EFFECT OF TRANSFORMERS ERROR
The decline in production in recent years has led to a decrease in loads in a number of nodes of the power system, as well as a decrease in industrial consumption, which in turn has caused the occurrence of negative errors in automated power control and metering systems (AMR). The reason for this was the occurrence of a negative error in the primary current and voltage sensors, which are used as current and voltage transformers. This work is devoted to the study of the causes of errors and ways to eliminate the underreporting of power consumption in AMR systems.
Error current transformers (current and angle) due to the presence of magnetizing current and are calculated by the formulas [1, 2]:
current error
(one)
where lm  the average length of the magnetic flux in the magnetic circuit, m;
z2 is the resistance of the secondary current branch (impedance of the secondary circuit and the secondary winding), Ohm;
f is the frequency of alternating current, Hz;
Sm  the actual cross section of the magnetic circuit, m2;
j is the loss angle, and a is the phase angle between the secondary emf.
E2 and secondary current I2, deg .;
angular error
(2)
The main influence on the magnitude of the errors of current transformers is their current loading and the resistance value of the secondary circuit. With the reduction of electricity consumption by industrial enterprises, the load on current transformers often does not exceed 5–15%, which leads to a significant increase in errors.
The limiting values of current and angle errors of current transformers for measurements (according to GOST 774689) are given in the table.
Accuracy class 
Primary current,% nominal 
Marginal error 
Secondary load,% nominal, with cos j _{2}= 0.8 

