Aging of Polyolefin Electrical Insulation - ACS Symposium Series

30

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Aging of Polyolefin Electrical Insulation K. D. KISS, H. C. DOEPKEN, JR., and N. SRINIVAS Phelps Dodge Cable and Wire Company, Yonkers, NY 10702 B. S. BERNSTEIN Electric Power Research Institute, Washington, DC 20006

Polyolefins are the preferred insulating materials due to a fortuitous combination of their properties: high resistivity and dielectric strength, low dielec t r i c constant and dissipation factor, low specific gravity, moderate melting range and good processability, adaptability to stabilization and compatability with additives and f i l l e r s and economy and availability on large scale. In power transmission and distribution cables rated 5 kV and above low density polyethylene (ΡΕ), crosslinked low density polyethylene (XLPE) and ethylene -propylene rubbers (EPR) are used in large quantities. A recent survey (1) shows that the combined length of underground power cables exceeds 190,000 miles in the U.S.A. Field data covering over 25% of this total re veals dielectric failures attributable to premature ageing beginning approximately 3 to 8 years after the installation (Figure 1). This is considered a serious indicator of potential hazard and has precipitated a major effort to define the problem areas, understand the causes with a view of eliminating or at least mini mizing them. Background Ageing Process i n S o l i d D i e l e c t r i c s . "Ageing" and l i f e time" are terms based on b i o l o g i c a l analogies, and, though widely used describe the investigated phenomena with limited accuracy. Kelen ( 2 ) suggests the use of the term "endurance", which i s the opposite though not the exact reverse of ageing. 0-8412-0485-3/79/47-095-433$08.50/0 ©

1979 A m e r i c a n C h e m i c a l Society

Eby; Durability of Macromolecular Materials ACS Symposium Series; American Chemical Society: Washington, DC, 1979.


DURABILITY O F M A C R O M O L E C U L A R M A T E R I A L S

1962

1965

1970

1975 Time, years

Figure 1.

Field performance of high voltage cables

Annealing Tree Formation

Figure 2.

Schematic life curve



30.

KISS E T A L .

Polyolefin

Electrical

Insulation

435

The inherent d i e l e c t r i c strength of polyethylene measured on t h i n f i l m s i s estimated as 600 to 800 kV/=

Whelan l o i d a l

(12)

presents

the

equation

for

two

hyperbo-

points: E max ^

V r t a n h l

x /

(fiTT j

( )

r

5

where:

This

correlation

calculation electrodes oratories at

the

the

of in

in

t i p

turn

may

t i a t e

adopted

stress

fold

(14).

gradual

Aschcraft

needle

studies.

protrusion

the

by

enhancement

double

the

trigger

Though

was

the

hundred

surface

= point to point dist.

treeing

of

free

= radius conductive point

stress

e l l i p s o i d ,

several

r C

the

test

used

or

on

the

enhancement to

level

immediate

the

of

of

in on

ratio may

d i e l e c t r i c

some of

breakdown

polymers

made

s p e c i f i c a l l y

for

high

occasional

ants

and

contribute

to

deterioration

properties. as

gels

Some or

of

the

these

prematurely

ethylene

particles

which

in

depending

on

color

in

or

i n i -

deterioration. clean,

such

in

to

protrusion

remarkably

nature

axes

increase

are

occur

lab-

radius

amount

insulation e l e c t r i c

the

the

the

smooth,

stress

for

(JL3) t i p

Depending

compared This

at

may

heat

appear

history.

are

voltage

contaminof

polymeric

corsslinked amber

to

Figure

in

poly-

dark 5

d i -

brown

shows


one


30.

KISS E T A L .

Polyolefin

Figure 5.

