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ra
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ro
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K
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w
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s
:
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p
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I
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s
tan
tan
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u
s
p
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wer
Or
th
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g
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p
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c
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m
p
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en
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R
ea
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p
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T
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is i
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CC B
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C
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A
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Ko
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b
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Un
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T
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Facu
lty
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f
E
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in
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Dep
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Ma
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Me
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I
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I
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r
[
4
]
–
[
6
]
as
in
th
e
ca
s
e
o
f
s
in
u
s
o
id
al
wav
ef
o
r
m
s
(
4
)
.
An
o
v
er
v
iew
o
f
th
e
d
ev
elo
p
m
en
t
o
f
p
o
wer
th
eo
r
y
ca
n
b
e
f
o
u
n
d
in
r
e
v
ie
w
p
ap
er
s
[
7
]
–
[
1
2
]
.
B
u
t
ap
p
ar
en
t
p
o
wer
is
n
o
t
an
ad
d
itiv
e
q
u
an
tity
.
Als
o
,
th
e
n
ewly
f
o
r
m
ed
p
o
wer
co
m
p
o
n
en
ts
ar
e
m
o
s
t
o
f
ten
n
o
n
ad
d
itiv
e.
T
h
e
y
ar
e
s
u
itab
le
f
o
r
d
escr
ib
i
n
g
th
e
en
er
g
y
p
r
o
p
er
ties
o
f
an
o
b
ject
o
n
l
y
in
u
n
u
s
u
al
ca
s
es.
B
y
an
alo
g
y
to
th
e
f
o
r
m
u
la
f
o
r
ac
tiv
e
p
o
wer
ca
lcu
lated
f
r
o
m
Fo
u
r
ier
s
er
ies
=
∑
∞
=
1
.
(
6
)
C
.
I
.
B
u
d
ea
n
u
[
1
3
]
d
ef
in
ed
th
e
r
ea
ctiv
e
p
o
wer
o
f
d
is
to
r
ted
wav
ef
o
r
m
s
.
=
∑
∞
=
1
(
7
)
w
h
er
e:
n
in
d
icate
s
th
e
h
ar
m
o
n
ic
n
u
m
b
er
,
n
is
th
e
p
h
ase
s
h
if
t
b
etwe
en
th
e
n
-
th
h
ar
m
o
n
i
c
o
f
th
e
c
u
r
r
en
t
an
d
v
o
ltag
e,
an
d
U
n
an
d
I
n
ar
e
t
h
e
R
MS
v
alu
es o
f
th
e
h
ar
m
o
n
ics.
I
lio
v
ici’
s
id
ea
[
1
4
]
o
f
m
ea
s
u
r
in
g
r
ea
ctiv
e
p
o
wer
th
r
o
u
g
h
th
e
s
ca
lar
p
r
o
d
u
ct
o
f
v
o
lta
g
e
an
d
o
r
th
o
g
o
n
al
f
u
n
ctio
n
s
t
o
c
u
r
r
en
t
h
as
n
o
t
g
a
in
ed
ac
ce
p
ta
n
ce
s
in
ce
th
e
r
esu
lts
o
b
tain
ed
in
th
is
wa
y
m
a
y
e
x
ce
ed
th
e
ap
p
ar
en
t
p
o
wer
v
alu
e
[
1
5
]
,
[
1
6
]
.
H
o
w
e
v
e
r
,
t
h
i
s
m
e
t
h
o
d
-
r
e
p
l
a
c
i
n
g
o
n
e
o
f
t
h
e
v
o
l
t
a
g
e
o
r
c
u
r
r
e
n
t
q
u
a
n
t
i
t
i
es
i
n
t
h
e
a
c
t
i
v
e
p
o
w
e
r
f
o
r
m
u
l
a
(
2
)
w
i
t
h
a
n
o
r
t
h
o
g
o
n
a
l
f
u
n
c
t
i
o
n
w
a
s
p
r
o
p
o
s
e
d
i
n
t
h
e
I
E
E
E
1
4
5
9
-
2
0
1
0
s
t
a
n
d
a
r
d
[
1
7
]
w
h
e
n
c
a
l
c
u
l
a
ti
n
g
p
o
w
e
r
f
o
r
s
i
n
u
s
o
id
a
l
w
a
v
e
f
o
r
m
s
.
T
h
is
s
t
a
n
d
a
r
d
i
s
a
n
at
t
e
m
p
t
t
o
s
ta
n
d
a
r
d
i
z
e
a
n
d
s
y
s
t
e
m
a
ti
z
e
t
h
e
m
e
t
h
o
d
o
f
d
e
f
i
n
i
n
g
a
n
d
m
e
a
s
u
r
i
n
g
r
e
a
c
t
i
v
e
p
o
w
e
r
-
d
e
d
i
c
at
e
d
t
o
e
n
g
i
n
e
e
r
i
n
g
a
p
p
l
i
c
a
ti
o
n
s
.
2.
I
NS
T
AN
T
ANEOU
S P
O
WE
R
AND
ACT
I
V
E
P
O
WE
R
I
f
elec
tr
ic
en
er
g
y
is
tr
an
s
f
er
r
ed
b
etwe
en
an
o
b
ject
an
d
th
e
r
est
o
f
th
e
elec
tr
ic
p
o
wer
s
y
s
tem
b
y
cu
r
r
en
ts
i
k
in
n
+1
co
n
d
u
ct
o
r
s
,
s
ee
Fig
u
r
e
1
,
th
en
f
r
o
m
t
h
e
en
er
g
y
co
n
s
er
v
ati
o
n
law
it
f
o
llo
ws
th
at
th
e
in
s
tan
tan
eo
u
s
p
o
wer
o
f
th
e
o
b
j
ec
t is
,
=
∑
=
1
.
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
1
0
2
-
110
104
Vo
ltag
es
u
k
in
(
8
)
ar
e
d
e
f
in
ed
b
y
th
e
n
ec
ess
ar
y
co
n
d
itio
n
.
∑
=
0
=
1
(
9
)
Fig
u
r
e
1
.
An
elec
tr
ical
o
b
ject
I
f
f
r
o
m
(
9
)
o
n
e
ca
lcu
lates,
f
o
r
in
s
tan
ce
,
cu
r
r
e
n
t
in
an
d
s
u
b
s
titu
tes
it
in
to
eq
u
atio
n
(
8
)
,
t
h
e
n
o
n
e
will
g
et
,
=
∑
(
−
)
−
1
=
1
,
(
1
0
)
A
cc
o
r
d
in
g
to
wh
ich
v
o
ltag
es
u
k
in
(
8
)
ar
e
n
o
t
u
n
i
q
u
e,
i.e
.
,
th
ey
ca
n
b
e
th
e
d
if
f
er
e
n
ce
b
etwe
en
th
e
p
o
ten
tials
o
f
th
e
p
ar
ticu
lar
co
n
d
u
cto
r
s
a
n
d
th
e
p
o
ten
tial
o
f
t
h
e
n
-
th
o
r
an
y
o
th
er
co
n
d
u
cto
r
.
Als
o
,
o
n
e
ca
n
ad
d
o
n
e
m
o
r
e
co
n
d
u
ct
o
r
(
in
wh
ic
h
th
e
cu
r
r
e
n
t
is
alwa
y
s
eq
u
al
to
ze
r
o
)
to
th
e
n
co
n
d
u
cto
r
s
an
d
s
tar
tin
g
f
r
o
m
th
is
co
n
d
u
cto
r
m
ea
s
u
r
e
all
v
o
ltag
es
u
k
.
