Dynamic programming strategy in optimal controller design for a wind turbine system

Abstract

In this article, an optimal controller is proposed to extract maximum wind energy from the available wind speed. The very fluctuating nature of wind speed has made the process of extracting wind energy complicated. To extract and optimize such a complicated system, a dynamic programming-based optimal control approach is well suited to non-linear wind turbine system models and restrictions. The performance of this control method is tested via MATLAB software. The outcomes of the system have a 7 up to 8.5 tip speed ratio optimal value and the aerodynamic efficiency has a 0.411 conversion value. With the proposed controller, the energy captured is improved by 13.841% and 1.15% for piecewise step input and randomly generated wind speed respectively compared to standard torque control. The lower percentage improvement, in this case, is due to the limited range of the wind speed value given for the simulation. Generally, the optimal control method is globally maximizing wind energy capture for each time step via forward and backward recursion of dynamic programming rather than normal torque control.

Keywords:

• Dynamic programming
• Wind energy
• Optimal control
• Optimization

Reviewing Editor:

• Ai Qingsong, Wuhan University of Technology, China

Subjects:

• Technology
• Engineering & Technology
• Biomedical Engineering
• Biosensors
• Medical Devices
• Electrical & Electronic Engineering
• Intelligent Systems
• Power Electronics
• Instrumentation, Measurement & Testing
• Power Engineering
• Systems & Controls
• Power & Energy
• Renewable Energy
• Transport & Vehicle Engineering

1. Introduction

Wind turbine capacity has expanded dramatically over the last few decades, from a few tens of KW to today’s multi-MW level (Srivastava et al., 2021). Advanced generators, advanced power converter systems, and control solutions must be developed to make wind turbine units better suitable for power grid integration due to the continuous growth in the power level of wind turbines and their higher penetration into the power grid (Jiao et al., 2019). The kinetic energy of the wind is transformed into usable electrical energy by rotating machinery known as a wind turbine. By allowing the rotor speed to adapt to changes in wind speed, variable speed operation was created to increase aerodynamic efficiency in the partial load region. This method reduces drive train strain, making it the most recent trend in wind energy conversion (Santosh Kumar & Suresh Kumar, 2018). The main goal of a wind turbine system operating at half load is to track the maximum aerodynamic power coefficient to absorb as much wind energy as possible. Such power coefficients have been tracked using a variety of control techniques. Standard torque control is one of the control algorithms. It maximizes wind energy capture based on the global maximum assumption of the aerodynamic power coefficient. These controllers presume that the global maximum power coefficient is always known, despite their high performance and simplicity of use. Unfortunately, not all wind turbine systems fit this assumption, especially when generator speeds are constrained by demands for extended service lives and inexpensive electrical components (Aittaleb, 2020; Apata & Oyedokun, 2020). To maximize wind power generation under these circumstances, the optimal controller must be applied. These control techniques can be used to direct the behavior of wind turbines in the future based on a nonlinear turbine model, variation of wind speed. It uses deterministic dynamic programming algorithm to convert an optimal control problem into a discrete optimization problem with constrained. This algorithm optimize wind turbine variables such as turbine rotor speed trajectory, tip speed ratio, pitch angle, generator input torque, and aerodynamic efficiency by preceding forward in time and evaluates the optimal energy capture at every node in the discretized state-time space by proceeding backward in time. In this study, the effectiveness of maximizing energy capture from available wind speed and dynamic wind conditions is demonstrated by comparing the suggested control strategy to standard torque control, in MATLAB simulation. The article contribution is to clearly show the performance of the proposed strategy in relative to the conventional torqe control methods. The next parts of this article are comprised of five sections; wind turbine aerodynamics, optimal control, dynamic programming, result and discussion, and conclusion.

2. System modelling

2.1. Wind turbine aerodynamics

Betz’s law illustrates the theoretical maximum power that can be obtained from the wind. The extracted power can be given by Cortes-Vega et al. (2021) and Coelho (2022) (1) $$P_{\mathrm{\text{extract}}}=\frac{1}{2}\rho \mathrm{\pi }{R}^2\frac{V_{\mathrm{a}}+V_b}{2}(V_b^2-V_a^2)$$(1) where $p_{\mathrm{\text{extract}}}$ (power extract) is the maximum power that can be obtained from the wind, $v_a$ is the wind speed after passing through the turbine, $v_{b }$ is the wind speed before passing through the turbine. ρ, R are the air density and radius of the blade respectively.

