# Adaptive-MPPT-Based Control of Improved Photovoltaic Virtual Synchronous Generators

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## Abstract

**:**

## 1. Introduction

## 2. Overview of Fundamental Problems

- (1)
- PV maximum available power is adequate.

- (2)
- PV maximum available power is inadequate.

## 3. Methods

#### 3.1. PV-Boost Control

#### 3.1.1. Overall Control Scheme of Pre-Stage PV-Boost

_{pv-ref}, which is obtained through the adaptive-MPPT control, and the actual value U

_{pv}generate the PWM modulated signals D through PI control. The theoretical analysis of adaptive-MPPT algorithm will be elaborated in Section 3.1.2.

#### 3.1.2. Adaptive-MPPT Algorithm

_{pv}and ordinate P

_{pv}represent the PV output voltage and output power, respectively. P

_{max}is the PV maximum output power, which corresponds to the voltage U

_{mpp}. Additionally, A, B and M are possible PV operating points, where M is the maximum power point.

_{need}is less than the PV maximum available power P

_{max}, PV exists at two operating points: A and B. Through quantitative and qualitative verification, Refs. [23,24] indicate that the PV stable operation area is [U

_{mpp}, U

_{oc}]. Thus, combined with the actual operating conditions, the adaptive-MPPT should be equipped with the dynamic regulation features as follows:

- When P
_{need}< P_{max}, PV works at B point within [U_{mpp}, U_{oc}] to output power equal to P_{need}. - When P
_{need}≥ P_{max}, PV works at M point to output maximum power P_{max}.

_{dc}, this paper designs the adaptive-MPPT algorithm based on an improved incremental conductance method in light of the following four control goals, as described in Figure 6.

- (1)
- Ensure that PV operates within the stable operating area [U
_{mpp}, U_{oc}]. - (2)
- Whether the DC bus voltage U
_{dc}is stable at the set reference value U_{dc-ref}is used as a criterion for judging whether supply and demand match. - (3)
- When the PV output power is in surplus, adaptive-MPPT causes the DC bus voltage to remain at the set reference value U
_{dc-ref}constantly. - (4)
- When the PV maximum output is insufficient at a given time, U
_{dc}< U_{dc-ref}, adaptive-MPPT runs MPP to determine maintain maximum output.

- (1)
- When the PV system starts for the first time, the slope is $\mathrm{d}{I}_{\mathrm{pv}}/\mathrm{d}{U}_{\mathrm{pv}}+{I}_{\mathrm{pv}}/{U}_{\mathrm{pv}}>0$. To prevent PV from operating in unstable areas, the algorithm enables PV run to [U
_{mpp}, U_{oc}] with y = 1, which ensures accurate tracking in the stable region all the time. - (2)
- In the stable area, according to difference-value ΔU
_{dc}sign of the actual DC bus voltage U_{dc}and set value U_{dc-ref}, PV regulates output power to meet supply-demand matching, i.e., P_{pv}= P_{need}. There are three main situations.- When ΔU
_{dc}(k) > 0, in this case, P_{pv}(k) > P_{need}(k), the PV output power should be reduced, so the voltage judgement sign is x = −1. - When ΔU
_{dc}(k) < 0, in this case, P_{pv}(k) < P_{need}(k), the PV output power ought to increase, so the voltage judgement sign is x = 1. - When ΔU
_{dc}(k) = 0, in this case, P_{pv}(k) = P_{need}(k), the voltage judgement sign is x = 0.

Nevertheless, since the actual adjustment direction is opposite to the voltage judgment sign in the stable area, the PV regulates with y = −x. Most notably, If the PV maximum output power is less than the load or the dispatch demand invariably, ΔU_{dc}is always less than zero, so y = −x = −1. Thus, this algorithm jumps out of the ΔU_{dc}judgment step and turns into the traditional MPPT control based on the conductance increment method. - (3)
- The actual step size $y\times \lambda $ is obtained, thereby refreshing the PV voltage value U
_{pv}.

- In the case of sufficient PV power, adaptive-MPPT enables two-stage PV to transmit power in accordance with the load or dispatching requirements, while guaranteeing DC bus voltage U
_{dc}= U_{dc-ref}. - Under conditions where PV maximum output power is inadequate, adaptive-MPPT automatically switches to traditional MPPT control, always outputting maximum power to decrease the power shortage. At this moment, the DC bus voltage is no longer controlled.

#### 3.2. Inverter Control

#### 3.2.1. VSG Basic Modeling

_{m}is the mechanical power; P

_{e}is the electromagnetic power; J and D represent the inertia and damping, respectively; ω is the rotor angular frequency; ω

_{g}is the actual angular frequency of the grid; e

_{abc}, u

_{abc}and i

_{abc}are the excitation voltage, terminal voltage and stator current of SG respectively, which correspond to input voltage, output voltage and output current in the inverter; R is the armature resistance and L is the synchronous reactance.

