Restoring System Stability by Underfrequency Load Shedding in Circumstances of Sudden Supply Deficiency

RESTORING SYSTEM STABILITY BY UNDERFREQUENCY LOAD SHEDDING IN CIRCUMSTANCES OF SUDDEN SUPPLY DEFICIENCY P. Harrison BBC Broum Boveri & Co., Baden, Switzerland

Abstract. The factors upon which a load shedding programme is built up are explained. A method of deriving a programme is described, which differs from previous practice in that it inherently returns the frequency to near rating. The possibility of the frequency stabilising at a low level is only a secondary risk and a back-up scheme to cope with this situation is also described. Keywords.

Load shedding; System stability; System failure and recovery.

INTRODUCTION

This paper is concerned with the application of underfrequency load shedding to restoring a stable situation in the deficient islands. The same considerations may be applicable at the highest voltage level when using underfrequency relays to form the islands.

Various features of an electrical power system influence its vulnerability to complete system collapse. Some of these apply equally to most modern systems, others arise from the local situation. A common feature, for example, is the the trend to larger machine ratings for economic reasons, but with the disadvantage that the loss of one of these units cannot always be covered by the available reserves. On the other hand, instability may be a constant threat in a particular system, because of the distance between the centres of generation and load, with the risk of tripping generators or lines. System design and also operating routines therefore play an important role and the proper choice of both is a pre-condition of a successful load shedding scheme. In the case of a large hierarchially organised system of networks at different voltage levels, underfrequency load shedding will be only one of at least three functions which are necessary, if serious disruptions at the highest level are not to lead to a disorderly disintegration of the whole system. The other two are means of dividing the system up into predetermined "islands", and means of frequency control in the islands so that they can ultimately be re-synchronised to the grid. The islands must have a minimum of generation to make the whole thing worthwhile. The actual amount varies with situation, but 40 to 50 percent would be a reasonable figure. The fact that some of the islands were not generating 100 percent of their requirement before the event means that other islands will have an excess of generation, so that in these further measures such a braking resistors may be necessary to guard against overfrequency (1).

SYSTEM BEHAVIOUR WHEN OVERLOADED WITH A VIEW TO LOAD SHEDDING Where after some event the load connected to an electrical system exceeds the power being generated by it, i t will respond with a reduction in frequency. The exact dynamic behaviour of the frequency, however, is difficult to calculate because of constant changes in such parameters as system configuration, degree of generation self-sufficiency, energy deficit, nature of the load etc. Therefore a number of simplifications and approximations have to be made which, on the other hand, have proved sufficiently accurate when establishing practical load shedding programmes. Firstly, governor action is normally neglected, because the level of the spinning reserves varies greatly and in any event could not be made available fast enough (typically at the most about 20 percent of the reserves in the first 5 to 10 s). The rate at which frequency will fall and possibly stabilise at a lower level depends on three factors: the percentage overload, the inertia of the system and the load reduction factor of the system. From the point of view of the load shedding programme, it is the maximum percentage overload which is of interest, as this determines the overall frequency range of the scheme and the overall block of load which must be shed. The

13

P. Harrison

14

value should be a practical one relating the essential loads to the available generation. Clearly the system must be operated so that the generation within the island can always cover the load deemed to be essential, if the bulk supply infeed were to be lost. This constraint could override purely economic operating considerations. In any event, the information required is available from system operations, where the dispatcher has at his disposal the prospective levels of import and local generation for each day and each hour of the year. Prognoses will normally also exist for a number of years in advance. Thus the maximum percentage loss of bulk supply can be determined, so that percentage overload

=

load - local generation x 100 local generation

The inertia of the physical mass of the rotating machines enables an electrical system to absorb load surges to some degree. This ability is expressed as the inertia constant H and defined as: kinetic energy total apparent power of the rotating machines

H

(s)

For a 50 Hzr system this can be written: H = 12,3

GD2

where GD p S

2

moment of inertia number of pole pairs apparent power

Typical values are: small industrial units larger turbo-alternators pump-storage machines other hydro machines

5 to 4 to 3 to 2 to

8 s

7 s 4 s 3 s

H for a complete system can be derived from the constants of the individual machines connected to it, but in practice it is better to determine H by a staged test. Depending on the nature of the load, system loading actually reduces with frequency. If this were not so, it would not be possible for the frequency to stabilise at a lower level (other than with load shedding). Stabilisation at a frequency below rating means that generation and load are balanced. The percentage reduction in load for a 1 percent reduction in frequency is referred to as d Studies of various systems indicate values of d within the range of 1,2 to 3 or even 7-8 percent (2). Fig. 1 and Fig. 2 show the relationship between the three quantities percentage overload, inertia constant and load reduction and their influence on frequency for given values of each. This subject is dealt with in greater detail in (2).

