Matlab/ Simulink Simulation Results

148 | P a g e PI controller can successfully operate the system at optimum speed. The optimization of the rotor design (pitch angle, geometry, number of blades) done using CFD. Simulation shows that rotor with curved blades improves the efficiency of the turbine. It should be noted that the CFD model only includes the turbine blade and hub geometries. Other turbine components, such as the clamp support, were not considered in this simulation.

Nevertheless, the reasonable agreement between the CFD results and the blade element momentum method calculations provides confidence in the results obtained with both numerical methods.The CFD simulation represents is a step in the development of a CFD methodology to characterize the turbine performance. In future research should be done to develop a numerical model by considering realistic inlet velocity profiles and turbulence levels. Also include structural elements of the turbine, such as the support, in future simulations.

7.2 Matlab/ Simulink Simulation Results

Matlab/Simulink has been selected to carry out the overall modeling task of MCECS.

Simulink is a platform, is often used for model-based design of dynamic systems. The software package provides an interactive graphical presentation of results and a customizable set of block libraries, and also options for specialized application. This makes it the best candidate for accomplishing the objective of fostering interdisciplinary integration (hydrodynamics and electro mechanics). In addition Simulink can be used in conjunction with Matlab to allow user to develop algorithm, data visualization, data analysis and numerical computation. It can also control physical setups. The time stepping of the simulation is chosen to be fixed.

149 | P a g e The dimensions of the turbine are measured directly from the prototype. The efficiency of the turbine is derived through potential flow theory. Generator parameters are determined experimentally within the lab settings. Testing and steady-state analysis are carried out to determine generator efficiency. The PMSG inertia and damping constant are calculated analytically. Finally the generator model is validated through separate modelling exercises. The rectifier parameters are taken from manufacturer’s specifications. The efficiency of rectifier is identified through lab testing. Similarly the parameters of customized boost converter are taken from the design and validated

150 | P a g e Fig. 7.4 Matlab/ Simulink Model of Marine Current Energy Conversion System

152 | P a g e Table 7.1 shows the parameters of the marine turbine, PMSG, dc-dc converter used in the simulation. The sampling frequency used for the simulation is 100 kHz .

Table 7.1 Parameters of turbine, PMSG and DC-DC converter

Fig. 7.5 presents the step responses of the system for different flow speed. The flow speed is varied from 0.8 m/s to 1.25 m/s. The trajectory of the generator reference torque always follows the turbine optimum torque as shown in Fig. 7.5(b). Thus, at any flow speed, it is always possible to track the optimum turbine torque using the proposed control strategy without using any flow sensors. Fig. 7.5(c) shows the developed electromagnetic torque of the PMSG. The developed electromagnetic torque is controlled so that it always tracks the reference torque which is evident in the figures. In Fig. 7.5(d), the reference current and

153 | P a g e the input dc current of the converter are displayed. The proportional integral controller ensures that the developed torque and the input current strictly follow the reference generator torque and the command current. Fig. 7.5(e) depicts the reference speed and the measured speed of the PMSG. It is observed that the PMSG always operates at the optimum reference speed for any given flow speed. Fig. 7.6 shows the output power of the proposed marine energy conversion system. The system always produces maximum power at any flow speed. Therefore the PI controller always operates the system at maximum power point. Also the controller provides good steady state and dynamic performances and exhibits excellent tracking capabilities.

Fig. 7.5 (a)

154 | P a g e Fig. 7.5 (b)

Fig. 7.5 (c)

155 | P a g e Fig. 7.5 (d)

Fig. 7.5(e)

Fig. 7.5 Response of the system for step changes in flow speed: (a) flow speed, (b) optimum turbine torque and reference generator torque, (c) reference and developed generator torque, (d) reference current and instantaneous input current of the converter and (e) reference generator speed and instantaneous generator speed.

156 | P a g e Fig. 7.6 Output power of Marine Current Energy Conversion System

Fig. 7.7 presents the step responses of the system for different flow speed. The speed is varied from 0.8 m/s to 1.5 m/s. The trajectory of the generator reference torque always follows the turbine optimum torque as shown in Fig. 7.7(b). Thus, at any flow speed, it is always possible to track the optimum turbine torque using the proposed control strategy without using any flow sensors. Fig. 7.7(c) shows the developed electromagnetic torque of the PMSG. The developed electromagnetic torque is controlled so that it always tracks the reference torque which is evident in the figures. In Fig. 7.7(d), the reference current and the input dc current of the converter are displayed. The backstepping controller ensures that the developed torque and the input current strictly follow the reference generator torque and the command current. Fig. 7.7(e) depicts the reference speed and the measured speed of the PMSG. It is observed that the PMSG always operates at the optimum reference speed for any given flow speed.

157 | P a g e Fig. 7.8 illustrates the output voltage, the output current and the output power of the proposed marine energy conversion system. The system always produces maximum power at any flow speed. Thus, the proposed controller always operates the system at maximum power point. The adaptive performance of the proposed controller is depicted in Fig 7.9. The trajectories of the estimated load resistance and the estimated input voltage follow that of the actual load resistance and the actual input voltage. Thus, the proposed controller provides good steady state and dynamic performances and exhibits excellent tracking capabilities. Fig. 7.10 provides the boundless and stability of the proposed controller. The input current and the output voltage errors _u and , respectively, converge to zero within finite time. The virtual control law α₁ also matches the output dc voltage of the system. This proves the stability of the proposed controller.

Time(s) Fig. 7.7(a)

158 | P a g e Time (s)

Fig. 7.7 (b)

Time (s) Fig. 7.7(c)

159 | P a g e Time(s)

Fig. 7.7 (d)

Time (s) Fig. 7.7 (e)

Fig. 7.7 Response of the system for step changes in (a) flow speed(m/s), (b) optimum turbine torque and reference generator torque(N-m), (c) reference and developed generator torque(N-m), (d) reference current and instantaneous input current of the converter(A) and (e) reference generator speed and instantaneous generator speed(rad/s).

160 | P a g e

Time(s) Fig. 7.8(a)

Time(s) Fig. 7.8(b)

161 | P a g e Time(s)

Fig. 7.8 (c)

Fig. 7.8 (a) Output load voltage (V), (b) output load current (A) and (c) Output power (W) of the system

Time (s) Fig. 7.9 (a)

162 | P a g e

Time (s) Fig. 7.9 (b)

Fig. 7.9 (a) Exact and estimated load resistance (ohm) and (b) exact and estimated input voltage (V)

Time (s) Fig. 7.10(a)

163 | P a g e Time(s)

Fig. 7.10 (b)

Time(s) Fig. 7.10(c)

Fig. 7.10 Performance of the proposed controller (a) Input current error z1, (b) Output voltage error z2 and (c) Virtual voltage control law α1

164 | P a g e