Intelligent ann - based load - frequency control strategies for an interconnected hydropower system

itable for applying the ANN-
Kỹ thuật điều khiển & Điện tử 
N. D. Trung, , N. V. Tiem, “Intelligent ANN-based load-frequency  hydropower system.” 46 
based controllers. This section introduces two of typical such ANN-based controllers, 
namely ANN-based NARMA and ANN-based MRAC. 
Figure 3. The architecture of an ANN-based NARMA model. 
To apply the first ANN – based LFC controller, we recall the power system model 
described by a discrete state-space model created from (4) and (5): 
[ 1] . [ ] . [ ] ( [ ], [ ]),x k A x k B u k f x k u k (11) 
[ ] . [ ].y k C x k (12) 
The above model can be expressed as a NARMA (Nonlinear Autoregressive Moving 
Average) model shown below: 
[ ] ( [ ], [ 1], ... [ 1], [ ], [ 1], ... [ 1])y k d F y k y k y k n u k u k u k m 
(13) 
where d, m, and n denote the relative order, input delays, and output delays, 
respectively. The real output y[k+d] must be forced to follow the reference value yref[k+d]. 
This is an effective way when a NARMA-L2 model has been used [10]. In principle, the 
algorithm of a NARMA-L2 model is based on the removal of non-linear elements of the 
given system to generate an approximately linear system. According to such a principle, 
the control signal derived from the NARMA-L2 model should be calculated as: 
[ ] [ ], [ 1],... [ 1], [ ], [ 1],... [ 1]
[ 1] .
[ ], [ 1],... [ 1], [ ], [ 1],... [ 1]
refy k d h y k y k y k n u k u k u k m
u k
g y k y k y k n u k u k u k m
(14) 
Such controllers are applied in our power control system by using two multi-layer 
ANNs to obtain the approximate computation of h(•) and g(•). The detailed architecture of 
an ANN-based NARMA-L2 model is represented in figure 3. The effectiveness of the 
controller will be demonstrated in Section 4 of the current paper. 
3.3. MRAC-based LFC controller 
The principle of the control strategy using a MRAC-based LFC controller is presented 
in figure 4. Here, two neural networks are used in each model applied in the ith control-
area: ANN-controller and ANN-identification plant. The inputs of an ANN-controller are 
Nghiên cứu khoa học công nghệ 
Tạp chí Nghiên cứu KH&CN quân sự, Số 65, 02 - 2020 47
similar to the ANN-NARMA controllers as mentioned above, while the second neural 
network used to identify the corresponding control-area uses the output of the first 
network, u(k), as its input. In addition, a Reference area model is also used in this control 
architecture to evaluate the error of its output and the real ACE in order to train the ANN-
controller. Thus, the ANN-controller is trained along with the ith control-area model to 
track the corresponding reference model. This control strategy is defined as a direct ANN-
MRAC scheme since the generated error will be propagated backwards through the 
controller. 
To implement such control scheme, the ith control-area model is identified first to 
imitate the forward model of the control plant. In this work, we use the ANN-identification 
model with a 2-10-2 architecture to achieve the training error of 10-4. Also, a 5-13-2 
architecture is designed for each ANN-controller to obtain the similar training error. The 
full parameters of the proposed control strategy are indicated in Table 3 (see Appendix C) 
of this paper. 
After training the ANN-identification plant, it is then embedded in the control system 
to combine with the ANN-controller. Consequently, the ANN-controller is trained more 
effectively through the ANN-identification model in order to achieve the desired control 
characteristics. The accuracy of these control properties depends on the choice of a 
suitable Reference area model. At last, simulation results of this control architecture will 
also be implemented in the next section to verify its control applicapility. 
Figure 4. Control structure of ANN-based MRAC model. 
4. SIMULATION RESULTS AND DISCUSSION 
This section presents numerical simulation results using MATLAB package to verify 
feasibility of control strategies proposed for the LFC of a two-area hydropower system. 
The current study proposes two simulation scenarios of the load changes: 
(i) In the first scenario, the load changes appear in each area at different starting points 
and magnitudes (see figure 6(a)). 
(ii) In the second scenario, the load change appears randomly and continuously in the 
first area (see figure 9 (a)). 
The major functions of the LFC are to damp the oscillations of the net frequency and 
tie power flow of the hydropower network. It means that the output vector 
1 2 ,12[ ( ), ( ), ( )]
T
tiey f t f t P t must be converged towards the zero-steady state with good 
control indexed. In this section, three LFC controllers are studied, including PID, NARMA 
and MRAC. To execute the last two ANN-based LFC controllers, the following steps need 
Kỹ thuật điều khiển & Điện tử 
N. D. Trung, , N. V. Tiem, “Intelligent ANN-based load-frequency  hydropower system.” 48 
to be performed: 
Step 1: Design a reference model to the control system. 
Step 2: Executing plant identification. In this work, we use parameters for plant 
identification as shown in Table 3 (see appendix C). 
The plant identification needs a process of generating training data, then training 
network. This process is described in figure 5. 
Step 3: Training the ANN controller. This is the last step to complete the ANN-based 
controllers. Figure 5 shows the best validation performance for the NARMA controller as 
a typical example. 
After the above three steps, the ANN-based controllers are ready to be applied for the 
LFC problem in a two-area interconnected hydropower system model. It is noted that there 
is a scaling factor behind each ANN-based LFC controller. It can be found that both “trial 
and error” and optimization methods are able to be applied to determine a suitable value 
for such scaling factors. In this paper, the optimization method based on the PSO (partical 
swarm optimization) mechanism is applied to this determination. 
Figure 5. Training process of two ANN-based LFC controllers – typical results. 
0 20 40 60 80
-1
-0.5
0
0.5
1
Input
0 20 40 60 80
0
0.2
0.4
0.6
0.8
Plant Output
0 20 40 60 80
time (s)
-2
-1
0
1
2
10-3 Error
0 20 40 60 80
time (s)
0
0.2
0.4
0.6
0.8
NN Output
Nghiên c
Tạp chí Nghi
second simulation context is being dedicated in 
compare performances of the LFC controllers, 
indexes
technique to determine the optimal gains behind
given as:
Figures 6
An objective function which is considered to be
Figure 6. 
ứu khoa học công nghệ 
as: 
ên c
-8 and Table 1 present simulation results for the first scenario. Meanwhile, the 
(c) Dynamic response of frequency deviation in the second area.
ứu KH&CN 
Simulation results for the first simulation scenario
(b) Dynamic response of frequency deviation in the first area;
quân s
ự, Số
IAE ACE t dt
ISE ACE t dt
ITAE ACE t tdt
ITSE ACE t tdt
J f f P
 65
, 02
0
T
 - 20
0
T

