249068 B CN 106249068B
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刘鑫
梁仕斌
姚陈果
刘涛
王磊
田庆生
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Yunnan Electric Power Technology Co ltd
Electric Power Research Institute of Yunnan Power Grid Co Ltd
Yunnan Electric Power Test and Research Institute Group Co Ltd
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Yunnan Electric Power Technology Co ltd
Electric Power Research Institute of Yunnan Power Grid Co Ltd
Yunnan Electric Power Test and Research Institute Group Co Ltd
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Abstract

一种铁磁元件空载特性的低频测量方法，主要包括如下步骤：第一步：根据T型等效电路，建立高压侧开路等效电路，在低压侧施加2个频率不同的低频正弦波，计算各个频率下的铁心损耗；第二步：计算单位周期产生的单位磁滞和涡流损耗We和Wh，并计算折算至工频下的铁心损耗PCoren；第三步：根据涡流电流补偿算法计算折算至工频下的励磁电流Iexn、谐波含量K(k)、励磁电压Un；第四步：计算空载损耗Pn；第五步：绘制PCoren‑Un，Iexn‑Un关系曲线，以及K(k)‑Un谐波含量表格。该方法采用低频电源代替工频电源开展试验可以成倍减低试验电源容量、减小试验设备体积和重量，使试验成本更低。

Figure 201610536618

A low-frequency measurement method for no-load characteristics of a ferromagnetic component mainly includes the following steps: Step 1: Establish an open-circuit equivalent circuit on a high-voltage side according to a T-type equivalent circuit, and apply two low-frequency sine waves with different frequencies on the low-voltage side, Calculate the core loss at each frequency; Step 2: Calculate the unit hysteresis and eddy current losses We and W h generated per unit cycle, and calculate the core loss P Coren converted to the power frequency; Step 3: Compensate according to the eddy current The algorithm calculates the excitation current I exn , harmonic content K (k) , excitation voltage U n converted to the power frequency; the fourth step: calculates the no-load loss P n ; the fifth step: draws P Coren ‑U n , I exn ‑U n relationship curve, and K (k) ‑U n harmonic content table. In this method, the low-frequency power supply is used instead of the power-frequency power supply to carry out the test, which can double the capacity of the test power supply, reduce the volume and weight of the test equipment, and make the test cost lower.

Figure 201610536618

Description

Low-frequency measurement method for no-load characteristic of ferromagnetic element
Technical Field
The invention belongs to the technical field of ferromagnetic element no-load characteristic measurement, mainly comprises no-load loss, excitation characteristic and no-load current harmonic content measurement, and particularly relates to ferromagnetic elements such as a transformer, a mutual inductor, a reactor and the like.
Background
Ferromagnetic elements such as transformers, reactors and the like are used as the most important power transmission and transformation equipment in a power system, and the performance of the ferromagnetic elements directly influences the safe and economic operation of the power system. The no-load loss, excitation characteristics and no-load current harmonic content of the ferromagnetic element are important indexes for reflecting the performance of the iron core of the ferromagnetic element. GB1094.1-2013 power transformer first part: general guidelines, which require no-load loss and no-load current measurement as routine tests, can be used to inspect and find local defects and global defects in the magnetic circuit of the test article. The test guide of the JB/T501-2006 power transformer provides: when no-load test is carried out, rated voltage with rated frequency is supplied to a high-voltage side winding (generally a low-voltage winding) in each winding of a test sample, and the other windings are opened; the measurement of the no-load current harmonic of the transformer is a special test, and the saturation degree of the iron core is checked by detecting the composition and the value of the no-load current harmonic, so that the rationality of the design is verified. Section 1 of the experimental guide for the GB22071.1-2008 transformer: current transformers and GB22071.2-2008 mutual inductor test guide 2 part: voltage transformers "all specify the need for excitation characteristic testing of voltage (current) transformers. GB 1094.6-2011 power transformer part 6: the reactor "also stipulates that the reactor must perform no-load loss measurement. However, with the increase of the voltage level of the power grid, the voltage level and the capacity of ferromagnetic elements such as a transformer are gradually increased, and the capacity, the volume and the weight of test equipment required in the no-load test are often very large, so that the no-load test procedure is complex, and the personal safety of operators cannot be guaranteed.
Therefore, it is necessary to find a new testing method for the no-load characteristic of ferromagnetic components, which can simplify the testing process and reduce the weight and volume of the testing equipment.
Disclosure of Invention
Aiming at the defects of the existing ferromagnetic element no-load characteristic measuring method, the invention provides a ferromagnetic element no-load test by adopting a low-frequency power supply. As can be seen from E ═ 4.44fN Φ, the core saturation voltage of the ferromagnetic element is substantially proportional to the power supply frequency, and under the excitation of the low-frequency power supply, the power supply voltage can be greatly reduced, while the no-load current is substantially unchanged, so that the capacity of the test power supply can be reduced by times. And measuring the no-load loss, the no-load current and the harmonic characteristics thereof under the low frequency, and calculating the no-load loss, the no-load current and the harmonic contents thereof converted to the power frequency test condition according to a related algorithm, thereby achieving the purpose of replacing the power frequency test with the low frequency test. Tests prove that the method has better consistency with a power frequency test method directly adopted.
In order to achieve the purpose, the invention adopts the following technical scheme:
a low-frequency measurement method for no-load characteristics of a ferromagnetic element is characterized by comprising the following steps:
1. an equivalent circuit model of the open circuit on the high-voltage side of the ferromagnetic element is established, and is shown in figure 1. Wherein R isdcIs a direct current resistance on the winding, LσFor leakage inductance of the side winding, ReNonlinear inductor L with hysteresis loop for equivalent resistance of eddy current lossmFor exciting inductance, hysteresis loss PhIs contained in LmIn (1). i.e. iex(t) is an excitation current, im(t) is a flow through LmMagnetizing current of ie(t) is the eddy current loss equivalent current, u (t) is the excitation voltage applied to the winding;
2. the no-load loss of the ferromagnetic element is mainly core loss, and the core loss mainly comprises magnetic hysteresis loss and eddy current loss:
Figure BDA0001044651200000021
in the formula, PhAnd PeHysteresis loss and eddy current loss, respectively; ceDetermining the resistivity for the eddy current loss coefficient; chThe hysteresis loss coefficient and the material property are determined; b ismIs the peak value of the magnetic flux of the iron core; f is the frequency; v is the volume of the iron core; delta is the thickness of the silicon steel sheet; wh(W/Hz) and We(W/Hz2) Unit hysteresis and eddy current loss are generated for each magnetization period, respectively. Thus if B at different frequencies is guaranteedmIf they are consistent, W can be considerede、WhIs constant, and when the U/f under different frequencies is consistent in the test, B can be considered asmAre equal. W is determined by the core losses at two different frequencieshAnd WeA value of (d);
3. and (3) opening the high-voltage side of the winding, applying voltage to the low-voltage side, and recording voltage and current data when the U/f is equal under two different frequencies. Calculation formula of iron loss:
Figure BDA0001044651200000022
where u (t) is the voltage applied across the winding, iex(t) is the excitation current, IexIs its valid value;
4. calculating the corresponding iron loss under each frequency to obtain:
Figure BDA0001044651200000023
5. from equation (3), solving the equation can obtain WeAnd WhComprises the following steps:
Figure BDA0001044651200000024
6. thus, the iron loss at power frequency is translated:
Figure BDA0001044651200000025
wherein f isnA nominal frequency, typically 50Hz or 60 Hz;
7. iron loss current can be divided into hysteresis loss current and eddy current loss current:
Figure BDA0001044651200000026
in the formula IFe、Ih、IeFor effective value of corresponding current, from E to KvfNBmS, knowing that E is proportional to the frequency f, the eddy current loss current ieHysteresis loss current i proportional to the frequency first powerhIndependent of frequency. And because of B at different frequenciesmAre equal to each other, so that imAnd (3) equality, converting to the exciting current under the power frequency:
8. loss of current i due to eddy currentseProportional to the frequency first power, convert to the eddy current at power frequency:
Ien＝Ie·fn/f (7)
9. as shown in fig. 1, since the eddy current contains only the fundamental component, it is only necessary to compensate the eddy current to the fundamental component of the excitation current when calculating the excitation current, and the phasor diagram is as shown in fig. 2, and is converted to the fundamental component of the excitation current at power frequency:
Figure BDA0001044651200000031
10. converting to exciting current under power frequency:
Figure BDA0001044651200000032
wherein, Iex(k)The current effective value of the kth harmonic wave under low frequency is obtained;
11. percent of no-load current harmonics:
Figure BDA0001044651200000033
K(k)the kth harmonic current accounts for the effective value of the fundamental current, and even harmonic content is the same as that of the fundamental current due to symmetrical positive and negative semi-axes of the waveformThis is zero. Therefore k is 1,3,5,7 …, k>1 hour, the amplitude of the idle current higher harmonic under low frequency and power frequency excitation is equal, i.e. Iexn(k)＝Iex(k)；
12. Converting to no-load loss at rated frequency:
Figure BDA0001044651200000034
13. because the voltage drop on the leakage inductance is very small and can be ignored when the leakage inductance is in no load, the leakage inductance is converted into the excitation voltage under the rated frequency:
Un＝E·fn/f+Iexn·Rdc(12)。
thus, the excitation voltage U converted to power frequency can be obtainednThe corresponding relation between the power frequency excitation voltage effective value and the no-load loss, the excitation current and the no-load current harmonic content under the power frequency achieves the purpose of replacing the power frequency test by adopting a low frequency test.
Compared with the prior art, the invention has the following advantages:
1. the low-frequency sine wave power supply is adopted for testing, so that the capacity, volume and weight of the testing power supply can be reduced by times, the testing process is more convenient, and the cost is lower;
2. the testing voltage is reduced, the requirement on the insulation performance of the testing equipment is low, and the safety of testing personnel is guaranteed.
Drawings
In order to make the method and principle of the present invention for measuring the no-load characteristic of a ferromagnetic element clearer, the present invention will be further described in detail with reference to the accompanying drawings, wherein:
fig. 1 is an equivalent circuit diagram of an open circuit on a high-voltage side of a ferromagnetic element according to an embodiment of the present invention;
fig. 2 is a phasor diagram illustrating field current compensation for a ferromagnetic element according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a preferred embodiment of a low-frequency measurement method for an unloaded characteristic of a ferromagnetic element according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a method for measuring an unloaded characteristic of a ferromagnetic element according to an embodiment of the present invention;
fig. 5 is a comparison between the measurement by the method and the actual measurement at power frequency provided by the embodiment of the present invention, (a) is a comparison between no-load loss measurement, and (b) is a comparison between excitation characteristic measurement.
Detailed Description
In order to enable a person skilled in the art to better understand the technical solution of the present invention, the following will clearly and completely describe the technical solution in the embodiments of the present invention with reference to the accompanying drawings and the detailed description, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The measurement process is as follows:
fig. 4 is a schematic view of the measurement method of the present invention.
Step 100: according to the T-type equivalent circuit model, an equivalent circuit with one side (high voltage side) of the ferromagnetic element open is established, as shown in FIG. 1, wherein RdcIs a direct current resistance on the winding, LσFor leakage inductance of the side winding, ReNonlinear inductor L with hysteresis loop for equivalent resistance of eddy current lossmFor exciting inductance, hysteresis loss PhIs contained in LmIn (1). i.e. iex(t) is an excitation current, im(t) is a flow through LmMagnetizing current of ie(t) is the eddy current loss equivalent current, u (t) is the excitation voltage applied to the winding;
step 200: a schematic diagram of a measurement process of a preferred embodiment provided by the invention is shown in fig. 2, a high-voltage side is open-circuited, a low-frequency sine wave with 2 frequencies is applied to a low-voltage side (U/f is ensured to be equal under different frequencies), a data acquisition device records corresponding voltage and current data, and the iron core loss under each frequency is calculated according to a formula (2);
step 300: the unit hysteresis loss W in each magnetization period is calculated from the expressions (3) to (4)hAnd eddy current loss We；
Step 400: calculating the core loss P converted to power frequency according to the formula (5)Coren；
Step 500: calculating the eddy current I converted to power frequency according to the formulas (6) to (8)eFundamental component of exciting current Iexn(1)；
Step 600: calculating the exciting current I converted to power frequency according to the formulas (9) to (10)exnAnd its harmonic content K(k)；
Step 700: calculating the no-load loss P converted to power frequency according to the formula (11)n；
Step 800: calculating the excitation voltage effective value U converted to power frequency according to the formula (12)n；
Step 900: drawing PCoren-Un，Iexn-UnRelation curve, and K(k)-UnTable of harmonic content.
