Very interesting Process optimisation with the help of Hopfield neural networks. Can surely be done by other methods but this is a new way and has been applied practically.

1. An Optimal Power-Dispatching Control
System
for the Electrochemical Process of Zinc Based
on
Back-propagation and Hopfield Neural
Networks
Chunhua Yang, Geert Deconinck, Senior Member, IEEE, and
Weihua Gu, IEEE TRANSACTIONS ON INDUSTRIAL
ELECTRONICS, VOL. 50, NO. 5, OCTOBER 2003
Presented by: - Soumyadeep Nag

2. Aim
• The main aim of this project was to reduce the electricity consumed and associated
cost by a Zinc smeltery under a dynamic pricing environment
• To reduce the consumption during the peaks and increase the consumption during the
valley periods of dynamic pricing by optimizing the current supplied
Data Collection
• 4 months of data consisting of 6 values of the ratio Cs/Czn for 20 different current
densities giving a total of 120 experiments from where the current efficiency, cell
voltage and energy consumed were measured.
Procedure
• Modeling the process with Feed forward NN
• Modeling the constraints and framing the energy function
• Optimization with Hopfield NN
• Training the NNs with error back propagation algorithm
Results
• Implementation of the algorithm into the plant
• .7% reduction of cost per ton of zinc produced = 3052.2 kWhr/t to 3030.5 kWhr/t
• Yearly savings of 7,844,588$
Abstract

3. Arrangement of cells
Series connection of cells
Anode
cathode

4. Plant under consideration
• Zhuzhou smeltery – 250,000 tons of zinc/year
• Energy consumed – 800 million units
• Consists of 2 units – Unit A has 240 cells and Unit B
has 208 cells
• Dynamic pricing - 4 pricing periods
A = basic price = .054 $/kWhr

5. The electrochemical process of zinc
extraction
•The aim is to decrease the current
density during the period of high price
and increase the current density during
the period of low price
•Zinc output directly depends upon the
amount of current, or current density,
that passes through the electrodes
• However, too high or too low current
density may affect efficiency of the
process, product quality and may lead to
irregular production
SALPHERITE  Roasting
• 2ZnS + 3O2  2ZnO + 2SO2
Leaching
• ZnO + H2SO4  ZnSO4 + H2O
Electrolysis  Electro wining
• ZnSO4 + H2O = Zn + H2SO4 + 1/2O2

6. Objective functions and constraints
- Quantitative constraint
for daily output
- Qualitative constraint
imposed on current
density

7. Structure of a Hopfield network
• Symmetric
• Single layered
• Fully connected

8. Energy Function for Training the
Hopfield NN

9. Modified Energy Function

10. Training the Hopfield NN

11. Measured and computed data for the
120 experiments

12. Measured and computed data for the
120 experiments

13. Architecture of BPNN-V and BPNN-ῃ

14. Training the Hopfield NN

15. Training the BPNN
MSE for cell voltage
MSE for current
efficiency
Adjusting the weights
with error back
propagation
x(l) is the matrix of current weights and
biases

16. Results
BPNN modification with new samples
Obtaining the optimized schedule
Rectifier control and sensor
information collection including
current
Tracks the optimal current
Regulated rectifiers with SCRs after
the transformer that are current
controlled Provide alarms - Record data -
Diagnose faults – Generate trend
curves

17. Results
Quantity Change
Decrease in energy
consumed per ton of zinc
0.7%
Production deviation .5%
Total annual decrease in cost
of energy consumed
$ 7,844,588
Cost of energy saved due to
reduction in power
consumed during peak hours
$ 1 985 903
Cost of energy saved due to
increase in power consumed
during valley periods
$5,858,675
• Not only does it reduce the cost of production but it also relieves the grid during peak
load hours and levels the load by increasing the power consumed during the off – peak
hours, hence stabilizing the grid.

18. Test Code
w(1,1)=swarm(j,1,1);
w(1,2)=swarm(j,1,2);
w(2,1)=swarm(j,1,3);
w(2,2)=swarm(j,1,4);
b(1)= swarm(j,1,5);
b(2)= swarm(j,1,6);
y=w*O+b';
O(1)=(5/(1+exp(-y(1)))+5)';
O(2)=(6/(1+exp(-y(2)))+1)';
J(j)=(O(1)-9)^2+(O(2)-5)^2;
if J(j)<abs(swarm(:, 4, 1))
O
for dim=1:6
swarm(j, 3, dim) = swarm(j, 1, dim);
end
swarm(j, 4, 1) = J(j);
end
end

19. Test functions
J(j)=(x1-9)^2+(y-5)^2;
J(j)=(100*(x2-x1^2)^2 +(x1-1)^2);
J(j) = -20*exp(-.2*sqrt(.5*(x1^2+x2^2)))-
exp(.5*(cos(2*pi*x1)+cos(2*pi*x2)))+exp(1)+2
0;
Sphere function
Rosenbrock function
Ackley’s function
X1, x2 = 9,5
X1, x2 = 1,1
X1, x2 = 0,0

20. Results – Sphere function
X =
9.0000
4.9873
weights and biases
w =
0.0846 0.1352
0.0135 0.0972
b = 0.0223 0.0997
Value of the energy function
ans =
1.6226e-004

21. Results – Rosenbrock function
X=
1.0140
1.0288
weights and biases
w =
0.0157 0.0278
0.0302 0.0221
b = -0.0254 -0.0049
Value of the energy function
ans = 2.2793e-004

22. Ackley’s Function
O =
1.0e-003 *
0.1282
-0.0329
Value of the energy function
ans = 3.7479e-004
weights and biases
w =
0.0008 0.0055
0.0015 -0.0180
b =
1.0e-004 *
0.6434 -0.5106

23. Thank you