Current error. Phase displacement and accuracy class

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2 Introduction Current transformer is an instrument transformer in which the secondary current, in normal conditions of use, is substantially proportional to the primary current and differs in phase from it by an angle which is approximately zero for an appropriate direction of the connections.

3 Current error The error which a transformer introduces into the measurement of a current arises from the fact that the actual transformation ratio is not equal to the rated transformation ratio. The higher the exciting current or core loss the larger the error. The current error expressed in percent is given by the formula: Phase displacement and accuracy class Phase displacement = The difference in phase between the primary and secondary current vectors, the direction of the vectors being so chosen that the angle is zero for a perfect transformer. Accuracy class = A designation assigned to a current transformer the error of which (Current error, phase displacement, composite error) remain with specified limits under prescribed conditions of use. Burden Burden = The impedance of the secondary circuit in ohms and power factor. The burden is usually expressed as the apparent power (S) in volt-amperes absorbed at a specified power-factor at the rated secondary current.

4 Secondary winding impedance (internal burden) Z s Secondary load impedance Z 0 The secondary load S = V 0 I s (cos φ = 0.8 ind for example) As a matter of safety, the secondary circuits of a current transformer should never be opened under load, because these would then be no secondary mmf to oppose the primary mmf, and all the primary current would become exciting current and thus might induce a very high voltage in the secondary. Rated thermal and dynamic currents Rated short-time thermal current = The r.m.s. value of the primary current which a transformer will withstand for one second without suffering harmful effects, the secondary winding being short-circuited. Rated continuous thermal current = The value of the current which can be permitted to flow continuously in the primary winding, the secondary winding being connected to the rated burden, without the temperature rise exceeding the values specified. Rated dynamic current = The peak value of the primary current which a transformer will withstand without damaged electrically or mechanically by the resulting electromagnetic forces, the secondary winding being short-circuited.

5 General Measuring current transformer = A current transformer intended to supply indicating instruments, integrating meters and similar apparatus. Definitions Composite error = Under steady-state conditions, the r.m.s value of the difference between: a) the instantaneous values of the primary current

6 b) the instantaneous values of the actual secondary current multiplied by the rated transformation ratio. The composite error ε c is generally expressed as a percentage of the r.m.s. values of the primary current according to the formula: K n = rated transformation ratio I p = r.m.s. value of the primary current i p = instantaneous value of the primary current i s = instantaneous value of the secondary current T= duration of one cycle Rated instrument limit primary current = The value of the minimum primary current at which the composite error of the measuring current transformer is equal to or greater than 10%, the secondary burden being equal to the rated burden Instrument security factor = The ratio of rated instrument limit primary current to the rated primary current. Accuracy requirements For measuring current transformers the accuracy class is designated by the highest permissible percentage current error at rated current prescribed for the accuracy class concerned. The standard accuracy classes for measuring current transformers are: 0,1-0,2-0,

7 Accuracy class +/- Percentage current error at percentage of rated current +/- Phase displacement at percentage of rated current shown below shown below Minutes Centiradians ,1 0,4 0,2 0,1 0, ,45 0,24 0,15 0,15 0,2 0,75 0,35 0,2 0, ,9 0,45 0,3 0,3 0,5 1,5 1,5 0,5 0, ,7 1,35 0,9 0,9 1 3,0 3,0 1,0 1, ,4 2,7 1,8 1,8 Class +/- Percentage current error at percentage of rated current shown below [SFS 2874:E] Marking The rating plate shall carry the appropriate information in accordance general marking. The accuracy class and instrument security factor shall be indicated following the indication of corresponding rated output (e.g. 15 VA Class 0,5 F s 10). F s = instrument security factor Current transformers having an extended current rating shall have this rating indicated immediately following the class designation (e.g. 15 VA Class 0,5 ext. 150%).

8 General Protective current transformer = A current transformer intended to supply protective relays. Definitions Composite error = Under steady-state conditions, the r.m.s value of the difference between: a) the instantaneous values of the primary current

9 b) the instantaneous values of the actual secondary current multiplied by the rated transformation ratio. The composite error ε c is generally expressed as a percentage of the r.m.s. values of the primary current according to the formula: K n = rated transformation ratio I p = r.m.s. value of the primary current i p = instantaneous value of the primary current i s = instantaneous value of the secondary current T= duration of one cycle Rated accuracy limit primary current = The value of primary current up to which the transformer will comply with the requirements for composite error. Accuracy limit factor = The ratio of the rated accuracy limit primary current to the rated primary current. Secondary limiting e.m.f = The product of the accuracy limit factor, the rated secondary current and the vectorial sum of the rated burden and the impedance of the secondary winding. Accuracy requirements For protective current transformers the accuracy class is designated by the highest permissible percentage composite error at the rated accuracy limit primary current prescribed for the accuracy class concerned, followed by the letter "P" (meaning protection) at ratecurrent prescribed for the accuracy class concerned. The standard accuracy classes for protective current transformers are: 5 P and 10 P

