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An adaptive load shedding method with time-based design for isolatedpower systems

S.-J. Huang*, C.-C. Huang

Department of Electrical Engineering, National Cheng Kung University, Tainan, Taiwan, 70101

Abstract

When an isolated power system encounters a serious disturbance or a large generator unit trip, the system frequency may drop if total

generating power is not able to supply the load demand sufficiently. Since an isolated power system possesses a lower inertia with limited

reserves, load shedding becomes a critical solution to restore system frequency. In this paper, the initial rate of change of frequency is firstdetected. A designated time interval and a modification algorithm that considers the maximum frequency change at the last step are

integrated to complete a load shedding task. Features of the method include the easy determination of shedding loads and fast trip of the

load in anticipation of avoiding the occurrence of over-shedding or under-shedding. Numerical simulations have solidified the effectiveness

of the proposed method for the application. 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Load shedding; Isolated power system

1. Introduction

When an isolated power system encounters a serious

disturbance or a large generator trip, the system frequency

may drop once the total generating power could not supply

the load demand sufficiently. It is known that an isolatedpower system should be self-sufficient to provide security,

reliability and economy of electricity. In such a system, the

speed of frequency decay due to loss of generation is parti-

cularly significant. Therefore, more attention should be paid

to the load shedding scheme design [13].

Several studies have been proposed to restore the system

operation frequency after serious disturbances. One of these

strategies is throughthe under-frequencyloadshedding design

[4,5]. This approach is simple and easy to implement;

however, its poor coordination capability may deteriorate the

overall performance. Efforts to improve under-frequency load

shedding using the rate of change of frequency as additional

control variables have been suggested [610]. These methods

primarily shed the load when therate of change offrequency is

higher than a designated value. Among these methods, a low-

order linear system frequency response model based on the

idea of average frequency was proposed, where the essential

characteristics of the system frequency response was seen

accurately estimated in their test cases [6]. This is followed

by an adaptive methodology that was applied for the setting of

under-frequency relays based on the initial rate of change of

the frequency at the relay [7]. Because conventional under-

frequency loadshedding schemes canonlyhandle a maximum

of 50% load, a hybrid load-shedding scheme was also

suggested. This hybrid system includes at least one time-coor-

dinated step in addition to several frequency-coordinatedsteps. By this hybrid, it is able to shed 70% and more of the

loadfrom the system[11]. On accountof tediouscomputations

required for determining the amount of overload and the load

shed per step, a neural network approach has also been

employed to calculate the minimum frequency during a forced

outage of a generating unit [12].

This paper proposes the detection of the initial rate of

change of frequency with predetermined time intervals to

formulate an appropriate load shedding strategy. Mean-

while, to avoid load-shedding failures, a modification

method considering the maximum change of frequency at

the last step is embedded in order to adjust the required total

amount of shed load. By this modification, the load-shed-

ding scheme can be more effective in restoring the system

frequency, which also overcomes the coordination difficulty

of the problems. Numerical simulations support the

proposed method in good agreement.

2. Problem formulation

2.1. Analysis model

Fig. 1 shows the linear frequency response model that

Electrical Power and Energy Systems 22 (2000) 5158

0142-0615/00/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved.

PII: S0142-0615(99) 00035-6

www.elsevier.com/locate/ijepes

* Corresponding author. Tel.: 886-6-276-0711; fax: 886-6-234-

5482.

E-mail address:[email protected] (S.-J. Huang)

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represents the frequency characteristics of an isolated power

system, where all parameters are in per unit on an MVA

base equal to the total rating of the generating units in the

island. This frequency response model is formulated based

on neglecting non-linearity and all but the largest time

constants in the generating unit inertia and reheat time

constant of generating units in the isolated system. Note

that in modeling, the generation is assumed dominated by

reheat steam turbine generators. In Fig. 1, the change in thespeed changer setting Prefand the change in load demand

PLare two inputs. Other parameters in this model are FHP,

GM and s, where FHP is the high-pressure turbine power

fraction, GM the mechanical power gain factor and s the

differential operator. Most steam turbine generators in

service today are of the reheating type, in which about

one-third of the power is developed in the high-pressure

section. When the steam leaves the high pressure turbine,

it returns to the reheater and then flows to the intermediate

and low pressure sections of the turbine, where the remain-

ing two-thirds of the power is developed.

