Distribution transformer harmonic loss calculation method
By calculating hysteresis loss, eddy current loss, resistance loss, harmonic loss and stray loss, and adding them, the problem of poor calculation accuracy of the distribution transformer harmonic loss in the prior art is solved, and high-precision loss calculation is realized in a non-sine grid environment.
Patent Information
- Application Number
- CN202411663284.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-20
- Publication Date
- 2025-03-07
Smart Images
Figure CN119575251A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a method for calculating harmonic losses in an electric power system. Background Art
[0002] With the continuous expansion of the scale of power systems and the continuous increase of nonlinear devices such as various high-power switchgear, frequency converters and AC arc welders in power systems, a large number of high-order harmonics are contained in the power network, causing a large degree of distortion of voltage and current waveforms, and the "harmonic pollution" of the power system is becoming more and more serious. In the case of harmonics, transformer losses can no longer be ignored; and in the existing distribution transformer harmonic loss method, it is unable to adapt to the non-sinusoidal power grid environment, resulting in poor accuracy of the distribution transformer harmonic loss calculation results. Summary of the invention
[0003] The purpose of the present invention is to solve the problem of poor accuracy of calculation results of existing distribution transformer harmonic loss methods, and propose a distribution transformer harmonic loss calculation method.
[0004] A method for calculating harmonic losses of a distribution transformer according to the present invention comprises the following steps:
[0005] Calculate the hysteresis loss of the distribution transformer and the eddy current loss of the distribution transformer to obtain the harmonic iron loss;
[0006] Calculate the resistance loss of the distribution transformer winding, the harmonic loss of the distribution transformer winding and the stray loss of the distribution transformer; obtain the harmonic copper loss;
[0007] Add the harmonic iron loss and the harmonic copper loss to get the harmonic loss of the distribution transformer.
[0008] Furthermore, the calculation formula for the hysteresis loss of the distribution transformer is:
[0009]
[0010] Among them, P H is the hysteresis loss of the distribution transformer; C1 is the characteristic constant of the silicon steel sheet material in the distribution transformer; V is the volume of the ferromagnetic material in the distribution transformer; f is the fundamental frequency; B m is the maximum magnetic density of the ferromagnetic material in the distribution transformer.
[0011] Furthermore, the eddy current loss calculation formula of the distribution transformer is:
[0012]
[0013] Among them, P Wis the eddy current loss of the distribution transformer; P1 is the eddy current loss generated by the first harmonic; P2 is the eddy current loss generated by the second harmonic; P3 is the eddy current loss generated by the third harmonic; P h Indicates the eddy current loss generated by the hth harmonic; U h represents the hth harmonic voltage; U1 is the fundamental voltage; C eh is the immersion depth of electromagnetic waves.
[0014] Furthermore, the electromagnetic wave is injected into the depth C eh The calculation formula is:
[0015]
[0016] Among them, ξ is the intermediate variable of the electromagnetic wave input depth, Δ is the core thickness of the distribution transformer; u is the core permeability of the distribution transformer; γ is the core conductivity of the distribution transformer; f is the fundamental frequency.
[0017] Furthermore, the harmonic copper loss calculation formula is:
[0018] P LL =P R +F HL-EC ·P EC-O +F HL-OSL ·P OSL-O
[0019] Among them, P LL is the harmonic copper loss; P R is the resistance loss of the distribution transformer winding; P EC-O is the harmonic loss of the distribution transformer winding; F HL-EC is the eddy current harmonic loss factor; P OSL-O is the stray loss of the distribution transformer; F HL-OSL is the stray harmonic loss factor of the distribution transformer.
[0020] Furthermore, the calculation formulas for the eddy current harmonic loss factor and the stray harmonic loss factor are:
[0021]
[0022] Where h represents the harmonic order; I1 represents the fundamental current; I h Represents the hth harmonic current.
[0023] Furthermore, the calculation formula for the resistance loss of the distribution transformer winding is:
[0024]
[0025] Among them, P Ris the resistance loss of the distribution transformer winding; I 1-R is the primary rated current value; I 2-R is the secondary rated current value; R1 is the fundamental resistance of the primary winding; R2 is the fundamental resistance of the secondary winding; K is the type constant of the distribution transformer. When the distribution transformer is a single-phase transformer, K is 1; when the distribution transformer is a three-phase transformer, K is 1.5.
