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Load Shedding A pply Neural Network and Power Sensitivity Theory

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Published by :  
International Journal of Engineering Research & Technology (IJERT)  
http://www.ijert.org  
ISSN: 2278-0181  
Vol. 7 Issue 04, April-2018  
Load Shedding Apply Neural Network and  
Power Sensitivity Theory  
L.T. Nghia1, T.T. Giang1, Q.H. Anh1 P.T.T. Binh2  
,
Bui.NguyenXuan. Vu1  
1Faculty of Electrical and Electronics Engineering, HCMC University of Technology and Education  
Hochiminh city, Vietnam  
2Faculty of Electrical and Electronics Engineering, HCMC University of Technology  
Hochiminh city, Vietnam  
Abstract—This paper proposed the method load shedding on the  
basis of the combination of Generalized Regression Neural  
Network, power sensitivity theory and Phase Electrical Distance  
theories to recover the frequency to allowable limit in the event loss  
a generator occurring in the electric system. The phase electrical  
distance calculation intended to calculate the distance between the  
generator outage and the load to align the load buses in ascending.  
The phase electrical distance sequence as compared to the fault  
generator. From there, the loads on the buses which are near the  
generator outage will be cut firstly, then the next loads until the  
system return to stable. The effectiveness of the proposed method  
are tested on the IEEE 39 Bus New England 10 Generators, which  
demonstrated the effective the proposed method.  
improve the frequency response and to reduce the risk of  
unstable electric system.  
This paper proposes the method of load shedding under pre-  
designed load shedding rules based on phase electrical distance  
method and power sensitivity theory. ANN neural networks are  
used to identify and classify load shedding control strategies  
based on the designed rules. The effectiveness of the proposed  
method has been tested on the IEEE 39 Bus New England.  
II.  
MATERIALS AND METHODS.  
A. Generalized regression neural network.  
Keywords: Load Shedding, Phase Electrical Distance,  
Power Sensitivity, Neural Network, Frequency Control.  
I.  
INTRODUCTION.  
Load shedding is an effective method for restoring electrical  
system frequencies by reducing the load to suit the power  
supply. Most of the studies related to load shedding are based  
on rate change of frequency and voltage of the power system.  
H. Bevrani and et al [1] presented an overview of the key  
issues in the use of frequency rate change (df/dt) in power  
system emergency control schemes. The role of df/dt in  
designing effective under frequency load shedding (UFLS) plan  
was discussed. The impact of new variable renewable sources  
(such as wind and solar units) on system frequency gradient is  
analyzed, and the need for the revising of frequency  
performance standards, re-tuning of automatic UFLS relays,  
and use of ∆f/∆t rather than df/dt are emphasized.  
Fig. 1. Generalized regression neural network.  
GRNN (Generalized Regression Neural Network) is a  
powerful tool in the application for identification problems.  
GRNN is basically the same as fig. 1 including input layer,  
radial function hidden layer and linear output layer. Neuron  
network operation must include the spread parameter whose  
optimum value is determined by the experimental error.  
Urban Rudez and et al [2] studied a novel approach to  
underfrequency load shedding is using the frequency second  
derivative as a source of information for a forecast of the  
frequency trajectory. A Newton method based approximation  
and the interpolation of the frequency second derivative are  
continuously performed in order to forecast the minimum  
frequency value using a numerical integration.  
F. Shokooh and et al [3] introduced the new technology of  
intelligent load shedding application in a large industrial  
facility.  