LOAD SHEDDING PROGRAMME

The frequency in an interconnected system is the same at all voltage levels and all consumers are affected equally by an overload. Conversely, load shed at any voltage level will improve the situation of the whole system. Although to arrest frequency decline and to raise the frequency subsequently to near rating more load has to be shed than corresponds to the deficit, as little as possible above that absolutely necessary should be shed. In fact if too much load is shed, the system may become unstable. A me sure of fine control must therefore be included. A further consideration is that certain categories of load are usually given prioritory. To satisfy these demands underfrequency load shedding must be applied at the distribution voltage level, where the number of feeders having the appropriate ratings and permitting the grouping of consumers are available. As already stated, one speaks of percentage overload, that is, the load is referred to the available generation. On the other hand, the percentage load which is shed is referred to the load. For example, if 20 percent of the load is shed in response to an initial overload of 60 percent, the remaining overload is 28 percent. This of course assumes that the percentage of load allocated to a particular load shedding step remains reasonably reliable with fluctuations in total load. Each percentage step should therefore have about the same cross-section of types of consumers, which may come in conflict with grading the consumers according to priority. If the programme is to be successful, the frequency excursion must be reversed before the underfrequency relays of the generators can isolate the machines from the system. Hitherto, the lowest frequency setting for load shedding has been chosen 1 Hz above this value, usually 48 or 48,5 Hz in a 50 Hz system. One to three further steps would then be evenly spaced up to 49 or 49,5 Hz. In this paper an attempt will be made to indicate a more purposeful procedure for arriving at the frequency settings. The objective of the following procedure is not just to prevent system collapse, but also to bring the frequency back towards rating. Firstly the total load to be shed for the worst practical overload should be chosen about 5 to la percent above that which would be required to merely stabilise the frequency i.e. total load to max. overload p.u. 1 + max. overload be shed For example, an overload of 60 percent requires 37,5 percent to be shed to stabilise the frequency. By neglecting d and choosing 45 percent the frequency must return to rating. The first block of load is chosen in relation to the spinning reserves. Assuming these to be 5 percent then the first block should be la percent. The remaining 35 percent

15

Restoring system stability can be split for the moment into two blocks of 10 percent and 25 percent. Intervention by the load shedding scheme is not required for small overloads for which spinning reserves can be mobilised given sufficient time. The frequency setting for shedding the first block of load is therefore also selected in relation to the spinning reserves and the influence of the load reduction factor d. From Fig. 3 can be seen that if the load reduction factor of the system were d= 3, the frequency would stabilise at a little above 49,2 Hz for a 5 percent overload. A frequency setting of 49,1 Hz means that in theory the load shedding scheme would not intervene for overloads less than 5,75 percent. At this overload and after mobilising the spinning reserves the frequency could be expected to settle at about 49,87 Hz (d = 3 ), which can be tolerated until measures can be taken such as the starting of a gas turbine. An arbitrary setting of 49,5 Hz, on the other hand would shed 10 percent load for an overload of only 3 percent. The frequency settings for the other two chosen blocks of load can now be determined using the equations of table 1. These give the frequency reached for stage 1, stages 1 and 2 and stages 1, 2 and 3 when in each case the load shed corresponds to the initial overload. The operating times of relay and circuit breaker are taken into account and the percentage load shed must be referred to the overload and expressed in p.u. For example, the first stage on its own will cope with an overload of 0,11 p.u. The first and second stages together can cope with an overload of 0,25 p.u., whereby the first stage corresponds to 0,125 p.u. In the table f' is then the level at which the frequency would theoretically be stabilised by action of stage 1. By choosing the frequency setting of stage 2 just above this value, the theoretical possibility of the frequency stabilising between fl and f2 is eliminated. Similarly f" is the frequency at which action of stages 1 and 2 would cause stabilisation and just above which the setting of stage 3 must be chosen. As initially the total load to be shed was chosen to be greater than would be necessary for the maximum overload, there should be no theoretical stabilisation below tripping of stage 2. Fig. 4 shows the result of a typical calculation using table 1. From this can also be seen the influence of varying the ratio of load shed by stages 2 and 3. For instance, increasing the percentage of stage 2 lowers the frequency setting of stage 3 and also the lowest frequency that would be reached for the maximum overload. Examination in the manner of table 1 and Fig. 4 quickly reveals that considering safe relay operating time and average distribution circuit breaker time, it is not possible to arrest frequency decline before 47,5 Hz for overloads around 90 to 100 percent and a