[0026] Compared with the prior art, the present invention has the following beneficial effects:
[0027] The method for calculating the harmonic loss of a distribution transformer described in the present invention can well adapt to a non-sinusoidal power grid environment. Even if the power grid contains a large amount of harmonics, the method can accurately measure the power consumption values of linear and nonlinear users. According to the method for calculating the harmonic loss of a distribution transformer described in the present invention, the harmonic loss of the distribution transformer is calculated, and an eddy current harmonic loss factor and a stray harmonic loss factor of the distribution transformer are introduced, thereby improving the accuracy of the calculation result. BRIEF DESCRIPTION OF THE DRAWINGS
[0028] Figure 1 This is a flowchart of a method for calculating harmonic losses of a distribution transformer described in a specific implementation method 1. DETAILED DESCRIPTION
[0029] Specific implementation method 1. Combination Figure 1 To illustrate this embodiment, a method for calculating harmonic loss of a distribution transformer described in this embodiment includes the following steps:
[0030] Calculate the hysteresis loss of the distribution transformer and the eddy current loss of the distribution transformer to obtain the harmonic iron loss;
[0031] Calculate the resistance loss of the distribution transformer winding, the harmonic loss of the distribution transformer winding and the stray loss of the distribution transformer; obtain the harmonic copper loss;
[0032] Add the harmonic iron loss and the harmonic copper loss to get the harmonic loss of the distribution transformer.
[0033] In this embodiment, the transformer loss is divided into two parts: no-load loss and load loss; no-load loss is also called harmonic iron loss, which mainly includes the hysteresis loss of the distribution transformer and the eddy current loss of the distribution transformer and has nothing to do with the load; therefore, the harmonic iron loss is equal to the sum of the hysteresis loss of the distribution transformer and the eddy current loss of the distribution transformer; load loss is also called harmonic copper loss, which includes the resistance loss of the distribution transformer winding, the harmonic loss of the distribution transformer winding and the stray loss of the distribution transformer; in the harmonic case, the harmonic iron loss is mainly affected by the harmonic voltage, and the harmonic copper loss is mainly affected by the harmonic current.
[0034] Specific implementation method 2: This implementation method further limits the method for calculating the harmonic loss of a distribution transformer described in specific implementation method 1. In this implementation method, the hysteresis loss calculation formula of the distribution transformer is:
[0035]
[0036] Among them, P H is the hysteresis loss of the distribution transformer; C1 is the characteristic constant of the silicon steel sheet material in the distribution transformer; V is the volume of the ferromagnetic material in the distribution transformer; f is the fundamental frequency; B m is the maximum magnetic density of the ferromagnetic material in the distribution transformer.
[0037] Combined with the common use of distribution transformers, the S11-50 / 10 distribution transformer is selected, and the transformer connection group number is: Dyn11. The nameplate parameters of the selected distribution transformer are shown in the following table.
[0038] Table 1 Line and transformer parameters
[0039]
[0040]
[0041] In this embodiment, the hysteresis phenomenon of the ferromagnetic material produces hysteresis loss, and the magnitude of the hysteresis loss is related to the maximum magnetic flux density B. m In addition, due to the magnetization process, an alternating magnetic field is required, so the magnitude of the hysteresis loss is also affected by the frequency. When the system contains harmonics, the higher the harmonic voltage content, the greater the hysteresis loss. The relationship between harmonic voltage and hysteresis loss can be expressed as:
[0042]
[0043] Where P h Indicates the eddy current loss generated by the hth harmonic; U h represents the hth harmonic voltage; U1 represents the fundamental voltage; φ h represents the initial phase angle of the hth harmonic voltage; S represents the ferromagnetic material coefficient.
