=Paper=
{{Paper
|id=Vol-3126/paper27
|storemode=property
|title=Investigation of measurement errors of electrical signals characteristics of energy supply systems
|pdfUrl=https://ceur-ws.org/Vol-3126/paper27.pdf
|volume=Vol-3126
|authors=Larysa Hatsenko,Anton Lutsenko,Oleg Skopintsev,Serhii Pohasii
}}
==Investigation of measurement errors of electrical signals characteristics of energy supply systems==
https://ceur-ws.org/Vol-3126/paper27.pdf
Investigation of Measurement Errors of Electrical Signals
Characteristics of Energy Supply Systems
Larysa Hatsenko 1, Anton Lutsenko 2, Oleg Skopintsev 3 , Serhii Pohasii 4
1
State University of Infrastructure and Technology, Kyiv, Ukraine
2,3
Ivan Kozhedub Kharkiv National Air Force University, Kharkiv, Ukraine
4
Simon Kuznets Kharkiv National University of Economics, Kharkiv, Ukraine
Abstract
The study substantiates the current scientific and technical problem of developing precision
methods for measuring the parameters of electrical signals (usually harmonic voltages), which
will allow to create a fairly simple control equipment with desired characteristics. The method
of measuring the frequency (period) of a sinusoidal signal based on the conversion of voltage
into the frequency of pulses is investigated. This method has pronounced filtering properties
with respect to interference. In particular, if the interference is harmonic with a frequency
multiple of the frequency of the measured signal, the error caused by interference is virtually
absent. The method of measuring phase shift with intermediate voltage-frequency conversion
is investigated. This method eliminates the dependence of the measurement result on the
frequency of the studied signals. This expands the frequency range and increases accuracy.
Also, this method has a short measurement time, no more than one or two periods of the studied
signals, which is especially important when measuring infrared frequency signals. The method
of power measurement with intermediate voltage-frequency conversion is investigated. This
method reduces the power measurement error with increasing broadband interference.
Keywords 1
Error, electrical signal, power supply system, method, obstacle
methods for measuring the parameters of
1. Introduction electrical signals (usually harmonic voltages),
which will create a fairly simple and at the same
time with the desired characteristics of the control
Increasing the requirements for electricity equipment
quality indicators of energy supply systems of In this regard, there is an urgent scientific and
water transport vehicles requires improvement of technical problem in the field of monitoring the
methods and means of their control [1, 2]. technical condition of energy supply systems of
However, the further development of such water transport: improving methods of synthesis
measuring instruments is largely constrained by
of equipment for monitoring the technical
the level of their technical characteristics (errors
condition of energy supply systems of water
in measuring electricity quality indicators) at low transport by reducing their errors in measuring the
cost. Today it is not economically necessary to use characteristics of electrical signals.
high-precision control equipment on water
vehicles, which is constantly in harsh operating
conditions [3, 4]. Therefore, a very important
scientific and technical task is to develop precise
ISIT 2021: II International Scientific and Practical Conference
«Intellectual Systems and Information Technologies», September
13–19, 2021, Odesa, Ukraine
EMAIL: sergeyg@i.ua (A. 1); Lutsenko_Ant@gmail.com (A. 2);
Skopintsev@gmail.com (A. 3); spogasiy1978@gmail.com (A. 4);
ORCID: 0000-0003-1210-5726 (A. 1); 0000-0002-7242-625X (A.
2); 0000-0002-4483-5339 (A. 3); 0000-0002-4540-3693 (A. 4)
©️ 2021 Copyright for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
2. Investigation of measurement Therefore, the topic of the article, aimed at
studying the errors in measuring the
errors of electrical signals characteristics of the electrical signal of the power
characteristics supply systems of water transport vehicles, is
2.1. Literature analysis relevant.
A significant number of publications are 2.2. Frequency measurement
devoted to the problem of monitoring the method with intermediate voltage-
technical condition of power supply systems of
various technical systems [5 - 17]. frequency conversion
Thus, the article [5] considers the method of
monitoring the technical condition of electronic The method of measuring the frequency
circuits that are part of power supply systems. In (period) of a sinusoidal signal based on the
[6 - 9] the results of research of methods of conversion of voltage into pulse frequency is as
synthesis of the equipment of control of a follows.