Electrical

Insulation

Gel particle in XLPE (10 ym)


441


442

DURABILITY O F

MACROMOLECULAR

MATERIALS

of these i n the center, the v e r t i c a l r i p p l e s are a r t i f a c t s caused by the c u t t i n g blade f o r c i n g the r e s i s t i n g g e l forward. Inorganic p a r t i c l e s (Fig. 6) such as meta l l i c f i l i n g s contribute to tree i n i t i a t i o n and hence gradual d e t e r i o r a t i o n . Along with contaminant nature, t h e i r shape, d i r e c t i o n and l o c a t i o n may amplify t h e i r detrimental e f f e c t . Those imbedded at the conductor s h i e l d - i n s u l a t i o n i n t e r f a c e (Figure 8) may act as protrusions and cause l o c a l i z e d s t r e s s enhancement. C e l l u l o s i c fibrous p a r t i c l e s (Figure 7) (15-20 mils, 0.38 to 0.51 mm) at about 10 per l i n e a r foot of cable were shown by Bahder (15) to lower the average AC breakdown strength by 40%. E x i s t i n g s p e c i f i c a t i o n s for 5 to 69 kV cables proh i b i t "any translucent material that i s l a r g e r than 50 m i l (2 mm) i n i t s r a d i a l vector p r o j e c t i o n " and "any contaminant larger than 10 mils (0.4 mm) i n i t s largest dimension" and l i m i t s those 2 to 5 mils (0.08 to 0.2 mm) to 15 per cubic inch (0.92 per ccm) (9.). Part of the contaminants may be present i n the p e l l e t i z e d raw materials, another part o r i g i n a t e s from m a t e r i a l handling and processing. The extrusion process and the a p p l i c a t i o n of screens removes the larger p a r t i c l e s or breaks them down. Ionic contamination may occur during the service l i f e due to corrosion products of the conductor or of the m e t a l l i c s h i e l d s entering the i n s u l a t i o n . Voids or c a v i t i e s are the most numerous of the imp e r f e c t i o n s . Their number i n steam cured XLPE i s e s t i mated as 10^ per cubic cm. (16) Their combined volume amounts to l e s s than 1% of the t o t a l , which computes as about 30 jam average diameter assuming s p h e r i c a l shape. This s p h e r i c a l shape probably applies to the majority of them though ovaloid shapes, roundish ones with i r regular corners, polygonals with s l i g h t l y rounded corners and long, narrow cracks have also been found ( F i g . 9); the l a t t e r ones may o r i g i n a t e from round voids. Void d i s t r i b u t i o n i s not uniform (15, 17). In the r a d i a l d i r e c t i o n of the cable r e l a t i v e l y few are l o c a t ed at the conductor side and at the outside surface, and the d i s t r i b u t i o n curve peaks between the midpoint and the outer surface (18). This d i s t r i b u t i o n i s associated with the e f f e c t of steam used to cure XLPE. The s o l u b i l i t y of water i s very low (50 to 70 ppm)



30.

KISS E T A L .

Polyolefin

Figure 6.

Figure 7.

Electrical

Insulation

Contamination in XLPE (600 fim)

Fibrous contamination (25 ym)


443

DURABILITY O F M A C R O M O L E C U L A R


444

Figure 8.

MATERIALS

Contamination at conductor shield-insulation interface (15 fim)

Figure 9.

Void (5 fim) and cracks



30.

KISS E T

AL.

Polyolefin

Electrical

Insulation

445

(19) i n polyethylene at room temperature, but reaches 4000 - 5000 ppm under the conditions p r e v a i l i n g i n the steam tube. Thus, most of t h i s absorbed water forms a d i s t i n c t separate phase when the crosslinked cable i s cooled and i s probably responsible f o r the majority of the voids. E s p e c i a l l y harmful are the voids at the conductor s h i e l d - i n s u l a t i o n i n t e r f a c e (Figure 10) which, when f i l l e d with a conductive l i q u i d , may act as protrusions. Even i n XLPE cables cured under dry conditions some voids e x i s t . These are thought to be due to the c o a l escence of c a t a l y s t by-products or i n t e r s p h e r u l i t i c space caused by c r y s t a l l i z a t i o n of the cooling polyethylene. Relative to the morphological structure, the larger voids were shown by P h i l l i p s (17) to occur at the i n t e r s t i c e s of spherulites, and the smaller ones along the s p h e r u l i t i c d i v i d e r s . S i m i l a r views were presented by Patsch (20). An opposing view (16, 21) places them i n the center of the spherulite l i k e structures (Figure 11) . In the f r e s h l y made XLPE cable the c a v i t i e s are f i l l e d with e i t h e r a gas (water vapor, a i r , nitrogen, methane, low molecular weight hydrocarbons) or a l i q u i d (water or organic l i q u i d s from the by-products of the decomposed curing agent). Even r a d i a t i o n crosslinked polyethylene contains voids, presumably caused by the evolution of hydrogen or low molecular weight hydrocarbons (22) (Figure 12). Both the gaseous and the l i q u i d by-products may escape gradually. Thermal treatment was shown to diminish void number and s i z e (18). This would necessitate an increase i n density and such an increase was reported by N i t t a and a l (6_) . E l e c t r i c stress and d i e l e c t r i c heating among other factors could r e s u l t i n a rearrangement of void d i s t r i b u t i o n , shape, s i z e and number, and i s a p o s s i b l e cause of some slowly occurring changes during s e r v i c e . Ageing Parameters Several of the t y p i c a l factors e f f e c t i n g service l i f e or ageing of polymers i n other a p p l i c a t i o n s can be eliminated on the basis that e i t h e r by themselves or i n combination they appear to cause less damage than