Then the efficiency can be calculated as Cortes-Vega et al. (2021) (2) $$\mathrm{\text{efficiency}}=\frac{P_{\mathrm{\text{extract}}}\mathrm{ }}{P_{\mathit{\text{wind}}}\mathrm{ }}\mathrm{ }$$(2) where, (3) $$P_{\mathrm{\text{wind}}}=\frac{1}{2}\mathit{\rho \pi }{R}^2{V}_b^3$$(3)

In Afanasieva et al. (2018), the dynamics of the wind turbine can be represented by the following equation, assuming the drivetrain is stiff and its energy loss is minimal: (4) $$\dot{\omega }=\frac{1}{J_{\mathrm{r}}}\left({\tau }_{\mathrm{\text{aero}}}-{\tau }_{\mathrm{c}}\right)$$(4) where J_r is the combined rotational inertia of the rotor, gearbox, generator, and shafts, ${\tau }_{\mathrm{\text{aero}}}$ is aerodynamic torque, which drives the turbine, and ${\tau }_{\mathrm{c}}$ is the reactive torque (Cortes-Vega et al., 2021). (5) $${\tau }_{\mathrm{\text{aero}}}=\frac{P_{\mathrm{\text{cap}}}}{{\omega }_{\mathrm{r}}}$$(5) $P_{\mathrm{\text{cap}}}$ depicts the wind energy gathered. The aerodynamic power coefficient (C_p) establishes the relationship between the captured wind power $P_{\mathrm{\text{cap}}}$ and the available wind power ($P_{\mathrm{\text{wind}}}$). This coefficient indicates how well wind energy is converted into mechanical energy. It is characterized by (6) $$C_{\mathrm{p}}=\frac{P_{\mathrm{\text{cap}}}}{P_{\mathrm{\text{wind}}}}$$(6)

Finally, the aerodynamic power coefficient is developed as in Equation (7)(7) $$C_p=C_1(\frac{C_2}{{\lambda }_i}-C_3\beta -C_4)e^{\frac{C_5}{{\lambda }_i}}$$(7) . (7) $$C_p=C_1(\frac{C_2}{{\lambda }_i}-C_3\beta -C_4)e^{\frac{C_5}{{\lambda }_i}}$$(7) where, (8) $${\lambda }_i=\frac{1}{\lambda +0.08\beta }-\frac{0.035}{{\beta }^3+1}$$(8)

The value from C1 to C6 and x are constant and given in Table 1.

Table 1. Value of aerodynamic power coefficient (Cortes-Vega et al., 2021).

Variable	$C_1$	$C_2$	$C_3$	$C_4$	$C_5$
Value	0.51760	116.00	0.40	5.00	21.00

The reactive torque: (9) $${\mathrm{\tau }}_c={\mathrm{\tau }}_g{\mathrm{N}}_g$$(9) where ${\tau }_g$ the turbine generator torque and N_g the gearbox ratio defined as generator shaft speed over the wind turbine rotor speed ${ (w}_r).$

By combining the above equation, the dynamics of wind turbines can be derived: (10) $$\dot{w}=\frac{1}{J_r}\left(\frac{\pi }{8}{D}_r^2\rho C_p\frac{v_w^3}{w_r}-{\mathrm{\tau }}_g{\mathrm{N}}_g\right)$$(10) (11) $${\tau }_g=(\frac{\frac{\pi }{2}{R}^2\rho C_p\left(\lambda ,\beta \right)v_w^3}{w_r}-J_r\frac{\mathit{\text{dw}}}{\mathit{\text{dt}}})/\mathit{\text{Ng}}$$(11)

The total wind energy captured over a time interval can be calculated as; (12) $$E_{\mathit{\text{cap}}}=\underset{t_0}{\overset{t_f}{\int }}{P}_{\mathit{\text{cap}}}\mathit{\text{dt}}=\underset{t_0}{\overset{t_f}{\int }}{P}_{\mathit{\text{wind}}}.C_{p\mathrm{ }}\mathit{\text{dt}}=\frac{\pi }{8}\rho D_r^2.\underset{t_0}{\overset{t_f}{\int }}{v}_w^3.C_p\mathit{\text{dt}}$$(12)

The graph in Figure 1 is a two-dimensional plot of C_p as a function of λ (tip speed ratio) and (pitch angle). Each C_p curve represents a distinct value of β. The dashed blue curve is made up of several segments that represent the highest conceivable values of $C_p$ between λ and β. Each segment may correspond to a different β depending on the value of λ.