The foregoing are merely exemplary embodiments of the present invention, which enable those skilled in the art to understand or practice the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (5)

1.一种铁磁元件空载特性的低频测量方法，其特征在于，包括如下步骤：1. a low-frequency measurement method of ferromagnetic element no-load characteristic, is characterized in that, comprises the steps: 步骤一：根据T型等效电路，建立高压侧开路等效电路，其中，所述高压侧开路等效电路为励磁电感L m和涡流等效电阻R e并联后，再与绕组直流电阻R dc和绕组漏感L σ串联形成，磁滞损耗P h包含在励磁电感L m中，在低压侧施加2个频率不同的低频正弦波，计算各频率下的铁心损耗，其中：Step 1: According to the T-type equivalent circuit, establish the high-voltage side open-circuit equivalent circuit, wherein the high-voltage side open-circuit equivalent circuit is that the excitation inductance L m and the eddy current equivalent resistance R e are connected in parallel, and then connected to the winding DC resistance R dc . It is formed in series with the winding leakage inductance L σ , the hysteresis loss P h is included in the excitation inductance L m , and two low-frequency sine waves with different frequencies are applied to the low-voltage side to calculate the core loss at each frequency, where: 根据
Figure 370797DEST_PATH_IMAGE001
计算各频率下的铁心损耗；according to
Figure 370797DEST_PATH_IMAGE001
Calculate the core loss at each frequency; 式中，u(t)是施加在绕组两端的电压，i ex(t)是励磁电流，I ex是其有效值；where u ( t ) is the voltage applied across the winding, i ex ( t ) is the excitation current, and I ex is its effective value; 步骤二：采用插值法计算频率不同、相等E/f时的铁心损耗，计算不同电压下单位周期产生的单位磁滞和涡流损耗We和Wh，并计算折算至工频下的铁心损耗P Coren，其中：Step 2: Use the interpolation method to calculate the core loss at different frequencies and equal E /f, calculate the unit hysteresis and eddy current losses We and W h generated per unit period under different voltages, and calculate the core loss P converted to the power frequency Coren , where: 根据
Figure 404481DEST_PATH_IMAGE002
计算不同电压下单位周期产生的单位磁滞和涡流损耗We和Wh；according to
Figure 404481DEST_PATH_IMAGE002
Calculate the unit hysteresis and eddy current losses We and W h generated per unit cycle at different voltages; 根据
Figure 333123DEST_PATH_IMAGE003
计算折算至工频下的铁心损耗P Coren；according to
Figure 333123DEST_PATH_IMAGE003
Calculate the core loss P Coren converted to the power frequency; 其中，f n 为额定频率，为50Hz或者60Hz， E为感应电动势，f为施加的电源频率；Among them, f n is the rated frequency, which is 50Hz or 60Hz, E is the induced electromotive force, and f is the applied power frequency; 步骤三：根据涡流电流补偿到励磁电流基波分量分折算算法计算折算至工频下的励磁电流I exn、谐波含量K(k )、励磁电压U n，其中：Step 3: Calculate the excitation current I exn , the harmonic content K (k ), and the excitation voltage U n converted to the power frequency according to the eddy current compensation to the fundamental wave component of the excitation current, where: 根据
Figure 124361DEST_PATH_IMAGE004
，
Figure 999913DEST_PATH_IMAGE005
计算折算至工频下的励磁电流I exn；according to
Figure 124361DEST_PATH_IMAGE004
,
Figure 999913DEST_PATH_IMAGE005
Calculate the excitation current I exn converted to the power frequency; 根据
Figure 888104DEST_PATH_IMAGE006
计算折算至工频下的励磁电流K(k )；according to
Figure 888104DEST_PATH_IMAGE006
Calculate the excitation current K (k ) converted to the power frequency; 根据
Figure 722068DEST_PATH_IMAGE007
计算折算至工频下的励磁电压U n；according to
Figure 722068DEST_PATH_IMAGE007
Calculate the excitation voltage U n converted to the power frequency; 其中，