T
h
u
s
,
ea
ch
co
m
m
o
n
p
o
in
t
with
an
y
p
o
ten
tial
ca
n
b
e
r
ef
er
e
n
ce
,
b
u
t
u
s
u
ally
a
p
o
i
n
t
with
ze
r
o
p
o
te
n
tial is ad
o
p
ted
f
o
r
th
is
p
u
r
p
o
s
e
[
1
4
]
.
Dep
en
d
in
g
o
n
th
e
p
o
ten
tial
o
f
th
e
a
d
o
p
te
d
co
m
m
o
n
p
o
in
t,
th
e
o
b
ject
ca
n
b
e
v
ar
i
o
u
s
ly
d
iv
id
ed
i
n
to
p
ar
ts
ass
o
ciate
d
with
th
e
p
ar
ti
cu
lar
co
n
d
u
cto
r
s
an
d
th
e
t
o
tal
p
o
wer
will
b
e
th
e
s
u
m
o
f
th
e
p
o
wer
s
o
f
all
th
e
p
ar
ts
.
A
q
u
a
n
tity
h
a
v
in
g
th
is
p
r
o
p
er
ty
is
ad
d
itiv
e
a
n
d
s
atis
f
ie
s
th
e
p
r
in
cip
le
o
f
en
er
g
y
c
o
n
s
er
v
atio
n
.
T
h
e
s
am
e
p
r
o
ce
d
u
r
e
is
f
o
llo
wed
f
o
r
t
h
e
r
em
ain
in
g
co
n
d
u
ct
o
r
s
.
Sin
ce
in
s
tan
tan
eo
u
s
p
o
wer
is
an
ad
d
itiv
e
q
u
an
tity
,
it
is
e
n
o
u
g
h
to
an
aly
ze
o
n
ly
o
n
e
ar
b
itra
r
il
y
s
elec
ted
p
ar
t
o
f
th
e
o
b
ject,
a
s
s
ig
n
ed
to
o
n
e
(
th
e
k
-
th
)
cu
r
r
en
t
co
n
d
u
ctin
g
wir
e.
W
h
en
elec
tr
ic
en
er
g
y
is
co
n
v
er
ted
in
to
wo
r
k
a
n
d
h
ea
t,
th
e
av
er
a
g
e
in
s
tan
tan
eo
u
s
p
o
wer
o
f
th
e
elec
tr
ical
o
b
ject,
in
en
er
g
y
co
n
v
er
s
io
n
p
er
io
d
T
is
n
o
t
eq
u
al
to
ze
r
o
s
in
ce
th
is
in
s
tan
tan
eo
u
s
p
o
wer
p
ar
am
eter
(
ca
lled
ac
tiv
e
p
o
we
r
)
is
also
th
e
s
ca
lar
p
r
o
d
u
ct
o
f
v
o
ltag
e
a
n
d
cu
r
r
en
t,
r
ef
er
r
ed
to
th
e
p
e
r
io
d
,
i.e
.
it
s
p
ec
if
ies
th
e
elec
tr
ic
cu
r
r
en
t
wo
r
k
in
a
u
n
it
tim
e
(
1
)
.
B
ein
g
d
ef
in
ed
b
y
t
h
e
lin
ea
r
o
p
er
atio
n
o
n
th
e
ad
d
itiv
e
q
u
a
n
tity
(
in
s
tan
tan
eo
u
s
p
o
wer
)
,
ac
tiv
e
p
o
wer
is
an
ad
d
itiv
e
q
u
a
n
tity
.
T
im
e
T
is
a
p
er
io
d
if
th
e
cu
r
r
en
t
o
r
v
o
ltag
e
wav
ef
o
r
m
is
p
er
io
d
ic
.
G
en
er
ally
,
it
is
an
in
ter
v
al
o
f
c
o
n
tin
u
o
u
s
f
u
n
ctio
n
s
u
,
i
wh
ich
h
av
e
th
e
s
am
e
v
a
lu
es a
t th
e
in
ter
v
al’
s
en
d
s
.
R
ef
er
r
in
g
to
Far
ad
a
y
’
s
law
u
(
t)
=
d
/d
t
o
r
th
e
d
e
f
in
itio
n
o
f
cu
r
r
en
t
in
ten
s
ity
i(
t)
=
d
q
/d
t
,
th
e
in
s
tan
tan
eo
u
s
p
o
wer
o
f
th
e
s
y
s
tem
ca
n
b
e
wr
itten
as:
(
)
=
(
)
,
or
(
)
=
(
)
.
(
1
1
)
B
y
ch
an
g
in
g
th
e
in
teg
r
atio
n
lim
its
in
f
o
r
m
u
la
(
2
)
we
o
b
t
ain
th
at
ac
tiv
e
p
o
wer
ca
n
also
b
e
g
e
o
m
etr
ically
d
ef
in
ed
as f
o
llo
ws
=
1
∮
(
1
2
)
o
r
in
th
e
s
ec
o
n
d
f
o
r
m
=
1
∮
,
(
1
3
)
wh
er
e:
-
a
m
a
g
n
etic
f
lu
x
,
q
-
an
elec
tr
ic
ch
a
r
g
e
=
∫
,
=
∫
i
.
(
1
4
)
i
1
i
n
i
n
-
1
i
k
i
2
u
1
u
2
u
k
u
n
-
1
u
n
E
l
e
c
t
r
i
c
a
l
o
b
j
e
c
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Gen
era
liz
a
tio
n
o
f rea
ctive
p
o
w
er d
efin
itio
n
fo
r
p
erio
d
ica
l wa
ve
fo
r
ms
(
Grz
eg
o
r
z
K
o
s
o
b
u
d
z
ki
)
105
Acc
o
r
d
in
g
t
o
(
1
2
)
an
d
(
1
3
)
,
t
h
e
s
u
r
f
ac
e
ar
ea
s
o
f
th
e
clo
s
ed
l
o
o
p
s
f
o
r
m
ed
b
y
th
e
c
h
ar
ac
ter
i
s
tics
o
f
th
e
o
b
ject’
s
co
m
p
o
n
en
ts
in
co
o
r
d
in
ates
i,
o
r
in
c
o
o
r
d
i
n
ates
u
,
q
r
ep
r
esen
t
th
e
g
eo
m
etr
ic
p
ictu
r
e
o
f
ac
tiv
e
p
o
wer
(
th
e
am
o
u
n
t
o
f
e
n
er
g
y
d
eliv
er
ed
o
r
r
ec
eiv
ed
d
u
r
i
n
g
o
n
e
p
e
r
io
d
T)
.
Fo
r
s
in
u
s
o
id
al
cu
r
r
en
t
an
d
v
o
ltag
e
wav
ef
o
r
m
s
-
m
u
tu
ally
s
h
if
ted
b
y
an
an
g
le
d
if
f
er
en
t f
r
o
m
0
an
d
1
8
0
d
eg
r
ee
s
-
th
e
lo
o
p
h
as th
e
s
h
ap
e
o
f
a
n
ellip
s
e.
3.
RE
AC
T
I
V
E
P
O
WE
R
R
ea
ctiv
e
p
o
wer
is
to
d
escr
ib
e
th
e
en
er
g
y
p
r
o
c
ess
es
ar
is
in
g
f
r
o
m
th
e
ex
is
ten
ce
o
f
elec
tr
ic
en
er
g
y
in
th
e
f
o
r
m
o
f
elec
tr
ic,
m
a
g
n
eti
c,
an
d
elec
tr
o
m
ag
n
etic
f
ield
s
.
