Investigation of Measurement Errors Characteristics of Energy Supply Systems

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

1. Introduction

Increasing the requirements for electricity quality indicators of energy supply systems of water transport vehicles requires improvement of methods and means of their control [ 1, 2 ]. However, the further development of such measuring instruments is largely constrained by the level of their technical characteristics (errors in measuring electricity quality indicators) at low cost. Today it is not economically necessary to use 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 methods for measuring the parameters of electrical signals (usually harmonic voltages), which will create a fairly simple and at the same time with the desired characteristics of the control equipment

In this regard, there is an urgent scientific and technical problem in the field of monitoring the technical condition of energy supply systems of water transport: improving methods of synthesis of equipment for monitoring the technical condition of energy supply systems of water transport by reducing their errors in measuring the characteristics of electrical signals.

2. Investigation

errors of characteristics

2.1. Literature analysis of measurement electrical signals

A significant number of publications are devoted to the problem of monitoring the technical condition of power supply systems of various technical systems [ 5 - 17 ].

Thus, the article [ 5 ] considers the method of monitoring the technical condition of electronic circuits that are part of power supply systems. In [ 6 - 9 ] the results of research of methods of synthesis of the equipment of control of a technical condition of radio electronic systems of water transport vehicles are presented. However, in such works the estimation of errors of measurement of parameters of the electronic equipment at control of a technical condition is not resulted.

In the publications [ 10 - 14 ] the questions of functioning of modern electric and electronic systems are considered, the factors which essentially influence definition of their technical condition are allocated.

In [ 15 - 17 ] the results of efficiency of technical condition control of a power supply systems at operation of water transport vehicles and in the field of development of the digital control equipment are presented. However, in such works there are no results of research of influence of features of operation of the control equipment in the aggressive environment (sea and river environment) on an error of measurement of electric signals characteristics at control of a technical condition.

Thus, the most critical for the synthesis of equipment for monitoring the technical condition of energy supply systems of water transport are: the lack of results of estimation errors in measuring the characteristics of electrical signals; lack of results of evaluation of the influence of interference on the measurement error of the characteristics of electrical signals; lack of a reasonable universal method for measuring the characteristics of electrical signals with minimal errors under interference.

The results of the analysis of modern literature show the lack of universal methods for the synthesis of equipment for monitoring the technical condition of energy supply systems of water transport to ensure minimal errors in measuring the characteristics of electrical signals. Therefore, the topic of the article, aimed at studying the errors in measuring the characteristics of the electrical signal of the power supply systems of water transport vehicles, is relevant. 2.2. Frequency measurement method with intermediate voltagefrequency conversion

The method of measuring the frequency (period) of a sinusoidal signal based on the conversion of voltage into pulse frequency is as follows.

Let the signal under study be described by an expression u(t)  m sint  (t), (1) where Vm is the amplitude of the measured signal;  is circular frequency of the studied signal;  t  is stationary interference that is present in the input signal.

This signal will be proportional pulse frequency f ( t )  K f m sint  K f  ( t ), converted into

a (2) where K f is voltage to frequency conversion factor.

Frequency-modulation pulse f ( t ) the signal is integrated at intervals equal to the half-cycle of the input signal, where the number of output impulses:

T / 2 (3) NT   f ( t )dt .

0

Substituting the ratio (2) in the formula (3), we find (4) T 2 NT  K f m  [ sint  ( t )]dt 

0 T T 2 2  K f Vm  sintdt  K f  ( t )dt  0 0

 N  NT  N , K f VmT

 NT  К f VmT

 where is informative, useful component of the measurement result, proportional to the period T of the signal u( t ) ; 0  K f  2 N  K f  ( t )dt is error introduced by the obstacle.

Taking into account only the useful component of the measurement result, we write

T 

K f Vm NT  KT NT ,

Vm where KT 

is coefficient of proportionality.

The frequency of the studied signal will be determined from the ratio f  1 T 

Vm KT NT 

K f Vm

NT 1

. where K f 

KT

As can be seen from ratio (6) the result of frequency measurement f depends on the amplitude Vm of harmonic signal. To eliminate this dependence, the studied signal can be subjected to amplitude normalization, ie to achieve Vm= const.

Then expression (6) can be written as f  d f NT , where d f  K f Vm is discreteness of frequency measurement.

For error analysis N , introduced by interference, fully applied estimates that the averaging algorithm 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, then error N  0 . 2.3. Method of measuring phase shift with intermediate voltagefrequency conversion

Suppose it is necessary to measure the phase shift between two sinusoidal signals described by expressions

u1( t )  V1m sint ; u2( t )  V2m sin(t  ) , where V1m , V2m is the amplitude of the measured signals;  is circular frequency of the studied signal; (5) (6) (7) (8)  is measured phase shift.

The algorithm for measuring the phase shift is as follows:

a) one of the input signals, for example u2( t ), u3( t )  should be differentiated U2( T )

 KV2m cos(t  ) , (9) t where K is the transmission factor of the differentiation unit;

b) received signal V3( t ) proportional to the frequency of the pulses f ( t )  K f u3( t )  K f KV2m cos(t  ) ; (10) will become c) frequency pulses f ( t ) are counted (integrated) twice:

– once for the time interval between voltage transitions u1( t ) and u2( t ) through zero; – another time during the time interval between voltage transitions u2( t ) through zero and maximum;

1  N1   f ( t )d(t )   0

  K f KV2m  cos(t  )d(t ) 

0  K f KV2m sin ,

  signals, which is especially important when measuring infrared frequency signals.

Another variant of the method of measuring the phase shift with intermediate voltagefrequency conversion is possible. In it, the signal module is subjected to frequency conversion selection of the phases:       K f V2m

 2 N2m  K f V2m  . (25)



Limits of change of absolute errors in measurement of sizes N1 and N2 :

sin2  2 .