In the above model, the inertia constant of H and thereheater time constant ofTRH are important. For the inertia

constant of H, it is defined as the ratio of the moment of

inertia of the generator rotating components to the generat-

ing capacity of the unit. This constant is available from the

manufacturer of generating units, with the typical value of

28 s. Calculation of this constant in a system is also

expressed as follows:

HH1MVA1 H2MVA2 HnMVAn

MVA1 MVA2 MVAn1

The other time constant that is critical to the system is the

reheater time constant, TRH. This constant is usually of therange between 6 and 12 s, and tends to dominate the

response of the largest fraction of turbine power output

[6]. The remaining parameters of this model shown in Fig.

1 are the incremental frequency off, the damping factor of

D, and the inverse of the governor regulation of 1R

2.2. Formulation

With the above analysis model, let us now consider a

simple situation where Pref 0 and a step change happens

in load demand of PL. The frequency variation in the

frequency domain is then calculated as follows:

fs bR1 TRHs

ss2 2ns 2n

PL 2

where

b 2HRtRH1

n bDR GM05

b2n

2HR DR GMFHPTRH3

By applying the inverse Laplace transform, the change of

frequency as function of time when a step of change in the

load can be written:

ft bR

2n1 rent cosht PL 4

where

r1 2nT

2RH 2nTRH

1 2

05

h n1 2

05

tan1 nTRH

1 2

Since Eq. (4) is expressed in the closed form, we can readily

compute the initial slope of the response at t 0Therefore,

m0 dft

dt t0

PL

2H 5

By differentiating Eq. (4) with respect to the time variable of

tand let the post-differentiated result be equal to zero, the

result oftmreveals the time when the variation of frequencyis maximum. This result is also expressed as below:

tm 1

htan1

hTRH

nTRH 1

6

Substitutetminto Eq. (4), the outcome can be simplified as:

fmax kPL 7

where k is a constant. This equation illuminates that the

maximum frequency variation can be deemed proportional

to the system disturbances.

S.-J. Huang, C.-C. Huang / Electrical Power and Energy Systems 22 (2000) 515852

frefP

-

+

sT

F

RH

HP

+

1

1

R

1

MG

+

+

-

+

LP

DHs+2

1

HPF

Fig. 1. Analysis model.

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3. Design of load-shedding scheme

The load-shedding scheme is designed to determine a

workable balance between providing maximum system

protection and minimal service interruption. The design

procedure for the proposed load-shedding scheme is listed

as follows:

Step1 (obtain system parameters): As an example of the

computation of the proposed method, consider an isolated

area whose system parameters are D 10R 006H

45 GM 090 FHP 033 and TRH 75 We can then

calculate the following values, including b 02469 n

04869 08158 r 50046 h 02816 and

13696By substituting these values into Eq. (4), we can

obtain the frequency variations in the function of time:

ft 00625PL1 50046e03972t cos02816t

13696 8

Moreover, by Eq. (6), the value oftm can be calculated as2.9044 s. By substituting thistminto Eq. (8) and comparing

the results with Eq. (7), the value of k was found to be

0.1196.

Step 2 (select the first shedding frequency(f1) and mini-

mum allowable operating frequency (fmin)): Many utilities

have set the first step of load shedding at 59.5 Hz. This

choice was made based on several reasons [7,14]. First, all

of the larger turbine-generators on the system are not rated

for continuous operation below 59.5 Hz. Thus, setting the

initial load shedding frequency at a relatively high value,

such as 59.5 Hz, tends to limit the maximum frequency

deviation. Second, a load-shedding program starting at59.5 Hz would be more effective in minimizing the depth

of the under-frequency response for a heavy overload than

would a similar program which had a lower first shedding

frequency. Third, the first shedding frequency should not be

too close to normal frequency. In this way, the tripping on

severe but non-emergency frequency swings can be

avoided. In this paper, the 59.5 Hz was also selected as

shedding frequency at the first step shedding frequency.