Figure 10. Void at conductor shield-insulation interface (4 fim)

Figure 11. Voids in center of spherulitic structures (5 fim)


MATERIALS


30.

KISS E T A L .

Polyolefin

Electrical

Insulation

Figure 12. Voids in radiation cross-linked polyethylene (1-8 fim)


447


448 others, ageing

therefore


of

Environment.

ultraviolet

whelming et

tection carbon

in

this

black

of

commonly

at

XLPE

a

oxygen

linking

of

e l e c t r i c a l

treeing

The a

fact

major

thermal dealing or

parent

to

concern

or

of

treatment

heat

Mangaraj

(16)

parameters frequency

the

such

as

and

in

in

per

a

the

of

factor

a n t i -

the

crosssystems

the on

reported preventing

limitation

the

with and

was

temperature

potential

concern. by

effect

with

in

compreeffect and

(6)

work

in

that

concentration

ap-

conductor

or

Nitta the

stabil-

is

this

of

(24)

other or

(26).

E l e c t r i c a l

of

by

a

investigations

emergency

of

to

was

performance,

effect

antioxidant

stress,

of

Beneficial

noted

comwould

due

temperature

performance

Most

is

temperature

deleterious

f i e l d

se

insulation

variety

others.

mechanical

prevented

on

operating

to

largely

t e l e -

satisfactory

is

amines

potential

major

acceleration

Mechanical

de-

in

during

provide

investigations.

among

combines

most

the

stabilizer

conductor

indirectly

either

laboratory

area

for

No

allowed

hensive

The

complicating

interest

Obviously,

considered

temperatures,

to

on

thiophenols,

interaction

aromatic

elevated

endurance. up

of

a v a i l -

(14).

of

directly

on

generated

temperature

degradation.

variable

on

out-

enhanced

efficient

A

oxidative

appear

the

of

is

based

or

highly

potential

point

jackpro-

data

years

limited

are

(25).

radicals

effect of

32

application.

diamine

found

and

over-

outer

presented

the

systems

Specific

beneficial

plex.

underground

the

employed

effect

(23)

insulation

A

ity

the

insulation the

adequate

by

(24).

The

providing

and

types

free

being

key

in

site.

applications

with

The

covering

paraphenylene

process.

buried.

the

protection

imply

role

the

since

of

of

is

of

surviving

Florida

in

cables

is

Gilroy PE

antioxidant

general

oxidants are

determining

limited,

thus

s t a b i l i t y

communication in

black

used

rivatives same

cables

respect.

protective

a b i l i t y

the

a

Exposure

very

containing

exposure

the

is

of

carbon

Oxidative by

light

majority

contains

door

playing

process.

Effect to

not

MATERIALS

axial

Stress.

and

Excessive the

radial axial

conductor

With

reference

deformations elongation

which

serves


as

are is an

30.

KISS E T A L .

internal high ly

the

designed

i a l

The

flow

of

either beyond

i s

with

a

e a r l i e r . fact i s

single

This that

assumptions

questionable kV/mm) l e v e l ,

(8

kv/mm)is other

i n

conclusions. a

applied

type

short

by

are

the

cable

predict

at

the

which term

generating

and i t s stress

v a l i d -

levels

could

present,

result

acceptance at

limit to

and prevent occur

stress,

despite

r e s t r i c t i v e

withstand

operating long

i n

l i f e ,

would

to

I t s conditions

data,

suitable

in

presented

used

set

and

referred

manufacturers.

tests

i n

(2)

basis

voluntary

some

failures

time

A t

5 minute a

by i t s e l f

test

using

voltage

service

controlled

service

no

associated

factors

postulating

project

although

be

parameter.

theoretical

Similarly, to

high

during

stress

widely

l i f e

shows

d i s t i n c t

i n

to

equation

i s

service

limit.

