# New Intelligent Control Strategy Hybrid Grey–RCMAC Algorithm for Ocean Wave Power Generation Systems

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## Abstract

**:**

## 1. Introduction

## 2. Modeling of the Studied System

#### 2.1. Structure of the System

#### 2.2. Wells Turbine Modeling

_{A}and V

_{B}are the axial velocity and blade tip speed, respectively, k is the Wells turbine coefficient, C

_{1}–C

_{8}are constants, and $\alpha $ is the arctangent of the V

_{A}to V

_{B}ratio.

#### 2.3. PMSG Modeling

- ${v}_{d},\text{}{v}_{q}=$d, q axis stator voltages
- ${i}_{d},\text{}{i}_{q}=$d, q axis stator currents
- ${L}_{d},\text{}{L}_{q}=$d, q axis stator inductances
- ${\lambda}_{d},\text{}{\lambda}_{q}=$d, q axis stator flux linkages
- $R=$ stator resistance
- ${\omega}_{s}=$ inverter frequency
- ${I}_{fd}=$ equivalent d-axis magnetizing current
- ${L}_{md}=$d-axis mutual inductance

## 3. Design of Maximum Power Point Tracking (MPPT) Controller Based on RCMAC with Grey Forecasting

#### 3.1. The Online Grey Dynamic Prediction Model

#### 3.2. Recurrent CMAC Controller

#### 3.2.1. RCMAC Structure

^{−1}denotes a time delay. This RCMAC comprises input, association memory, receptive field, weight memory, and output spaces. Signal propagation for each layer is introduced as follows:

- Input Layer: For a given C = [$e(k+1)$, $ce(k+1)$], each input variable c
_{i}can be quantized into discrete reference states. - Association Memory Layer: To effectively assign each input state in learning. Herein, the Gaussian function (receptive field basis function) is built into the hypercube block as Equation (14). In the bell-shaped manner of the Gaussian function, when the discontinuous input state is closer to the center of a certain cube, the output is more affected by the cube, and vice versa. The farther the impact is, the smaller it is.

**,**and scale parameter, ${S}_{ij}$. Additionally, this block’s input can be expressed as follows:

- Receptive Field Layer: The multidimensional receptive field function is expressed as follows:$${b}_{j}={\Pi}_{i=1}^{N}{\psi}_{ij}=exp\left[-\left({\displaystyle {\sum}_{i=1}^{N}\frac{{({c}_{ri}-{L}_{ij})}^{2}}{{S}_{ij}^{2}}}\right)\right]$$
- Weight Memory Layer: This space specifies adjustable weights of the receptive field layer results as follows:$${w}_{k}={\left[{w}_{1k},{w}_{2k},\cdots {w}_{{N}_{R}k}\right]}^{T}\phantom{\rule{0ex}{0ex}}\mathrm{for}\text{}k\text{}=\text{}1,\text{}2,\dots ,\text{}m$$
- Output Layer: The output of RCMAC mathematic form and also the control effort of the proposed controller is obtained as follows:$${i}_{qs}^{*}={y}_{0}={w}_{k}^{T}b={\displaystyle {\sum}_{j=1}^{{N}_{R}}{w}_{jk}}\mathrm{exp}\left[-\left({\displaystyle {\sum}_{i=1}^{N}\frac{{({c}_{ri}-{L}_{ij})}^{2}}{{S}_{ij}^{2}}}\right)\right]$$

#### 3.2.2. RCMAC Learning Algorithm

_{c}is defined as follows:

#### 3.3. Adjust Learning Rates with IPSO

_{1}and R

_{2}are two pseudo-random sequences used to simulate the randomness of the algorithm. For each m, $R{c}_{i}^{m}$ and $pb{t}_{i}^{m}$ are the current positions and current best position of oneself, respectively. The velocity updating law is shown in Equation (28). Besides, the inertia weight $w$ is set to 0 and IPSO can reduce parameter settings. Acceleration coefficients ${c}_{1}$ and ${c}_{2}$ can be modified using Equations (29) and (30). These settings are known as time-varying acceleration coefficients and are expressed as follows [29]:

_{max}is the maximum number of iterations, ${c}_{1i}$ and ${c}_{2i}$ are the initial parameters settings, and ${c}_{1f}$ and ${c}_{2f}$ are the final parameters settings.