first stage setting of 49 Hz. In such cases, the third stage is replaced by a df/dt unit interlocked for security reasons by a discrete frequency enabling setting. As load must be shed as quickly as possible for high overloads and the operating time of the breaker limits any reduction that can be achieved, the discrete frequency setting must be as high as possible conducive to secure operation, perhaps 49,6 or 49,7 Hz. The slope at which the df/dt unit is to be set is derived from the overload corresponding to the load shed by stages 1 and 2. For example, in Fig. 4 stages 1 and 2 shed together 20 percent, corresponding to an overload of 25 percent. The slope in this case is then fo x overload df/dt 2 H 50 x 0,25 2 x 4 1,56 Hz/s By choosing a slightly lesser lope, say 1,5 Hz/S, the same overlapping of the operation of the stages as before is achieved. This arrangement is correct for instantaneous overloads of the prescribed amount. If, however, a case can be envisaged where a second event causes a slow frequency decline after stages 1 and 2 had been shed, stage 3 would not be replaced but a supplementary df/dt unit fitted which would trip all the stages. Whatever the load shedding programme neither the data upon which it is based nor the percentages of load shed can be expected to be consistent. It can be said, however, that an adverse discrepancy will always be reflected by the frequency stabilising between two stages. To obviate this possibility, each stage can be equipped with a back-up timer which will trip the next block of load if the stage does not reset within a predetermined time. The timer setting would be related to the ability of the machines to sustain a frequency in the respective band. This scheme adds a block of load which would be tripped by the back-up timer of the lowest frequency step. HARDWARE Fig. 5 shows a digital frequency relay specifically designed for underfrequency load shedding applications. A quartz reference and digital techniques provide the necessary accuracy and high resolution. A total of four stages can be accommodated, one or two of which can be df/dt units. Fig. 6 shows a complete scheme in a single package comprising underfrequency relay, backup timers, feeder selection facilities and supervision and remote signalling units. In the version illustrated each of up to 60 feeders has a selector plug, enabling it to be allocated to any of the four frequency stages of the underfrequency relay. From left to right the units are four-stage underfrequen-

P.

16

Harrison

cy relay, auxiliary supply unit, two backup timer units with a total. of four timers, supervision of internal supplies, quartz etc., remote signalling unit, tripping unit and three feeder selector units for 20 feeders each. A fourth feeder selector unit can be accommodated on the extreme right.

unfortunately varies and is to some degree unpredictable. The programmes must therefore include back-up timers for shedding additional load, if the frequency remains below pick-up for too long.

REFERENCES CONCLUSION Underfrequency load shedding is a valuable instrument for restoring a balance between the load and the available generation in an island system. Underfrequency is not necessarily a reliable criterion for forming the islands in a large bulk supply grid. It is not sufficient for a load shedding programme to restrain frequency decline; it should also be designed to bring system frequency back to near rating. For high overloads discrete frequency setting may prove inadequate to halt the frequency above the minimum frequency of the generator, because of relay and circuit breaker operating times in relation to df/dt. A supplementary df/dt measuring unit can provide a solution in such cases, but for security reasons this must be interlocked to only operate below a fixed frequency setting. Load shedding programmes will vary depending on the objectives and the nature of the system. They are derived from system data which

1

Summary of stability control systems used in the Pacific Northwest. Prepared by branch of substation and control engineering, October 1, 1979, U.S. Dept. of Energy/ Bonneville Power Administration

2

Lokay H.E. and Burtnyk V. Application of underfrequency relays for automatic load shedding. IEEE Transactions, Vol. PAS-87, No. 3, March 1968

3

Oelwegaerdt A., Norback K., Blondell R. and Lohage L. Load shedding in Sweden according to system requirements and frequency relay testing CIGRE 1972, 34-09

4

Slatem R.R. and Taylor A.L. Some protection, underfrequency load shedding and testing aspects of the ESCOM network. Transactions S.A. Institue of Electrical Engineers, December 1976, Section 3

Restoring system stability

17

flHzl 50

~

48

10% Overload

~

V

~ \\,

46

\ 44

42

40

""

' - 10

""

~

"

'\..