As for the selection of minimum allowable frequency,

because the TPC limits system frequency deviation within

^ 4% (i.e. ^ 2.4 Hz for 60 Hz base), the minimum allow-

able operating frequency of fmin is equal to 57.6 Hz. Thus,

the value of the maximum change of frequency fmaxbecomes576 595595 00319 pu

Step 3 (determine the number of steps (N) and the time

interval between consecutive steps (t)): Steps of the shed

load should be carefully chosen. Over- or under-shedding

might happen under a small disturbance when a large step

size is selected, while coordination problems might happen

when many steps are decided. Experience has shown that

three to five steps are adequate selections [13,14]. Hence, in

this paper, the three, four and five steps were all adopted for

the evaluation of the proposed method.

An under-frequency relay is often incorporated with a

time delay in order to decrease the impact caused by the

system surges. This time delay may result in a longer trip

reaction such that the frequency may decline, and hence

result in unnecessary generator protection relay trips. To

deal with this problem, a time-based procedure was

proposed to shed the load in each predetermined time inter-

val. By this method, because each length of time step was

known, the time delay will not be required and the coordi-

nation problem can also be solved. This time interval can be

determined based on the system characteristics and types of

under-frequency relays. The length of each time step is not

necessarily equal to each other; while in this paper, time

intervals were all set at t 01 s for easy manipulation.

Step 4 (calculate the total amount of load shed PLS):

The worst possible disturbance is subject to the speculation,

while the load-shedding plan is inherently limit based on

this assumption. Although the larger system upsets are seen

less probable than small upsets, there is a certain probability

that a large disturbance happens [15,16]. In the load-shed-

ding study, once the frequency deviation curve is known, wecan obtain the initial rate of change of frequency ofm0based

on this curve. The overload calculated by using Eq. (5)

becomes PL 2Hm0

With the time tm obtained in Step 1 and the maximum

change of frequency fmaxin Step 2, we can solve the PL,minwith the aid of Eq. (8); and then, the total amount of load

shed can be obtained by the following equation:

PLS 2Hm0 PLmin 9

Step 5 (determine the amount of load shed per step

(PLS,i)): Once the total amount of load to be shed is

known, the load shed per step can be obtained throughdividing by the number of shedding steps. In the method,

each successive step was designed to shed a larger amount

of load than the preceding step [17,18]. This design feature

allows the protection scheme to drop smaller amounts of

load when the degree of overload is less serious. Note that

for an isolated system, fewer steps and larger load shed per

step are required when compared with the interconnected

systems.

Step6 (plot the system frequency change curve): By the

information on the amount of load shed per step, the over-

load PL, and the time interval t, the system frequency

change curve off(t) and f(t) can be plotted through the aid

of Eqs. (4) and (9), respectively. Therefore, we can evaluatethe minimal operation frequency value. If the minimum

operation frequency is seen higher than the minimum allow-

able value offmin, the load shedding is claimed accomplished

and the system has reached a new steady state. Otherwise,

an additional modification step should be activated. As for

the modification task, it will be discussed in the next step.

Step7 (modification) A modification task is required for

the case when the minimum operation frequency is lower

than the minimum allowable operation frequency fmin.

Under this scenario, it reveals that the amount of load to

be shed is still insufficient to restore the system frequency.

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To justify the total amount of shed load, a necessary task is

to get the shedding frequency fi at each step. When the

frequency at the last step is termed as fL, this value can be

computed by the following Eqs. (10)(12) iteratively:

PL1 PL PLS1 10

PLi1 PLi PLSi1 i 1 2 3 N 1 11

fi1 fi1

f

ti i 1 2 3 N

1 12where PLis the initial system overload, PL,ithe overload

after thei-th step, PLS,ithe amount of shed load at the i-th

step, fti frequency variation after the i-th step during

time interval t, andfi the frequency at the i-th step.

Now, the frequency at the last step is obtained; therefore,

we can immediately calculate the maximum allowable

change of frequency at the last step, namely, fmax

fmin fLfL in p.u./s. Similar to Eq. (7), the modified

expression can be rewritten as below:

fmin fL

fLkPmax 13

Eq. (13) can be also rearranged as:

Pmax

1

k

fmin

fL 1

14

At this stage, the modified amount of shed of load is calcu-

lated as follows:

PLS PL Pmax 15

By Eqs. (5) and (14), Eq. (15) can be further formulated as

follows:

P

LS

2Hm0

1

k

fmin fL

fL

16

whereP LSrepresents the total amount of shed load after the

modification, and Pmax the maximum allowable overload

after the last step. This equation informs the new amount of

load to be shed in anticipation of restoring the system

frequency.