Conventional methods of system load shedding often have  
to wait until the frequency drops below the allowable threshold  
to make the load shedding decision. However, due to the  
complexity of the power system, it is imperative to treat it  
promptly after a fault in order to minimize the damage, to  
B. Phase electrical distance [4]  
The definition of phase electrical distance between the two  
nodes by using the elements of the matrix [dθ/dP] is the inverse  
matrix from the power sensitivity matrix [dP/dθ], as follows:  
DP(i,j)=(dθi/dPi)+(dθj/dPj)-(dθj/dPi)-(dθi/dPj)  
(1)  
The components [dθ/dP] are extracted from the Jacobian  
matrix. There are two interpretations of the phase electrical  
distance:  
(2)  
j
j
i
i
j
D (i, j) =  
+
-
-
P
P
P
P
P
i
j
i
Write this distance in another way:  
(3)  
j
j
j
i
j
i
D (i, j) =  
-
+
-
P
P
P
P
P
i
i
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ISSN: 2278-0181  
Vol. 7 Issue 04, April-2018  
PowerWorld simulation software to shed for each generator in  
trouble at different load levels. (including 41 load levels from  
60% to 100%). Dismissed until the rotor angle, frequency and  
voltage of the buses are within the allowable range of stopping,  
so that for each case the incident will have the number of load  
shedding corresponding to that case. The incident data collected  
would correspond to a number of load shedding from the trained  
neuron function.  
Location of load shedding: Use phase electrical distance for  
calculating distance between nodes. The load shedding position  
will be based on the distances from the generator outage  
(generator bus) to the remaining load buses to the load shedding  
order, or in other words the priority of the nodes closer to the  
generator will be first off, because these load nodes directly  
affect the generator is the most trouble.  
æ
ç
ö
÷
is phase difference between j and i caused by a  
j
j
i
j
-
ç
ç
è
÷
÷
ø
P
P
active power injection in j.  
æ
ç
ç
è
ö
is phase difference between i and j caused by a  
j
÷
÷
ø
i
-
P
P
i
i
active power injection in i.  
Then else:  
(4)  
j
j
j
i
i
j
D (i, j) =  
-
+
-
P
P
P
P
P
i
i
æ
ç
ö
is variation in phase of j caused by a active power  
÷
j
j
j
-
ç
ç
è
÷
÷
ø
P
P
i
The flowchart load shedding process is shown in Fig. 3 and  
4.  
transit from j to i.  
æ
ç
ö
is variation in phase of i caused by a active power  
÷
i
i
-
ç
ç
è
÷
÷
ø
P
P
i
j
transit from i to j.  
Two nodes electrically very close will always have a very  
small phase difference corresponding to the small distance D.  
Therefore, in the event of a loss of generator, it should be cut  
the load at the buses which near the generator in advance.  
Fig. 3. Flowchart load shedding online  
Fig. 2. The block diagram of the relationship between the generator j and  
the loads  
With:  
D ( j,1) < D ( j,2) < D ( j,3)....< D ( j,n)  
P
P
P
P
Prioritized load shedding: Load 1 à Load 2 à Load 3 à …  
à Load n  
III.  
PROPOSED METHODS.  
A. Set up load shedding program.  
Load shedding are based on three main factors: the timing,  
the amount of load to be shed and the location of load shedding  
The timing: The system data is sent to the control center for  
continuous measurement, when the system frequency is within  
the allowable range of 59.7Hz<f<60.3Hz, the system frequency  
is within the allowable value, whereas if the system frequency  
is outside of the allowable range, the load shedding program  
will start, the neuron function will be activated to identify the  
generator with the fault and the load shedding sequence. The  
time is calculated after the time of the incident is 300ms. This  
interval includes time intervals: measurement of data  
acquisition, data transfer, data processing, and load circuit  
breaker operation. [5]  
Fig. 4. Flowchart simulator sampling and neural network training  
The amount of load to be shed: After obtaining the load  
shedding sequence list for each generator failure, use the offline  
Fig. 5. The process of developing a load shedding strategy  
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The process of developing a load shedding strategy,  
including steps:  
From: Dp(i,j) = (δθi/δPi) + (δθj/δPj) - (δθj/δPi) - (δθi/δPj), with  
(δθi/δPi), (δθj/δPj), (δθj/δPi) and (δθi/δPj) are the corresponding  
elements in row i colum j in matrix [J1].  