Figure 735023DEST_PATH_IMAGE008
为工频下的励磁电流基波分量，
Figure 414266DEST_PATH_IMAGE009
为低频下的励磁电流基波分量有效值，
Figure 354366DEST_PATH_IMAGE010
为折算到工频下的涡流电流有效值，
Figure 359231DEST_PATH_IMAGE011
为低频下的涡流损耗电流的有效值，
Figure 187379DEST_PATH_IMAGE012
为低频下的涡流电流与励磁电流基波分量之间的相位差，
Figure 404733DEST_PATH_IMAGE013
为工频下励磁电流的第k次谐波有效值，
Figure 470778DEST_PATH_IMAGE014
为低频下励磁电流第k次谐波电流有效值；in,
Figure 735023DEST_PATH_IMAGE008
is the fundamental component of the excitation current at the power frequency,
Figure 414266DEST_PATH_IMAGE009
is the effective value of the fundamental component of the excitation current at low frequencies,
Figure 354366DEST_PATH_IMAGE010
is the effective value of the eddy current converted to the power frequency,
Figure 359231DEST_PATH_IMAGE011
is the effective value of the eddy current loss current at low frequency,
Figure 187379DEST_PATH_IMAGE012
is the phase difference between the eddy current at low frequency and the fundamental component of the excitation current,
Figure 404733DEST_PATH_IMAGE013
is the effective value of the kth harmonic of the excitation current at the power frequency,
Figure 470778DEST_PATH_IMAGE014
is the effective value of the k-th harmonic current of the excitation current at low frequency; 步骤四：根据对折算到工频下的铁损耗和铜损耗来计算空载损耗P n，其中根据
Figure 177703DEST_PATH_IMAGE015
计算空载损耗P n；Step 4: Calculate the no-load loss P n according to the iron loss and copper loss converted to the power frequency, where according to
Figure 177703DEST_PATH_IMAGE015
Calculate the no-load loss P n ; 步骤五：绘制P Coren-U n，I exn-U n关系曲线，以及K(k)-U n谐波含量表格。Step 5: Plot P Coren - U n , I exn - U n relationship curve, and K (k) - U n harmonic content table. 2.根据权利要求1所述的铁磁元件空载特性的低频测量方法，其特征在于，步骤一所述的铁心损耗是保证铁磁元件不同频率下U/f相等，以保证不同频率下的磁通Bm相等条件下的铁心损耗。2. The low-frequency measurement method of ferromagnetic element no-load characteristics according to claim 1, wherein the iron core loss in step 1 is to ensure that U/f is equal under different frequencies of the ferromagnetic element, to ensure that the Core loss under the condition of equal magnetic flux B m . 3.根据权利要求1所述的铁磁元件空载特性的低频测量方法，其特征在于，所述的步骤二所述的We和Wh是根据求解两个频率下的铁心损耗二元一次方程组得到。3. the low-frequency measuring method of ferromagnetic element no-load characteristic according to claim 1, is characterized in that, described in described step 2 We and Wh are according to solving the core loss binary quadratic equation system under two frequencies get. 4.根据权利要求1所述的铁磁元件空载特性的低频测量方法，其特征在于，所述的步骤三所述的涡流电流补偿算法因涡流电流只含基波分量，只将涡流电流补偿到励磁电流的基波分量上。4. The low-frequency measurement method for no-load characteristics of a ferromagnetic element according to claim 1, wherein the eddy current compensation algorithm described in the step 3 only contains the fundamental wave component because the eddy current only compensates the eddy current. to the fundamental component of the excitation current. 5.根据权利要求1所述的一种铁磁元件空载特性的低频测量方法，其特征在于，所述的步骤四所述的铜损耗是根据折算到工频下的励磁电流代入到欧姆定律中计算得到。5. The low-frequency measurement method of the no-load characteristic of a ferromagnetic element according to claim 1, wherein the copper loss described in the step 4 is substituted into Ohm's law according to the excitation current converted to the power frequency calculated in.
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