4. Numerical simulations

To verify the proposed algorithm, numerical simulations

have been performed. For an isolated system, the maximum

load subject to a shedding schedule may include all loads.

Therefore, in the simulation, the maximum disturbance at

100% of the generation (i.e. PL 10 pu) in an isolated

power system was investigated. Under this situation, the

initial rate of change of frequency m0 can be obtained

through Eq. (5),m0 01111 pusThe value ofPL,minwas thus computed as 0.267 p.u. By Eq. (9), the total

amount of shed load PLS was concluded to be 0.733 p.u.

As mentioned above, the 3, 4 and 5 steps were selectedas the number of shedding steps. In each case, two

strategies (Strategy A, B) for shedding the load are

considered:

Strategy A: The loads are shed equally in each step.

Strategy B: The loads are shed in the geometry mean

form. Namely, the load shed at the second step is of the

half amount of load shed at the first step.

Tables 1 and 2 tabulate the load shed by strategy A and

strategy B, respectively. In Table 1, the load can be seen

shed equally at each step. For example, if the 3-step shed-

ding-load is selected, the amount of the shed load at eachstep is equal to 07333 0244 pu While in Table 2, by

strategy B, each step of shed load will be 0733 47

0419 pu 0733 27 0209 pu and 0733 17

0105 pu In these tables, we use the scheme 1A-3 to

symbolize the 3-step load-shedding by strategy A, and the

scheme 1B-3 to symbolize the 3-step load-shedding by strat-

egy B. Figs. 2 and 3 plot the frequency change curve by

these strategies, respectively. From these figures, the mini-

mum frequency is seen lower than fmin 576 Hz by both

strategies. The load shedding process was not successfully

accomplished.

To improve the above load-shedding process, the Step 7

mentioned in Section 3 has been adopted. In this modifica-tion process, the shedding frequency at the last step, fL, was

first calculated. Table 3 shows the shedding frequency at

each step. In the table, the fL of 58.694, 58.294 and

57.899 Hz that is seen for the scheme 1A-3, 1A-4 and 1A-

5 at their individual final step. Similarly, the fL values of

58.895, 58.648 and 58.431 Hz is seen for the scheme 1B-3,

1B-4 and 1B-5, respectively. Now, by substituting these

values of fL into Eq. (16), the amount of total shed load

can be determined. Table 4 lists the required shed-load

before and after modification. For example, after the modi-

fication process, the new amount of load required to shed for


Table 1

Amount of load shed per step by Strategy A

Scheme Amount of load shed per step (p.u.)

1 2 3 4 5

1A-3 0.245 0.244 0.244

1A-4 0.184 0.183 0.183 0.1831A-5 0.147 0.147 0.147 0.146 0.146

Table 2

Amount of load shed per step by Strategy B


1 2 3 4 5

1B-3 0.419 0.209 0.105

1B-4 0.391 0.195 0.098 0.049

1B-5 0.378 0.189 0.095 0.047 0.024

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Fig. 2. Load frequency curve of Scheme 1A.

Fig. 3. Load frequency curve of Scheme 1B.

Table 3

Shedding frequency of Strategy A

Strategy Shedding frequency at each step (Hz)

1 2 3 4 5

1A-3 59.5 59.018 58.694

1A-4 59.5 58.979 58.578 58.294

1A-5 59.5 58.955 58.508 58.157 57.899

1B-3 59.5 59.129 58.895

1B-4 59.5 59.111 58.848 58.648

1B-5 59.5 59.103 58.828 58.614 58.431

Table 4

Required shed load before and after modification

Strategy Total amount of load shed (p.u.)