0
T

0
T
1 2 ,12
20
we consider four typ
figures 9, 10 and Table 2. Here, 
( )
( )
( )
( )
an ANN

2

2
 a candidate for the optimization 
tie
-based LFC controller can be 
 (a) Load changes;
ical control quality 
(1
(1
(17
(18
(19
49
to 
5)
6)
)
)
)
Kỹ thuật điều khiển & Điện tử 
N. D. Trung, , N. V. Tiem, “Intelligent ANN-based load-frequency  hydropower system.” 50 
From figures 6-10 and Tables 1-2, there is overwhelming evidence for the notion that 
both ANN-based LFC controllers obtained much better control quality in comparison with 
the PID regulator. Therefore, they are completely able to replace with the conventional 
PID regulators when solving the LFC problem. 
Figure 7. Tie-line power flow in the first simulation perspective. 
Figure 8. Objective function for the first simulation scenario. 
Table 1. Comparative results based on several control criteria in the first simulation case. 
P
ti
e
1
,2
(p
u
)
0 50 100 150 200 250 300
time (s)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
O
b
je
ct
iv
e
 f
u
n
ct
io
n
 (
p
u
)
PID
NARMA
MRAC
Criteria PID NARMA MRAC 
 ACE1 ACE2 ACE1 ACE2 ACE1 ACE2 
IAE 8.6040 9.0902 2.4292 2.9809 3.0097 3.4023 
ISE 0.4119 0.5678 0.0792 0.1844 0.0942 0.2010 
ITAE 1233.0 1317.0 215.6 325.8 293.0 374.8 
ITSE*10-3 6243.2 9055.6 850.4 2575.7 1059.8 2836.0 
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Tạp chí Nghiên cứu KH&CN quân sự, Số 65, 02 - 2020 51
Figure 9. Simulation results for the second scenario 
(a) Load change in the first area; 
(b) Fluctuations of net frequency deviation in the first area. 
Figure 10. Objective functions for the second simulation case. 
0 50 100 150 200 250 300
time (s)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
O
b
je
ct
iv
e
 f
u
n
ct
io
n
 (
p
u
)
PID
NARMA
MRAC
Kỹ thuật điều khiển & Điện tử 
N. D. Trung, , N. V. Tiem, “Intelligent ANN-based load-frequency  hydropower system.” 52 
Table 2. Two main control criteria for the second simulation case. 
5. CONCLUSION 
In this paper, two intelligent LFC strategies based on artificial neural networks have 
been investigated. In addition, a simulation process has been implemented using 
MATLAB/Simulink® package for a typical case of two-control-area hydropower system to 
verify the effectiveness of such two robust controllers proposed in this study. 
Subsequently, simulation results that have been achieved in comparison with the 
conventional LFC strategy using PID regulators demonstrated that such two intelligent 
controllers are the best choices for the solutions of the LFC problem. Further research in 
this area may include increasing complexity of the interconnected power systems 
consisting of more control-areas as well as types of power plants: thermal, hydro and 
renewable systems in dealing with the LFC problem. 
APPENDICES 
Appendix A 
Nomenclature 
fn nominal frequency, fn = 50Hz 
f real frequency of the network, Hz 
tieP tie line power flow, p.u. 
∆f1,2 (t) frequency deviations of the first and second areas, in time domain, p.u. 
∆F1,2 (s) frequency deviations of the first and second areas, in Laplace domain, p.u. 
1,2 ( )ACE t Area control error, in time domain 
1 2( ), ( )u t u t control signal for the first and the second areas 
1,2DP load changes in the first and the second areas, p.u. 
,12tieP tie-line power flow deviation, p.u. 
i
gT time constant of governor, s 
,w iT time constant of hydro turbine unit, s 