The Jacobian matrix has the following general form:  
Fig. 6. General Jacobian matrix  
Step 1: Extract the Jacobian matrix J1  
Step 2: Inverse J1  
Fig. 8. Sampling process  
Step 3: Apply phase electrical distance formula  
Step 4: Building the relationship between the nodes containing  
the generator and the nodes containing the load.  
Step 5: Arranges the order of the load shedding with the  
corresponding generator failure.  
B. Application ANN to identify the failure.  
Identification of failure in electrical systems is often  
difficult due to its complexity. Traditional failure identification  
methods are often unsuitable, which can cause problems not to  
be resolved in time to endanger the system. Thus, the ANN  
method with advantages of computational speed as well as  
efficiency will best solve these difficult problems that other  
traditional methods cannot solve.  
Fig. 9. Neural network training model with inputs and outputs  
IV.  
TESTING ON THE IEEE 39 BUS NEW ENGLAND  
First, need to build data sets for ANN learning. This  
database is based on parameters at different load levels of the  
system (rate change of generator power, load power, voltage at  
buses, power variation on line, rate change of frequency at  
buses). The database must meet the following requirements:  
The database must fully display the status of the operation  
and must show all the various failure scenarios.  
The database created should ensure objectivity of the  
parameters of the test power system.  
The process of creating a database based on simulation  
PowerWorld and is done through the following stages:  
Fig. 10. The IEEE 39 bus New England  
The proposed method is tested on The IEEE 39 bus New  
England, using Powerworld software to collect samples and  
Matlab software for neural network training.  
Fig. 7. Simulation steps for input, output sampling  
A. Calculate the phase electrical distance.  
The phase electrical distance calculation is done in the  
following steps:  
Step 1: Take the Jacobian matrix J1 from Powerworld  
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Vol. 7 Issue 04, April-2018  
TABLE 2. Proposed load shedding strategy  
Bus  
Bus Bus  
30 32  
Bus  
33  
Bus  
34  
Bus  
35  
Bus  
36  
Bus  
37  
Bus  
38  
Bus  
39  
Order  
1
Load Load Load Load Load Load Load Load Load  
25 20 20 23 23 25 29 39  
Load Load Load Load Load Load Load Load Load  
16 16 21 21 28  
Load Load Load Load Load Load Load Load Load  
18 24 24 16 24 26 26  
Load Load Load Load Load Load Load Load Load  
15 15 24 16 18 27  
Load Load Load Load Load Load Load Load Load  
16 12 21 21 15 15 27 25  
Load Load Load Load Load Load Load Load Load  
26 15 18 18 18 18 18 18  
Load Load Load Load Load Load Load Load Load  
27 16 16 25  
Load Load Load Load Load Load Load Load Load  
15 18 23 23 15 16 16  
Load Load Load Load Load Load Load Load Load  
24 24 27 27 24 15 15  
Load Load Load Load Load Load Load Load Load  
25 27 27 26 26 24 27  
Load Load Load Load Load Load Load Load Load  
27 26 26 25 25 24  
Load Load Load Load Load Load Load Load Load  
21 21 25 25 21 21 26  
Load Load Load Load Load Load Load Load Load  
39 26 39 21  
Load Load Load Load Load Load Load Load Load  
23 23 20 20 23 12  
Load Load Load Load Load Load Load Load Load  
12 39 12 12 12 12 28 23 23  
Load Load Load Load Load Load Load Load Load  
28 20 39 39 39 39 29 39 20  
Load Load Load Load Load Load Load Load Load  
29 28 28 28 28 28 12 12 28  
Load Load Load Load Load Load Load Load Load  
20 29 29 29 29 29 20 20 29  
4
2
3
3
7
3
8
8
7
4
4
3
3
5
4
6
Fig. 11. The Jacobian matrix  
4
7
Step 2: Use the inv function of matlab to invert the matrix  
Step 3: Apply phase electrical distance formula: Dp(j,i) =  
3
3
3
3
3
J1.  