technical condition of radio electronic systems of Let the signal under study be described by an
water transport vehicles are presented. However, expression
in such works the estimation of errors of u(t ) m sin t (t ), (1)
measurement of parameters of the electronic where Vm is the amplitude of the measured signal;
equipment at control of a technical condition is is circular frequency of the studied signal;
not resulted. t is stationary interference that is present in
In the publications [10 - 14] the questions of
functioning of modern electric and electronic the input signal.
systems are considered, the factors which This signal will be converted into a
essentially influence definition of their technical proportional pulse frequency
condition are allocated. f ( t ) K f m sin t K f ( t ), (2)
In [15 - 17] the results of efficiency of where K f is voltage to frequency conversion
technical condition control of a power supply
factor.
systems at operation of water transport vehicles
Frequency-modulation pulse f ( t ) the signal
and in the field of development of the digital
control equipment are presented. However, in is integrated at intervals equal to the half-cycle of
such works there are no results of research of the input signal, where the number of output
influence of features of operation of the control impulses:
equipment in the aggressive environment (sea and
T/2 (3)
NT f ( t )dt .
river environment) on an error of measurement of
0
electric signals characteristics at control of a
Substituting the ratio (2) in the formula (3), we
technical condition.
find
Thus, the most critical for the synthesis of
T
equipment for monitoring the technical condition
2
of energy supply systems of water transport are: NT K f m [ sint ( t )] dt
the lack of results of estimation errors in 0
measuring the characteristics of electrical signals; T T
lack of results of evaluation of the influence of 2 2 (4)
interference on the measurement error of the K f Vm sin tdt K f ( t )dt
characteristics of electrical signals; lack of a 0 0
reasonable universal method for measuring the K f VmT
characteristics of electrical signals with minimal N NT N ,
errors under interference.
The results of the analysis of modern literature К f VmT
where NT is informative, useful
show the lack of universal methods for the
synthesis of equipment for monitoring the component of the measurement result,
technical condition of energy supply systems of proportional to the period T of the signal u( t ) ;
water transport to ensure minimal errors in
measuring the characteristics of electrical signals.
is measured phase shift.
2 The algorithm for measuring the phase shift is
N K f ( t )dt is error introduced by the as follows:
0
a) one of the input signals, for example u2 ( t ),
obstacle.
Taking into account only the useful component should be differentiated
U 2 ( T )
of the measurement result, we write u3 ( t ) K V2m cos( t ) , (9)
N K t
T T T NT , (5) where K is the transmission factor of the
K f Vm Vm
differentiation unit;
where K T is coefficient of proportionality. b) received signal V3 ( t ) will become
Kf proportional to the frequency of the pulses
The frequency of the studied signal will be f ( t ) K f u3 ( t ) K f K V2m cos( t ) ; (10)
determined from the ratio
c) frequency pulses f ( t ) are counted
1 Vm K f Vm
f (6) (integrated) twice:
T KT NT NT – once for the time interval between voltage
1 transitions u1( t ) and u2 ( t ) through zero;
where K f .
KT – another time during the time interval
As can be seen from ratio (6) the result of between voltage transitions u2 ( t ) through zero
frequency measurement f depends on the and maximum;
amplitude Vm of harmonic signal. To eliminate 1
f ( t )d ( t )
0
this dependence, the studied signal can be N1
subjected to amplitude normalization, ie to
achieve Vm= const. (11)
Then expression (6) can be written as K f K V2m cos( t )d ( t )
df 0
f , (7) K f K V2m sin ,
NT
where d f K f Vm is discreteness of frequency
1 2
f ( t )d ( t )
measurement. N2
For error analysis N , introduced by
(12)
interference, fully applied estimates that the
averaging algorithm has pronounced filtering 2
properties with respect to interference. In
K f K V2m cos( t )d ( t )
particular, if the interference is harmonic with a
frequency multiple of the frequency of the K f K V2m ;
measured signal, then error N 0 . d) phase shift measurement will be
determined from the following expression
2.3. Method of measuring phase N
arcsin 1 . (13)
N2
shift with intermediate voltage-
The considered method of phase shift
frequency conversion measurement has the following advantages.
