Evaluation of Voltage Phase Fluctuations in Power Networks with Rapid Variable Loads

International Journal of Innovative Research in Advanced Engineering (IJIRAE) ISSN: 2349-2763
Issue 02, Volume 4 (February 2017) www.ijirae.com
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Evaluation of Voltage Phase Fluctuations in Power
Networks with Rapid Variable Loads
A. Lipsky *
Y. Hemo N.Miteva
Dept. of Electrical and Electronic Engineering IEC Dept. of Electrical and Electronic Engineering
Ariel University, Israel Ariel University, Israel
Abstract— This paper presents a method for calculation of the voltage phase fluctuations in power networks due to
the operation of the electrical energy consumers with rapid variable nature of the active and reactive power
consumption. The operation of these power consumers leads to the simultaneous occurrence of the voltage frequency
and voltage phase fluctuations in the power system load nodes. The voltage frequency fluctuations appear because of
mechanical transients in power station "generator – turbine” blocks of energy system. Voltage phase fluctuations are
associated with variations of the value of the transverse component of the voltage drop on the equivalent power system
impedance, in relation to a concrete power system node. Considering the processes of power consumption value
variations caused by above mentioned consumers as random processes with known parameters and types of
correlation functions of consumers’ load diagrams, are obtained expressions which give the possibility to assess the
variances of the corresponding voltage phase fluctuation graphs in the analysed power system node. The carried out
calculations allow defining the conditions that depend on the permissible calculation accuracy, when it can neglect
the influence of the voltage frequency variations in the power system under assessing the voltage phase fluctuation
values in the power system node, where rapid variable consumers are connected. The analysis of the calculation
results allows also revealing the basic parameters of the power spectrum of rapid variable power consumption graphs
of users. These parameters have a practical influence on the values of the error assessments for voltage phase value
fluctuations at power system nodes.
Keywords—Voltage phases variations, voltage frequency variations, power systems, rapid variable loads.
I. INTRODUCTION
Some of the mighty power consumers such as electric arc furnaces (EAF), rolling mills (RM), welding machines, etc.
have rapidly varying loads graphs [1, 2, etc.]. The main frequency of power consumption variations for power networks
with EAF is not larger than 1 Hz, for networks with RM frequency of these variations is about 0.1 Hz and less [3, 4]. The
considered loads consume from the power network varying reactive and active powers. Rapid variations of the reactive
power consumption lead, as known, to the voltage fluctuations in the power networks and to flicker. These processes are
identified by the relevant standards, for example, EN 50160 [5].
Active power consumption variations mainly effect on the voltage phase fluctuations at the power network nodes, where
rapid variable consumers are connected. These voltage phase fluctuations caused by changes in the magnitude of the
transverse component of the voltage drop on the power network equivalent impedance, which is the external impedance
for power system node with rapid variable loads [6]. Active power consumption variations also lead to the appearance of
larger or smaller voltage frequency fluctuations in the power networks. These voltage frequency fluctuations occur due to
mechanical transients in "generator – turbine” blocks of electrical system power plants [7]. Thus, the operation of
electricity consumers with rapid variable load leads to simultaneous fluctuations of the voltage phase and the voltage
frequency at power network node, where these power users are connected.
Voltage frequency and voltage phase fluctuations are not defined and not standardized by relevant electric power quality
standards, for example, [5 and others]. Nevertheless, the presence of voltage phase and voltage frequency fluctuations
can adversely affect the efficiency and performance of various types of electrical equipment connected to the same power
network load nodes where discussed consumers are connected. For example, there are problems for the measurements
associated with the voltage period measurement in power network, which lead to the time measurement errors [8, 9, etc.].