" '-7',

--- -- --- .:::: ---

....... "- ........ _........ _ - - _ 50%Overload ........... ....-. ---. --------==_-.--

.......

- --

L-_~_~_+~----_+-----_+_-____:l~

o

10

20

30

Fig. 1: Frequency decay due to system overload for d

t[sl

2

flHz] 50 d=6

V " 48

d= 6

'-

-

46

44

- - H=4 - - H=7

42

40 0

5

10

15

t[s]

Fig. 2: Influence of load reduction factor d on frequency decay for a 50% overload

P.

18

Harrison

f[Hz]

50

d-1 1+ -d-Po

49 f

=

1 + Po

• fo

Po in p. u.

48

47

46 d=2

o

20

3

60

40

80

a) f[Hz]

50

'8

'2

49

+--t---+--+--+---+--~---I--+~-+---+-­

o

2

4

6

8

b) Fig. 3: Frequency decay versus overload Po for different load reduction factors d

10

Po [%]

TABLE 1 overload Po

P1

P1

1 - P1

1 - P1

P1 + Pz

P1

1- I P1+ PZ)

1-( P + P ) 1 Z

1

f/:

=P

'I

t"

= P1

Pz

-p

time to shed stage

frequency stabilises at

load shed referred to overload

= f1

-

f1

fa· t r +cb (P1"+ PZ") ZH

-

ZH( f o- f1 )

fa' t r +cb ' P{ ZH

pq Z p" P" 1+ Z

-

fa· P1

I

+tr+c b=t{

ZH(fo-f1) t t ~ f 0 (P / + Pi') + r+ctf 1 1

If - f ) 1 Z

ZHlfo-f Z ) q

1- I ~ + P ) - Z Z

fIR'; P o 1+ 2

1 1 )

+

t =t;, r+cb 2

:;od et> tI)

rt

o

ti

1-"

P1+ PZ + P 3 1- (~+PZ+P3)

P1

f;~

=P{ 1-1~ +P +P ) 2 3

= f1 -

f· t (P~+p.~+p.~) o r+cb 1 Z 3 2H

-

Pi+ P; Pf+ pi +P'3

p.~

(f1- f 2) -

3

P.j +Pt + P:3'"

(f - f

Z

3 )

ZHlfo - f 1 )

66

fa (~"+ Pi"+ P

'< tI)

+t - t~ 3') r+cb - 1

tI)

rt

m P

2Hlfo -f Z)

p~

2

1- (P1+ P2+ P3)

= 2

f o (~~+P2+P3)

tI)

t~

+t r +cb = 2

rt ~

0"

1-'-

I-'

1-" rt

P3 1-1 P1+PZ+P3 )

2H(f -f ) o 3

pili = 3

fol P,t+Pi"+ P31

fa = ra ted frequency f1 , f 2, f 3 = frequency settings, stages 1,2 1 3 P1 , PZ' P3 = load shed by stages 1,2,3 in p.u. full load

'< 1>

.. t r +cb =t3

t r + cb = relay + breaker time t1', t1~' t 1"'=operating times, till load t ~ t ,* shed by stages 1, Z,3

2' Z

t~

3

P1', P1~ Pt=~, ~,P3 referred to Po Pi, P2~' p~

3

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P. Harrison

20

2 50

t[sl

_=:_-------------+---------------+--

I

I I

----T------_J_

49-1 49

I

I I I

I

.... -------------------·25cyo

~--

48-7

\

48

250ms

\ \-82

\

•~\

\

H =4 trel.= 150ms tc.b. = 100ms

limit for 45% ..1~q£2!!.ed

47

f[Hzl

Fig. 4: Example of load shedding programme designed to bring the frequency back to rating

Restoring system stability

21

.

-

Fig. 5: Four stage digital underfrequency relay. As shown stage A is a df/dt unit, whilst B, C and D are discrete measuring units

Fig. 6: Complete load shedding and back-up scheme with underfrequency relay, back-up timer and feeder selection facility