## 4. Simulation Results and Discussion

_{PMSG}= 20 MW, 3.75 A, 3000 rpm, J = 1.32 × 10

^{−3}Nms

^{2}, B = 5.78 × 10

^{−3}Nm s/rad, V = 15 KV, PF = 0.975, f = 60 Hz, C

_{dc}= 0.6 pu, and T

_{R}= 0.69/33 kV.

#### 4.1. MPPT System Performance

#### 4.2. Wells Turbine Variable Axial Velocities

#### 4.3. Dynamic Load Switching

#### 4.4. Short-Circuit Fault of Power Grid

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Dynamic responses to speed changes for the studied system: (

**a**) Wells turbine’s rotor speed response, (

**b**) the real power response of WECS, (

**c**) the reactive power response of WECS, and (

**d**) dynamic voltage amplitude response of AC bus on power grid side.

**Figure 5.**Dynamic responses to pressure drop for the studied system: (

**a**) the pressure variation, (

**b**) the real power response of WECS (Case 1), (

**c**) Wells turbine’s rotor speed response (Case 1), (

**d**) the real power response of WECS (Case 2), and (

**e**) Wells turbine’s rotor speed response (Case 2).

**Figure 6.**Dynamic responses of the studied system with load changes: (

**a**) Wells turbine’s rotor speed response, (

**b**) the real power response of WECS, (

**c**) the reactive power response of WECS, and (

**d**) dynamic voltage amplitude response of AC bus on power grid side.

**Figure 7.**Transient responses of the studied system when a fault occurs: (

**a**) generator speed of WECS (

**b**) real power of WECS, (

**c**) reactive power of WECS, and (

**d**) transient voltage amplitude response of AC bus on power grid side.

Controller | Power Efficiency (%) | Max Error of Torque Coefficient C_{t} (%) | MPPT Accuracy (%) | Transient Response (s) |
---|---|---|---|---|

Grey–RCMAC | 90.9 | 0.65 | 0.41 | 1.65 |

RCMAC | 86.7 | 10.11 | 1.12 | 2.27 |

CMAC | 80.1 | 15.61 | 2.29 | 3.51 |

RFNN | 84.3 | 14.35 | 2.19 | 2.72 |

PI | 77.5 | 22.65 | 2.82 | 4.57 |

**Table 2.**Comparison results for five methods for the Wells turbine rotational speed change: (a) real power of WECS, (b) reactive power of WECS, and (c) dynamic voltage amplitude response of AC bus on power grid side.

(a) Real Power of Wells Turbine | ||||

Controller | Convergence Time (s) | CPU Execution Time | Mean Square Error (10^{−3}) | Accuracy (%) |

(10^{2} s) | ||||

Grey–RCMAC | 11.99 | 5.61 | 4.01 | 95.99 |

RCMAC | 12.67 | 5.92 | 6.21 | 93.79 |

CMAC | 9.15 | 4.30 | 10.73 | 89.27 |

RFNN | 8.11 | 3.81 | 8.52 | 91.48 |

PI | 13.50 | 6.34 | 21.15 | 78.85 |

(b) Reactive Power of Wells Turbine | ||||

Controller | Convergence Time (s) | CPU Execution Time(10^{2} s) | Mean Square Error (10^{−2}) | Accuracy (%) |

Grey–RCMAC | 10.83 | 5.09 | 4.28 | 95.72 |

RCMAC | 12.50 | 5.875 | 7.15 | 92.85 |

CMAC | 13.93 | 6.54 | 12.11 | 87.89 |

RFNN | 9.72 | 4.56 | 10.95 | 89.05 |

PI | 11.67 | 5.48 | 18.59 | 81.41 |

(c) Dynamic Voltage Amplitude Response of AC Bus on Power Grid Side | ||||

Controller | Convergence Time (s) | CPU Execution Time(10^{2} s) | Mean Square Error (pu) | Accuracy (%) |

Grey–RCMAC | 4.33 | 3.313 | 0.167 | 98.33 |

RCMAC | 4.50 | 3.443 | 0.835 | 91.65 |

CMAC | 5.81 | 4.444 | 1.161 | 88.39 |

RFNN | 5.87 | 4.490 | 0.677 | 93.23 |

PI | N/A | N/A | 1.502 | 85 |

**Table 3.**Comparison for five methods under the load switching: (a) real power of WECS, (b) reactive power of WECS, and (c) dynamic voltage amplitude response of AC bus on power grid side.

