Data set for the article titled “Application of Modern Non-Linear Control
Techniques for the Integration of Compressed Air Energy Storage with Medium
and Low Voltage Grid”


Figure 3

For the system in Equation (1) in the article, with L = 8.2 mH, R = 82 Ohm, C = 1120 uF, RLoad = 100
Ohm, Vc = 450 V, I = 10.12 A and D = 0.55 the root locus of the transfer function in Figure 3a shows
the non-ASPR character of the system. Since, the direct MRAC technique cannot be applied to the
system with non-minimum phase a PFC is designed to make it minimum phase. However, in order to
keep the system dynamics intact, it must be ensured that the augmented plant output should be
almost same as the actual plant output with this modification.

To design the PFC, it must be ensured that the plant is stabilizable using any controller. So, a PI
controller is designed by root locus method to shift poles to the left side of the s-plane as:

                              C(s)=(0.0001s+0.03)/s……………………             (4)

Now, to make the system minimum phase and of relative degree one, a PFC is designed as inverse of
a PD compensator D(s) that stabilizes the series combination of C(s)G(s). The PFC is thus designed
using the root locus method as:

                              PFC= [D(s)]-1=0.001/(0.001s+1)…………. (5)

Figure 3b shows the root locus of the augmented system G^' (s)=C(s)G(s)+PFC which is now minimum
phase and of relative degree one and hence the MRAC technique can be applied to this augmented
system.

The dataset for this figure is given in file named Fig3RootLocusData.zip. The dataset can be accessed
in MATLAB to regenerate the figure.



Figure 6 and Figure 7

The performance of the DC side controller has been investigated for different in-put voltage and load
conditions. Figure 6 shows the DC-link voltage for variation in the input voltage from the CAES keeping
the load constant at RLoad = 100 Ohm. The boost converter starts operating from t = 1 s and then for
variation in the CAES input voltage, the output DC-link voltage is found to be maintained at 450 V.

The corresponding inductor and output currents of the boost converter are shown in Figure 7. It is
seen that at the starting of the boost converter the current peak is very high but at the later stage for
variation in the voltage the current peaks are within limit. This starting current can be limited by using
a charging resistor in series with the boost converter and once the current is within limit it is short-
circuited.

The dataset for this figure is given in file named Fig6_7_Input_output_voltage_current_Data.zip. The
dataset can be accessed in MATLAB to regenerate the figure.
Figure 8

The transient response of the boost converter with a standard PI controller and MRAC controller for
two loading conditions is shown in Figure 8. The gains of the PI controller are chosen to be Kp = 0.1
and Ki = 1 for minimum settling time possible for the system under test with acceptable ripple of 2%
and without overshoot condition.

The response shows that with the MRAC controller the output voltage settles to reference voltage in
0.121 s whereas with the PI controller, it settles in 0.528 s for a fall of 50 V in the input voltage at t =
1.71 s and RLoad = 10 Ohm. Similarly, for RLoad = 100 Ohm the settling time for the output voltage
remains almost same for the same dip in the input voltage but, comparatively larger oscillations are
added in case of PI con-troller. This proves the faster operation and better damping property of the
MRAC

The dataset for this figure is given in file named Fig8_MRAC_PI_Comparison_data.zip. The dataset can
be accessed in MATLAB to regenerate the figure.



Figure 9

Figure 9a shows the inverter output voltage for different power flow conditions. The switch S3
between inverter side and grid has been closed at t = 0.1 s. It can be seen from Figure 9b that inverter
phase-A reference voltage and the grid voltage of phase-A are synchronized with each other for
successful integration with the grid. The com-mand for power requirement by the grid has been given
at t = 0.15 s and the grid cur-rent increases accordingly to meet the power demand of 600 W, keeping
the voltage unchanged. The corresponding inverter currents in d-q reference frame have been shown
in Figure 9c. At t = 0.6 s the power demand rises from 600 W to 1500 W and again at t = 1.2 s it reduces
to 600 W. From Figure 9d it is clear that the inverter system is able to comply the power demand
requirement by the grid successfully.

The dataset for this figure is given in file named Fig9Data.zip. The dataset can be accessed in MATLAB
to regenerate the figure.