First, it eliminates the dependence of the
Suppose it is necessary to measure the phase measurement result (13) on the frequency of the
shift between two sinusoidal signals described by studied signals, which ultimately leads to an
expressions expansion of the frequency range and increase
u1( t ) V1m sin t ; accuracy, because the effect of instability of the
(8)
u2 ( t ) V2m sin( t ) , frequency of the measured signals is eliminated.
where V1m , V2m is the amplitude of the The measurement result also does not depend on
the amplitude of the studied signals.
measured signals; Secondly, it has a short measurement time, no
is circular frequency of the studied signal; more than one or two periods of the studied
signals, which is especially important when
measuring infrared frequency signals. t1 ; t2 ; t3 .
2
Another variant of the method of measuring Given the error 1 і 2 from expression
the phase shift with intermediate voltage-
(16) we find
frequency conversion is possible. In it, the signal
2 K f V2m
module is subjected to frequency conversion 1
N1 f ( t )d ( t )
u2 ( t ) :
1
u 2 ( t ) V2m sin( t ) , (14) 2
2
f ( t ) K f V2m sin( t ) . (15) K f V2m (19)
sin( t )d ( t )
Expression (15) will be integrated twice: in the
1
2
interval from ( ) to (cos cos 2 sin sin 2 sin 1 ).
2
1 Given that errors 1 , 2 and 3 low, we
f ( t )d ( t )
N1 have
cos 2 1 ; sin 1 1 ;
2 (20)
sin 2 2 .
1
K f V2m sin( t ) d ( t )
(16) Then expression (19) takes the form
K f V2m (21)
2 N1 N1 ( 1 2 sin ) .
K f V2m Similarly, from expression (17) we obtain
cos ;
1
3
is at intervals from (
) to ( )
N2
f ( t )d ( t )
2 1
2
1
f ( t )d ( t ) K f V2m 3
N2
sin( t )d ( t )
2 1
2
1 (22)
K f V2m sin( t ) d ( t ) K f V2 m
(17)
(cos 3 sin 1 )
2 K f V2 m
K f V2m N2 1 .
.
From relations (21) and (22) we find the
absolute measurement errors
In this case, the measurement result is found K f V2m
by the formula N1 N1 N ( 1 2 sin )
arccos N , (18)
;
where N N1 N 2 . (23)
K f V2m
In addition to the instrumental error of voltage- N 2 N 2 N 2 1 .
frequency conversion, one of the dominant errors
of this method of measuring phase shifts is the Thinking 1 2 max , we
error due to the inaccuracy of the formation of obtain the error limits
time intervals during which the frequency K f V2m (24)
integration f ( t ) and the formation of N1m 1( 1 sin ) ;
intermediate results N1 і N 2 . Let's estimate this
K f V2m (25)
error. N 2m .
Denote by 1 , 2 і 3 phase errors of
Limits of change of absolute errors in
selection of the moments corresponding to
measurement of sizes N1 and N 2 :
phases:
K f V2m K f V2m (26) From the signal u1( t ) the variable component
N1 2 .
is allocated
K f V2m (27) u( t ) K M UI cos( 2t ) , (31)
N 2 . and its module with the help of a voltage-
Using expressions (19) and (22), we find the frequency converter will be converted into a pulse
absolute error of definition cos : frequency
f ( t ) K M UI cos( 2t ) . (32)
N N
N 1 1 Depending on the type of measured power
N2 N2
signal f ( t ) integrates over a period of time.
cos 2 cos sin 2 sin sin 1
cos When measuring active power, the time
cos 3 sin 1 interval of integration or frequency averaging
cos 2 cos sin 2 sin sin 1 f ( t ) concluded between t 2 and T 8 , which is
cos 3 cos sin 1 . equal to the phase interval from 2 to 4 .
cos 3 sin 1 Integrating frequency f ( t ) within the given
Taking into account equations (20) we obtain limits, we find:
sin cos sin sin sin
N 1 4 1
f ( t )d ( t ) K f K M UI
cos sin N1
(28)
(cos sin 1 ). 2
1
4 (33)
The component error of phase shift cos( 2t ) d ( t )
measurement introduced by the inaccuracy of the
integration intervals is found from expression (18) 2
N (29) K f KM T
N , UI cos ,
N 1 2 2
N where P UI cos is measured active power of
where N is determined from the ratio (28)
the circuit;
K f KM
2.4. Power measurement method K is coefficient of
2
with intermediate voltage-frequency proportionality.
