Energy and Power Engineering, 2013, 5, 442-447
doi:10.4236/epe.2013.54B085 Published Online July 2013 (http://www.scirp.org/journal/epe)
A Method for the Design of UFLS Scheme with Dynamic
Zhaoou Song1, Junyon g Liu 1, Youbo Liu1, Masoud Bazargan2, Wuxing Liang2
1School of Electrical Engineering and Information, Sichuan University, Chengdu, China
2LSTOM Grid Research & Technology Centre, Stafford ST17 4LX, UK
Received March, 2013
This paper presents an adaptive Under Frequency Load Shedding scheme based on Wide Area Measurement System.
Due to the lack of enough adaptability to the operation state of the system, the traditional successive approximation un-
der frequency load shedding method will cause excessive cut or undercut problems inevitably. This method consists
first in a comprehensive weight index including load characteristics and inertias of generators. Then active-power defi-
cit calculation based on the Low-order Frequency Response Model, concerning the effect of voltage was put forward.
Finally, a dynamic correction of the load shedding amount was proposed to modify the scheme. This approach was ap-
plied to IEEE-39 system and the simulation results indicated that the proposed method was effective in reducing the
load shedding amount as well as the frequency recovery time.
Keywords: UFLS; WAMS; Active- power Deficit; Comprehensive Weight
As the last resort against system blackouts, UFLS schemes
implemented today are conventional and adaptive schemes.
The former one is generally based on off-line calculation,
shedding a predefined amount of load in case frequency
and/or the rate of change of frequency (ROCOF) fall below
a certain threshold with a time delay. While the latter one
allocates the active- power deficit in each load shedding
step, taking online conditions into account.
Reference  proposes a new methodology based on
risk management and quantitative analysis for the time
response curves, and coordination between UFLS and
UVLS is studied. A UFLS scheme, based on non-recur-
ve Newton algorithm to estimate the frequency and the
frequency change ratio, is put forward . Concerning
the frequency characteristic difference of different load
nodes, reference  puts forward a load shedding scheme
base on comprehensive weights. References [4, 5] pro-
pose a low-order model to calculate the response of the
system with disturbance. A load shedding method ensur-
ing the stability of both frequency and voltage is studied
in . In a word, references mentioned above are all
based on the low-order frequency response model to
calculate the deficit power. Nevertheless, the model ig-
nores the effect of voltage on the deficit power, resulting
in some error in the deficit power calculation.
The literatures mentioned above, irrespective of the
effect of generator inertia on the grid dynamic frequency,
seldom analyze the correlation properties of these two
coupling parameters in UFLS. Besides, in the multi-
machine system, there is a close relationship between the
frequency variation and generator inertia time constant.
As a result, the effect of generator inertia on the fre-
quency shall not be neglected.
This paper proposes a new adaptive UFLS based on
WAMS. The main elements of the proposed WAMS-
based scheme are given below.
1) A power deficit calculation based on WAMS con-
sidering voltage effect factor.
2) A comprehensive load shedding criterion construc-
tion concerning load characteristics and the effect of ge-
nerators on loads.
3) A dynamic correction of load shedding amount in
accordance with the system self regulation ability and
real-time frequency change rate.
2. Comprehensive Load Shedding Criterion
Considering the differences of load frequency character-
istic and generation unit inertia, calculate the comprehen-
sive weights of each node in the process of load shedding.
Based on the weights obtained to allocate the load shed-
ding amount and determine the location.
2.1. The Path Distribution Weight of Generator
In multi-machine system, the frequency variation with
Copyright © 2013 SciRes. EPE
Z. O. SONG ET AL. 443
active power disturbance has a close relationship with
generator inertial time constant and disturbance site.
Calculate the frequency change rate instantly when the
disturbance occurs (3 time cycles after the disturbance),
and use Equation (4) to calculate the deficit power Pde-
fi(i=1,2,…n) of each unit to measure generator distur-
bance degree. In under-frequency state, the larger deficit
power is, the greater degree of unit is. The nearby load of
unit with large deficit power should be given priority to
be cut to stabilize the system as soon as possible. Choose
the maximum value Pdemax as the base value to normalize
all the P
defi. The disturbance degree weight then can be
max/ijdefi defPP ,
In which, n stands for the number of generators; m is
the number of loads; βij is the weight of jth load which is
near to ith generator. As the analysis mentioned above,
the larger βij is, the greater disturbance degree of unit is.
