Maximum Power Point Tracking for Photovoltaic System Using Model Predictive Control - Intelligent Computing for Sustainable Energy and Environment - page 520

to penalize big changes in input signal. For the numerical optimization to be
tractable, the predictive state x ( k + i/k ) should be replaced by equivalent re-
lations in terms of design variables i.e. manipulated variable-d, auxiliary logic
variable- δ and auxiliary continuous variable-z. Then the predictive output could
be expressed as

y ( k + i/k )= ζ + Ωγ ( k + i/k ) (7)

Where r ( k + i/k )=[ d ( k ) , ··· ,d ( k + M − 1) ,δ ( k ) , ··· ,δ ( k + M − 1) ,z ( k ) , ··· ],

ζ = C ( A , ,A P ) T x ( k ),

···

⎛ ⎞

B ··· 0 R ··· 0 G ··· 0

⎝ ⎠

A B ··· A R A G

0 ··· 0 ··· 0

Ω = C

. . . . . . . . .

A P− 1 B ··· A P−M B A P− 1 R A P−M RA P− 1 G A P−M G ··· ···

By substitution of y ( k + i/k ) into performance function of the system J, an
easy-to-tract form of optimization problem is obtained as follows:

γ T Hγ +2 f T γ

min
γ

⎧
⎨
⎩

(5)
0 ≤ d ( k + i/k ) ≤ 1
y min ≤

(8)

s.t.

y ( k + i/k ) ≤ y max

Where H = Ω T Q y Ω + Q m ,f =2 ζ T Q y ζ− 2 d 0 Q m . This control problem could be
converted to solving the corresponding Mixed Integer Quadratic Programming
(MIQP) problem with matlab function miqp.m. The optimal control sequence
is γ ∗M− 1
t

=[ d t (0) , ,d t ( M 1) ,δ t (0) , ,δ t ( M 1) ,z t (0) ,

]at the time of
t. Only d ∗ (0) is required when controlled the system. At the time of t = t +1,
repeat the above steps to realize rolling optimization.
In this paper, light intensity, temperature and output voltage of photovoltaic
cell should be measured in every sampling period in order to readjust the ref-
erence current I*. In the predictive control strategy, aforementioned procedures
should be performed at each time step. The numerical optimization is performed
and the first element of computed control sequence is applied to the system.
During this procedure, constraints based on components restriction, such as the
diode reverse current, limit the output current within I max ; duty cycle d ( k )
should be valued between 0 and 1, and the volatility of d ( k ) should be reduced,
avoiding the damage to the power switch and unnecessary energy loss caused by
frequent operation.

··· − ··· − ···

5 Simulation Results

In this work, the hybrid system toolbox is used for simulation. The predictive
horizon P=3, the control horizon M=2, Q y =1, Q m =0.01, Ts=50 μ s, number