conversion When measuring the reactive power, the
frequency integration is carried out in the time
The essence of the method consists in interval from 0 to t 2 or in the phase range from
converting the voltage proportional to the 0 to 2 :
instantaneous power into the pulse frequency,
which is then integrated over a certain time 1 2 1
f ( t )dtt K f K M UI
interval, depending on the type of measured value N2
– active, reactive or full power. 0
Let the voltage and current in the investigated
circuit be determined by the expression
2 (34)
cos( 2t ) d ( t )
u( t ) U m sin t , i( t ) I m sin( t ) . 0
By signals u( t ) and i( t ) a voltage K f KM
proportional to their product is formed TUI sin K T Q,
2
u1( t ) K M u( t )i( t ) (30) where Q UI sin is measured reactive power.
K M UI cos cos( 2t ), In the mode of measurement of full power
where K M is the transfer factor of the multiple averaging is conducted in a time interval from
block; t 2 до t 2 T 8 or in the phase range from
U , I is rms value according to voltage and 2 до ( 2 ) 4 :
current.
f t f uM t sin t .
1 2 4
N3 f ( t )d ( t ) Frequency f t we will integrate for the
2 averaging interval equal to half of the q-th period
of the carrier frequency, and obtain the number of
1 2 4 (35) pulses
K f K M UI cos( 2t ) d ( t )
t q 2 t q
2
Nq f ( t )dt K f uM t sin t dt . (40)
2
K f KM
TUI K T S . tq tq
2 Given that in the q-th half-cycle of the carrier
where S UI is full power in the studied circuit.
u M t q Vq that is, has a strictly defined value
To eliminate the dependence of the power
measurement results on the frequency (period) of equal to the amplitude of the carrier, we obtain
the studied signals, it is necessary to convert the t q 2
period of one of the signals into a code N, for N q K f Vq sin t dt
example, by the method of discrete number. We tq (41)
will get N T dT or T dT NT , where dT is f
2
discreteness of period measurement. Substituting K f Vq Vq .
this equality in formulas (33), (34), (35), we get
From expression (41) we find the amplitude of
N (36)
N p K9 1 KK 9 dT P P P , the carrier frequency in the q-th half-cycle of the
NT AM signal
N (37) f (42)
NQ K9 2 KK 9 dT Q Q P , Vq Nq
. Nq
NT f f
N (38) Knowing the amplitude of the carrier,
N S K 9 3 KK 9 dT S S P ,
NT determine the root mean square value of the
amplitude-modulated signal
2
where P is discreteness of 1 n 2 f n
K F K M K 9 dT V AM Vq N q2
power measurement;
n q 1 f n q 1
(43)
K9 is the transfer factor of the code divider. n
AM N q2 ,
q 1
2.5. Method for measuring the RMS where f is coefficient of
AM
value of the amplitude-modulated f n
signal with intermediate voltage- proportionality,
frequency conversion 2T
n M is the number of samples or codes,
T
The expression for the amplitude-modulated instantaneous values of the AM signal for the
(AM) signal is written as follows enveloping period.
u( t ) uM ( t ) sin t , (39) The developed method of measuring the RMS
value of the AM signal has a high noise immunity.
where u M ( t ) – signal enveloping or modulating Let's show it.
the signal with a period M ; We present the investigated signal by the sum
2 of the AM signal and the stationary interference
2f is the circular frequency of the u( t ) uM t sin t ( t ) ,
carrier, the initial phase of which is simplified to where t is stationary interference that is
zero to simplify the records; present in the input signal.
T, f is period and carrier frequency. Then to the result of measuring the value N q ,
AM signal module due to the relation (41) an error is introduced
u( t ) U M sin t , f (44)
Nq Nq .
convert to a proportional frequency of pulses f
The variance of this error: result on the frequency of the studied signals,
which ultimately leads to an expansion of the
tq
N q t t dtdt
2 frequency range and increase accuracy, because
2
2f | |
the effect of instability of the frequency of the
tq measured signals is eliminated. The measurement
result also does not depend on the amplitude of the
tq
r t t dtdt
2
studied signals. Has a short measurement time, no
2f 2 | |
tq
more than one or two periods of the studied
(45) signals.
t q 2
2f 2 r t t dtdt
| |
4. References
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