Cand. tech. sci
Kostinskiy S.S., the master Vasil'eva C.V.
Federal
state budget educational institution of higher professional education
"Platov
South-Russian State Polytechnic University (Novocherkassky polytechnic institute),
the Russian Federation
Way of definition of losses of active
electric energy in the transformer, based on the control of
temperature without current measurement in windings
The provisions. The expressions are resulted, allowing
to spend an estimation of losses for a non-uniform operating mode of the
transformer on the basis of the decision of the differential equation of
thermal balance with definition of separate parametres of the transformer on
its rating data. An experimental research of the received expression with
application of exact gauges 0,6 % not exceeding on the average have shown a
sufficient applicable error of definition of losses on the temperature
measurements. The function chart of the counter of losses is resulted and the
reference to the registered computer program using the received expression is
given.
Key words: power savings,
the counter of
losses, technical losses of the electric power,
the transformer,
òon-uniform
load pattern,
losses of active electric energy, heat account differential
equation, thermal time constant of the transformer, losses of idling of the
transformer, losses of short circuit of the transformer.
Now
the problem of an energy conservation and increase of power efficiency from the
branch has turned to the state. The energy conservation is the directed complex
of the measures which main objective is reduction of volume of the energy consumed
from external sources [1]. The municipal loadings which are, as a
rule, single-phase and leading stray load losses, arising owing to a deviation
of merit numbers of the electric power from standard meanings have considerably
increased [2]. The electric
energy lost in the transformer in the course of transformation of an
alternating current, is allocated in the form of heat in windings, magnetic
system and other parts of the transformer [3].
At real loadings transformer loading changes, owing to
what the size of losses changes. In this connection at definition of losses of
the electric power it is necessary to find power loss in the transformer on
each i-th time interval dt. For each element of a design under
the formula resulted in [4]:
, (1)
where Θi+1 – temperature
of a separate device of the transformer in the end of an interval dt.
Θi – temperature of a separate device of the
transformer;
T – the transformer heating time constant;
ΔPn – total nominal losses
of active power in the transformer
Θ∞n – the erected temperature of the
transformer in the nominal condition.
Total losses of active power in the transformer in
time dt develop of losses in each n-th element of the
transformer:
.
Losses of electric energy in time dt:
.
For the purpose of inspection of working capacity of
the expression (1) adapted for the dry transformer, experiment on the
single-phase dry transformer with use of the measuring equipment, passed
metrological checking has been made. Temperature sensor of the transformer have
been fixed on magnetic system and a winding, the sensor for measurement of an
ambient temperature near to the transformer also has been provided.
By means of the block of active and inductive loading
for the transformer with nominal power 500 ÂÀ the load
pattern shown in figure 1 has been set. At the moment of a minimum total power made 80 ÂÀ, at the moment of a maximum 440 ÂÀ.
Fig. 1. Transformer load pattern at experiment
carrying out at a variable load pattern: 1 – the curve of total
power; 2 – the curve of active power
The chart of change of the calculated and measured
losses of active power in the transformer during the measurement period is
shown in figure 2.
Fig. 2. The chart of change of losses of active power in the
transformer during the measurement period: 1 – the measured values;
2 – the calculated values; 3 – approximation of the
measured values by a polynom of 7-th order;
4 – approximation of the calculated values by a polynom of 7-th order
The chart of an error of calculation of losses of the
active electric power in the transformer under the formula (1) in comparison
with the valid (measured) losses is resulted in figure 3.
Fig. 3. The chart of an error of calculation of losses of the
active electric power in the transformer from time: 1 – the
calculated values; 2 – approximation of the calculated values by a
polynom of 7-th order
Average value of quantity of an error of calculation
of losses of the active electric power in the transformer during measurement
has made – 0,6 %.
Electric power meter of losses of the active electric
power are applied to definition of losses for example [5] which principle of
work is based on the Joule's law. A lack of such electric power meter is that
they define energy of losses in transformer windings, but losses also include
losses in magnetic system, a tank, and as losses from asymmetry and
nonsinusoidal a current. For the account of losses also it is necessary to know
resistance of object on which measurement which changes depending on heating
and environment temperature are made. Told all above leads to decrease in
accuracy of measurement of losses of electric energy.
With the account above the resulted equation (1) and
for elimination specified above lacks more low in figure 4 the function chart
of the developed counter of losses is resulted.