_{N}and Q

_{N}are the rated active power and reactive power, respectively; P and Q are the active power and reactive power of VSG; D

_{p}is the P-ω droop coefficient and D

_{q}is the Q-U droop coefficient; U

_{N}is the rated voltage amplitude; ω

_{N}is the rated angular frequency.

_{e}.

#### 3.2.2. Improved-VSG Control

_{dc}will discharge. If this power shortage is larger, the DC bus voltage may constantly drop or even collapse, which endangers the stability of the system. To settle this problem, Figure 8 puts forward the improved-VSG control method which comprises of VSG basic control and additional control.

_{dc}and the set-point U

_{dc-ref}is regulated by PI control to obtain an additional control variable ΔX; moreover, ΔX ≤ 0. The working mode of the additional control is as below:

- In off-grid mode, switch S
_{B}is closed, while switch S_{A}is open, so ΔX is introduced into the reactive power loop to revise the reactive power reference Q_{N}′, i.e., Q_{N}′ = Q_{N}+ ΔX ≤ Q_{N}. - In grid-connected mode, switch S
_{A}is closed. Since voltage is sustained by the bulk power system, switch S_{B}is open. Active power reference P_{N}′ is modified by ΔX, i.e., P_{N}′ = P_{N}+ ΔX ≤ P_{N}.

- (1)
- When the PV output power is surplus, pre-stage adaptive-MPPT changes the working point to achieve P
_{pv}= P_{need}, so that the DC bus voltage can stabilize at the reference value U_{dc-ref}. Thus, ΔX = 0, the additional control is inoperative, in this case, the adaptive-MPPT cooperates with VSG basic control. - (2)
- When the PV maximum output is insufficient, i.e., P
_{max}< P_{need}, although MPPT keeps PV outputting maximum power at all times, it still cannot meet the load or dispatch power requirements. Consequently, the DC bus capacitance will discharge, with the result that U_{dc}failed to keep at U_{dc-ref}. If the power difference-value is higher, U_{dc}will continue to fall until it collapses. In such situations, additional control takes effect.- In off-grid mode, load power is related to voltage. ΔX acts on the reactive power loop to indirectly decrease the voltage amplitude, so as to reduce the inverter output power, which lowers the decline degree of U
_{dc}to improve the PV steadiness. - In grid-connected mode, the dispatching power is greater than the PV maximum output, resulting in insufficient power. ΔX is led into the active power loop to lessen dispatching power reference value, which prevents U
_{dc}from falling ceaselessly.

_{dc}is jointly controlled by the pre-stage adaptive-MPPT and the post-stage improved-VSG, the two stages of control do not affect each other. When P

_{pv}> P

_{need}, the pre-stage U

_{dc}plays a role, but the post-stage U

_{dc}does not perform due to ΔX = 0; when P

_{pv}< P

_{need}, the adaptive-MPPT changes into the traditional MPPT, in which U

_{dc}is not governed. At this point, the post-stage U

_{dc}is under control on account of ΔX < 0.

_{max}> P

_{need}, and after 1 s, P

_{max}< P

_{need}. The simulation results are shown in Figure 9, in which the blue line represents the improved-VSG control and the red line is the VSG basic control.

_{max}< P

_{need}, U

_{dc}with VSG, basic control drops considerably whether in off-grid mode or grid-connected mode. Especially in the grid-connected mode, this case is more serious. However, when adopting the improved-VSG control, although PV maximum output cannot meet the power demand, it is manifestly known from the blue line in Figure 9 that the improved-VSG control can forestall incessant falling of U

_{dc}and drastically reduce the U

_{dc}drop degree to guarantee PV system stability. Therefore, later simulation validation will make use of the proposed improved-VSG control.

- In situations of adequate PV power, the adaptive-MPPT-controlled pre-stage DC/DC converter accomplishes stability of the DC bus voltage, which can be considered a constant DC source. At this point, post-stage improved-VSG control mainly causes the inverter to present inertia, damping and primary regulation characteristics of the SG, that is, achieving VSG basic function.
- When the PV power is inadequate, the DC bus voltage is not managed by pre-stage DC/DC circuit anymore, since adaptive-MPPT changes into a traditional MPPT. Under this condition, additional control of the improved-VSG is effective to prevent the continuous drop of the DC bus voltage, thus enhancing the stability of the PV system.

#### 3.2.3. Complete Control Scheme of Post-Stage Inverter

_{dc}should be attached to the PV-Boost circuit, whose control method is discussed in Figure 4.