Figure 1. C_p versus TSR with different pitch angles.

The plot shows that a pitch angle of 15°–25° produces the maximum achievable power coefficient at low values of λ, that is, λ < λ1 (L1). For high values of λ, that is, λ > λ2 (L2), achievable maxima of C_p are generated by pitch angles of 1° or 2°. For the range of λ between λ1 and λ2 all of the achievable maxima of Cp are on the 0° pitch angle curve, including the global maximum of C_p. Due to constraints governed by the rotor speed and wind speed, the global maximum of C_p is not always achievable. In this instance, achieving the highest attainable Cp requires the best tuning of pitch angle (β). The magnitude of the power grows together with the wind speed. The relationship between wind-generated mechanical energy and rotor speed for three different wind speeds—10, 11, and 12 m/s—is shown in Figure 2. Maximizing wind energy capture is equivalent to improving the integral term in Equation (12)(12) $$E_{\mathit{\text{cap}}}=\underset{t_0}{\overset{t_f}{\int }}{P}_{\mathit{\text{cap}}}\mathit{\text{dt}}=\underset{t_0}{\overset{t_f}{\int }}{P}_{\mathit{\text{wind}}}.C_{p\mathrm{ }}\mathit{\text{dt}}=\frac{\pi }{8}\rho D_r^2.\underset{t_0}{\overset{t_f}{\int }}{v}_w^3.C_p\mathit{\text{dt}}$$(12) . For the case of steady-state operation, C_p should be maintained as its global maximum value to maximize the wind energy capture. However, the transient of the turbine may cause it to fall into any zone of Cp as illustrated in Figure 1, due to the variation in wind speed or the constraint on rotor speed.

Figure 2. Mechanical power versus rotor speed for different wind speeds.

3. Controller design

3.1 Optimal controller design

The STC control approach depends on global maximum power coefficient. It assumes that global maximum power coefficient (${\left(c_p\right)}_{\mathrm{\text{max}}}$) knowledge is always obtainable. The turbine generator torque is controlled in this approach using a feedback control law (Doekemeijer et al., 2019), which is stated as follows. (13) $${\mathrm{\tau }}_c={\mathrm{\tau }}_g{\mathrm{N}}_g=k_{\tau }{\omega }_r^2$$(13) where (14) $$k_{\tau }=\frac{1}{2}{\rho }_{\mathit{\text{air}}}\pi R_r^5\frac{{\left(c_p\right)}_{\mathrm{\text{max}}}}{{\lambda }_{\mathrm{*}}^3}=\frac{1}{2}{\rho }_{\mathit{\text{air}}}\pi R_r^5\frac{\left.c_p({\lambda }_{\mathrm{*}},{\beta }_{\mathrm{*}}\right)}{{\lambda }_{\mathrm{*}}^3}$$(14)

When substituting this in Equation (10)(10) $$\dot{w}=\frac{1}{J_r}\left(\frac{\pi }{8}{D}_r^2\rho C_p\frac{v_w^3}{w_r}-{\mathrm{\tau }}_g{\mathrm{N}}_g\right)$$(10) , the model has the following forms. (15) $$\stackrel{·}{\omega }=\frac{1}{2J_r}{\rho }_{\mathit{\text{air}}}\pi R_r^5{\omega }_r^2[\frac{C_p}{{\lambda }^3}-\frac{{\left(C_p\right)}_{\mathrm{\text{max}}}}{{\lambda }_{\mathrm{*}}^3}]$$(15)