8
4
4
9
Dp(i,j) = (δθi/δPi) + (δθj/δPj) - (δθj/δPi) - (δθi/δPj)  
4
4
From the above formula, use the matlab software to set the  
matrix related to the phase electrical distance between the nodes  
in the network together, called the matrix Dp.  
Step 4: From the relational parameters between the buses in  
the system to the phase electrical distance, the relationship  
between the nodes containing the generator and the nodes  
containing the load is shown in Table 1.  
10  
11  
12  
13  
14  
15  
16  
17  
18  
8
8
7
7
4
8
8
8
8
7
7
8
7
7
7
TABLE 1. Table summarizes the relationship between the nodes containing  
the generator and the nodes containing the load on phase electrical distance.  
Bus 30 Bus 32 Bus 33 Bus 34 Bus 35 Bus 36 Bus 37 Bus 38 Bus 39  
Bus 3 0.027 0.041 0.047 0.064 0.045 0.057 0.040 0.065 0.038  
Bus 4 0.037 0.031 0.050 0.067 0.047 0.060 0.048 0.072 0.038  
Bus 7 0.045 0.033 0.058 0.075 0.055 0.068 0.056 0.080 0.037  
Bus 8 0.044 0.033 0.057 0.075 0.055 0.067 0.055 0.080 0.035  
Bus 12 0.061 0.041 0.071 0.088 0.069 0.081 0.072 0.096 0.059  
Bus 15 0.041 0.041 0.039 0.056 0.036 0.048 0.051 0.071 0.047  
Bus 16 0.039 0.044 0.031 0.048 0.029 0.041 0.048 0.067 0.046  
Bus 18 0.034 0.045 0.043 0.060 0.041 0.053 0.044 0.064 0.044  
Bus 20 0.070 0.074 0.028 0.018 0.060 0.072 0.079 0.097 0.077  
Bus 21 0.049 0.053 0.041 0.058 0.023 0.039 0.058 0.076 0.056  
Bus 23 0.056 0.061 0.048 0.066 0.021 0.024 0.065 0.084 0.063  
Bus 24 0.044 0.048 0.036 0.053 0.030 0.041 0.053 0.071 0.051  
Bus 25 0.027 0.054 0.058 0.075 0.055 0.068 0.022 0.061 0.045  
Bus 26 0.040 0.058 0.056 0.074 0.054 0.066 0.041 0.042 0.053  
Bus 27 0.040 0.054 0.050 0.067 0.048 0.060 0.044 0.053 0.051  
Bus 28 0.065 0.083 0.082 0.099 0.079 0.092 0.067 0.026 0.079  
Bus 29 0.067 0.085 0.084 0.101 0.081 0.093 0.068 0.015 0.080  
Bus 39 0.053 0.062 0.078 0.095 0.075 0.087 0.066 0.094 0.000  
Explanation: According to the suggested strategy table  
above, if there is a fault at generator 30, the load shedding order  
will be Load 25 à Load 3 à Load 18 à ... until the system is  
stabilized again. Similarly, for the remaining generators.  
B. Test load shedding on the IEEE 39 bus New England  
by Powerwold.  
Process simulation sampling with the IEEE 10 generators 39  
bus are made as follows:  
Assuming the fault generator is 34, at load level 100%, the  
frequency and deviation of the rotor angle become unstable.  
Fig. 12. Diagram of rotor angle generator and frequency of bus at fault  
generator 34 load level 100%  
Step 5: Arranges the order of the load shedding with the  
corresponding generators failure.  
When the bus frequency and rotor angle exceeded the  
allowable range, load shedding are made according to the  
strategic proposed. In this case, just shed the Load 20, the rotor  
frequency and angle have stabilized.  
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V.  
COMPARISON OF SUGGESTED METHOD WITH  
OTHER METHODS.  