(27)

under

l i f e

without

acceptance

mortality" e s s a r i l y

present

with

stress

Tanaka

accelerated

lacks

deficiencies

areas

contributing

the

include

(6

a t i v e l y

matersuch

(20)

strength

the key ageing

from

c r i t e r i a

of

internal by

variable

(28).

in

and

one

means

during

Patsch

E l e c t r i c a l

by

i t

test

(9.)

or

correlation

as

major

at

inherent

other

95% c o n f i d e n c e

of

questionable

c r i t e r i a

the

poor-

especially

applied

by

at

due t o

i n i t i a l l y

effects.

other

projections

i t y

solved

developed

cusp

the

considered

as

the

i s

are not

whether or

reported

characterized

l i f e

may o c c u r

range

supports

section

d i e l e c t r i c

formation.

combination effect

the

on the

been

with tree above

stress cable

development

has

cross

problems

deleterious

insulation The

at

and can be

made

pattern

l i f e

deformation

temperature

long

these

internal

have

effect

or a

449

Insulation

changes.

freshly

could

is

of

limitations

the

Radial

shields

However,

design

Electrical

allowed

the weight

point.


support.

end o f

when

as

Polyolefin

but

performance

150

of

V/mil

200

This

V/mil test

pinpoint the

"infant

after

a

r e l -

do n o t

nec-

under

f i e l d

certain

types

conditions. Higher of f u l

frequency

processes tool

to

leading study

testing to

tree

accelerates

premature formation

failure,

and

is

a

use-

(29.) .

Treeing When pated

f i e l d

lifetime

performance i n

solid

indicated

d i e l e c t r i c

lower

than

insulation,


a n t i c i close

450


inspection of

of

dendritic

the

site

of

d i e l e c t r i c

established trees

and


cables.

recovered

between

the

to

understand

of

assessing The

the

longest

this

tree

strength

of

p a r t i a l l y

observations the

nature effect

the

i t

only

nearby the

tree

than

the

longest

a

trees

phenomena ageing

is

strength the

be

to

examined

and

caused

the

remaining

level*

excessive

tree-

point

catastrophic the

where

failure.

Since

breakdown process., i t

failure

nearby

view

and

tolerable

the

in

effort

with a

process

that

of

aged

major

p r a c t i c a l l y view

destroyed

can

that

the

a

was

types

is

assumed

had

to

be

to

be

the

tree

longer f i r s t

f a i l . Types

the

of

Trees.

appearance

16).

Other

terms

like

dendrite,

of

The

some

broccoli, etc

•

(X)

Though

and

overlapping

some

four

types

of

no

The short,

very

which

is

Since

this

cal

tree

unique is

They the

hollow They

are

down.

In

interface lation weeks

corona be

fast

shield or

in

as

the

of

or

tape

to

lined a

fine

within cause

in

they the a

can

at

a

chemi-

without

higher

decomposed high

stain-

initiated

consist

hypodermic

of polymer.

syringe

stress

may

insulation initiated

conductor insulation

failure.

as

shield.

the

stresses

They

be

trees.

tree,

conductor

immediate

with

type

the and

(J5)

discharge

at

by

importance.

with

propagation

exists,

design,

voltage.

is

accepted,

chemical

observe

insulation

through

service

to

a

used

to

delta,

them

Lanctoe

broccoli

e l e c t r i c a l

channels of

and by

of

13

by

e l e c t r i c a l

limited

easy

by

insulation

months

with

frequently

resulting

actual of

colored,

inception

rate

trees,

is

s t i l l

as

described

are

described

nomenclature

water

(Figures

streamer,

controversy

is

descriptive

describe

c l a s s i f i e d

cables a

f i l l e d

Their

extremely

and

caused

connected

can

(14).

to

trees

imperfections

than

t i e ,

considered

E l e c t r i c a l ing.

bow way

dark

to

not

adequately

plume,

are

is

structures

Another

tree

dense, is

are

trees,

chemical

"tree"

the

uniform

trees

electrochemical

word

of

structures

origin.

at

to

causes

usually

these

on

accepted

breakdown

tree

initiated

of

near

Correlation

breakdown

that to

(30).

presence 13)

certain

their

is

failures

the

(Figure

of

minimizing

lowers

revealed

"trees'*

presence

generally

ing

or

the

These

possibly

cables

structures

MATERIALS

shield and

Under

at or

take

be

breakthe insudays,

laboratory



30.