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The fluctuations of voltage period duration can lead to the following: to errors in estimation of losses in dielectrics when
spectral analysis techniques are used [10], to errors in evaluation of the average and the RMS periodic signal values [11],
to additional errors for electric power meters, etc.
Voltage period duration fluctuations lead to the incorrect operation of control devices, of various protection devices and
systems [12] and so on. To take in account and to reduce the negative effects of the presence of voltage phase and
frequency fluctuations in power system load nodes it is necessary to estimate correctly the magnitude of these
fluctuations in each concrete case. Thus, there is a problem to estimate the magnitude of the voltage phase fluctuations in
power systems load nodes, caused by the effect of rapid variable loads on power networks, taking into account the
simultaneous presence of voltage phase and voltage frequency fluctuations.
Due to the problematic possibility of correct calculation of voltage frequency fluctuations in the electrical system load
nodes where are connected a large number of different electric power stations, within the framework of the analyzed
problem the great practical importance has the determination of the conditions which allow to neglect the magnitudes of
the voltage frequency fluctuations under the evaluation of the voltage phase fluctuation magnitudes.
II. CHARACTERISTICS OF MODE PARAMETER VARIATION PROCESSES IN POWER NETWORKS
WITH RAPID VARIABLE LOADS
Under theoretical analysis of the static stability processes at power system load nodes (Fig. 1, point B) with powerful
rapid variable loads, which are external to the load node under consideration, the power system is represented as a
generalized power system with a generalized or equivalent unit "generator - turbine" G (Fig. 1) and an equivalent
impedance in relation to the considered power system load nodes eqz (Fig. 1) [7].
Fig. 1 Scheme for evaluation of voltage frequency and voltage phase at a power system particular point.
In Fig. 1 ''
S is a sub-transient short-circuit power at the point B of the power system, Tr is a power load transformer, L1
and L2 are electricity consumers in the power network with rapid variable load, A is a point of clamps location for
equivalent "turbine – generator" block. And even in such simplified scheme the calculation of the voltage frequency
fluctuations at the point B in the scheme (Fig.1) presents some difficulties due to the lack and (or) the ambiguity of the
initial information about the parameters of the equivalent "generator - turbine" unit and its control systems, as well as
about the equivalent power network run between generator clamps at the point A and the power system point B under
consideration. Therefore, it is advisable to determine the conditions under which the magnitudes of the voltage
frequency fluctuations caused by mechanical transients, can be neglected in comparison with the magnitudes of the
voltage frequency fluctuations at a specific network point (point B), caused by the voltage phase fluctuations. A formal
comparison of the voltage phase and frequency fluctuations can be done on the basis of the known equation
( )
( )
d t
t
dt

  [13].
III. EVALUATION OF VOLTAGE FREQUENCY FLUCTUATIONS AT POINT B (FIG. 1)
Consider the case (Fig. 1) when an equivalent generating unit operates on a system with constant voltage, i.e., the voltage
at the point A remains unchanged when the load under consideration operates. Further, we will consider the power
system consisting of thermal power stations. It is known that during sudden load changes in power systems with mixed-
generating units these changes are perceived mainly by thermal power stations [14].

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In practice, there are different voltage frequency and power control systems of different “turbine - generator" blocks.
Consider the power system, reduced to one equivalent "turbine - generator" unit without intermediate superheating, and
equipped with a turbine speed control system.
With suitable for practical calculation accuracy, the process of the frequency variation  in the power system with
thermal power stations depends on variations of active power consumption, P , is characterized by the following
transfer function [15]:
( ) 1
( ) ;
( ) j
p
W p
P p T p A

 
 
(1)
1
.L
t
A K
S
 
Here jT is the mechanical inertia time constant of the equivalent "turbine - generator" unit, LK is the load regulating
effect coefficient on active power, tS is the offset value of control system performance, which characterizes the slope of
the static characteristic of the turbine control mechanism. Considering the process of load active power consumption
variations as a stationary normal random process, one can determine the variance of the voltage frequency fluctuations
due to mechanical transients in the "generator - turbine" unit in the discussed system as:
2
.
0
2 ( ) ( )G PD W j G d  

   (2)
where ( )PG 
is the power spectrum of the process of load active power consumption variations, ( )W j is the module
of the frequency transfer function corresponding to the operator transfer function (1).
In many cases, the power spectrum of the active power consumption of discussed load types can be approximated by the
following expression [16]:
 
2 2 2
0
22 2 2 2 2
0 0
2
( )
4
P
PG
   

     



 
  
, (3)
which corresponds to the following correlation function [17].
2
0 0
0
( ) cos sinPK e
  
     



 
  
 
. (4)
Here  and 0 are the damping coefficient of the correlation function and its main frequency of variations, respectively.
IV. EVALUATION OF VOLTAGE PHASE VARIATIONS AT POINT B (FIG. 1)
The magnitude of the angle between the voltages at A and B points (Fig.1) in the high-voltage power networks taking
into account the features of their network parameters can be estimated as [7]:
''
2 ''
( ) ( )
( ) L L
B
P t X P t
t
U S

 
   (5)
where ''
S is the sub-transient short-circuit power at the B point in the Fig. 1, ''
X is power system sub-transient reactance
corresponding to this power.
Taking into account the last equation, the power spectrum of the voltage phase variations at B point (Fig. 1) is
represented as:
 
2
''
1
( ) ( )PG G
S
   (6)

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Considering that ( )
( )
d t
t
dt

  , the power spectrum of voltage frequency fluctuations due to voltage phase fluctuations is
defined as follows [17]:
 
2
2
''
1
( ) ( )PG G
S
     (7)
Taking into consideration the equation (3) the variance of voltage frequency fluctuations at the B point of the discussed
scheme, caused by voltage phases fluctuations, can be estimated as
   