Shed these sort of loads first can facilitate the recovery of
With regard to the ownership of the load, the shortest
electric distance from load node to generator is adopted
to differentiate the ownership. Assume the number of
node is a, the number of edge is b, calculate the adja-
cency according to the weighted power system network
theory. Apply Floyd algorithm to the matrix WG to fig-
ure out the shortest electric distance matrix D. Calculate
all the electric distance from jth load node to all the gen-
erators according to matrix D, choose the shortest dis-
tance to obtain the load weight βij.
2.2. Load Frequency Characteristic Weight
Load active-frequency characteristic refers to the charac-
teristic that the load active power varies with the change
In which, ai is the proportion of load which is propor-
tional to the i times of frequency; PLN is the rated load of
system; fN is the rated frequency.
In real power system, the load which is proportional to
the 3 times of frequency is rather fewer; Equation (12)
can be simplified by Equation (13):
Further, we can obtain:
In which, KL is the load frequency regulation coeffi-
cient and each load corresponds to different KL.
When the frequency drops, the load with bigger KL
absorbs less active power from the system. Therefore,
calculate the reciprocals of KL1，KL2，KL3…KLm and
choose the maximum value(1/KLmin) as the base value to
normalize all the coefficients. The load static characteris-
tic weight then can be expressed by:
In which, KLj is the frequency regulation coefficient of
jth load node; KLmin is minimum value of m coefficients.
The analysis indicates that shed the load with small KL
first can reduce the absorption of active power from sys-
tem, facilitating the recovery of frequency. The greater λj
is, the KL is smaller, in order to make full use of load
self frequency regulation ability, the load with greater λj
should be chosen as the key target of load shedding.
2.3. The Comprehensive Weight
Considering the load static characteristic and the distur-
bance degree load weight comprehensively, a weighted
product of these two weights is proposed. In the process
of load shedding, the real-time frequency variation of
each node can be provided by WAMS, which can be uti-
lized to calculate the load characteristic and disturbance
degree, so as to figure out the comprehensive weight of
each load node to act as the criterion of load shedding
amount and site.
Define the comprehensive weight as:
In the process of UFLS, the load with greater compre-
hensive weight is preferred to be assigned large shedding
amount to recover the system as soon as possible.
3. Deficit Power Calculation Base on WAMS
3.1. Deficit Power Calculation Based on
Frequency Response Model
In order to estimate the deficit power of whole system
accurately, it is reasonable to imagine an equivalent gen-
eration unit that describes the average behavior of all the
generators. This equivalent unit is called COI. The inertia
constant and frequency of COI are defined respectively
In which, fi is the frequency of ith generator；n is the
number of generators.
Copyright © 2013 SciRes. EPE
Z. O. SONG ET AL.
In which, Hi is the inertia constant of ith generator；Si
is the rated power of ith generator.
According to the frequency variation curve the WAMS
provided, the frequency variation rate of the initial dis-
turbance moment can be calculated by numerical calcu-
df nf nf n
Then the deficit power can be obtained by:
In which, the fN is the rated frequency.
3.2. The Voltage Influence Factors of Deficit
The frequency response model ignores the effect of vol-
tage on the deficit in the initial disturbance moment.