KISS E T A L .

Polyolefin

Electrical

Figure 13.

Figure 14.

Insulation

Dendritic tree

Electrochemical tree


451



Figure 15.

Figure 16.

Water tree

Bowtie tree (40 fim)


MATERIALS

30.

KISS E T A L .

conditions

Polyolefin

high

Electrical

stress

is

453

Insulation

used

to

accelerate

their

formation. Electrochemical w a t e r - f i l l e d

voids

ed

by

channels.

very

stresses age,


(or water)

of

fine

s i g n i f i c a n t l y

i . e . ,

charge. a r i l y

i n

the

slowly

(29)

and evidence breakdown They

e l e c t r i c a l

trees.

or

iron

methylene

salts

chemical used

or

t i e at

may s t a i n (31)

have

voids

conductor aligned The

been

do

the in

(5.)

or

alkaline referred

though

the

not

necessnecessarily insulation

appearance such

they as

than

as

copper

can be

solution. to

volt-

d i s -

propagate

f u l l

chemicals

them i n

(not

They

they

diffuse

(Figure

or

stained

Electro-

water

two terms

or

to

to

the

effect

ageing,

failure

on the

service

However,

their

be

the

calculate

trees,

are

often

widely i s

of

place

below

eter.

used

1 2 kv/mm i n

In practice

small

enough

operating

to

i t

avoid

Even which

propagate

i f

weaken

not the

i n

that

less

possible

to

to

17)

is

i n i t i a t e 3.8

kv/mm i n

2 5 jam i n the i n

a

According

discharge

keep

discharges

i n

possi-

discharge

than

when direct-

stress I t

(32).

and no p a r t i a l

p a r t i a l

trees,

f a i l u r e

(Figure

to

insulation

takes

diam-

voids

voids

at

stress.

Electrochemical levels,

is

of

level

voids

p a r t i a l

voids

They

direction.

electrochemi-

level.

stress

induce

2 5 0 jam d i a m e t e r ,

and

requires

correlation to

shield.

E l e c t r i c a l

spherical

i n i -

either

contribution

and cause

inception

are to

f i e l d

on the q u a l i t y

t h e minimum

necessary

voids

their

e l e c t r i -

They

insulation

e l e c t r i c a l

formation

i n

either

connected

e l e c t r i c a l

fast

corona

discharges

this

stress

the

of

o r i g i n . not

conditions.

ly.

to

of

depends

void

p a r t i a l

i n

and hence

can propagate

above

can be

contaminants

shield

on

i n i t i a t e d ,

16)

nature

p a r a l l e l

relative

trees

premature

to

that

at

p a r t i a l

phase

bridging

Dissolved

trees

are

ble

when

chemicals,

the

and

exists

consist connect-

inception

measurable

liquid

to be

i n i t i a t e d

corona

prerequisite.

electrochemical

tiated

cal

a

can be

the

of

appear

may n o t

interchangeably. Bow

c a l

They

a r e more

blue

trees

containing

a

even

thickness.

by

of

i s

trees

may o r

below

absence

The presence

water)

cause

which

trees

slowly

immediately insulation

turn

cause

form but

do

causing

at

r e l a t i v e l y

cause the

a n d may s i r e

failures.

The

low

stress

deterioration.

failure

they

e l e c t r i c a l increasing

may

trees rate


of


454

DURABILITY O F M A C R O M O L E C U L A R M A T E R I A L S

V o i d Diameter,

Figure 17.

nm

Calculated partial discharge inception voltage


30.

KISS E T A L .

failures slow

with

the

subject

major

l i f e

to

major

from

Institute

chemical

trees

major

ductors iments 300,000

trees

course

of

applied

were

growth. kHz

frequency

maximum

i n i t i a t i o n

of

insulation

surface.