Di
 load damping factor, p.u. MW/Hz 
Mi generator inertia constant, p.u. 
Tij
 tie-line time constant, sec 
Bi frequency bias factor, MW/p.u.Hz 
Ri speed regulation constant, Hz/MW 
,g iG transfer function of the governor unit 
Criteria PID NARMA MRAC 
IAE 39.1473 24.9040 24.6673 
ISE 6.7665 2.8997 2.8608 
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Tạp chí Nghiên cứu KH&CN quân sự, Số 65, 02 - 2020 53
,t iG transfer function of the hydro turbine unit 
,PiG transfer function of the rotor inertia and load (power system) 
Appendix B 
Two-area interconnected power system parameters: 
1 2 48.7g gT T s ; 1 2 1w wT T s 
1 2 1 2 1 2 1 2 120.513; 0.6; 1; 2.4; 0.0707;r rT T M M D D R R T 
Load changes: 
Scenario 1:
,1
,1
0.1( )
0.2( )
D
D
D
P pu
P
P pu
at starting times: 20s and 50s. 
Scenario 2: ∆PD1 is a uniform random number function generates uniformly distributed 
random numbers over an interval of [-1; 1]. 
 ∆PD2 is the same to ∆PD2 in the first scenario. 
Appendix C 
Table 3. Parameters for the proposed two ANN-based controllers. 
Parameters NARMA MRAC 
MRC Controller Plant Model 
Size of Hidden layer 8 15 14 
Sampling internal (s) 0.01 0.05 0.05 
No. Delayed Ref. inputs N/A 2 N/A 
No. Delayed Plant inputs 3 N/A 2 
No. Delayed Plant outputs 2 2 2 
No. Delayed controller outputs N/A 2 N/A 
Training samples 10000 15000 10000 
Training epochs 100 10 30 
Training function trainlm trainlm trainlm 
Trained error 10-5 10-4 10-4 
REFERENCES 
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[5]. R. C. Dorf and R. H. Bishop, Modern Control Systems, Pearson Prentice Hall, 2008. 
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[7]. Bimal KB. Modern power electronics and AC drives. Upper Saddle River, NJ, USA: 
Prentice Hall PTR, 2002. 
[8]. Hykin S. Neural network. USA: Mac Miller, 1994. 
[9]. Norgaard M., Poulsen N. K., Hansen L. K., Ravn O. Neural Networks for Modelling 
and Control of Dynamic Systems. Springer, 2003. 
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TÓM TẮT 
CÁC CHIẾN LƯỢC ĐIỀU KHIỂN TẦN SỐ - PHỤ TẢI THÔNG MINH DỰA TRÊN 
TRÍ TUỆ NHÂN TẠO CHO MỘT HỆ THỐNG THỦY ĐIỆN LIÊN KẾT 
Điều khiển tần số tải (LFC) là một trong những bài toán điều khiển quan trọng 
nhất trong hệ thống điện nói chung và hệ thống nhà máy thủy điện nói riêng. Nhiệm 
vụ chủ yếu của chiến lược điều khiển này khi áp dụng cho một hệ thống các nhà 
máy thủy điện liên kết là để duy trì tần số lưới và công suất trao đổi trên đường dây 
tại các giá trị danh định. Cùng với sự phát triển nhanh chóng của khoa học kỹ 
thuật, các bộ điều khiển tần số tải truyền thống như PID đã được thay thế bởi các 
bộ điều khiển thông minh. Bài báo này giới thiệu hai bộ điều khiển thông minh ứng 
dụng trí tuệ nhân tạo, đó là NARMA và MRAC. Các kết quả mô phỏng đạt được từ 
việc áp dụng hai bộ điều khiển này cho bài toán kiểm soát tần số phụ tải của một hệ 
thống thủy điện hai vùng điều khiển liên kết đã chứng tỏ tính khả thi và ưu việt của 
các chiến lược điều khiển đã đề xuất. 
Từ khóa: LFC; Hệ thống thủy điện liên kết; Thay đổi tải; Độ lệch tần số; Công suất tro đổi đường dây; Chỉ số 
chất lượng điều khiển. 
Received, 13th December, 2019 
Revised, 10th January, 2020 
Published, 17th February, 2020 
Author affiliations: 
1 Electric Power University; 
2 National Center for Technological Progress; 
3University of Transport and Communications. 
*Corresponding author: trungnd@epu.edu.vn.