P LS PLS Increment

1A-3 0.733 0.8442 0.1112

1A-4 0.733 0.9005 0.1675

1A-5 0.733 0.9568 0.2238

1B-3 0.733 0.8162 0.0832

1B-4 0.733 0.8506 0.1176

1B-5 0.733 0.8811 0.1481

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0 2 4 6 8 10 12 14 1657.5

58

58.5

59

59.5

60

60.5

Time [Sec]

Frequen

cy[Hz]

Scheme 2B-5

Scheme 2B-4Scheme 2B-3


Table 5

Modified amount of load shed per step by Strategy A


1 2 3 4 5

2A-3 0.2814 0.2814 0.2814

2A-4 0.2252 0.2251 0.2251 0.2251

2A-5 0.1914 0.1914 0.1914 0.1913 0.1913

Table 6

Modified amount of load shed per step by Strategy B


1 2 3 4 5

2B-3 0.4824 0.2412 0.1206

2B-4 0.4803 0.2401 0.1201 0.0600

2B-5 0.4939 0.2469 0.1235 0.0617 0.0308

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the scheme 1A-3, P LS, will be:

1A-3 P LS 10 1

01196

576 58694

58694

08442 pu

Hence, the increment amount of total shed load becomes

08442 0733 01112 puSimilarly, the new amount of

load required to shed for the scheme 1B-3, P LS, can be

computed:

1B-3 P

LS

10 1

01196

576 58895

58895

08162 pu




Table 7

Modified amount of load shed per step by Strategy A


1 2 3 4 5

3A-3 0.2721 0.2721 0.2720

3A-4 0.2127 0.2127 0.2126 0.2126

3A-5 0.1763 0.1762 0.1762 0.1762 0.1762

Table 8

Modified amount of load shed per step by Strategy B


1 2 3 4 5

3B-3 0.4664 0.2332 0.1166

3B-4 0.4537 0.2268 0.1135 0.0566

3B-5 0.4548 0.2274 0.1137 0.0568 0.0284

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Now, because the total amount of load to be shed is

different from the above case, the above scheme 1A is modi-

fied to be schemes 2A and 2B, while the scheme 1B is

modified to be 3A and 3B. Tables 5 and 6 list the newly

determined amount of load shed per step after the modifica-

tion by strategy A and strategy B, respectively. By this new

amount of shed load, Figs. 4 and 5 plot the respective

frequency curve by strategy A and strategy B.

Similarly, for the modified amount of shed load from

Scheme 1B, Tables 7 and 8 list the amount of shed load

per step by strategy A and strategy B, respectively. By the

new amount of shed load, Figs. 6 and 7 individually plot the

frequency curve by strategy A and strategy B.

From the above results, the operation frequency of Figs.

4, 5 and 7 is seen higher than 57.6 Hz, which have demon-

strated the effectiveness of the proposed method. However,

seen from Fig. 6, it does not complete the load-shedding

task. The reason why Fig. 6 failed is that Scheme 3A was

modified from Scheme 1B, and the shed load of Scheme 3A

is less drastic than Scheme 1B. Therefore, the load may notbe shed sufficiently in time, and the frequency drops down

to be lower than the value offmin. The frequency restoration

was thus not successfully accomplished. This outcome also

explains the critical importance of the load-shedding

scheme to the system protection performance.

5. Conclusions

A time-based load shedding protection scheme is

proposed in this paper. In the method, the rate of change

of frequency was detected as the initial value. A predeter-

mined time interval and a modification algorithm thatincludes the maximum frequency change at the last step

are embedded to organize a load shedding strategy. By

case studies with numerical simulations, the proposed

method is verified with simplicity, flexibility, and success

for load shedding problems considering power system

dynamics nature and protection component nature. It can

be a useful integration of load shedding algorithm with a

practical value. Currently, by the assistance of Taiwan

Power Company engineers, a research project is carried

on the extension of the proposed method to cover the control

of pump-storage generating units in Taiwan Power Systems.

The results will be reported in the near future.

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Shyh-Jier Huang received his PhD degree in Electrical Engineering

from the University of Washington, Seattle, in 1994. Currently, he is

with Department of Electrical Engineering and is the project manager

in Computational Intelligence Applied to Power (CIAP) laboratory at

National Cheng Kung University, Taiwan. He has worked research

projects at the University of California, Berkeley from 1989 to 1991.

He received Research Awards from National Science Council, Taiwan,

from 1996 to 1999. He is a member of IEEE PES, CSS, CS and SMC.

His main areas of interest are power system analysis, neural networks

and fuzzy control.

Chin-Chyr Huang received his MS degree from National Cheng Kung

University in 1992. He is pursuing his PhD degree in the same univer-

sity. His major interests are power system analysis and fuzzy controls.

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