18,

show

t i a l l y

that

with

effect i n

temperature trees, est

trees

trends.

increased

summary a

In

methods

Figure

from

600 t o

actual

fore

i t

i s

ance

of

this

a

3.4,

to

5.0

and

made

8.0 of

70 d a y s .

summarized penetrate PE

as

tree

and a t

were

i n an

60 t o

The

the i n

inner

Figure

exponenthe

appears

0 . 7 5 mm

t o

be

at

accelerating

factor

8000

70°C

the

Hz.

stress

and the

time.

of

of

the

scatter

of

specimens to

i n i t i a t i o n

to

A t

t h e number

length

Large

lengths

about

of

longdata

and

of

establish and the

simultaneously.

various 60

of

propaThe

trees

600 H z ,

but

shows minor

Hz.

the

frequency

contributor

correlation

emerged

correlates

applied

the

8000

the were

scratching

evaluation

service,

not

up

by

i n

for

stress 2,

number

from

during

to

progresses

19

increase

of

a high both

the trees

i n

drastic

effect

with

experOver

methods

temperature

as

of

length

of

Using con-

XLPE.

kv/mm

Obviously, of

rate

range

square

accelerating

length

frequency

average

the use

s t a t i s t i c a l gation

of the

i n

stress

i n

The

the

accelerated

observations

required as

electro-

(29).

conditions.

Voltage

results,

growth

and 3.4

their

mandated

time

Power

of

obtained.

induced

The

that

formation. or

and measured

tree

was

as high

studied

their

aqueous

70°C

applied

Tree

twice

The was

the

the

insulation. least

trees

the

real

quantify

round

stresses

at

and treeing

and of

was t o

i n f l u e n t i a l

voltage

i n

E l e c t r i c effects

and s t a t i s t i c a l

applied

believed

materials

f o r

Parameters.

Average

kV/mm w e r e

average

under

the data

most

6.8

work

observed

analyze

condition

the

# 1 4 AWG s o l i d

the project,

to

i s

reflect

treeing.

ageing

0 . 7 5 mm i n s u l a t i o n ,

Accelerating the

this

performed

could

treeing.

the

cable

responsible

with

and with were

of

by

evaluate

extruded

objective wires

i t

d i e l e c t r i c

funded

to

i n

parameters

coated

to

electrochemical was

Research primary

l i f e

electrochemical

qualifications,

study

455

Insulation

service

due t o

contribution

results A

Electrical

increasing

deterioration

Though


Polyolefin

i s

to i t s

i s

ageing.

constant, The

a p p l i c a b i l i t y

there-

s i g n i f i c to


accel-



Figure 18.

Effect of applied stress on tree growth


MATERIALS


KISS E T A L .

Polyolefin

Figure 19.

Electrical

Insulation

Effect of frequency on tree growth



458

DURABILITY

OF MACROMOLECULAR MATERIALS

erate ageing i n laboratory i n v e s t i g a t i o n s , and p o s s i b l y to serve as a q u a l i t y c o n t r o l technique. The e f f e c t of temperature on tree growth i s complex and required s t a t i s t i c a l evaluation of a large number of samples. At 4600 Hz and 30°C, 3.4 kv/mm stress the growth rate was 5 to 8 times higher f o r PE than f o r XLPE. Increasing the temperature to 90°C lowered the rate f o r both i n s u l a t i o n s by a f a c t o r of about 2. In both cases 0.1 NCuSO^ increased the rate obtained with l o c a l (Yonkers) tap water. Figure 20 presents the trend as days to penetrate the 0.75 mm i n s u l a t i o n by the longest t r e e . S i m i l a r trends were found f o r average tree lengths. EPR, on the other hand, shows s l i g h t l y increasing rates with higher temperatures. Organic chemicals as additives to e i t h e r PE or XLPE influence tree growth. The comparison of antioxidants, peroxides, and t h e i r decomposition products was r e v e a l ing. The most commonly used c r o s s l i n k i n g agent, d i cumyl peroxide (dicup), i s t y p i c a l l y applied at about 2% l e v e l i n the c r o s s l i n k a b l e polymer. In the crossl i n k i n g process, decomposition products are generated and amount to the same 2% or s l i g h t l y l e s s . Their r e l a t i v e r a t i o s vary somewhat according to the reported values (33.) . The bulk appear to be cumyl alcohol, with lesser amounts of acetophenone and traces of

Aging of Polyolefin Electrical Insulation - ACS Symposium Series

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