## 4. Results

#### 4.1. Simulation System and Simulation Parameters

#### 4.2. Verification Process

#### 4.2.1. Off-Grid Mode

- (1)
- Variation of Load Demand

_{max}= 15 kW and the corresponding output voltage is U

_{mpp}= 370 V. Before 1 s, the power demand of the load is 12 kW, which is reduced to 10 kW at 1 s but increased to 18 kW at 1.5 s. Figure 12 displays the system dynamic response waveforms in the case of varying load requirements.

_{max}> P

_{need}, so the PV power is surplus. Thus, it can be seen in Figure 12a,d that PV power controlled by adaptive-MPPT changes the operating point to make inverter output power match the load demand. Additionally, before 1.5 s, Figure 12b shows that PV output voltage is greater than U

_{mpp}= 370 V, i.e., U

_{pv}> U

_{mpp}, which means that PV works in the stable area [U

_{mpp}, U

_{oc}]. Furthermore, DC bus voltage stabilizes at the set value 800 V owing to system power balance in Figure 12c, and inverter output voltage is identical to the AC rated voltage in Figure 12f. After 1.5 s, the load demand power increases to 18 kW, which is greater than the PV maximum output power of 15 kW, i.e., P

_{max}< P

_{need}; as a result, the PV power is inadequate. In this case, Figure 12a,b indicates that PV works at MPP point (370 V, 15 kW) to output maximum power. In addition, due to power shortage, the DC bus voltage reduces to 625 V in Figure 12c and the inverter output voltage falls below the rated AC voltage in Figure 12f. During the above power regulation process, Figure 12e shows that VSG frequency is involved in regulating according to the active droop coefficient.

- (2)
- Variation of PV Maximum Output Power

_{max}> P

_{need}. Figure 13a,d demonstrates that the PV power decreases the output power to enable inverter output of 10 kW power, which is equal to the load requirement. Despite the increased light intensity, the PV output remains unchanged due to the constant load demand in Figure 13a. We can see from Figure 13b that PV output voltage is 398 V before 1 s and 428 V between 1~1.5 s, which are more than 370 V and 380 V, respectively, so the PV power based on the adaptive-MPPT algorithm adjusts the working point in the stable region [U

_{mpp}, U

_{oc}]. The VSG frequency in Figure 13e also stays constant on account of power demand invariability. Due to supply-demand matching before 1.5 s, the DC bus voltage can hold at 800 V in Figure 13c and the amplitude of the inverter output voltage is 311.13 V. After 1.5 s, P

_{max}< P

_{need}, it can be seen from Figure 13a,b that PV power runs at the MPP point (9.5 kW, 342 V), which proves that adaptive-MPPT can be transformed into a traditional MPPT control when PV maximum is inadequate. VSG frequency regulation in Figure 13e depends on the droop characteristic. Figure 13c shows that the improved-VSG let the DC bus voltage stabilize at 670 V. Due to the existence of power shortage, the inverter output voltage is below the rated amplitude 311.13 V.

#### 4.2.2. Grid-Connected Mode

- (1)
- Variation of Dispatching Power Demand

_{max}= 15 kW, which corresponds to output voltage U

_{mpp}= 370 V. Before 1 s, the dispatching power instruction was 11 kW, which decreased to 9 kW at 1 s and increased to 16 kW at 1.5 s. In this case, the simulation results are expressed in Figure 14.

_{max}> P

_{need}. Thus, can be observed in Figure 14a,b,d that PV adaptively regulates in the stable interval (U

_{pv}> 370 V), so that the inverter outputs power of 11 kW and 7 kW, which are identical to the dispatch orders. On account of system power balance, the DC bus voltage maintains at 800 V in Figure 14c. After 1.5 s, the dispatching requirements surpass the PV maximum power, i.e., P

_{max}= 15 kW < P

_{need}= 16 kW. At this time, PV power operates at the MPP point (15 kW, 370 V) to achieve full output. Moreover, improved-VSG causes the DC bus voltage to settle at 710 V, so as to ensure its stability. Throughout the adjustment process, because of the rigid support offered by the bulk power grid, the VSG frequency in Figure 14e maintains at the rated value of 50 Hz after slight fluctuations, and the inverter output voltage in Figure 14f is the same as the AC voltage of the bulk power grid.

- (2)
- Variation of PV Maximum Output Power

^{2}before 1 s, but it rises to 1200 W/m

^{2}at 1 s and then weakens to 700 W/m

^{2}at 1.5 s. Other relevant PV parameters of the PV power and voltage are indicated in Table 2. Figure 15 gives the simulation waveforms in grid-connected mode when the PV maximum output power changes.