current 
corner 

min 
hail 

0.2 
five

± 0.75

± 30

± 0.9


0.5 
five

± 1.5

± 90

± 2.5

25100 
The results of the calculation of the angular and current errors of current transformers of the type TPOL 600/5, accuracy class 0.5, produced by formulas (1) and (2), are shown in fig. 1 and 2 (thin line  calculated curve, bold line  approximation). The type of the approximating expression and the criterion of agreement between the calculated and approximating curves are shown in the figures.
Fig.
one
Fig.
2
For the ranges of change (1  10% and 10  100%) of the primary current from the nominal value, the mathematical models of the current error of the most common current transformers are:
TPOL10600 / 5
Df [%] = 0.8428 * ln I1  1.9617 for 1 <I1 <10%
Df [%] = 0.0841 * ln I1  0.3919 for 10 <I1 <100%
TLSh102000/5
Df [%] = 0.7227 * ln I1  1.6815 for 1 <I1 <10%
Df [%] = 0.0722 * ln I1  0.3353 for 10 <I1 <100%
TPSHFD10 3000/5
Df [%] = 0.5986 * ln I1  1.2261 for 1 <I1 <10%
Df [%] = 0.0597 * ln I1  0.1111 for 10 <I1 <100%
The values of the primary current I1 of the current transformer in the formulas should be substituted as a percentage of the nominal value.
Investigations of current transformer errors performed at NITSE showed acceptable convergence of theoretical and experimental results. In fig. 3 shows the results of an experimental study of TT type TPLM10200 / 5, accuracy class 0.5.
The results of the study of current errors of various types of current transformers with a primary rated current of 75  600 A made it possible to draw the following conclusions:
Fig.
3
 in the range of variation of the primary current from the nominal value of 1–25%, the current error has a negative sign;
 with an increase in the primary current, the absolute value of the current error decreases;
 experimental studies confirm the correctness of the mathematical model of the current error of the current transformer;
 taking into account the current error of the current transformer in the automated metering system will reduce the unbalance value at substations;
 the amount of electricity supplied to consumers due to the negative current error of current transformers is underestimated in comparison with the actual value; Therefore, taking into account the current error of the current transformer in AMR will allow more accurate assessment of the amount of electricity supplied to consumers and get a certain economic effect, which will be evaluated further.
The second source of error in the measurement of electricity is a voltage transformer.
According to [3, 4], the voltage error is determined as follows: DU = DUн + DUх (3)
where DUn is the voltage error due to the load current,%;
DUx  voltage error due to noload current,%.
Using the vector diagram, it is possible to express with sufficient accuracy the error components of the voltage transformer as follows:
where U2 is the voltage of the secondary winding of the transformer, V;
Ia is the active component of the noload current, reduced to the secondary winding of the transformer, A;
r'1 is the reduced resistance of the primary winding of the transformer, reduced to the secondary winding, Ohm;
I'p  reduced reactive component of the noload current, reduced to the secondary winding of the transformer, A;
x'1  reactance of the primary winding of the transformer, reduced to the secondary winding, Ohm;
I2 is the load current of the transformer, A;
r2 is the resistance of the secondary winding of the transformer, Ohm;
cosj2  load power factor, rel.
unit;
x  inductive resistance of the transformer, Ohm.
The angular error of the voltage transformer is defined as
,
where d'x is the angular error due to the noload current;
d'n is the angular error due to the load current.
The components of the angular error are defined as
;
The results of the calculation of the voltage transformer errors are shown in fig. 4 and 5. The magnitude of the secondary load I2 has the main influence on the error of the voltage transformer.
Fig.
four
Fig.
five
The dependence of the error of the voltage transformer on the load factor for power (the ratio of the actual load of the secondary winding of the voltage transformer to the nominal value of the load) is
DU [%] =  0.73 * Cs + 0.35,
where Cs is the voltage transformer loading on the secondary winding, rel.
units
The obtained expressions for the errors of current transformers and voltage transformers allow to increase the accuracy of electricity metering at substations.
The effectiveness of the introduction of AMR in substations depends
 from the cost of the introduction of AMR;
 from the economic effect obtained as a result of implementation.
At present, the accounting of sold electricity and the calculation of the energy balance at most substations is carried out using electromagnetic meters without taking into account the errors of current transformers and voltage transformers.
Frequently, voltage transformers operate when the secondary winding is loaded several times more than the nominal, that is, with a negative error. A large part of the load of the voltage transformer consists of measuring instruments connected to them, in particular, electromagnetic active energy meters. For example, induction meters of the type SAZUI670M, whose power consumption is 4 watts, are installed at the Sverdlovskaya substation. As a result of the introduction of automated metering systems, induction meters will be replaced by electronic ones, such as a frequency alarm system, the power consumption of which is two times less  2 watts.
In this case, the load factor of the voltage transformer is halved to a value of 1.1 and, therefore, the error of the voltage transformer is reduced from 1.15% to 0.5%. Reducing the error of the voltage transformer will lead to an increase in the accuracy of metering of electricity supplied to consumers.
Accounting for current errors of current transformers and voltage in the system of automated system of commercial accounting of power consumption gives an economic effect. To assess the economic effect of the introduction of AMR, an estimated calculation was made of the annual electricity consumption at the Sverdlovskaya substation, taking into account the errors of current and voltage transformers. The calculation was made as follows:
 According to the available data for the characteristic winter and summer days of the year (1997 and 1998), the hourly active power values were calculated (taking into account the errors of the current and voltage transformers) by input and outgoing lines using the formula
Rfact = P * KI * KU,
where P is the average hourly power values, determined by the readings of electricity meters;
KI  coefficient taking into account the current error of the current transformer, KU  coefficient taking into account the error of the voltage transformer.KI = 1  (Df _{I}/ 100), KU = 1  (Df _{U}/ 100),
where Df _{I}is the current error of the current transformer, Df _{U}is the error of the voltage transformer.  Determined the power consumption for the characteristic winter and summer days taking into account the errors of the current and voltage transformers (Wc. Fact and Wl. Fact) and without taking into account the errors (Wc and Wl) on the input and outgoing lines:
Wz. Fact = S pfaktz,
W lact = S Rfact. L,
W3 = S P3,
Wl = S Rl.  Calculated the value of the annual consumption of active electricity input and outgoing lines by the formulas
W.act = Wc. Fact * Nc + W. Fact * Nl,
Wg = Wc * Nz + Wl * Nl,
where N3 = 213 and NL = 152 is the number of winter and summer days per year.  The effect of the introduction of AMR is determined by the formula DW = SWg. Fact  SWg,
where SWg. fact and SWg  annual electricity consumption by outgoing feeders with and without errors of current and voltage transformers, respectively.
We will estimate the economic effect for two options.
 When taking into account the automated metering system of current transformer current errors and reducing voltage transformer errors due to the reduced energy consumption of electronic meters, the effect will be:
according to 1997 data
DW = 331021094326683013 = 4338081 kW * h / year;according to 1998 data
DW = 294647641290512594 = 4135047 kWh / year.In monetary terms, the economic effect (E) is equal (when the cost of electricity is 0.4 rub / kW * h)
E = 1735 ... 1650 thousand rubles per year.  Taking into account only the reduction in the errors of voltage transformers due to the reduced energy consumption of electronic meters, the effect will be:
according to 1997 data
DW = 328316428326683013 = 1633415 kW * h / year;according to 1998 data
DW = 292196976290512594 = 1684382 kWh / year.In monetary terms, the economic effect is equal (when the cost of electricity is 0.4 rubles / kWh)
E = 653 ... 674 thousand rubles per year.
In conclusion, we can draw the following conclusions:
 reduction of loads in a number of nodes of the power system, as well as a decrease in electricity consumption by the industry led to the occurrence of negative errors in current transformers and, accordingly, to a commercial undercount of energy consumed;
 to eliminate the undercount of electricity consumption, it is necessary to introduce correction factors;
 taking into account the errors of current transformers in the ASCAE, as well as reducing the errors of the voltage transformer due to the introduction of new electronic meters lead to a significant economic effect.
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