(a) Real Power of Wells Turbine | ||||

Controller | Convergence Time (s) | CPU Execution Time (10^{2} s) | Mean Square Error (10^{−2}) | Accuracy (%) |

Grey–RCMAC | 5.66 | 4.30 | 3.080 | 96.92 |

RCMAC | 7.50 | 5.07 | 5.390 | 94.61 |

CMAC | 6.28 | 4.77 | 7.912 | 92.09 |

RFNN | 8.18 | 6.21 | 6.667 | 93.33 |

PI | 8.00 | 6.08 | 9.230 | 90.77 |

(b) Reactive Power of Wells Turbine | ||||

Controller | Convergence Time (s) | CPU Execution Time (10^{2} s) | Mean Square Error (10^{−2}) | Accuracy (%) |

Grey–RCMAC | 5.66 | 4.07 | 5.001 | 94.99 |

RCMAC | 7.66 | 5.51 | 13.336 | 86.66 |

CMAC | 7.04 | 5.06 | 14.912 | 85.08 |

RFNN | 6.15 | 4.67 | 9.730 | 90.27 |

PI | 7.83 | 5.63 | 21.667 | 78.33 |

(c) Dynamic Voltage Amplitude Response of AC Bus on Power Grid Side | ||||

Controller | Convergence Time (s) | CPU Execution Time (10^{2} s) | Mean Square Error (10^{−2}) | Accuracy (%) |

Grey–RCMAC | 6.00 | 4.56 | 5.001 | 94.99 |

RCMAC | 7.66 | 5.82 | 8.335 | 91.66 |

CMAC | 7.16 | 5.44 | 10.721 | 89.28 |

RFNN | 6.74 | 5.12 | 7.056 | 92.94 |

PI | 8.00 | 6.08 | 13.333 | 86.67 |

**Table 4.**Comparison for five controllers when a fault occurs: (a) real power of WECS, (b) reactive power of WECS, and (c) transient voltage amplitude response of AC bus on power grid side.

(a) Real Power of WECS | ||||

Controller | Convergence Time (s) | CPU Execution Time(10^{2} s) | Mean Square Error (10^{−2}) | Accuracy (%) |

Grey–RCMAC | 2.40 | 1.82 | 7.50 | 92.50 |

RCMAC | 2.65 | 2.01 | 15.00 | 85.00 |

CMAC | 3.11 | 2.36 | 16.56 | 83.44 |

RFNN | 2.45 | 186 | 11.91 | 88.09 |

PI | 3.60 | 2.73 | 20.00 | 80.00 |

(b) Reactive Power of WECS | ||||

Controller | Convergence Time (s) | CPU Execution Time(10^{2} s) | Mean Square Error (10^{−2}) | Accuracy (%) |

Grey–RCMAC | 2.25 | 1.71 | 5.01 | 94.99 |

RCMAC | 2.75 | 2.09 | 11.25 | 88.75 |

CMAC | 3.71 | 2.82 | 13.53 | 86.47 |

RFNN | 3.04 | 2.31 | 8.03 | 91.97 |

PI | 4.31 | 3.28 | 16.25 | 83.75 |

(c) Transient Voltage Amplitude Response of AC Bus on Power Grid Side | ||||

Controller | Convergence Time (s) | CPU Execution Time (10^{2} s) | Mean Square Error (10^{−2}) | Accuracy (%) |

Grey–RCMAC | 2.55 | 1.93 | 5.00 | 95.00 |

RCMAC | 2.90 | 2.20 | 12.50 | 87.5 |

CMAC | 3.57 | 2.71 | 15.08 | 84.92 |

RFNN | 2.86 | 2.17 | 8.91 | 91.09 |

PI | 4.52 | 3.43 | 18.75 | 81.25 |

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## Share and Cite

**MDPI and ACS Style**

Lu, K.-H.; Hong, C.-M.; Han, Z.; Yu, L.
New Intelligent Control Strategy Hybrid Grey–RCMAC Algorithm for Ocean Wave Power Generation Systems. *Energies* **2020**, *13*, 241.
https://doi.org/10.3390/en13010241

**AMA Style**

Lu K-H, Hong C-M, Han Z, Yu L.
New Intelligent Control Strategy Hybrid Grey–RCMAC Algorithm for Ocean Wave Power Generation Systems. *Energies*. 2020; 13(1):241.
https://doi.org/10.3390/en13010241

**Chicago/Turabian Style**

Lu, Kai-Hung, Chih-Ming Hong, Zhigang Han, and Lei Yu.
2020. "New Intelligent Control Strategy Hybrid Grey–RCMAC Algorithm for Ocean Wave Power Generation Systems" *Energies* 13, no. 1: 241.
https://doi.org/10.3390/en13010241