However, in the process of frequency decrease, node
voltage also drops in the meantime, which reflects an
existence of a coupling relationship between the active
power deficit and the reactive power deficit [7,8]. In the
1~2 seconds of disturbance, voltage variation acts as the
leading role in the effect on the change of load active
power, henceforth, the frequency replaces the voltage to
play a decisive role. Due to the fact that the change of
load reflects the deficit active power, at the initial distur-
bance moment, the voltage will change immediately;
therefore, the instantaneous response of load to the volt-
age variation can not be ignored. The load model con-
cerning the influence of voltage is built below:
On the basis of , the deficit power calculations con-
sidering the effect of load voltage mutation are given as
hedtur LPPP (14)
In which, Ptur is the output of turbine; PL is the load;
Pshed is the deficit power concerning the voltage influence;
m is the number of load nodes; PL0,j is the active power of
jth load node before disturbance, U0,jis the voltage of jth
load node before disturbance, Uj is the voltage of jth load
node after disturbance; α is the voltage influence factor
and α=1 is chosen in this paper. The calculation result of
Equation (9) is chosen as the base value of load shedding
4. UFLS Scheme with Dynamic Correction
On the basis of the measurement data provided by
WAMS, calculate the deficit power using Equation (9) as
the base UFLS shedding amount. With reference to the
real UFLS, the conditions for activation of individual
steps are equal to the following threshold frequencies:
49.2 Hz, 49 Hz, 48.8 Hz. All of the four predefined dis-
tributions Pshed,k(k =1,2,3) are set in accordance with the
traditional UFLS scheme: 30%, 30%, 40% of the deficit
Due to the effect of speed governor and load frequency
characteristic, after each load shedding step implemented,
the frequency change rate does not remain constant,
which will lead to the change of deficit power. Prior to
the implementation of load shedding, the frequency de-
creases dramatically, i.e. the frequency drop rate is the
largest. After each load shedding step, the frequency is
relieved, which in return reduces the deficit power, re-
ducing the corresponding load shedding amount. How-
ever, the traditional scheme lacks of the correction of
load shedding, which will inevitably result in overcut, so
it’s necessary to adjust the predefined load shedding steps
to the primary frequency-control reaction. It is obvious
from Equation(4) that the deficit power is a nearly linear
function of frequency change rate, in general, the x%
lowering of Pdef is reflected in an x% lowering of fre-
quency change rate. Based on this linearity concept, be-
fore the kth shedding step is activated, with the use of
WAMS, monitor the changes in dfCOI/dt between two
neighboring shedding steps and compare it to the ini-
tial(dfCOI ，max/dt)value, and the percentage change of
dfCOI/dt is calculated:
COI kCOI k
Keeping in mind the presented linearity concept, the
frequency variation rate change gradient Δk% demon-
strates the change in deficit power. As a result, the up-
coming shedding step can be altered from its predefined
value Pshed,k according to:
,,%shed kshed kkPP
After the achievement of kth shedding amount, the re-
quirement of control rapidity is taken into account to
Copyright © 2013 SciRes. EPE
Z. O. SONG ET AL. 445
introduce a new method to distribute the P’shed,k in com-
bination with the proposed comprehensive load weight.
The shedding amount of each load node is calculated by:
In which, M is a set of all load nodes. Consequently,
activate each shedding step according to the thresholds to
gradually restore the frequency.
The detailed process of UFLS is shown in Figure 1.
5. Test System Proposed UFLS Scheme
A load shedding procedure was tested on an island of a
39-bus IEEE test system, which is given in Figure 2.
Figure 1. Flow chart of UFLS.
Figure 2. IEEE39 nodes power system.
At 4 seconds, line 25-26, 3-18, 4-14 and 6-11 are cut
simultaneously; area 1 becomes an isolated grid with a
large deficit power. Figure 3 demonstrates the variation
of frequency provided by WAMS at the very moment
that the grid splits.
This paper selects the data from WAMS within 3 time
cycles after disturbance, using Equation (3) calculates
and averages, as the system frequency variation rate of
this moment. At the instant that frequency drops, calcu-
lates the deficit power of this moment using Equation (5)
as the base load shedding amount. The variation of volt-
age while islanding is shown in Figure 4.
The combination with Figure 3 and Figure 4 indicates
that the voltage of load nodes also plunges dramatically
at the instant frequency declines, especially 1-2 s after
disturbance. Henceforth, due to the regulation of excita-
tion system, the voltage gradually restores while the fre-
quency continues to decrease. It verifies that the voltage
variation plays the leading role on the change of load
active power at the initial stage of disturbance; the fre-
quency replaces it as main factor afterwards. Irrespective
of the influence of voltage, the deficit power is: Pdef
=5.5025 p.u and it is P
def =5.3911 p.u when voltage is
010 20 30 4050 60
Figure 3. The frequency variation curve while islanding.
0.94 10 20 30 40 50
Figure 4. The voltage variation curve while islanding.
Copyright © 2013 SciRes. EPE
Z. O. SONG ET AL.
taken into account. It is obvious that the voltage mutation
can not be ignored in the estimation of deficit power. It
will cause great error or even likely lead to problems such
as overcut without concerning the influence of voltage.
It is a fact that the estimated deficit power is not identi-
cal to the actual value. It is vital to modify the loadshed-
ding amount of each stage to ensure a precise control.
The frequency variation rate of inertia center is re-
corded maximum at the beginning of disturbance:
max(dfCOI/dt)=-0.8695 Hz/s. When the frequency reaches
the first frequency threshold 49.2 Hz, the dfCOI/dt is
measured and Δ1%=4.9% is calculated by Equation (11).