The control law in Equation (13)(13) $${\mathrm{\tau }}_c={\mathrm{\tau }}_g{\mathrm{N}}_g=k_{\tau }{\omega }_r^2$$(13) causes the turbine to accelerate toward the desired set point when the rotor speed is too slow and to decelerate when it is too fast. This generator torque control law will, therefore, in steady-state conditions, balance the aerodynamic and load torques to control the turbine speed to the optimal tip speed ratio (${\lambda }_{*}$) and pitch angle $({\beta }_{*}$). Even though standard control of region two wind turbines is widely adopted due to its ease of implementation and excellent performance, it has various flaws that result in significant power losses. The first of these is that the gain $k_{\tau }$ cannot be determined with any degree of accuracy. Second, even if it is assumed that $k_{\tau };$ can be precisely calculated by simulation, variations in wind speed drive the turbine to operate a majority of the time off the peak of its C_p–λ curve, resulting in reduced energy capture (Afanasieva et al., 2018). Therefore, to overcome the STC's shortcomings, this article offers dynamic programming approach for optimization. It is a numerical approach based on Bellman’s optimality principle for determining the control law that offers the global maximum value for a given objective function while satisfying the system constraints (Sun et al., 2019).

In this article, Bolza-type optimal control problems were used. So, the performance index is derived from Equation (3)(3) $$P_{\mathrm{\text{wind}}}=\frac{1}{2}\mathit{\rho \pi }{R}^2{V}_b^3$$(3) up to (10) (16) $$\mathrm{\text{max}}\mathit{ J}=E\left(N\right)+\frac{\pi }{8}\rho D_r^2.\sum _{k=0}^{N-1}\underset{t_0}{\overset{t_f}{\int }}{v}_w^3.C_p(\frac{R{\omega }_r}{v_w},\beta )\mathit{\text{dt}}$$(16)

Subjected to: (17) $$\dot{w_r}=\frac{1}{J_r}\left(\frac{\pi }{8}{D}_r^2\rho C_p(\lambda ,\beta )\frac{v_w^3}{w_r}-{\mathrm{\tau }}_g{\mathrm{N}}_g\right)$$(17) (18) $$x\left(0\right)=x_0$$(18) (19) $$({{\omega }_r)}_{\mathrm{\text{min}}}\le {\omega }_r\le ({{\omega }_r)}_{\mathrm{\text{max}}}$$(19) (20) $$({{\tau }_g)}_{\mathrm{\text{min}}}\le {\tau }_g\le ({{\tau }_g)}_{\mathrm{\text{max}}}$$(20) (21) $${\mathrm{\beta }}_{\mathrm{\text{min}}}\le \mathrm{\beta }\le {\mathrm{\beta }}_{\mathrm{\text{min}}}$$(21) where, $({{\omega }_r)}_{\mathrm{\text{min}}}$ is the minimum turbine rotor speed, $({{\omega }_r)}_{\mathrm{\text{max}}}$ is the maximum turbine speed. The continuous-time model must first be discretized in time before using dynamic programming to solve the continuous-time control problem. So, let’s describe the system using (22) $$x\left(k+1\right)=F\left(x\left(k\right),u\left(k\right),k\right),k=0,1,\dots N-1$$(22) (23) $$x(k+1)=T_s*\frac{1}{J_r}(\frac{\pi }{8}{D}_r^2\rho C_p(\frac{R*x(k)}{v_w},u(k))\frac{v_w^3}{x\left(k\right)}-{\mathrm{\tau }}_g(k){\mathrm{N}}_g)+x\left(k\right)$$(23) with the state variable x_k ∈ X_k and the control signal u_k ∈ U_k. And the cost function be (24) $$J_k\left(x\left(\mathrm{k}\right)\right)=J=\mathrm{E}\left(x\left(k_f\right),k_f\right)+\sum _{k=0}^{\mathrm{N}-1}\mathrm{E}\left(x\right(k),u(k\left)\right)$$(24) where, x(k), and u(k) are the n and r dimensional state and control vectors, respectively. By using the principle of optimality to find the optimal control u*(k) which is applied to the plant (22) gives optimal state x* (k). Assume for the moment that we considered the best control, state, and cost for each value from k + 1 to N. Then, we write using the principle of optimality at any point in time or stage k. (25) $$E_k^{*}\left(x\left(k\right)\right)=\mathrm{\text{max}}\hspace{0.17em}\left[E\left[x\left(k\right),u\left(k\right)\right]+E_{k+1}^{*}\left(x^{*}\left(k+1\right)\right)\right]$$(25) (26) $$J_k^{*}\left(x\left(k\right)\right)=\mathrm{\text{max}}\hspace{0.17em}\left(E_{k+1}\left(k+1\right)\right)+\frac{\pi }{8}{D}_r^2\rho \sum _{k=0}^{N-1}{T}_s*C_p\left(\mathit{R*}\frac{x\left(k\right)}{v_w},u_2\left(k\right)\right)*\frac{v_w^3}{x\left(k\right)}$$(26)