[0044] Specific implementation method three: This implementation method further limits the method for calculating the harmonic loss of a distribution transformer described in specific implementation method one. In this implementation method, the eddy current loss calculation formula of the distribution transformer is:
[0045]
[0046] Among them, P Wis the eddy current loss of the distribution transformer; P1 is the eddy current loss generated by the first harmonic; P2 is the eddy current loss generated by the second harmonic; P3 is the eddy current loss generated by the third harmonic; P h Indicates the eddy current loss generated by the hth harmonic; U h represents the hth harmonic voltage; U1 is the fundamental voltage; C eh is the immersion depth of electromagnetic waves.
[0047] In this embodiment, when harmonics are present, the eddy current loss of the transformer will also increase as the harmonic voltage increases.
[0048] Specific implementation method 4: This implementation method further limits the method for calculating harmonic loss of a distribution transformer described in specific implementation method 3. In this implementation method, the electromagnetic wave input depth C eh The calculation formula is:
[0049]
[0050] Among them, ξ is the intermediate variable of the electromagnetic wave input depth, Δ is the core thickness of the distribution transformer; u is the core permeability of the distribution transformer; γ is the core conductivity of the distribution transformer; f is the fundamental frequency.
[0051] In this embodiment, the core thickness Δ of the distribution transformer, the core permeability u of the distribution transformer, the core conductivity γ of the distribution transformer, and the fundamental frequency f can all be obtained through the factory parameters of the distribution transformer or in the test report.
[0052] Specific implementation method 5: This implementation method further limits the method for calculating harmonic loss of a distribution transformer described in specific implementation method 1. In this implementation method, the harmonic copper loss calculation formula is:
[0053] P LL =P R +F HL-EC ·P EC-O +F HL-OSL ·P OSL-O
[0054] Among them, P LL is the harmonic copper loss; P R is the resistance loss of the distribution transformer winding; P EC-O is the harmonic loss of the distribution transformer winding; F HL-EC is the eddy current harmonic loss factor; P OSL-O is the stray loss of the distribution transformer; F HL-OSL is the stray harmonic loss factor of the distribution transformer.
[0055] In this embodiment, the harmonic copper loss is the load loss of the transformer; the load loss of the transformer includes two parts: winding resistance loss and total stray loss; the total stray loss is caused by eddy current, and can be divided into winding eddy current loss generated in the transformer winding coil and other stray losses generated in the iron core, clamps and other parts according to their distribution positions. By introducing the harmonic loss factor and the stray harmonic loss factor of the distribution transformer, the test data under the harmonic background is given; the specific values of the harmonic loss of the distribution transformer winding and the stray loss of the distribution transformer are obtained by the actual measurement of the current amplitude by the electric meter.
[0056] Specific implementation method 6: This implementation method further limits the method for calculating the harmonic loss of a distribution transformer described in specific implementation method 5. In this implementation method, the calculation formulas for the eddy current harmonic loss factor and the stray harmonic loss factor are:
[0057]
[0058] Where h represents the harmonic order; I1 represents the fundamental current; I h Represents the hth harmonic current.
[0059] In this embodiment, the eddy current harmonic loss factor and the stray harmonic loss factor are used to correct the rated loss.
[0060] Specific implementation method 7: This implementation method further limits the method for calculating the harmonic loss of a distribution transformer described in specific implementation method 1 or 5. In this implementation method, the calculation formula for the resistance loss of the distribution transformer winding is:
[0061]
[0062] Among them, P R is the resistance loss of the distribution transformer winding; I 1-R is the primary rated current value; I 2-R is the secondary rated current value; R1 is the fundamental resistance of the primary winding; R2 is the fundamental resistance of the secondary winding; K is the type constant of the distribution transformer. When the distribution transformer is a single-phase transformer, K is 1; when the distribution transformer is a three-phase transformer, K is 1.5.
[0063] In this embodiment, the primary rated current of the distribution transformer is used as the line fundamental current, and the secondary rated current is used as the transformer fundamental current. The additional copper loss value of the distribution transformer under different harmonic orders and different content rates is calculated, and the calculation results are shown in Table 2.