A. Load shedding based on the AHP algorithm (Analytic  
Hierarchy Process) [6]  
AHP is the approach to making decisions. This method  
presents balanced assessment options and criteria, and  
integrates them into a final decision. AHP is particularly  
suitable for cases involving analysis and quantification, make  
decisions when there are multiple options depending on the  
criteria with multiple interactions.  
Fig. 13. Diagram of rotor angle generator and frequency of bus after shed  
Load 20  
Simulation proceeds from 60% to 100% load level at each  
load level causing the outage generators from generator 30 to  
39. After simulating and load shedding, the record is aggregated  
into sample. The result of the number of samples after the  
simulation of the case must load shedding when the generator  
fault is 369 samples.  
Table 3. The order of load shedding according to the AHP algorithm  
Order  
19  
18  
17  
16  
15  
14  
13  
12  
11  
10  
9
8
7
6
5
4
3
2
1
Load  
L39  
L4  
L8  
L20  
L7  
L27  
L29  
L15  
L16  
L3  
L24  
L28  
L21  
L25  
L23  
L26  
L18  
L12  
L31  
load center  
LC1  
LC1  
LC1  
LC2  
LC1  
LC3  
LC3  
LC2  
LC2  
LC4  
LC2  
LC3  
LC2  
LC4  
LC2  
LC3  
LC4  
LC1  
LC1  
Wdi  
0.37  
0.22  
0.22  
0.3  
Wkj  
0.467  
0.467  
0.467  
0.278  
0.467  
0.16  
Wij  
0.172543  
0.104727  
0.104727  
0.08208  
0.13  
0.33  
0.33  
0.17  
0.17  
0.49  
0.16  
0.20  
0.11  
0.31  
0.09  
0.14  
0.2  
0.061118  
0.053155  
0.053155  
0.048329  
0.048329  
0.047017  
0.043056  
0.031606  
0.030445  
0.029619  
0.025351  
0.022349  
0.018659  
0.011867  
0.011867  
C. Neural network training  
This section introduces the generalized regression neural  
network training model; the training process follows these  
steps:  
Step 1: Data collection, performs the collection via  
simulation on the PowerWorld software to retrieve data for each  
load level. Compile into a dataset, then split 85% of the sample  
for training and 15% of the sample for testing.  
Step 2: Create a network, implementing generalized  
regression neural network training should provide only input  
and output vector information along with spread constant, the  
procedure as follows:  
Create input_data is 85% of the samples (315 samples),  
output_data, input_test is 15% of the samples (54 samples).  
0.16  
0.278  
0.278  
0.10  
0.278  
0.16  
0.278  
0.10  
0.278  
0.16  
0.10  
0.467  
0.467  
0.03  
0.03  
B. Load shedding based on under frequency load  
shedding relays [7]  
Load shedding based on under frequency load shedding  
relays is the most commonly used method, which is still being  
used in many parts of the world, including Vietnam. When the  
grid frequency falls below the permitted threshold, the relay will  
be load shedding, prevents the system frequency declines.  
Without this load shedding control, the greatest possible  
consequence is the blackout, ie, the widespread outage.  
For example, the ERCOT load shedding program, has a load  
shedding plan under frequency load shedding shown in Table 4.  
Fig. 14. Neural network training structure  
Step 3: Create a interface.  
To facilitate training, monitoring, fault identification and  
load shedding. The creation of an appropriate interface program  
is necessary to enable the operator to easily monitor the  
operation of the system. Combined with the idea of creating a  
machine system that works on different power systems the  
interface is created as follows:  
Table 4. The ERCOT load shedding program  
Frequency  
59.3 Hz  
58.9 Hz  
58.5 Hz  
Load  
5% of total load  
15% of total load  
25% of total load  
C. Simulate and compare methods with each other.  
Fig. 15. The neural training system interface forecast load shedding in  
case of generator failure  
Fig. 16. Diagram of rotor angle and bus frequency after generator 34  
outage according to the proposed load shedding method.  