T
h
ey
a
r
e
elem
en
ta
r
y
p
r
o
ce
s
s
es
wh
ich
m
ay
r
u
n
ir
r
esp
ec
tiv
e
o
f
th
e
c
o
n
v
e
r
s
io
n
o
f
elec
tr
ic
en
er
g
y
in
t
o
wo
r
k
an
d
h
ea
t.
Sin
ce
th
e
g
e
n
er
al
d
ef
in
itio
n
o
f
ac
tiv
e
p
o
wer
is
b
ased
o
n
th
e
s
ca
lar
p
r
o
d
u
ct
o
f
two
f
u
n
ctio
n
s
:
u
a
n
d
i
,
(
2
)
,
a
g
en
er
alize
d
r
ea
ctiv
e
p
o
wer
d
e
f
in
itio
n
is
o
b
tain
ed
b
y
r
e
p
lacin
g
o
n
e
o
f
th
e
f
u
n
ctio
n
s
,
i.e
.
,
c
u
r
r
e
n
t
f
u
n
ctio
n
i
k
,
with
a
n
o
r
th
o
g
o
n
al
f
u
n
ctio
n
.
R
ea
ctiv
e
p
o
wer
d
ef
i
n
ed
in
th
is
way
is
an
ad
d
itiv
e
q
u
an
tity
.
A
f
u
n
ctio
n
o
r
t
h
o
g
o
n
al
to
p
e
r
io
d
ic
cu
r
r
en
t
i
is
ea
ch
o
f
it
s
o
d
d
-
o
r
d
er
tim
e
d
e
r
iv
ativ
es
an
d
ea
c
h
m
u
ltip
le
in
teg
r
als
with
o
d
d
m
u
ltip
licity
(
an
alo
g
o
u
s
ly
,
it
ca
n
b
e
d
o
n
e
with
v
o
ltag
e)
.
B
o
th
I
llo
v
ici
[
1
4
]
a
n
d
t
h
e
IEEE
1
4
5
9
-
2
0
1
0
[
1
7
]
s
tan
d
ar
d
m
en
tio
n
eq
u
iv
alen
tly
a
f
ir
s
t
-
o
r
d
er
f
u
n
ctio
n
: d
er
iv
ativ
e
o
r
in
t
eg
r
al.
Fro
m
all
th
e
f
u
n
ctio
n
s
o
n
l
y
o
n
e
–
th
e
f
ir
s
t
cu
r
r
en
t
d
er
i
v
ativ
e
–
f
o
r
m
s
with
v
o
ltag
e
u
a
s
ca
lar
p
r
o
d
u
ct
alwa
y
s
eq
u
al
to
ze
r
o
wh
en
th
e
elec
tr
ic
en
e
r
g
y
is
co
m
p
letely
d
is
s
ip
ated
in
th
e
o
b
je
ct
[
1
5
]
,
[
1
6
]
,
[
1
8
]
.
Geo
m
etr
ically
,
th
e
s
ca
lar
p
r
o
d
u
ct
o
f
th
e
v
o
ltag
e
a
n
d
th
e
c
u
r
r
en
t
d
e
r
iv
ativ
e
is
eq
u
al
to
th
e
s
ca
lar
p
r
o
d
u
ct
o
f
t
h
e
cu
r
r
en
t a
n
d
th
e
v
o
ltag
e
d
er
i
v
ativ
e
.
=
1
∫
=
−
1
∫
=
0
1
2
∮
0
=
−
1
2
∮
(
1
5
)
is
th
e
ar
ea
o
f
th
e
l
o
o
p
f
o
r
m
e
d
b
y
th
e
c
h
ar
ac
ter
is
tic
o
f
th
e
o
b
j
ec
t in
co
o
r
d
in
ates
i,
u
.
Als
o
,
f
ir
s
t
o
r
d
er
in
teg
r
als
(
1
4
)
ar
e
a
f
u
n
ctio
n
o
r
th
o
g
o
n
al
to
cu
r
r
e
n
t
i
an
d
to
v
o
ltag
e
u
.
T
h
e
in
teg
r
al
an
d
v
o
lta
g
e
u
f
o
r
m
t
h
e
s
ca
lar
p
r
o
d
u
ct.
=
∫
=
−
∫
=
0
∮
0
=
−
∮
(
1
6
)
wh
o
s
e
g
eo
m
etr
ic
p
ictu
r
e
is
th
e
ar
ea
o
f
t
h
e
lo
o
p
in
co
o
r
d
in
ate
s
q,
.
Fo
r
s
i
n
u
s
o
i
d
al
c
u
r
r
e
n
t
a
n
d
v
o
l
tag
e
w
av
ef
o
r
m
s
,
b
o
t
h
r
ea
cti
v
e
p
o
we
r
f
o
r
m
u
las
(
1
5
)
an
d
(
1
6
)
g
i
v
e
t
h
e
s
am
e
r
es
u
lts
.
R
ea
cti
v
e
p
o
we
r
s
ca
l
cu
lat
ed
f
r
o
m
(
1
5
)
a
n
d
(
1
6
)
g
i
v
e
d
i
f
f
er
en
t
v
al
u
es
o
n
ly
f
o
r
b
o
t
h
n
o
n
-
s
i
n
u
s
o
i
d
al
wav
ef
o
r
m
s
.
I
n
o
r
d
e
r
t
o
d
is
t
in
g
u
is
h
r
ea
cti
v
e
p
o
we
r
s
r
es
u
l
ti
n
g
f
r
o
m
f
o
r
m
u
l
a
(
2
)
-
b
y
in
s
er
tin
g
t
h
e
o
r
t
h
o
g
o
n
a
l
wav
ef
o
r
m
o
b
t
ai
n
e
d
b
y
a
p
p
l
y
i
n
g
d
i
f
f
er
en
tia
ti
o
n
,
t
h
e
i
n
d
e
x
d
w
as a
d
d
e
d
(
Q
d
)
,
w
h
i
le
in
th
e
c
as
e
o
f
i
n
t
eg
r
ati
o
n
t
h
e
in
d
e
x
i
was
a
d
d
e
d
(
Q
i
).
I
n
t
h
e
p
r
ese
n
c
e
o
f
n
o
n
-
s
in
u
s
o
i
d
a
l
v
o
l
tag
e
a
n
d
c
u
r
r
e
n
t
wa
v
e
f
o
r
m
s
,
t
h
e
r
ea
cti
v
e
p
o
we
r
s
Q
d
a
n
d
Q
i
ex
h
i
b
i
t
d
if
f
er
i
n
g
v
alu
es.
I
n
[
1
4
]
,
th
e
g
e
o
m
et
r
ic
m
ea
n
o
f
t
h
es
e
p
o
w
er
s
is
e
m
p
l
o
y
e
d
,
d
e
n
o
t
ed
as
eq
u
i
v
a
le
n
t
r
ea
cti
v
e
p
o
we
r
.
R
el
ati
o
n
s
(
1
5
)
a
n
d
(
1
6
)
in
t
h
e
f
r
eq
u
e
n
c
y
d
o
m
ai
n
ta
k
e
t
h
e
f
o
r
m
o
f
s
e
r
ies
.
=
∑
∞
=
1
(
1
7
)
=
∑
1
∞
=
1
.
(
1
8
)
Po
wer
Q
i
-
f
o
r
m
u
las
(
1
6
)
a
n
d
(
1
8
)
-
ar
e
n
o
t
r
ec
o
m
m
en
d
e
d
f
o
r
ca
lcu
latin
g
a
n
d
ca
n
n
o
t
b
e
t
h
e
b
asis
f
o
r
a
r
ea
ctiv
e
p
o
wer
d
e
f
in
itio
n
s
i
n
ce
Q
i
is
n
o
t
alwa
y
s
e
q
u
al
t
o
ze
r
o
wh
en
t
h
e
elec
tr
ic
e
n
er
g
y
in
th
e
o
b
ject
is
co
m
p
letely
d
is
s
ip
ated
.
Fo
r
a
v
o
ltag
e
h
av
in
g
th
e
f
i
r
s
t a
n
d
th
ir
d
h
ar
m
o
n
ic
.
=
1
s
in
+
3
c
os
3
,
(
1
9
)
wh
en
th
e
f
ac
t
o
r
o
f
v
o
ltag
e
an
d
cu
r
r
e
n
t
p
r
o
p
o
r
tio
n
ality
u
n
iq
u
ely
d
ep
e
n
d
s
o
n
v
o
ltag
e
in
a
cc
o
r
d
an
ce
with
th
e
eq
u
atio
n
.
(
)
=
0
+
2
2
,
(
2
0
)
C
h
ar
ac
ter
is
tics
in
co
o
r
d
in
ates
i,
u
a
n
d
in
co
o
r
d
in
ates
q,
,
with
wav
ef
o
r
m
s
as
in
Fig
u
r
e
2
ar
e
o
b
tain
ed
.
T
h
e
ch
ar
ac
ter
is
tic
in
co
o
r
d
in
ates
i
,
u
Fig
u
r
es
2
(
a)
is
a
lin
e
s
eg
m
en
t,
an
d
it
co
r
r
ec
tly
in
d
icate
s
th
e
ab
s
en
ce
o
f
r
ea
ctiv
e
p
o
wer
wh
ile
th
e
ch
ar
ac
ter
is
tic
in
co
o
r
d
in
ates
q,
Fig
u
r
es
2
(
b
)
f
o
r
m
s
a
lo
o
p
wh
o
s
e
ar
ea
is
n
o
t
eq
u
al
to
ze
r
o
.
T
h
e
en
er
g
y
d
is
s
ip
ated
d
u
r
in
g
o
n
e
p
er
i
o
d
is
e
q
u
al
to
th
e
ar
ea
o
f
th
e
lo
o
p
in
co
o
r
d
in
ates
u
,
q
-
Fig
u
r
e
3
(
a)
an
d
,i
-
Fig
u
r
e
3
(
b
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
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8
7
0
8
I
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t J E
lec
&
C
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m
p
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g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
1
0
2
-
110
106
(
a)
(
b
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Fig
u
r
e
2
.
R
ea
ctiv
e
p
o
wer
lo
o
p
s
.
T
a
h
e
ch
ar
ac
ter
is
tics
o
f
th
e
n
o
n
lin
ea
r
o
b
ject
co
m
p
letely
d
is
s
ip
atin
g
elec
tr
ic
en
er
g
y
,
(
a)
in
cu
r
r
e
n
t
-
v
o
ltag
e
co
o
r
d
in
ates
an
d
(
b
)
in
elec
tr
ic
ch
ar
g
e
-
m
ag
n
etic
f
lu
x
co
o
r
d
in
ates
.
T
h
e
ch
ar
ac
ter
is
tics
wer
e
o
b
tain
ed
f
r
o
m
(
1
9
)
a
n
d
(
2
0
)
f
o
r
: U
1
=1
V,
U
3
=1
/3
V,
= 2
, a
0
=1
Ω
,
a
2
= 1
Ω
/V2
(
a)
(
b
)
Fig
u
r
e
3
.
Activ
e
p
o
wer
lo
o
p
s
o
f
a
n
o
n
lin
ea
r
r
esis
to
r
in
(
a)
el
ec
tr
ic
ch
ar
g
e
-
v
o
ltag
e
co
o
r
d
in
ates a
n
d
(
b
)
cu
r
r
en
t
-
m
ag
n
etic
f
lu
x
c
o
o
r
d
in
ates
T
h
e
d
is
s
ip
atio
n
o
f
elec
tr
ic
en
e
r
g
y
a
n
d
th
e
ac
cu
m
u
latio
n
o
f
e
lectr
ic
en
er
g
y
in
th
e
f
o
r
m
o
f
a
n
elec
tr
ic
f
ield
an
d
a
m
ag
n
etic
f
ield
in
th
e
o
b
ject
ca
n
b
e
ap
p
r
o
x
im
at
ely
m
o
d
elled
b
y
a
n
elec
tr
ic
c
ir
cu
it
as
s
h
o
wn
in
F
ig
u
r
e
4
.
T
h
e
cu
r
r
en
t d
r
awn
b
y
th
is
cir
cu
it d
ep
e
n
d
s
o
n
t
h
e
a
p
p
lied
v
o
ltag
e,
ac
co
r
d
in
g
t
o
:
=
+
1
+
.
(
2
1
)
Fig
u
r
e
4
.
An
eq
u
iv
ale
n
t c
ir
cu
i
t o
f
th
e
o
b
ject
C
o
n
s
id
er
in
g
th
at
th
e
r
esis
tan
ce
wh
ich
m
o
d
els
en
er
g
y
d
is
s
ip
atio
n
m
u
s
t
u
n
iq
u
ely
d
e
p
en
d
o
n
v
o
ltag
e,
th
e
r
ea
ctiv
e
p
o
wer
o
f
a
n
e
q
u
iv
alen
t
cir
cu
it
p
ar
t
with
r
esis
tan
ce
R
is
eq
u
al
to
ze
r
o
.
I
f
t
h
e
o
b
ject
in
clu
d
es
f
er
r
o
m
a
g
n
etic
cir
cu
its
,
th
en
in
d
u
ctan
ce
L
o
f
th
e
eq
u
iv
alen
t
cir
cu
it
s
h
o
u
ld
b
e
tr
ea
ted
as
a
tim
e
-
d
ep
en
d
en
t
q
u
an
tity
.
T
h
u
s
,
th
e
r
ea
ctiv
e
p
o
wer
Q
d
o
f
a
co
m
p
o
n
en
t w
ith
i
n
d
u
ctan
ce
L
is
eq
u
al
t
o
,
C
R
i
L
u
E
l
e
c
t
r
i
c
a
l
o
b
j
e
c
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Gen
era
liz
a
tio
n
o
f rea
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p
o
w
er d
efin
itio
n
fo
r
p
erio
d
ica
l wa
ve
fo
r
ms
(
Grz
eg
o
r
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K
o
s
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u
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)
107
=
1
2
∫
0
(
1
)
+
1
2
∫
1
2
0
.
(
2
2
)
I
n
d
u
ctan
ce
L
o
f
th
e
eq
u
i
v
alen
t
cir
cu
it
co
m
p
o
n
en
t
m
o
d
ellin
g
th
e
o
cc
u
r
r
en
c
e
o
f
elec
tr
ic
en
er
g
y
in
th
e
f
o
r
m
a
m
ag
n
etic
f
ield
m
u
s
t
u
n
iq
u
ely
d
ep
en
d
o
n
e
q
u
iv
alen
t
f
lu
x
.
T
h
u
s
,
th
e
f
ir
s
t
in
teg
e
r
in
(
2
2
)
ca
n
b
e
wr
itten
as
a
lo
o
p
ar
ea
i
n
co
o
r
d
in
ates
,
f(
)
.
1
2
∫
0
(
1
)
=
∮
(
1
)
=
∮
(
)
=
0
.
(
2
3
)
Sin
ce
th
e
g
r
ap
h
o
f
p
er
i
o
d
ic
f
u
n
ctio
n
f
(
)
is
a
lin
e
s
eg
m
en
t,
th
e
lo
o
p
ar
ea
is
eq
u
al
to
z
er
o
.
T
h
u
s
,
r
ea
ctiv
e
p
o
wer
Q
d
o
f
th
e
in
d
u
ctan
ce
co
m
p
o
n
e
n
t c
an
b
e
d
eter
m
in
e
d
th
r
o
u
g
h
av
er
a
g
ed
in
d
u
ctan
ce
L
.
=
1
2
∫
1
2
0
=
2
1
2
,
(
2
4
)
wh
er
e
U
–
a
r
m
s
v
o
ltag
e.
T
h
e
r
ea
ctiv
e
p
o
wer
o
f
a
co
m
p
o
n
en
t w
ith
co
n
s
tan
t c
ap
ac
itan
ce
C
is
=
2
∫
0
2
2
=
−
2
∫
[
]
2
0
=
−
2
(
̇
)
2
,
(
2
5
)
wh
er
e
̇
–
a
r
m
s
v
alu
e
o
f
th
e
d
e
r
iv
ativ
e
o
f
v
o
ltag
e
u
.
T
h
e
r
ea
ctiv
e
p
o
wer
o
f
th
e
wh
o
le
eq
u
iv
alen
t c
ir
c
u
it
as sh
o
wn
in
F
ig
u
r
e
4
is
th
e
s
u
m
o
f
(
2
4
)
an
d
(
2
5
)
.
=
2
[
1
2
−
(
̇
)
2
]
.
(
2
6
)
I
t
f
o
llo
ws
f
r
o
m
(
2
6
)
th
at
th
e
r
ea
ctiv
e
p
o
wer
o
f
an
in
d
u
ctiv
e
o
b
ject
(
e.
g
.
,
a
n
elec
tr
ic
m
o
to
r
)
ca
n
b
e
co
m
p
en
s
ated
to
ze
r
o
b
y
m
ea
n
s
o
f
a
ca
p
ac
ito
r
with
a
p
r
o
p
e
r
ca
p
ac
itan
ce
.
T
h
e
o
p
tim
u
m
c
ap
ac
itan
ce
C
(
opt
)
is
ca
lcu
lated
f
r
o
m
th
e
r
ea
ctiv
e
p
o
wer
(
Q’
d
)
ze
r
o
in
g
c
o
n
d
itio
n
.
(
o
p
t
.
)
=
2
′
(
̇
)
2
(2
7
)
Gen
er
alize
d
r
ea
ctiv
e
p
o
wer
Q
d
is
m
ea
s
u
r
ed
b
ef
o
r
e
a
ca
p
ac
ito
r
with
ca
p
ac
itan
ce
C
(opt.
)
is
co
n
n
ec
ted
to
th
e
o
b
ject
o
r
b
ef
o
r
e
th
is
ca
p
ac
itan
ce
is
ch
an
g
ed
.
R
esu
lt
(
2
7
)
is
ex
ac
tly
eq
u
iv
alen
t
to
th
e
o
p
tim
u
m
ca
p
ac
itan
ce
,
o
b
tain
ed
u
n
d
er
d
if
f
er
en
t
a
s
s
u
m
p
tio
n
s
in
[
1
1
]
,
[
1
9
]
–
[
2
2
]
,
at
wh
ich
th
e
m
in
im
u
m
o
f
r
m
s
cu
r
r
en
t
o
c
cu
r
s
.
An
ex
am
p
le
ca
lcu
latio
n
f
o
r
m
in
im
izin
g
th
e
cu
r
r
en
t
o
f
a
n
in
d
u
ctio
n
m
o
to
r
u
s
in
g
a
ca
p
ac
ito
r
is
p
r
o
v
id
e
d
in
[
2
3
]
.
T
h
u
s
,
if
th
e
g
en
er
alize
d
r
ea
ctiv
e
p
o
wer
o
f
a
g
iv
en
co
n
d
u
cto
r
b
ec
o
m
es z
er
o
,
th
e
r
m
s
cu
r
r
e
n
t r
ea
ch
es a
m
in
im
u
m
wh
ich
d
o
es n
o
t d
ep
en
d
o
n
th
e
r
esis
tan
ce
in
th
e
eq
u
iv
alen
t
cir
cu
it.
T
h
is
p
r
o
p
er
t
y
ca
n
b
e
f
o
r
m
ally
p
r
o
v
ed
if
th
e
eq
u
iv
alen
t
r
esis
tan
ce
u
n
iq
u
ely
d
e
p
en
d
s
o
n
v
o
ltag
e
an
d
wh
e
n
th
e
in
d
u
c
tan
ce
u
n
iq
u
el
y
d
ep
e
n
d
s
o
n
t
h
e
m
ag
n
etic
f
lu
x
.
Me
asu
r
em
e
n
ts
s
h
o
w
th
at
wh
en
th
e
g
en
e
r
alize
d
r
ea
ctiv
e
p
o
we
r
Q
d
b
ec
o
m
es
ze
r
o
[
2
2
]
,
[
2
3
]
,
th
e
m
in
im
u
m
r
m
s
cu
r
r
en
t
o
c
cu
r
s
also
wh
en
th
e
ab
o
v
e
r
elatio
n
s
ar
e
n
o
n
-
u
n
iq
u
e.
R
ea
ctiv
e
p
o
wer
s
Q
d
an
d
Q
i
ca
n
b
e
u
s
ed
to
d
eter
m
in
e
th
e
c
o
n
s
tan
t
p
ar
am
eter
s
L
,
C
o
f
a
p
a
r
allel
o
r
s
er
ies
eq
u
iv
alen
t
cir
cu
it
o
f
th
e
r
ec
ei
v
er
[
1
0
]
.
A
n
ec
ess
ar
y
co
n
d
itio
n
i
s
th
at
th
e
v
alu
es
o
f
Q
d
an
d
Q
i
ar
e
d
i
f
f
er
en
t,
wh
ich
o
cc
u
r
s
wh
en
th
e
v
o
ltag
e
an
d
c
u
r
r
en
t a
r
e
n
o
n
-
s
in
u
s
o
id
al.
4.
M
E
T
H
O
DS
F
O
R
M
E
AS
UR
I
NG
RE
AC
T
I
VE
P
O
W
E
R
I
N
DIGIT
AL
M
E
T
E
RS
Mo
d
er
n
elec
tr
icity
m
eter
s
ar
e
co
m
p
o
s
ed
o
f
a
n
alo
g
u
e
-
to
-
d
ig
ital
co
n
v
e
r
ter
s
(
ADCs
)
f
o
r
m
ea
s
u
r
in
g
in
s
tan
tan
eo
u
s
v
o
ltag
e
an
d
c
u
r
r
en
t
v
alu
es,
an
d
a
s
ig
n
al
p
r
o
c
ess
in
g
u
n
it.
T
h
is
u
n
it
ca
lc
u
lates
p
o
wer
,
en
er
g
y
,
p
o
wer
f
ac
to
r
s
,
an
d
o
th
er
p
ar
a
m
eter
s
,
in
clu
d
in
g
th
o
s
e
r
elate
d
to
p
o
wer
q
u
ality
.
A
m
eter
ca
n
b
e
im
p
lem
en
te
d
as
a
s
p
ec
ialized
in
teg
r
ated
cir
c
u
it
(
as
s
h
o
wn
in
Fig
u
r
es
5
(
a
)
)
o
r
as
a
co
m
b
in
atio
n
o
f
a
m
icr
o
p
r
o
ce
s
s
o
r
with
ADCs
.
T
h
e
m
icr
o
p
r
o
ce
s
s
o
r
o
r
co
m
p
u
tatio
n
al
u
n
it
ca
n
b
e
p
r
o
g
r
am
m
e
d
to
d
eter
m
in
e
r
ea
cti
v
e
p
o
wer
(
en
er
g
y
)
ac
co
r
d
in
g
to
u
s
er
r
eq
u
ir
em
e
n
t
s
.
Fo
r
s
in
u
s
o
id
al
cu
r
r
en
t
an
d
v
o
ltag
e
wav
ef
o
r
m
s
,
all
d
ep
en
d
e
n
cies
p
r
esen
ted
in
t
h
e
p
r
ec
ed
i
n
g
s
ec
tio
n
y
ield
th
e
id
e
n
tical
v
alu
e
o
f
r
e
ac
tiv
e
p
o
wer
.
T
h
e
m
ete
r
m
an
u
f
ac
tu
r
er
is
n
o
t
co
n
s
tr
ain
ed
to
a
s
p
ec
if
ic
m
eth
o
d
f
o
r
m
ea
s
u
r
in
g
r
ea
ctiv
e
p
o
wer
.
T
h
ey
ca
n
ch
o
o
s
e
an
y
d
ep
en
d
en
cy
o
r
im
p
lem
e
n
t
th
e
alg
o
r
it
h
m
th
at
is
s
im
p
les
t
to
im
p
lem
en
t,
p
r
o
v
id
e
d
it
s
atis
f
ies
th
e
estab
lis
h
ed
d
esig
n
cr
iter
ia
(
e.
g
.
,
u
tili
za
tio
n
o
f
a
co
s
t
-
ef
f
ec
tiv
e
m
icr
o
p
r
o
ce
s
s
o
r
)
[
2
4
]
–
[
2
6
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
1
6
,
No
.
1
,
Feb
r
u
ar
y
20
2
6
:
1
0
2
-
110
108
On
e
s
u
ch
s
tr
aig
h
tf
o
r
war
d
alg
o
r
ith
m
in
v
o
lv
es
s
h
if
tin
g
th
e
v
o
ltag
e
s
am
p
les
r
elativ
e
to
t
h
e
cu
r
r
en
t
s
am
p
les
b
y
an
am
o
u
n
t
co
r
r
esp
o
n
d
in
g
to
o
n
e
-
q
u
ar
ter
o
f
th
e
p
er
io
d
o
f
th
e
m
e
asu
r
e
d
wav
ef
o
r
m
,
s
ee
Fig
u
r
e
5
(
b
)
.
T
h
is
9
0
-
d
eg
r
ee
p
h
ase
s
h
if
t
b
etwe
en
cu
r
r
en
t
an
d
v
o
ltag
e
o
cc
u
r
s
ex
clu
s
iv
ely
at
th
e
f
u
n
d
am
en
tal
f
r
eq
u
e
n
cy
.
Fo
r
h
ar
m
o
n
ics,
th
e
p
h
ase
s
h
if
t
is
m
u
ltip
lied
p
r
o
p
o
r
tio
n
ally
,
wh
ich
r
esu
lts
in
a
f
in
al
v
alu
e
th
at
is
th
e
s
u
m
o
f
t
h
e
f
u
n
d
am
en
tal
h
a
r
m
o
n
ic
r
ea
ctiv
e
p
o
wer
a
n
d
th
e
ac
tiv
e
o
r
r
ea
ctiv
e
p
o
wer
o
f
th
e
h
ar
m
o
n
ics (
2
7
)
.
4
=
1
∫
(
)
(
−
4
)
0
=
1
−
2
−
3
+
4
+
5
−
(
2
7
)
(
a)
(
b
)
Fig
u
r
e.
5
.
R
ea
ctiv
e
en
e
r
g
y
(
a)
I
C
Fu
n
ctio
n
al
b
lo
ck
d
iag
r
am
o
f
en
er
g
y
m
eter
in
g
d
ev
ice
ADE
9
0
7
8
–
[
2
7
]
a
n
d
(
b
)
r
ea
ctiv
e
p
o
wer
ca
lc
u
latio
n
f
r
o
m
9
0
º
p
h
ase
s
h
if
t (
2
7
)
,
AD
E
7
7
5
8
[
2
8
]
T
h
e
m
ea
s
u
r
em
en
t b
lo
ck
o
f
th
e
in
teg
r
ated
m
eter
m
ea
s
u
r
in
g
r
e
ac
tiv
e
en
er
g
y
f
r
o
m
th
e
"p
o
wer
tr
ian
g
le"
in
ac
co
r
d
an
ce
with
eq
u
atio
n
(
5
)
is
im
p
lem
en
ted
in
m
an
y
I
C
lik
e
[
2
9
]
.
Dif
f
e
r
en
ce
s
in
th
e
r
esu
lts
o
f
m
ea
s
u
r
in
g
th
e
r
ea
ctiv
e
e
n
er
g
y
o
f
o
b
jects,
r
esu
ltin
g
f
r
o
m
t
h
e
ca
lcu
latio
n
alg
o
r
ith
m
u
s
ed
in
th
e
m
eter
,
ar
e
d
is
cu
s
s
ed
m
an
y
tim
es
in
s
cien
tific
s
tu
d
ies,
e.
g
.
,
[
3
0
]
–
[
3
3
]
.
Stan
d
ar
d
izatio
n
r
eq
u
ir
em
en
ts
f
o
r
r
ea
ctiv
e
en
e
r
g
y
m
eter
s
s
tip
u
late
m
etr
o
lo
g
ical
v
er
if
icatio
n
u
n
d
er
s
in
u
s
o
id
al
co
n
d
itio
n
s
[
1
]
,
[
2
]
.
Me
ter
s
in
c
o
r
p
o
r
atin
g
h
ig
h
er
-
h
ar
m
o
n
ic
f
ilter
s
ef
f
ec
tiv
ely
f
u
n
ctio
n
as
f
u
n
d
a
m
en
tal
-
co
m
p
o
n
en
t
r
ea
ctiv
e
e
n
er
g
y
m
eter
s
,
d
is
tin
ct
f
r
o
m
a
ctiv
e
en
er
g
y
m
eter
s
.
Oth
er
ap
p
r
o
ac
h
es
to
m
ea
s
u
r
in
g
p
o
wer
an
d
r
ea
ctiv
e
en
er
g
y
a
r
e
b
ein
g
u
n
d
er
tak
e
n
[
3
4
]
–
[
3
6
]
.
T
h
ey
h
av
e
n
o
t
y
et
b
ee
n
im
p
lem
e
n
ted
in
co
m
m
er
cial
r
ea
ctiv
e
en
er
g
y
m
ete
r
s
.
Similar
ly
,
th
e
r
ec
o
m
m
en
d
a
tio
n
s
o
f
th
e
I
E
E
E
1459
-
2
0
1
0
s
tan
d
ar
d
[
1
7
]
h
av
e
n
o
t b
ee
n
im
p
lem
en
ted
.
5.
CO
NCLU
SI
O
N
T
h
er
e
is
n
o
u
n
iv
er
s
ally
ac
ce
p
ted
th
eo
r
y
o
f
r
ea
cti
v
e
p
o
wer
f
o
r
n
o
n
-
s
in
u
s
o
id
al
cu
r
r
en
t
a
n
d
v
o
ltag
e
wav
ef
o
r
m
s
.
Fu
n
d
am
en
tal
r
ea
c
tiv
e
en
er
g
y
m
eter
s
ar
e
u
s
ed
to
ac
co
u
n
t
f
o
r
r
ea
ctiv
e
en
er
g
y
.
T
h
e
m
eter
s
s
h
o
u
l
d
u
s
e
a
r
ea
ctiv
e
p
o
wer
m
ea
s
u
r
em
en
t
alg
o
r
ith
m
th
at
co
n
s
id
e
r
s
d
is
to
r
ted
wav
ef
o
r
m
s
.
A
u
n
iq
u
e
d
ef
in
itio
n
o
f
ad
d
itiv
e
r
ea
ctiv
e
p
o
wer
,
co
v
er
in
g
n
o
n
-
s
in
u
s
o
id
al,
p
e
r
io
d
ical
wav
ef
o
r
m
s
,
is
o
b
tain
ed
b
y
r
e
p
lacin
g
th
e
cu
r
r
en
t
in
th
e
eq
u
atio
n
(
th
e
s
ca
lar
p
r
o
d
u
ct
o
f
v
o
ltag
e
an
d
cu
r
r
e
n
t)
d
ef
in
in
g
ac
tiv
e
p
o
wer
with
a
s
p
ec
ial
o
r
th
o
g
o
n
al
f
u
n
ctio
n
–
a
d
e
r
iv
ativ
e
o
f
cu
r
r
en
t o
r
v
o
ltag
e.
Geo
m
etr
ically
,
th
e
s
ca
lar
p
r
o
d
u
ct
o
f
v
o
ltag
e
an
d
cu
r
r
e
n
t
d
er
iv
ativ
e
is
th
e
s
u
r
f
ac
e
ar
ea
o
f
th
e
lo
o
p
f
o
r
m
ed
b
y
th
e
o
b
ject
c
h
ar
ac
te
r
is
tic
in
cu
r
r
e
n
t
-
v
o
ltag
e
co
o
r
d
in
ates
(
i,
u
)
.
I
f
th
e
l
o
o
p
ar
ea
i
n
co
o
r
d
in
ates
i,
u
,
d
iv
id
ed
b
y
2
is
ad
o
p
ted
as
th
e
g
en
er
alize
d
d
e
f
in
itio
n
o
f
r
ea
ctiv
e
p
o
wer
f
o
r
p
er
io
d
ical
wav
ef
o
r
m
s
,
th
en
th
e
p
r
ev
io
u
s
ly
d
ef
in
e
d
r
ea
ctiv
e
p
o
wer
f
o
r
s
in
u
s
o
id
al
v
o
ltag
e
a
n
d
cu
r
r
en
t
wav
e
f
o
r
m
s
will
b
e
i
ts
s
p
ec
ial
ca
s
e.
T
h
e
ze
r
o
v
al
u
e
o
f
th
e
r
ea
ctiv
e
p
o
wer
Q
d
o
f
th
e
o
b
ject
in
d
icate
s
th
at
th
e
r
m
s
cu
r
r
en
t
i
n
th
is
o
b
ject
h
as
r
ea
ch
e
d
its
m
in
im
u
m
.
T
h
is
s
tate
ca
n
b
e
ac
h
iev
ed
b
y
co
n
n
ec
tin
g
a
ca
p
ac
i
to
r
–
a
s
im
p
le
p
ass
iv
e
co
m
p
en
s
ato
r
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
T
h
is
r
esear
ch
was
s
u
p
p
o
r
ted
b
y
r
esear
ch
f
u
n
d
s
o
f
th
e
Fac
u
lty
o
f
E
lectr
ical
E
n
g
in
ee
r
in
g
,
W
r
o
claw
Un
iv
er
s
ity
o
f
Scien
ce
an
d
T
ec
h
n
o
lo
g
y
(
2
0
2
5
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
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&
C
o
m
p
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n
g
I
SS
N:
2088
-
8
7
0
8
Gen
era
liz
a
tio
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f rea
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p
o
w
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efin
itio
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fo
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p
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fo
r
ms
(
Grz
eg
o
r
z
K
o
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b
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)
109
AUTHO
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to
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a
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y
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DATA AV
AI
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Data
av
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p
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th
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RE
F
E
R
E
NC
E
S
[
1
]
I
EC
,
“
I
EC
6
2
0
5
3
-
2
3
:
2
0
2
0
,
El
e
c
t
r
i
c
i
t
y
m
e
t
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r
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me
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t
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y
(
c
l
a
ss
e
s
2
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n
d
3
)
,
”
I
n
t
e
r
n
a
t
i
o
n
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l
E
l
e
c
t
ro
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h
n
i
c
a
l
C
o
m
m
i
ss
i
o
n
.
2
0
2
0
.
[
2
]
Eu
r
o
p
e
a
n
C
o
m
mi
t
t
e
e
f
o
r
E
l
e
c
t
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t
e
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h
n
i
c
a
l
S
t
a
n
d
a
r
d
i
z
a
t
i
o
n
,
“
EN
I
EC
6
2
0
5
3
-
2
4
:
2
0
2
1
:
E
l
e
c
t
r
i
c
i
t
y
me
t
e
r
i
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g
e
q
u
i
p
men
t
-
P
a
r
t
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c
u
l
a
r
r
e
q
u
i
r
e
m
e
n
t
s
-
P
a
r
t
2
4
:
S
t
a
t
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m
e
t
e
r
s
f
o
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f
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n
d
a
m
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n
t
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l
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p
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n
t
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y
(
c
l
a
sses
0
,
5
S
,
1
S
,
1
,
2
a
n
d
3
)
.
”
2
0
2
1
.
[
3
]
P
.
M
a
k
l
e
s
a
n
d
A
.
B
i
e
ń
,
“
R
e
a
c
t
i
v
e
e
n
e
r
g
y
me
a
su
r
e
me
n
t
s
i
ssu
e
s
i
n
t
h
e
a
s
p
e
c
t
o
f
l
e
g
a
l
r
e
g
u
l
a
t
i
o
n
s,
”
Prz
e
g
l
a
d
E
l
e
k
t
ro
t
e
c
h
n
i
c
z
n
y
,
v
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l
.
1
0
0
,
n
o
.
1
2
,
p
p
.
1
0
9
–
1
1
2
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2
0
2
4
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d
o
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:
1
0
.
1
5
1
9
9
/
4
8
.
2
0
2
4
.
1
2
.
2
4
.
[
4
]
F
.
M
o
n
t
o
y
a
,
“
A
c
t
i
v
e
,
r
e
a
c
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,
a
n
d
a
p
p
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p
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t
r
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c
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r
c
u
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t
s
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t
h
n
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n
-
si
n
u
so
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d
a
l
w
a
v
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f
o
r
ms
o
f
c
u
r
r
e
n
t
a
n
d
v
o
l
t
a
g
e
,
”
Przeg
l
ą
d
El
e
k
t
ro
t
e
c
h
n
i
c
z
n
y
,
n
o
.
7
--
8
,
2
0
2
3
.
[
5
]
L.
S
.
C
z
a
r
n
e
c
k
i
,
“
C
u
r
r
e
n
t
s’
p
h
y
si
c
a
l
c
o
m
p
o
n
e
n
t
s
(
C
P
C
)
c
o
n
c
e
p
t
:
A
f
u
n
d
a
me
n
t
a
l
o
f
p
o
w
e
r
t
h
e
o
r
y
,
”
i
n
I
S
N
C
C
2
0
0
8
:
9
t
h
C
o
n
f
e
re
n
c
e
-
S
e
m
i
n
a
r
,
Pr
o
c
e
e
d
i
n
g
s
o
f
t
h
e
I
n
t
e
r
n
a
t
i
o
n
a
l
S
c
h
o
o
l
o
n
N
o
n
si
n
u
so
i
d
a
l
C
u
rre
n
t
s
a
n
d
C
o
m
p
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n
s
a
t
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o
n
,
2
0
0
8
,
p
p
.
1
–
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1
,
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o
i
:
1
0
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1
1
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9
/
I
S
N
C
C
.
2
0
0
8
.
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6
2
7
4
8
3
.
[
6
]
L.
S
.
C
z
a
r
n
e
c
k
i
a
n
d
T
.
S
w
i
e
t
l
i
c
k
i
,
“
P
o
w
e
r
s
i
n
n
o
n
s
i
n
u
s
o
i
d
a
l
n
e
t
w
o
r
k
s
:
t
h
e
i
r
i
n
t
e
r
p
r
e
t
a
t
i
o
n
,
a
n
a
l
y
si
s,
a
n
d
me
a
su
r
e
me
n
t
,
”
I
EE
E
T
ra
n
s
a
c
t
i
o
n
s
o
n
I
n
s
t
ru
m
e
n
t
a
t
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o
n
a
n
d
Me
a
su
r
e
m
e
n
t
,
v
o
l
.
3
9
,
n
o
.
2
,
p
p
.
3
4
0
–
3
4
5
,
1
9
9
0
,
d
o
i
:
1
0
.
1
1
0
9
/
1
9
.
5
2
5
1
2
.
[
7
]
A
.
Ei
g
e
l
e
s
Em
a
n
u
e
l
,
“
P
o
w
e
r
s
i
n
n
o
n
si
n
u
s
o
i
d
a
l
s
i
t
u
a
t
i
o
n
s
a
r
e
v
i
e
w
o
f
d
e
f
i
n
i
t
i
o
n
s
a
n
d
p
h
y
s
i
c
a
l
mea
n
i
n
g
,
”
I
EE
E
T
ra
n
sa
c
t
i
o
n
s
o
n
Po
w
e
r D
e
l
i
v
e
r
y
,
v
o
l
.
5
,
n
o
.
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c
u
rre
n
tl
y
wo
r
k
s
a
t
t
h
e
F
a
c
u
l
ty
o
f
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
.
He
is
a
c
o
-
c
re
a
to
r
o
f
t
h
e
Re
se
a
rc
h
Lab
o
r
a
to
ry
a
c
c
re
d
it
e
d
(
2
0
0
4
-
2
0
1
6
)
b
y
th
e
P
o
li
s
h
Ce
n
tre
f
o
r
Ac
c
re
d
it
a
ti
o
n
,
m
e
e
ti
n
g
t
h
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re
q
u
ir
e
m
e
n
ts
o
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th
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P
N
EN
1
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2
5
sta
n
d
a
rd
.
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r
o
m
2
0
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4
t
o
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2
,
h
e
se
rv
e
d
a
s
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Tec
h
n
ica
l
M
a
n
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g
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r,
a
n
d
sin
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e
2
0
1
2
,
a
s
th
e
h
e
a
d
o
f
lab
o
ra
t
o
ry
.
His
re
se
a
rc
h
in
tere
sts
in
c
lu
d
e
e
lec
tro
m
a
g
n
e
ti
c
c
o
m
p
a
ti
b
il
i
ty
,
a
ss
e
ss
m
e
n
t
a
n
d
im
p
ro
v
e
m
e
n
t
o
f
p
o
we
r
q
u
a
li
ty
,
m
e
tro
lo
g
y
o
f
e
lec
tri
c
p
o
we
r
q
u
a
li
ty
,
a
c
ti
v
e
a
n
d
re
a
c
ti
v
e
e
n
e
rg
y
m
e
ters
,
re
a
c
ti
v
e
p
o
we
r
c
o
m
p
e
n
sa
ti
o
n
,
p
o
we
r
li
n
e
c
o
m
m
u
n
ica
ti
o
n
(
P
LC),
EM
C
in
ra
il
wa
y
p
o
we
r
s
u
p
p
ly
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
g
rz
e
g
o
rz
.
k
o
so
b
u
d
z
k
i@p
wr.e
d
u
.
p
l
.
Le
sz
e
k
Ła
d
n
i
a
k
wa
s
b
o
rn
in
Wr
o
c
law
in
P
o
lan
d
,
o
n
M
a
rc
h
7
,
1
9
5
5
.
He
c
o
m
p
lete
d
h
is
b
a
c
h
e
lo
r’s
a
n
d
m
a
ste
r’s
stu
d
ies
in
1
9
8
0
a
t
t
h
e
F
a
c
u
l
ty
o
f
El
e
c
tri
c
a
l
En
g
i
n
e
e
rin
g
a
t
Wr
o
c
law
Un
iv
e
rsit
y
o
f
Tec
h
n
o
l
o
g
y
.
He
re
c
e
iv
e
d
P
h
.
D
.
i
n
e
n
g
i
n
e
e
rin
g
in
1
9
8
8
f
o
r
t
h
e
d
isse
rtatio
n
ti
tl
e
d
:
“
S
tatisti
c
a
l
d
e
c
isio
n
m
e
th
o
d
f
o
r
e
v
a
lu
a
ti
o
n
o
f
m
e
a
su
rin
g
a
l
g
o
ri
th
m
s
f
o
r
d
ig
it
a
l
d
istan
t
p
ro
tec
ti
o
n
s
”
.
I
n
2
0
0
6
h
e
c
o
m
p
lete
d
p
o
st
-
g
ra
d
u
a
t
e
stu
d
ies
a
t
th
e
F
a
c
u
lt
y
o
f
P
h
y
sic
s
a
t
t
h
e
Un
i
v
e
rsity
o
f
Wa
rsa
w.
Be
twe
e
n
2
0
1
1
-
1
2
h
e
wa
s
e
m
p
lo
y
e
d
b
y
th
e
c
o
m
p
a
n
y
In
g
e
n
ieria
IDO
M
I
n
tern
a
ti
o
n
a
l
S
.
A.
t
o
d
e
sig
n
a
c
o
n
c
e
p
t
o
f
c
o
n
st
ru
c
ti
n
g
p
o
we
r
s
y
ste
m
s
fo
r
h
ig
h
-
sp
e
e
d
r
a
il
trac
ti
o
n
s
Wr
o
c
law
-
P
o
z
n
a
n
-
Wars
z
a
wa
a
n
d
a
n
a
ly
se
d
th
e
ir
imp
a
c
t
o
n
t
h
e
n
a
ti
o
n
a
l
e
n
e
rg
y
s
y
ste
m
.
He
sp
e
c
ialize
s
in
issu
e
s
re
latin
g
to
e
lec
t
rica
l
p
o
we
r
e
n
g
i
n
e
e
rin
g
,
i
n
p
a
rti
c
u
lar
o
f
si
g
n
a
l
p
ro
c
e
ss
in
g
f
o
r
sy
ste
m
p
r
o
tec
ti
o
n
a
n
d
p
o
we
r
q
u
a
li
ty
.
He
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
les
z
e
k
.
lad
n
iak
@p
wr.e
d
u
.
p
l
.
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