[0064] Table 2 Additional loss values of transformers under different harmonic content rates
[0065]
[0066] In actual projects, the data measured by the harmonic measurement device are mostly the content rate of each harmonic (that is, the ratio of each harmonic current to the fundamental current), so the following transformation is made:
[0067]
[0068] Among them, I R is the fundamental current flowing through the transformer winding; I is the harmonic current;
[0069] Rated harmonic loss P EC-R and rated other stray losses P OSL-R The proportion of the total stray loss remains basically unchanged. The standard determines the proportion of the two losses through a large amount of test data; for oil-immersed transformers, the proportions are 33% and 67%, respectively, and for dry-type transformers, the opposite is true. In summary, the total loss of the distribution transformer considering harmonics is:
[0070]
[0071] This method not only takes the skin effect into account, but also takes eddy current and hysteresis losses into account, and the calculation is more comprehensive; in addition, the calculation is mainly combined with actual measurement data, and the harmonic loss factor is introduced, so the result is more accurate.
[0072] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.
Claims
1. A method for calculating harmonic loss of a distribution transformer, characterized in that: The following steps are involved: Calculate the hysteresis loss of the distribution transformer and the eddy current loss of the distribution transformer to obtain the harmonic iron loss; Calculate the resistance loss of the distribution transformer winding, the harmonic loss of the distribution transformer winding and the stray loss of the distribution transformer to obtain the harmonic copper loss; Add the harmonic iron loss and the harmonic copper loss to get the harmonic loss of the distribution transformer.
2. A method for calculating harmonic loss of a distribution transformer according to claim 1, characterized in that: The calculation formula of the hysteresis loss of the distribution transformer is: Among them, P H is the hysteresis loss of the distribution transformer; C1 is the characteristic constant of the silicon steel sheet material in the distribution transformer; V is the volume of the ferromagnetic material in the distribution transformer; f is the fundamental frequency; B m is the maximum magnetic density of the ferromagnetic material in the distribution transformer.
3. A method for calculating harmonic loss of a distribution transformer according to claim 1, characterized in that: The calculation formula of the eddy current loss of the distribution transformer is: Among them, P W is the eddy current loss of the distribution transformer; P1 is the eddy current loss generated by the first harmonic; P2 is the eddy current loss generated by the second harmonic; P3 is the eddy current loss generated by the third harmonic; P h Indicates the eddy current loss generated by the hth harmonic; U h Indicates the hth harmonic voltage; U1 is the fundamental voltage; C eh is the immersion depth of electromagnetic waves.
4. A method for calculating harmonic loss of a distribution transformer according to claim 3, characterized in that: The electromagnetic wave is injected into the depth C eh The calculation formula is: Among them, ξ is the intermediate variable of the electromagnetic wave input depth, Δ is the core thickness of the distribution transformer; u is the core permeability of the distribution transformer; γ is the core conductivity of the distribution transformer; f is the fundamental frequency.
5. A method for calculating harmonic loss of a distribution transformer according to claim 1, characterized in that: The harmonic copper loss calculation formula is: P LL =P R +F HL-EC ·P EC-O +F HL-OSL ·P OSL-O Among them, P LL is the harmonic copper loss; P R is the resistance loss of the distribution transformer winding; P EC-O is the harmonic loss of the distribution transformer winding; F HL-EC is the eddy current harmonic loss factor; P OSL-O is the stray loss of the distribution transformer; F HL-OSL is the stray harmonic loss factor of the distribution transformer.
6. A method for calculating harmonic loss of a distribution transformer according to claim 5, characterized in that: The calculation formulas for the eddy current harmonic loss factor and the stray harmonic loss factor are: Where h represents the harmonic order; I1 represents the fundamental current; I h Represents the hth harmonic current.
7. A method for calculating harmonic loss of a distribution transformer according to claim 1 or 5, characterized in that: The calculation formula for the resistance loss of the distribution transformer winding is: Among them, P R is the resistance loss of the distribution transformer winding; I 1-R is the primary rated current value; I 2-R is the secondary rated current value; R1 is the fundamental resistance of the primary winding; R2 is the fundamental resistance of the secondary winding; K is the type constant of the distribution transformer. When the distribution transformer is a single-phase transformer, K is 1; when the distribution transformer is a three-phase transformer, K is 1.5.