The previous relationship represents the optimum control system’s application of the principle of optimality in mathematical form. It is also known as a dynamic programming functional equation. The ideal values for a single stage from k to k + 1 can therefore be found if the optimal control, state, and energy capture were discovered from any discrete dynamic programing stage k + 1 to the final stage N. For each time steps of the algorithm the optimal value of states, control inputs are calculated by forward proceeding till the system constraint limit. After get this optimal value the energy capture or cost function is optimized from the available optimal value of the system states and control inputs by considering final constraint. The general flow diagram for recursive dynamic programming is shown in Figure 3.

Figure 3. Recursive dynamic programming algorithm flow chart.

4. Results and discussions

With Piecewise Step input, (27) $$v_w\left(\mathrm{t}\right)=6+2.125\mathrm{*}\mathrm{\text{fix}}\left(\frac{\mathrm{t}-1}{15}\right)$$(27)

The performance of both optimal control using a dynamic programming technique and standard torque control by torque feedback control about turbine rotor speed were evaluated. As demonstrated in Figure 4, the STC control approach appears to converge to the optimal position faster than the optimal one. The reason for this is that the STC approach computes only the global optimal point of the pitch angle and C_p. Based on this maximum value of aerodynamic power coefficient value and pith angle this type of controller extract energy. But, this method will not be much useful when wind speed is varying continuously. After the wind speed gets a value above 6 m/s, the numerical optimal control mechanism has more performance than the STC control method. Discrete dynamic programing algorithm compute the optimal value of each variables of wind turbine by preceding backward and forward for each time step or discrete time. The forward preceding calculates the states (rotor speed of turbine speed), the control input unit (pitch angle and generator input torque), and tip speed ratio. The backward preceding calculates cost go function (energy capture) based on forwarded preceding optimal value of wind turbine variables. Due to this, it can be observed the total captured energy using the optimal numerical method is larger than that of the STC method. This is the result of the numerical method being superior at finding the optimal point for every value of the wind speed in contrast to the STC method which assumes the global optimal point only. Above 11 m/s, the numerical optimal control and standard torque control have approximately similar performance. But due to the state constraint, the numerical way of optimization tries to achieve the final state limits; that is why the DPM-type state has a greater value than STC.

Figure 4. DPM and STC wind energy capture using piecewise wind speed.

The steps of optimization of wind energy capture using random wind speed are follows the same procedures for each discrete time steps of dynamic programing algorithm. With random wind speed given in Equation (28)(28) $$v_w\left(\mathrm{t}\right)=10+0.87\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{25}t\right)+0.5\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{30}t\right)-0.625\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{65}t\right)+0.75\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{135}t\right)+0.65\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{235}t\right)+0.125\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{575}t\right)$$(28) , the numerical algorithm of dynamic programming method evaluation of the dynamic model of a nonlinear wind turbine system has better performance. The standard torque control method has easy implementation by assuming the aerodynamic power coefficient is at global maximum value, and the angle of attack is at zero degree, but due to the irregular nature of wind, this assumption is no further applicable to capture wind energy and generate maximum power. This is the reason why STC has less performance than the DPM method. Figure 5 presents the result of wind energy capture using DPM and STC with randomly generated wind speed given in Equation (28)(28) $$v_w\left(\mathrm{t}\right)=10+0.87\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{25}t\right)+0.5\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{30}t\right)-0.625\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{65}t\right)+0.75\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{135}t\right)+0.65\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{235}t\right)+0.125\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{575}t\right)$$(28) . (28) $$v_w\left(\mathrm{t}\right)=10+0.87\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{25}t\right)+0.5\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{30}t\right)-0.625\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{65}t\right)+0.75\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{135}t\right)+0.65\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{235}t\right)+0.125\mathrm{\text{sin}}\hspace{0.17em}\left(\frac{2}{575}t\right)$$(28)

Figure 5. DPM and STC wind energy capture using randomly generated wind speed.