10 Accuracy class Percentage current error at primary current in % Phase displacement at rated primary current Minutes 5 P +/- 1 +/- 60 +/- 1, P +/ Composite error at rated accuracy limit primary current in % Centiradians Marking The rating plate shall carry the appropriate information in accordance general marking. The rated accuracy limit factor shall be indicated following the corresponding output and accuracy class (e.g. 30 VA Class 5 P 10). 10 = Accuracy limit factor A current transformer satisfying the requirements of several combinations of output and accuracy class and accuracy class limit factor may be marked according to all of them. 15 VA Class 0,5 or 15 VA Class 0,5 30 VA Class 1 15 VA Class 1 ext 150% 30 VA Class 5 P VA Class 5 P 20

11 Standard values of rated currents and outputs The standard values of rated primary current are: 10-12, amperes And their decimal multiples of fractions. The preferred values are those underlined. The standard values of rated secondary current are: 1,2 and 5 amperes, but the preferred value is 5A. The standard values of rated output up to 30 VA are: 2,5-5, and 30 VA. Value above 30 VA may be selected to suit the application. (Recommended values: 45,60 VA)

12 Short-time current ratings Current transformer supplied with a fixed primary winding of conductor shall comply with the requirements of rating below. Thermal rating = A rated short-time thermal current shall be assigned to the transformer. Dynamic rating = The values of the rated dynamic current shall normally be 2,5 times the rated short-time thermal current and it shall be indicated on the rating plate when it is different from this value. Limits of temperature rise The temperature rise of a current transformer when carrying a primary current equal to the rated continuous thermal current, with a unity power-factor burden corresponding to the rated output, shall not exceed the appropriate value given in the table below. Class of insulation (in accordance with IEC Publication 85) All classes immersed in oil 60 All classes immersed in oil and hermetically sealed 65 All classes immersed in bituminous compound 50 Classes not immersed in oil or bituminous compound Y 45 A 60 E 75 B 85 F 110 H 135 Maximum temperature rise 0 C Terminal markings - general rules The terminal markings shall identify: the primary and secondary windings; the winding sections, if any; the relative polarities of windings and winding sections; the intermediate tapings, if any.

13 [SFS 2874:E] Graphic symbols of current transformers current transformer: one output at the secondary two alternative symbols two coils with the same core double core current transformer

14 Introduction In current transformer design, the core characteristics must be carefully selected because excitation current I e essentially subtracts from the metered current and affects the ratio and phase angle of the output current.

15 The higher the exciting current or core loss the larger the error Measuring current transformer Measuring or protective current transformers? Permeability of the core material high and core loss low => exciting current small (I fe<<) => current error small. The exciting current determines the maximum accuracy that can be achieved with a current transformer => Study accuracy classes Protective current transformer Permeability of the core material is low => When remanence is reduced to a lower level (increase the useful flux density, gapping), the voltage spikes produced by the leakage inductance due to the transformer saturation will be eliminated. In linear current transformers there are generally air gaps in the iron core to reduce the time constant and remanence. Such current transformers are used only to protect objects of major importance that require a short tripping time. Selecting core material When choosing a core material a reasonable value for B m (0,2... 0,3 T) typically results in L c and R fe values large enough to reduce the current flowing in these elements so as to satisfy the ratio and phase requirements. Window utilization factor The window utilization factor (K u = S 1 x S 2 x S 3 x S 4 ) is the amount of copper that appears in the window area or transformer of inductor. The window utilization factor is influenced by four different factors: (1) wire insulation, (2) wire lay (fill factor), (3) bobbin area and (4) insulation required for multilayer windings or between windings. In the design of high-current of low-current transformers, the ratio of conductor area over total wire area can vary from 0,941 to 0,673 depending on the wire size. The wire lay or fill factor can vary from 0,7 to 0,5, depending on the winding technique. The amount and the type of insulation are dependent on the voltage. [McLyman.]

16 A transformer intended to supply measuring instruments, meters, relays and other similar apparatus Effect of Gapping [McLyman.] Air gap increases the effective length of the magnetic path

17 Air-gapped current transformers These are auxiliary current transformers in which a small air gap is included in the core to produce a secondary voltage output proportional in magnitude to current in the primary winding. Sometimes termed transactors or quadrature current transformers, this form of current transformer has been used as an auxiliary component of unit protection schemes in which the outputs into multiple secondary circuits must remain linear for and proportioned to the widest practical range of input currents. [Protective Relays Application Guide.] Anti-remanence current transformers A variation in the overdimensioned class of current transformer has small gap(s) in the core magnetic circuit, thus reducing the possible remanent flux from approximately 90% of saturation value to some 10% only. These gap(s) are quite small, for example 0.12mm total, and so within the core saturation limits. Errors in current transformation are thereby significantly reduced when compared with those with the gapless type of core. [Protective Relays Application Guide.] Linear current transformers The linear current transformer constitutes an even more radial departure from the normal solid core CT in that it incorporates an appreciable air cap, for example mm. As its name implies the magnetic behaviour tends to linearization by the inclusion of this gap in the magnetic circuit. However, the purpose of introducing more reluctance into the magnetic circuit is to reduce the value of magnetizing reactance, this in turn reduces the secondary time-constant of the CT thereby reducing the overdimensioning factor necessary for faithful transformation. [Protective Relays Application Guide.] The time constant of the circuit depends on the inductance of the coil and on the resistance in the circuit in accordance to the following simple formula: