KB005
4
KILOVAR , BRIEFS FROM THE McGRAW-EDISON POWER SYSTEMS CAPACITOR PLANT Date November, 1985 GREENWOOD, SOUTH CAROLINA lssue 5 HARMONICS AND CAPACITORS APPLYING CAPACITORS IN THE HARMONIC ENVIRONMENT The two previous issues of Kilovar Briefs discussed the source of harmonics and effects of applying capacitors in a harmonic environment. This issue will discuss the proper application of capacitors in a harmonic environment. The economic benefits of applying capacitors to improve the system power factor can be achieved in a harmonic environment without compromising the system or the equipment. This i s accomplished by using the capacitor bank connected in series with a reactor as a filter circuit tuned to some specific frequency. The objectives of the filter design are as follows: 1. Provide the required vars for the system. 2. Assure that the filter is a very low impedance shunt at at critical characteristic harmonic frequencies of the path for the predominant harmonic currents or, 3. Tune the filter branch to be inductive so that the harmonic currents injected into the system are deamplified by the presence of the filter capacitor bank. In this article, we will discuss objective 3. A reactor is selected to tune the capacitor bank to a frequency that is below the first characteristic harmonic of the harmonic source. The advantage of this approach is: 1. Lower current ratings for the equipment. 2. Less stringent tuning requirements. Additional capacitor vars are required in filter applications to compensate for the var loss i n the tuning reactors. The filter tuning fre q uenc y is selected to be approximately 5% below the first characteristic harmonic of the system. In the case of a six pulse rectifer where the first characteristic harmonic is the 5th, the filter is tuned to a frequency of 4.7 times the fundamental power frequency. The equivalent circuit for a capacitor i n a harmonic environment i s shown in Figure 1A. Installing a reactor in series with the capacitor bank changes the equivalent circuit of Figure 1A to that shown i n Figure 1B. Figure 1A - Applying Capacitors Without Harmonic Protection Figure 1B Applying Capacitors With Harmonic Protection Pow Systems Division McGraw-Edison Company Post Office Box 1224 Greenwood,SC 29648
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Transcript of KB005
KILOVAR , BRIEFS FROM THE McGRAW-EDISON POWER SYSTEMS CAPACITOR PLANT
Date November, 1985 GREENWOOD, SOUTH CAROLINA lssue 5
HARMONICS AND CAPACITORS APPLYING CAPACITORS IN THE HARMONIC ENVIRONMENT
The t w o p r e v i o u s i s s u e s o f K i l o v a r B r i e f s d i s c u s s e d t h e s o u r c e o f h a r m o n i c s and e f f e c t s o f a p p l y i n g c a p a c i t o r s i n a h a r m o n i c e n v i r o n m e n t . T h i s i s s u e w i l l d i s c u s s t h e p r o p e r a p p l i c a t i o n o f c a p a c i t o r s i n a h a r m o n i c e n v i r o n m e n t .
The economic b e n e f i t s o f a p p l y i n g c a p a c i t o r s t o i m p r o v e t h e s y s t e m power f a c t o r c a n b e a c h i e v e d i n a h a r m o n i c e n v i r o n m e n t w i t h o u t c o m p r o m i s i n g t h e s y s t e m o r t h e e q u i p m e n t . T h i s i s a c c o m p l i s h e d b y u s i n g t h e c a p a c i t o r bank c o n n e c t e d i n s e r i e s w i t h a r e a c t o r as a f i l t e r c i r c u i t t u n e d t o some s p e c i f i c f r e q u e n c y .
The o b j e c t i v e s o f t h e f i l t e r d e s i g n a r e a s f o l l o w s : 1. P r o v i d e t h e r e q u i r e d v a r s f o r t h e sys tem. 2. A s s u r e t h a t t h e f i l t e r i s a v e r y l o w impedance s h u n t a t
a t c r i t i c a l c h a r a c t e r i s t i c h a r m o n i c f r e q u e n c i e s o f t h e p a t h f o r t h e p r e d o m i n a n t h a r m o n i c c u r r e n t s o r ,
3. Tune t h e f i l t e r b r a n c h t o b e i n d u c t i v e s o t h a t t h e h a r m o n i c c u r r e n t s i n j e c t e d i n t o t h e s y s t e m a r e d e a m p l i f i e d b y t h e p r e s e n c e o f t h e f i l t e r c a p a c i t o r bank.
I n t h i s a r t i c l e , we w i l l d i s c u s s o b j e c t i v e 3. A r e a c t o r i s s e l e c t e d t o t u n e t h e c a p a c i t o r bank t o a f r e q u e n c y t h a t i s b e l o w t h e f i r s t c h a r a c t e r i s t i c h a r m o n i c o f t h e h a r m o n i c sou rce . The a d v a n t a g e o f t h i s a p p r o a c h i s :
1. Lower c u r r e n t r a t i n g s f o r t h e e q u i p m e n t . 2. L e s s s t r i n g e n t t u n i n g r e q u i r e m e n t s .
A d d i t i o n a l c a p a c i t o r v a r s a r e r e q u i r e d i n f i l t e r a p p l i c a t i o n s t o compensa te f o r t h e v a r l o s s i n t h e t u n i n g r e a c t o r s .
The f i l t e r t u n i n g f r e q u e n c y i s s e l e c t e d t o b e a p p r o x i m a t e l y 5% b e l o w t h e f i r s t c h a r a c t e r i s t i c h a r m o n i c o f t h e system. I n t h e c a s e o f a s i x p u l s e r e c t i f e r w h e r e t h e f i r s t c h a r a c t e r i s t i c h a r m o n i c i s t h e 5 t h , t h e f i l t e r i s t u n e d t o a f r e q u e n c y o f 4.7 t i m e s t h e f u n d a m e n t a l power f r e q u e n c y .
The e q u i v a l e n t c i r c u i t f o r a c a p a c i t o r i n a h a r m o n i c e n v i r o n m e n t i s shown i n F i g u r e 1 A . I n s t a l l i n g a r e a c t o r i n s e r i e s w i t h t h e c a p a c i t o r bank changes t h e e q u i v a l e n t c i r c u i t o f F i g u r e 1 A t o t h a t shown i n F i g u r e 1B.
F i g u r e 1A - App ly ing C a p a c i t o r s W i t h o u t
Harmonic P r o t e c t i o n
F i g u r e 1B A p p l y i n g C a p a c i t o r s W i t h Harmonic P r o t e c t i o n
P o w Systems DivisionMcGraw-EdisonCompany Post OfficeBox 1224 Greenwood,SC 29648
The h a r m o n i c s p e c t r u m was d e f i n e d i n I s s u e 4 o f t h e K i l o v a r B r i e f s and t h e c i r c u i t i n F i g u r e 1A was a n a l y z e d . We now a n a l y z e t h e c i r c u i t shown i n f i g u r e 1B. The f i l t e r impedance i s c a l c u l a t e d a s :
The f i l t e r i s d e s i g n e d s o t h a t a t a f r e q u e n c y o f 4.7 t i m e s t h e f u n d a m e n t a l f r e q u e n c y t h e r e a c t o r and c a p a c i t o r a r e s e r i e s r e s o n a n t . T h a t i s :
T h i s a s s u r e s t h a t a t f r e q u e n c i e s g r e a t e r t h a n 4.7 t i m e s t h e f u n d a m e n t a l , t h e c a p a c i t o r r e a c t o r b r a n c h a p p e a r s i n d u c t i v e . S i n c e t h e s i x - p u l s e r e c t i f i e r p r o d u c e s no h a r m o n i c c u r r e n t b e l o w t h e 5 t h h a r m o n i c , h a r m o n i c c u r r e n t a m p l i c a t i o n c a n n o t o c c u r due t o t h e p r e s e n c e o f t h e power f a c t o r c o r r e c t i o n c a p a c i t o r .
. ,
R e c t i f i e r Network Impedance Spectrum Wi th A C a p a c i t o r F i l t e r Tuned To The 4 .7 Harmonic
P a r a l l e l Resonant
HARMONIC ORDER F i g u r e 2
T h i s i s b e s t i l l u s t r a t e d g r a p h i c a l l y i n F i g u r e 2. The f i l t e r impedance, Z F ( n ) , i s p l o t t e d as f u n c t i o n o f f r e q u e n c y . I t i s n o t e d t h a t i t c r o s s e s z e r o a t 4.7 t i m e s t h e f u n d a m e n t a l f r e q u e n c y . The parallel r e s o n a n t f r e q u e n c y i s d e t e r m i ned g r a p h i c a l l y as t h e i n t e r s e c t i o n o f t h e n e g a t i v e v a l u e o f Z S ( n ) w i t h ZF (n ) . I t i s o b s e r v e d t h a t t h e p a r a l l e l r e s o n a n t f r e q u e n c y a l w a y s o c c u r s a t a v a l u e l e s s t h a n t h e s e r i e s r e s o n a n t f r e q u e n c y o f t h e c a p a c i t o r / r e a c t o r f i l t e r sys tem. I f t h e f i l t e r t u n i n g p o i n t i s a t o r b e l o w t h e f i r s t c h a r a c t e r i s t i c h a r m o n i c f r e q u e n c y o f t h e m o t o r d r i v e , h a r m o n i c c u r r e n t a m p l i f i c a t i o n i s n o t a p rob lem.
The f i l t e r d e s i g n i s a n i t e r a t i v e p r o
o
c e s s a n d i s d e s c r i b e d be low. The r e a c t i v e power r a t i n g o f t h e c a p a c i t o r bank r e q u i r e d t o c o r r e c t t h e c o n v e r t e r power f a c t o r i s d e t e r m i n e d t h r o u g h n o r m a l power c o r r e c t i o n a n a l y s i s . From t h i s , t h e power f r e q u e n c y impedance o f t h e c a p a c i t o r bank i s c a l c u l a t e d as:
2 Z c ( l ) = (VLL) I Qcap ( 3 )
'The r e a c t o r impedance a t t h e power f r e q u e n c y r e q u i r e d t o t u n e t h e c a p a c i t o r bank i n t o r e s o n a n c e a t a h a r m o n i c , n, i s :
ZL ( l ) = ZC( l ) / n 2
(4) i
The p r e s e n c e o f t h e r e a c t o r i n s e r i e s w i t h t h e c a p a c i t o r causes a power f r e q u e n c y v o l t a g e r i s e t h a t t h e c a p a c i t o r bank must b e r a t e d t o w i t h s t a n d . I f h a r m o n i c v o l t a g e s a r e s i g n i f i c a n t , t h e i r m a g n i t u d e s h o u l d b e summed l i n e a r l y w i t h t h e power f r e q u e n c y v o l t a g e and t h e c a p a c i t o r banks s h o u l d b e r a t e d a p p r o x i m a t e l y as shown be low. T h i s l i n e t o l i n e v o l t a g e r i s e i s c a l c u l a t e d as:
A new c a p a c i t o r bank r e a c t i v e power r a t i n g i s t h e n c a l c u l a t e d f o r p u r p o s e o f s p e c i f y i n g t h e e q u i p m e n t .
(6)
The r e a c t i v e power r a t i n g Q c a p s h o u l d b e a d j u s t e d t o p i c k a s t a n d a r d s i z e bank r a t i n g . The may n e c e s s i t a t e r e c a l c u l a t i n g t h e c a p a c i t o r impedance, Z C ( l ) , and c o n s e q u e n t l y t h e r e a c t o r impedance,
The p r e s e n c e o f t h e f i l t e r r e a c t o r r e d u c e s t h e e f f e c t i v e K v a r o u t p u t o f t h e bank w h i c h i s c a l c u l a t e d a s f o l l o w s :
If t h e r e a c t i v e power o u t p u t o f t h e f i l t e r i s i n a d e q u a t e t h e c a p a c i t o r bank r e a c t i v e power r a t i n g s h o u l d b e i n c r e a s e d and t h e d e s i g n p r o c e d u r e r e p e a t e d i t e r a t i v e l y t o m a i n t a i n t h e p r o p e r power f a c t o r w i t h t h e g i v e n f i l t e r t u n i n g c o n s t r a i n t s .