^{2}, the PV maximum output power is 15 kW, which is more than the dispatching demand 12 kW. Accordingly, from Figure 15a,b,d, the PV managed by adaptive-MPPT alters the working point in the stable voltage range (U

_{pv}> 370 V) to enable inverter power output to meet dispatching power need of 12 kW. At 1 s, the light intensity is amplified to 1200 W/m

^{2}so that MPP point is (18.2 kW, 380 V). Even if the light intensity strengthens, PV still operates in the stable region (U

_{pv}> 380 V) to send invariant power owing to the constant dispatching power demand. Moreover, since this above regulation ensures supply-demand matching, Figure 15c shows that the DC bus voltage remains at the set value of 800 V. After 1.5 s, the light intensity weakens to 700 W/m

^{2}, at this moment, PV maximum output power fails to satisfy the dispatching power requirement, i.e., P

_{max}= 9.5 kW < P

_{need}= 12 kW, so it can be seen from Figure 15a,b that PV power transforms into traditional MPPT operation (9.5 kW, 342 V) to lower power shortage. Additionally, improved-VSG control takes effect to stabilize DC bus voltage at 655 V. Similar to the variation of the dispatching power demand in grid-connected mode, in the steady state, the VSG frequency in Figure 15e and inverter output voltage in Figure 15f are identical to the frequency and voltage of the bulk power grid.

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 12.**Waveforms in the off-grid mode when load demand changes (

**a**) PV output power; (

**b**) PV output voltage; (

**c**) DC bus voltage; (

**d**) Inverter output power; (

**e**) VSG frequency; (

**f**) Inverter output voltage.

**Figure 13.**Waveforms in the off-grid mode when PV maximum output power changes (

**a**) PV output power; (

**b**) PV output voltage; (

**c**) DC bus voltage; (

**d**) Inverter output power; (

**e**) VSG frequency; (

**f**) Inverter output voltage.

**Figure 14.**Waveforms in the grid-connected mode when dispatching power demand changes (

**a**) PV output power; (

**b**) PV output voltage; (

**c**) DC bus voltage; (

**d**) Inverter output power; (

**e**)VSG frequency; (

**f**) Inverter output voltage.

**Figure 15.**Waveforms in the grid-connected mode when PV maximum output power changes (

**a**) PV output power; (

**b**) PV output voltage; (

**c**) DC bus voltage; (

**d**) Inverter output power; (

**e**) VSG frequency; (

**f**) Inverter output voltage.

Parameters | Values | |
---|---|---|

Boost circuit parameters | PV-side capacitance, C | 30 μF |

Inductance, L | 1 mH | |

DC side capacitance, C_{dc} | 5000 μF | |

Filter parameters | The series inductance of the filter, L_{f} | 10 mH |

The parallel capacitance of the filter, C_{f} | 350 μF | |

System parameters | Reference value of DC voltage, U_{dc-ref} | 800 V |

Rated frequency | 50 Hz | |

The rated phase voltage of power system | 220 V | |

Inverter switching frequency | 5 kHz | |

Control parameters | The P-ω droop coefficient, D_{p} | 0.0003 |

The Q-U droop coefficient, D_{q} | 0.003 | |

The virtual inertia of VSG, J | 0.1 | |

The virtual damping of VSG, D | 20 | |

The proportionality factor of additional control in improved-VSG control, P_{Udc} | 50 | |

The integration factor of additional control in improved-VSG control, I_{Udc} | 0.01 |

Time (s) | Light Intensity (W/m^{2}) | P_{max} (kW) | U_{mpp} (V) |
---|---|---|---|

Before 1 s | 1000 | 15 | 370 |

1~1.5 s | 1200 | 18.2 | 380 |

After 1.5 s | 700 | 9.5 | 342 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yan, X.; Li, J.; Wang, L.; Zhao, S.; Li, T.; Lv, Z.; Wu, M. Adaptive-MPPT-Based Control of Improved Photovoltaic Virtual Synchronous Generators. *Energies* **2018**, *11*, 1834.
https://doi.org/10.3390/en11071834

**AMA Style**

Yan X, Li J, Wang L, Zhao S, Li T, Lv Z, Wu M. Adaptive-MPPT-Based Control of Improved Photovoltaic Virtual Synchronous Generators. *Energies*. 2018; 11(7):1834.
https://doi.org/10.3390/en11071834

**Chicago/Turabian Style**

Yan, Xiangwu, Jiajia Li, Ling Wang, Shuaishuai Zhao, Tie Li, Zhipeng Lv, and Ming Wu. 2018. "Adaptive-MPPT-Based Control of Improved Photovoltaic Virtual Synchronous Generators" *Energies* 11, no. 7: 1834.
https://doi.org/10.3390/en11071834