Applying Equation (13), the shedding amount of first
step is modified and the actual amount is: Pshed1’ =
30%-4.9% = 25.1%. Calculate the comprehensive weight
of each load node by Equation (11) and distribute the
load-shedding amount using Equation (14). The com-
parison of load shedding amount is listed in Table 1.
The load shedding corrections of each step are Δ2% =
1.4%, Δ3% = 0.47% respectively. The total shedding
amount with dynamic correction is 6.77% less than the
base value, which fully demonstrates the effectiveness of
the dynamic correction.
In order to validate the effectiveness of the proposed
comprehensive weight, three UFLS schemes with dy-
namic correction are compared. Scheme 1 is the one
proposed in this paper with 4 steps; Scheme 2 distributes
the shedding amount according to the load characteristics;
Scheme 3 sheds load by the load proportion, namely, the
lager the load is, the more it sheds. After the activation of
first step, the frequency recovery curves of each scheme
are shown in Figur e 5.
Table 1. The results of dynamic correction.
Load shedding steps
Scheme 1st step 2nd step 3rd step
Traditional scheme 30% 30% 40%
Dynamic scheme 25.1% 28.6% 39.53%
05 10 15 20 25 30 35 40 45 50 55 60
Figure 5. The frequency recovery curves of different under-
frequency load shedding sche mes after the first step.
It can be seen from Figure 5 that the proposed Scheme
1 can restrain the decrease of frequency quickly due to
the fact that enough load-shedding amounts are ensured
in the first step. The frequency stabilizes at 48.45668 Hz,
better than 48.41676 Hz of Scheme 2 and 48.37678 Hz
of Scheme 3.
After all the steps activated, the frequency recovery
curves are shown in Figure 6 and the shedding amounts
are listed in Table 2.
The recovery time of the scheme proposed in this pa-
per is 29.38 s, while Scheme 2 is 32.27 s and Scheme 3 is
34.96 s. The total load shedding amount of Scheme 1 is
5.0261 p.u, Scheme 2 is 5.0214 p.u and Scheme 3 is
5.0337 p.u. Without considering the load characteristics
or other factors, the recovery time and shedding amount
of Scheme 3 is unsatisfied. The shedding amount of first
step is largest in Scheme 1. However, it is of significance
to ensure the load shedding amount in first step to guar-
antee the frequency recovery. Although, the loads shed
of Scheme 1 are more than Scheme 2, the recovery curve
rises dramatically, better than that of Scheme 2 and 3.
Besides, the recovery time is shortest, which proves that
an effective control has been implemented at the key site
to meet the demand for control rapidity. Considering the
two aspects above, the UFLS scheme with dynamic cor-
rection makes full use of the self frequency recovery
ability to significantly reduce the total shedding amount
compared with the traditional one. Scheme 1 distributes
010 20 30 40 5060
Figure 6. The frequency recovery curves of different un-
der-frequency load shedding schemes.
Table 2. The total amount of shedding load of each scheme.
Scheme 1 Scheme 2 Scheme 3
1st step 1.3531 1.3474 1.3489
2nd step 1.5419 1.5432 1.5512
3rd step 2.1311 2.1308 2.1336
total 5.0261 5.0214 5.0337
Recovery time 29.38s 32.27s 34.96s
Copyright © 2013 SciRes. EPE
Z. O. SONG ET AL.
Copyright © 2013 SciRes. EPE
loadshedding amount in accordance with the synthetic
weigh proposed. Although the shedding amount of scheme1
is not the least, the frequency stabilizes faster at a small
cost. Therefore, Scheme 1 is optimal by a comprehensive
This paper proposes a new adaptive UFLS scheme base
on WAMS, the main research achievements and conclu-
sions are as follows:
1) Combine the UFLS with WAMS and modify the
traditional UFLS with adaptive UFLS, effectively short-
ening the time delay of frequency control.
2) The frequency variation rate of the COI is adopted
and the influence of voltage is taken into account to es-
timate the deficit power.
3) In order to lower the shedding amount, a procedure
is given for dynamically adjusting the amount of the
shedding steps to adapt to the primary frequency-control
response, which reduces the possibility of overcut and
unnecessary load losses.
4) A multi-factor comprehensive weight is proposed to
distribute the load shedding amount, which facilitates the
recovery of frequency as soon as possible.
The proposed method provides a new reference and
idea for the online application of frequency-control.
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