5. Conclusion

In this article, optimal controller design by using the numerical algorithm for HAWT orientation wind energy conversion system is investigated. Since WT has a complex non-linear dynamic system and the wind speed is determined by piecewise step input and sine function, deterministic dynamic programming of the numerical algorithm has to be used. This type of numerical algorithm solves continuous optimal control problems by converting them to discrete-time system form. Additionally, the dynamic programming algorithm is applicable for highly constrained and nonlinear system models, and it is used to optimize the cost function globally. The optimal values of wind turbine variables such as turbine rotor speed trajectory, tip speed ratio, pitch angle, generator input torque, aerodynamic efficiency are computed by preceding forward in time and evaluates the optimal energy capture at every node in the discretized state-time space by proceeding backward in time. From the simulation result, all wind turbine variables for both piecewise step and sine function-based input gives optimal values.

In general, the modeling results show that the system has an optimal tip speed ratio of 7.5 to 8.5 and an aerodynamic efficiency of 0.411. Furthermore, with the piecewise step input wind speed, the optimal controller captured 13.841% more energy and power than STC. The optimal controller gathered 1.15% more energy and power than the STC for the randomly generated wind speed pattern. The lower percentage improvement, in this case, is due to the limited range of the wind speed value given for the simulation.

For this article deterministic dynamic programing algorithm is applied from cut-in to rated wind speed ranges. Further researcher can be used this algorithm for above rated wind speed till to cut-off regions by considering wind energy optimization function with its constraints (Table 2).

Table 2. Parameters of the wind turbine system.

Rated power, Prated	100 KW
Rotor moment of inertia, Jr	2.6 × 10^4 Kg.m^2
Rotor diameter, Dr	18 m
Gear ratio, Gr	21.5858
Max. turbine rotor speed, (𝜔r) max	12 rad/sec
Min. turbine rotor speed, (𝜔r)min	2.75 rad/sec
Max. blade pitch angle,	25 degree
Min. blade pitch angle, 𝛽min	0 degree
Max. Generator input torque, (𝜏g)max	1500 Nm
Min. Generator input torque, (𝜏g)min	0 Nm
Global max. value of Cp (Cp)max	0.4212
Value of 𝜆 corresponding to (Cp)max, 𝜆∗	8.0
Value of 𝛽 corresponding to (Cp)max, 𝛽∗	0°
Rated wind speed	12.5 m/s

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Abibual Abate Mitaw

Abibual Abate Mitaw received the B.Sc. degree in electrical and computer engineering (industrial control engineering) from Hawassa University, Hawassa, Ethiopia, in 2015, and the M.Sc. degree in electrical and computer engineering (control science) from Addis Ababa Institute of Technology, Addis Ababa University, Addis Ababa, Ethiopia, in 2019. He is currently a Senior Lecturer with the B Woldia Institute of Technology, Woldia University. He has published two articles in the Scopus Web of Science Journals. His research interests include robotics, systems, control, electric vehicles, renewable energy, smart microgrids, energy systems, artificial intelligent, and machine learning.

Abrham Tadesse Kassie

Abrham Tadesse Kassie received the B.Sc. degree in electrical and computer engineering (industrial control engineering) from Hawassa University, Hawassa, Ethiopia, in 2015, and the M.Sc. degree in electrical and computer engineering (control and instrumentation engineering) from Addis Ababa Science and Technology University, Addis Ababa, Ethiopia, in 2019. He is currently a Senior Lecturer with the Bahir Dar Institute of Technology, Bahir Dar University. He serves as the Chair for the Control and Instrumentation Engineering, Bahir Dar Institute of Technology. He has published four articles in the Scopus Web of Science Journals. His research interests include robotics, systems, control, electric vehicles, renewable energy, smart microgrids, energy systems, artificial intelligent, and machine learning.

Dereje Shiferaw Negash

Dereje Shiferaw Negash received the M.Tech. and Ph.D. degrees from the Department of Electronics and Computer Engineering, Indian Institute of Technology Roorkee, India, in 2009 and 2011, respectively. He is currently an Assistant Professor with the School of Electrical and Computer Engineering, Addis Ababa University. His research interests include neural networks, fuzzy logic systems, genetic algorithms, and application of AI in nonlinear control and robotics.