Then expression (19) takes the form

2 K f V2m   sin3(t  )d(t )  

K f V2m 

(cos 3  sin 1 )   N2  K f V2m 1.



From relations (21) and (22) we find the absolute measurement errors N1  N1  N  

( 1  2 sin ) K f V2m  ; K f V2m   N1  K f V2m   2 .

(26) N2  K f V2m  . (27)



Using expressions (19) and (22), we find the absolute error of definition cos : N  N1  N1 

N2 N2  cos 2 cos  sin2 sin  sin1  cos  cos3  sin1  cos 2 cos  sin 2 sin  sin1    cos3 cos  sin1  .

cos3  sin1 N 

Taking into account equations (20) we obtain sin cos  sin sin  sin

cos  sin  

(cos  sin 1).

1 

The component error of phase shift measurement introduced by the inaccuracy of the integration intervals is found from expression (18)  N (29)  

N  N 1 N 2 , where N is determined from the ratio (28)  (28) 2.4. Power measurement method with intermediate voltage-frequency conversion

The essence of the method consists in converting the voltage proportional to the instantaneous power into the pulse frequency, which is then integrated over a certain time interval, depending on the type of measured value – active, reactive or full power.

Let the voltage and current in the investigated circuit be determined by the expression u( t )  Um sint , i( t )  Im sin(t  ) .

By signals u( t ) and i( t ) a voltage proportional to their product is formed u1( t )  KM u( t )i( t )  (30)  KMUI cos  cos( 2t  ), where KM is the transfer factor of the multiple block;

U ,I is rms value according to voltage and current. (33) (34)  K f KM TUI sin  K T  Q,

2 where Q  UI sin is measured reactive power.

In the mode of measurement of full power averaging is conducted in a time interval from t 2 до t 2  T 8 or in the phase range from  2 до ( 2 )  4 :

From the signal u1( t ) the variable component is allocated

u( t )  KMUI cos( 2t  ), (31) and its module with the help of a voltagefrequency converter will be converted into a pulse frequency

f ( t )  KM UI cos( 2t  ) . (32) Depending on the type of measured power signal f ( t ) integrates over a period of time.

When measuring active power, the time interval of integration or frequency averaging f ( t ) concluded between t 2 and T 8 , which is equal to the phase interval from  2 to  4 . Integrating frequency f ( t ) within the given limits, we find:

  

2 1 4  f ( t )d(t ) K f K M UI 1   4   cos( 2t  )d(t )  

K f KM T

UI cos     , 2 where P UI cos is measured active power of the circuit;

K 

K f KM

2 proportionality.

When measuring the reactive power, the frequency integration is carried out in the time interval from 0 to t 2 or in the phase range from is coefficient of 0 to  2 :

 1 2

 f ( t )dtt  K f KMUI  0 1   2   cos( 2t  )d(t )  2.5. Method for measuring the RMS value of the amplitude-modulated signal with intermediate voltagefrequency conversion where uM ( t ) – signal enveloping or modulating the signal with a period  M ;   2f 

 carrier, the initial phase of which is simplified to zero to simplify the records;

T, f is period and carrier frequency.

is the circular frequency of the AM signal module u( t )  U M sint , convert to a proportional frequency of pulses f t   f uM t sint .

Frequency f t  we will integrate for the averaging interval equal to half of the q-th period of the carrier frequency, and obtain the number of pulses

Nq 

 tq 2 tq 2  f ( t )dt  K f  uM t  sint dt . (40) tq tq

Given that in the q-th half-cycle of the carrier uM tq   Vq that is, has a strictly defined value equal to the amplitude of the carrier, we obtain tq 2 tq  f Nq  K f Vq  sint dt   K f Vq 2 

Vq .

Vq 

  f

Nq 

Nq . f  f  

From expression (41) we find the amplitude of the carrier frequency in the q-th half-cycle of the AM signal

Knowing the amplitude of the carrier, determine the root mean square value of the amplitude-modulated signal 1 n

Vq2  n q1

f n Nq2   f n q1 (41) (42) (43) VAM    AM where proportionality, n  Nq2 , q1  AM 

f  f n is coefficient of n  2TM is the number of samples or codes,

T instantaneous values of the AM signal for the enveloping period.

The developed method of measuring the RMS value of the AM signal has a high noise immunity. Let's show it.

We present the investigated signal by the sum of the AM signal and the stationary interference u( t )  uM tsint  ( t ) , where  t  is stationary interference that is present in the input signal.

Then to the result of measuring the value Nq , due to the relation (41) an error is introduced f (44) where  2 is interference dispersion;

rt  t| is normalized correlation function, r(0)=1;   is interference correlation time.

The relative value of the error introduced by the obstacles when measuring the q-th value of the envelope: (45) Nq   2.22  Vq Nq 2

Nq  .     Vq 

  2  (46)

From relation (46) it follows that the relative value of the error introduced by the interference, when measuring the q-th value of the amplitude of the envelope, will decrease with increasing broadband interference, ie when the condition    .

3. Conclusions

When analyzing the error introduced by interference, when using the method of converting voltage (phase, power) into frequency when measuring electrical parameters, the estimates that characterize the averaging algorithm are fully applied, ie it has pronounced filtering properties with respect to interference. That means that this method is noise-proof.

The method of measuring phase shift with intermediate voltage-frequency conversion is presented. The considered method of phase shift measurement has the following advantages. It eliminates the dependence of the measurement result on the frequency of the studied signals, which ultimately leads to an expansion of the frequency range and increase accuracy, because the effect of instability of the frequency of the measured signals is eliminated. The measurement result also does not depend on the amplitude of the studied signals. Has a short measurement time, no more than one or two periods of the studied signals. 4. References

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