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Vol. 7 Issue 04, April-2018  
ACKNOWLEDGMENT  
This research was supported by Ho Chi Minh City University  
of Technology and Education under a research at the Power  
System and Renewable Lab.  
REFERENCES  
[1]  
[2]  
H. Bevrani, Senior Member, IEEE, G. Ledwich, Senior  
Member, IEEE, and J. J. Ford. "On the Use of df/dt in Power  
System Emergency Control", 2009.  
Urban Rudez, Rafael Mihalic, Faculty of Electrical  
Engineering, University of Ljubljana, Trzaska 25, 1000  
Ljubljana, Slovenia. "A novel approach to underfrequency  
load shedding", 2011.  
Fig. 17. Diagram of rotor angle and bus frequency after generator 34  
outage according to the AHP method.  
[3]  
Farrokh Shokooh, J.J. Dai, Shervin Shokooh, Jacques Tastet,  
Hugo Castro, Tanuj Khandelwal, & Gary Donner, IEEE  
Industry Applications Magazine, "Intelligent load shedding,  
case study of the application in a large industrial facility", 21  
January 2011.  
[4]  
[5]  
Lagonotte Patrick, Labroratoire d'Automaticque et  
d'Informatique Industrielle, "The different electrical  
distances"  
Fig. 18. Diagram rotor angle and bus frequency after generator 34 outage  
according to the under frequency load shedding relay method.  
Tohid Shekari, Student Member, IEEE, Farrokh Aminifar,  
Senior Member, IEEE, and Majid Sanaye-Pasand, Senior  
Member, IEEE, "An Analytical Adaptive Load Shedding  
Scheme Against Severe Combinational Disturbances", 2015  
Nhan MaiNgoc, "Master Thesis: Study of load shedding  
using neural network and AHP algorithm", Ho Chi Minh  
City of University of Technology and Education, VietNam,  
2017  
Comparative results of the methods presented in Table 5.  
[6]  
Table 5. Comparative results of the methods  
Frequency  
recovery time  
(s)  
Frequency  
stability  
(Hz)  
Amount of  
load shedding  
(MW)  
Method  
[7]  
[8]  
Ercot, "Under frequency Load Shedding, 2006  
Proposed  
AHP  
45  
60,030  
60,157  
60,89  
628,000  
738,852  
1154,394  
D. Kottick, “Neural Network for Predicting the Operation of  
an Under Frequency Load Shedding System”, IEEE Trans.  
on Power Systems, Vol.11, No. 3, pp. 1350-58, 1996.  
55  
UFLS relay  
100  
In the case of generators 34 outage with a load level of  
100%, the proposed method has many advantages over the AHP  
method and the low frequency method, as follows:  
The amount of load shedding in at least 3 methods.  
The rotor angle recovery time is almost the same, but the  
frequency recovery time of the proposed method is earlier  
(about 20 ÷ 25s). System stability sooner and increased  
reliability in the supply.  
It can be seen that the load shedding is based on phase  
electrical distance are offset for both the remaining methods,  
with fast recovery times, optimum capacity load shedding and  
bus frequencies within the allowable range.  
VI.  
CONCLUSION.  
The paper proposed the method load shedding on the basis  
of the combination of Generalized Regression Neural Network,  
power sensitivity theory and Phase Electrical Distance theories  
to maintain a stable electrical system in the event loss a  
generator occurring in the electric system. The effect of the  
proposed method is to perform offline simulations on the IEEE  
39 Bus New England test system. The results of the comparison  
of the efficacy of the proposed method with the AHP method  
and low frequency method revealed that: The proposed method  
has a system frequency of recovery that is 18% faster than the  
AHP method, 55% faster than the low frequency method; The  
load shedding capacity was 15% less than the AHP method and  
45.6% less than the under frequency load shedding relay  
method.  
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