## 1 Introduction

## 2 Virtual synchronous generator

## 3 Adaptive virtual synchronous generator

_{m1}to P

_{m2}, the operating point moves along the power curve, from point “A” to point “C” and then from point “C” to point “A” with oscillatory motion about point “B.” The change in frequency in one cycle of the oscillation can be partitioned into four intervals as shown in Fig. 3 [26‐31].

_{ad}) for the power reference has a high value. At the second time interval, the \(\Delta \omega \) is positive but d\(\upomega \)/dt has a negative value that means there is deceleration, and at this time interval, the P

_{ad}has a low value. At third time interval, the \(\Delta \omega \) is negative and d\(\upomega \)/dt is also negative that means there is acceleration, and hence, P

_{ad}has a high value at this interval. At the last one, the \(\Delta \omega \) is negative but the d\(\upomega \)/dt is positive which means there is deceleration like the second one; therefore, P

_{ad}at this time has a low value. By this adaptive technique, the controller adopts the suitable value of power reference taking the power changes and frequency deviations into consideration. The conclusion of deducing the value of P

_{ad}according to the state of the system can be shortened as shown in Table 1 [31].

_{ad}) according to system state

Interval | \(\Delta \omega \) | d\(\upomega \)/dt | State | P _{ad} |
---|---|---|---|---|

t _{1}:t_{2} | + | + | Acceleration | High |

t _{2}:t_{3} | + | − | Deceleration | Low |

t _{3}:t_{4} | − | − | Acceleration | High |

t _{4}:t_{5} | − | + | Deceleration | Low |

_{ad}is increased and decreased according to the system state, and this increasing or decreasing can be determined by \(M\) factor as follows:

_{ad}, the second is (− 1) that points to the deceleration of the system and low value of P

_{ad}. The value of P

_{ad}is calculated adaptively according to \(M\) factor as follows:

_{ad}is the adaptive power reference, P

_{in}is the input power to the inverter, \(M\) is the adaptive change factor and \(\Delta \omega \) is the angular frequency deviation.

## 4 Adaptive neuro-fuzzy inference system

_{m}and B

_{m}represent the linguistic labels associated with this node function value. In other words, \({O}_{{A}_{\mathrm{m}}}^{1}\) and \({O}_{{B}_{\mathrm{m}}}^{1}\) denote the degree of membership functions of the A

_{m}and B

_{m}, respectively, and μ represents the membership function.

_{n}represents the firing strength of a rule as follows [35]:

_{n}, q

_{n}and r

_{n}are designed parameters. Square type nodes are used for this layer.

## 5 Proposed VSG with ANFIS

d\(\upomega \)/dt | \(\Delta \omega \) | ||||
---|---|---|---|---|---|

NL | NS | ZE | PS | PL | |

NL | PL | PS | ZE | NS | NL |

NS | PS | PS | ZE | NS | NS |

ZE | ZE | ZE | ZE | ZE | ZE |

PS | NS | NS | ZE | PS | PS |

PL | NL | NS | ZE | PS | PL |

## 6 Simulation results

Parameter | Value |
---|---|

Open circuit voltage (V _{oc})/module | 37.4 V |

Short circuit current (I _{sc})/module | 8.63 A |

Maximum power (P _{max})/module | 250 W |

Maximum power voltage (V _{mp})/module | 30.7 V |

Maximum power current (I _{mp})/module | 8.15 A |

Number of parallel/series modules | 8/10 modules |

DC-side capacitor | 4 μF |

Line voltage | 380 V |

System frequency | 50 Hz |

AC-side inductor | 400 mH |

AC-side capacitor | 950 μF |

### 6.1 Starting

### 6.2 Load increase

### 6.3 Load decrease

### 6.4 Islanding mode

#### 6.4.1 Heavy load

#### 6.4.2 Medium load

#### 6.4.3 Light load

### 6.5 Irradiance change

^{2}for 0.2 s then increased to 1100 W/m

^{2}. Regarding Fig. 16, (a) the active power, (b) the reactive power and (c) the frequency of the system are shown, respectively, when the system is controlled with the proposed VSG with ANFIS, adaptive VSG with fuzzy logic controller, conventional VSG and without virtual inertia.

^{2}then when the irradiance is decreased to 600 W/m

^{2}, the active power is decreased to 4.5 KW; then by increasing the irradiance to 1100 W/m

^{2}, the active power is increased to 14.2 KW. Likewise, the reactive power started at 1.95 KVar then decreased to 0.8 KVar then increased to 2.32 Kvar with respect to the irradiance change. Based on the system response, there is a reduction in the overshoot magnitude, and the system takes less time to reach the steady-state period when the proposed VSG with ANFIS is used. This means the preponderance of using the proposed VSG with ANFIS method in PV systems compared with the adaptive VSG with fuzzy logic controller, conventional VSG and without virtual inertia controller.

## 7 Experimental setup and results

### 7.1 Experimental setup

Parameter | Value |
---|---|

Open circuit voltage (V _{oc})/module | 37.4 V |

Short circuit current (I _{sc})/module | 8.63 A |

Maximum power (P _{max})/module | 250 W |

Maximum power voltage (V _{mp})/module | 30.7 V |

Maximum power current (I _{mp})/module | 8.15 A |

Number of modules | 1 Module |

DC-side capacitor | 400 μF |

System frequency | 50 Hz |

AC-side inductor | 5 mH |

AC-side capacitor | 50 μF |

Resistive load bank | 10 Ω |