Fig. 4. Function chart of the developed
device for realisation of a way of definition of losses in the transformer,
based on temperature measurement at a non-uniform load pattern: 1, 16 - the analogue-digital converter; 2, 3, 22, 23
- the one-vibrator, 4, 29, 30 - the division block; 5 - the generator of
rectangular impulses; 6 - the timer; 7 - timers-hours; 8 - the counter; 9 - the
indicator; 10 - a reprogrammed memory; 11 - the transceiver; 12 - the computer;
13 - the accumulating adder; 14, 15 - the temperature sensor; 17, 18, 19, 20 -
the subtracter; 21 - the block of subtraction from unit; 24, 25 - the memory
register; 26, 27, 28 - the multiplier; 31 - the adder; 32 - the block of the
task of parametres of the transformer; 33 - the erection block in negative
degree of the basis of the natural logarithm
As for calculation of losses by the developed method
the program for calculation of losses of the active electric power on the basis
of the control of temperature of dry power transformers is written and
registered at a non-uniform load
pattern [6].
Deductions.
1. The essence of an offered way of
definition of losses of the active electric power at a non-uniform load pattern consists in the single-phase transformer
that the temperature
of magnetic system is measured, a winding and environment and through intervals
of time of measurement an equal on two, three order less than a thermal
constant of time of the transformer, is calculated increments of temperatures
of magnetic system and a winding, differences between temperatures of the
magnetic environment, a winding and environment are defined. Losses of the
active electric power in the transformer are calculated under the formula (1).
2. At a non-uniform production schedule it is
expedient to count electric power losses in each element of a design of the
transformer separately taking into account the settlement established
temperature for each mode of loading of the transformer and invariable design
data of its elements. Such decision considers losses in windings, in magnetic
system, from the higher harmonics of a current and voltage, from asymmetry of
loading.
3. In the offered device (the counter of losses
of the active electric power in the transformer) is carried out definition of
losses of the active electric energy lost in the transformer for intervals of
time of equal on two, three order less of a thermal constant of time, and
allocated in the form of heat that allows to solve a task in view, at use of
the first 14 and the second 15 gauges of temperature which take transformer and
environment temperature and the parametres of the transformer received in a
nominal mode of its work, necessary for calculation.
4. The formula
(1) allows to consider all losses of the active electric power allocated in the
transformer in the form of heat at a non-uniform load pattern . Average value
of size of an error of calculation under the formula (1) during experiment has
made 0,6 %.
The
literature:
1. Vorotnitskiy V.E., Kalinkina M.A.,
Komkova E.V., Pyatigor V.I. [Decrease
in losses of the electric power in electric networks].
Energosberezhenie, 2005, no.2, pp. 2 – 6.
2. Troitskiy A.I., Kostinskiy S.S.,
Khimishev T.Z. [Definition of additional
losses depending on quality of electrical energy for an apartment house
on the basis of experimental data]. Izvestiya vysshikh uchebnykh zavedeniy. Elektromekhanika [Russian
Electromechanics], 2014, no.3, pp. 48 – 51.
3. Ivanov-Smolenskiy A.V.
Elektricheskie mashiny: Uchebnik dlya vuzov [Electric machines: the Textbook for high schools]. Moscow, Energy, 1980. 928 p.
4. Kostinskiy S.S.,
Mikhaylov V.V., Alekseeva D.S., Lopanskiy V.V. [Loss
evaluation of the active electric power in the transformer at a nonuniform load pattern]. Izvestiya vysshikh uchebnykh zavedeniy.
Elektromekhanika [Russian Electromechanics], 2015, no.2,
pp. 44 – 48.
5. Patent
na izobretenie ¹ 2380715. Schetchik poter' elektroenergii [The patent for
the invention ¹ 2380715. The counter of losses of the electric power].
6. Svidetel'stvo
o gosudarstvennoy registratsii programmy dlya EVM ¹ 2015662379. Raschet
poter' aktivnoy moshchnosti i elektroenergii na osnove kontrolya temperatury
sukhikh silovykh transformatorov raspredelitel'nykh setey pri neravnomernom
grafike nagruzki [The certificate on the state registration of the computer
program ¹ 2015662379. Calculation of losses of active power and the electric
power on the basis of the control of temperature of dry power transformers of
distributive networks at a non-uniform load pattern].