I
We w i l l now d e s i g n a f i l t e r t u n e d t o t h e 4.7 h a r m o n i c f o r t h e e x a m p l e p r o b l e m p r e s e n t e d i n I s s u e 4 o f . t h e K i l o v a r B r i e f s . A d e f i n i t i o n o f k e y p a r a m e t e r s i s summar ized b e l o w f o r t h e c i r c u i t i n f i g u r e 1 A .
'Load i s a s i x p u l s e t h y r i s t o r d r i v e s y s t e m (6300 K V A , 4160 V) 'Source i s a t r a n s f o r m e r (6300 K V A , 10% impedance) ' C a p a c i t o r bank i s 2400 K v a r , 4160 V ( 9 9 % power f a c t o r )
ZC( l ) = ( 4 1 6 0 ) 2 / (2400 x l03) = 7 . 2 1 ( from equation 3) 2 Z L ( l ) = 7.21 / (4.7) = .33 (from equation 4)
v 2 (n) 4460 v = (4160) (4.7 - 1) +
(from equation 5)
N e x t we s e l e c t a 4800 v o l t L- L v o l t a g e - r a t i n g ( t h e c l o s e s t s t a n d a r d r a t i n g ) f o r t h e c a p a c i t o r and c a l c u l a t e t h e K v a r r a t i n g
(7.21 x = 3196 Kvar ( from equation 6)
LGerard
Text Box
Ω
LGerard
Text Box
Ω
Nex t we choose a s t a n d a r d K v a r s i z e and r e c a l c u l a t e c a p a c i t o r andr e a c t o r impedance.
Let QCap
3 x ( f r o m equation 3)
= 7.68 = ( from equation 4)
The a c t u a l v a r o u t p u t o f t h e f i l t e r i s c a l c u l a t e d as :
t = (7.68 - x = 2361 Kvar ( from equation 7)
The power f a c t o r o f t h e c i r c u i t s h o u l d be checked t o make s u r e t h e f i l t e r r a t i n g i s adequate . F o r o u r examp le t h e power f a c t o r i s 99%.
T a b l e I summarizes t h e c i r c u i t c u r r e n t s and v o l t a g e s w i t h t h e 4.7 h a r m o n i c s f i l t e r i n s t a l l e d and u s i n g a 3000 K v a r , 4800 v o l t c a p a c i t o r bank.
THE S U M M A R Y OF CIRCUIT CURRENTS AND VOLTAGE WITH FILTER INSTALLED --
I H ( n ) I (n ) I s ( n ) Capacitor
Harmonic Voltage Order Amps Amps Amps Vol ts
2514.60
The l i n e a r sum o f t h e v o l t a g e s a c r o s s t h e c a p a c i t o r s i s 2806 v o l t s (L- N) . T h i s v a l u e i s used t o s e l e c t t h e c a p a c i t o r u n i t r a t i n g . T h i s app roach assumes t h a t t h e r e i s no phase s h i f t be tween h a r m o n i c components and r e p r e s e n t s t h e h i g h e s t v o l t a g e m a g n i t u d e t h e c a p a c i t o r d i e l e c t r i c s y s t e m w i l l b e exposed. As a r e s u l t , 2770 v o l t u n i t s a r e used i n t h e bank, w h i c h a r e t h e c l o s e s t s t a n d a r d r a t i n g a v a i l a b l e .
The t o t a l v o l t a g e d i s t o r t i o n ( d e f i n e d i n i s s u e # 4 o f t h e K i l o v a r B r i e f s ) i s 105% a t t h e bus compared t o 135% without t h e f i l t e r .
A S e v i d e n c e d b y t h i s example, c a p a c i t o r banks c a n be e f f e c t i v e l y a p p l i e d i n t h e h a r m o n i c e n v i r o n m e n t t h r o u g h t h e a p p l i c a t i o n s o f f i l t e r s . I n g e n e r a l , t h e a d d i t i o n a l c o s t o f t h e r e a c t o r equ ipment does n o t s i g n i f i c a n t l y i n c r e a s e t h e payback p o i n t o f t h e power f a c t o r c o m p e n s a t i o n equipmment.