 
2 2
2 2 2
. 02 2
'' ''
( )P P
PD G d
S S

 
    

 
 

   , (8)
where 2
P
and ( )PG 

are the variance of load active power consumption fluctuations and the normalized power
spectrum of this process.
The standard deviation of the voltage frequency variations due to voltage phase variations can be estimated as follows:
 2 2
0''
P
S


 
   . (9)
V. THE ERROR CAUSED BY NOT TAKING INTO ACCOUNT THE MECHANICAL TRANSIENTS
Processes of voltage frequency variations in the power system G , caused by mechanical transients, and variations of
formal frequency due to voltage phase fluctuations, caused by changes in active power consumption, are uncorrelated,
since it is not correlated process and its first derivative. [17] Therefore, the variance of the resulting voltage frequency
fluctuations at the point B of the power network (Fig.1) can be estimated as follows:
. .GD D D     (10)
where .GD
and .D 
are the variances of voltage frequency variation process due to mechanical transients and
voltage frequency variation process due to voltage phase fluctuations.
The error caused by not taking into account the voltage frequency fluctuations under evaluation of voltage phase
fluctuations can be estimated as:
.2
.
G
S
D
D


  (11)
Based on the above expressions after some transformations it can be written:
 
2
''
2
22 2 2 2 2 2 2 2
. 0 0
4 1 1
4gen eq J
S
d
P A T


      

 
           
 (12)
Or, based on the allowable magnitude of the error caused by not taking into account the mechanical transients, we can
estimate the maximum possible relations ''
. /gen eqP S in which the calculation error will be no more than allowed error
all :
   
2
.
2 22 2 2 2 2 2 2 2 2 ''
0 0 0
4 1 1
4
gen eq
all J
P
d
A T S


      

  
     
 (13)

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In accordance with the expression (13) calculations were carried out for different types of power consumers with rapid
variable load modes, including the two most powerful groups of different type consumers: metallurgical rolling mill
“1150” and the 200-ton electric arc furnaces. Some results of the calculations are shown below. In these calculations the
magnitude of the mechanical time constants is equal to 5, 10, 15 seconds, the load regulating effect coefficient is
assumed to be 2, the offset value of control system performance is equal to 0.1 [15]. Some obtained calculation results
are shown on Figs. 2 - 5.
Fig. 2 Permissible ratio ''
. /gen eqP S for rolling mills when 0 =0.15, 1/s

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The results shown in Figs. 2 - 5 were obtained for the following initial data:
1 0.01, 5 ; 2 0.01, 10 ; 3 0.01, 15 ; 4 0.05, 5 ;
5 0.05, 10 ; 0.05, 15 ; 7 0.1, 5 ; 8 0.1, 10 ; 9 0.1, 15
all j all j all j all j
all j all j all j all j all j
T s T s T s T s
T s T s T s T s T s
               
                  
As can see from the above graphs, the errors caused by the neglecting of voltage frequency variations in power network
under evaluation of the voltage phase fluctuations for the above considered parameters is practically independent of the
value of the standard deviation of the active power consumption variations.
In power networks with EAF the time constants magnitudes of system mechanical inertia in considered range of their
values do not affect the calculation results at any approved calculation accuracy. In power networks with RM this is
observed when adopted calculation accuracy is of 5% or less.
The parameters  and 0 of power spectrum of the active load process variations affect differently on the admissibility
of neglecting the voltage frequency fluctuations. For example, as shown on Fig. 2, for the power networks with rolling
mills when the permissible calculation error is 1%, the effect of the correlation function damping factor is considerable.
A slight influence of this parameter is observed for power systems with rolling mills when the allowed error is 5% or
more, and for power networks with EAF (Fig. 3) for all values of the permissible calculation accuracies. Essentially the
same effect has the parameter 0 (Fig. 3, 5).
VI. CONCLUSIONS
1. The limit ratio values of ''
. /gen eqP S were obtained for the power system load nodes with rapid variable loads, in
which it cannot be taken into account the mechanical transients in "turbine-generator" blocks of energy system power
stations for the evaluation of voltage phase fluctuations in these nodes.
2. From the carried out researches follows that in many cases, the characteristics of the power system mechanical inertia
do not affect the calculation accuracies, and therefore there is no need to define the time constant of the power system
mechanical inertia.
3. The permissible ''
. /gen eqP S values, for which it cannot be taken into account the mechanical transients in "turbine-
generator" blocks of power stations under the evaluation of voltage phase fluctuations, are determined only by the
parameters of the normalized correlation function of the active power consumption graphs.
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Estimation of Electrical Demand in Hot Rolling Mills”, IEEE Transaction on industry application, vol. 52, Issue
3, pp. 1-9, May-June 2016.

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