# Robust Control for Optimized Islanded and Grid-Connected Operation of Solar/Wind/Battery Hybrid Energy

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## Abstract

**:**

## 1. Introduction

- The development of a unified non-linear sliding mode MIMO controller ensuring a compliant, efficient, reliable, with low complexity, and safe operation of the components of the HRES both in standalone and grid-connected modes of the microgrid.
- Ensuring a continuous power supply through the DC-DC buck/boost integrated ESS that allows power into and out of the battery with controlled charging and discharging operation.
- Obviation of redundant converter incorporation with the integration of wind/PV hybrid RES using a back-to-back (B2B) converter topology and direct interconnection of solar PV to the DC-bus, hence facilitating higher efficiency and reducing power losses.
- Formulation of autonomous MPPT operation for the solar and wind energy sources that is operable on the rotor side converter (RSC) and grid side converter (GSC) configuration of the B2B converter.
- Investigation and evaluation of the proposed control architecture to perform following function: (i) stabilize the DC-bus and load voltages under the fluctuations of the generated RES power; (ii) achieving MPPT operation from solar and wind energy sources; and (iii) maintaining the power balance of the HRES during both on-grid and off-grid operations.

## 2. Related Works

## 3. Mathematical Modeling

#### 3.1. Wind Turbine Model

#### 3.2. PMSG Model

#### 3.3. Modeling of Solar PV Module

**Remark**

**1.**

#### 3.4. DC-DC Converter and Battery Modelling

**Remark**

**2.**

#### 3.5. GSC Modeling

#### 3.6. Grid Side Modeling

**Remark**

**3.**

#### 3.7. Overall Model of the Hybrid Microgrid

#### 3.8. MPPT Derivation

#### 3.8.1. Wind Turbine MPPT

#### 3.8.2. PV MPPT

## 4. Power Management

## 5. Control Design

- Harnessing the maximum power from the wind by optimally regulating the rotor speed, ${\omega}_{r}$, to track the wind speed variations.
- Achieving a unity power factor operation at the PMSG stator terminals by controlling ${I}_{ds}$.
- MPPT operation of the PV module by controlling ${V}_{pv}$.
- Meet the load voltage requirement by controlling the ${U}_{dl}$ and ${U}_{ql}$.
- Ensuring a smooth power management between the renewable energy sources, storage system, load and grid by controlling ${I}_{b}$.
- Regulating the DC-bus voltage by controlling ${V}_{dc}$.

#### Calculation of the Reference Signals

- The ${\omega}_{r}^{*}$ is computed as follows:$${\omega}_{r}^{*}=\frac{{\lambda}_{opt}{V}_{w}}{R}$$
- The ${I}_{ds}^{*}$ can be generated as follows: The stator’s power factor angle $\left({\Theta}_{s}\right)$ must remain zero in order to obtain unity power factor. The PMSG’s stator current angle $\left({\Theta}_{I}\right)$ and voltage phase angle $\left({\Theta}_{V}\right)$ are expressed by the following equations [56]:$${\Theta}_{I}=ta{n}^{-1}\left(\frac{{I}_{qs}}{{I}_{ds}}\right)$$$${\Theta}_{V}=ta{n}^{-1}\left(\frac{{V}_{qs}}{{V}_{ds}}\right)=ta{n}^{-1}\frac{{\omega}_{r}{\Lambda}_{r}-{\omega}_{r}{L}_{d}{I}_{ds}}{{\omega}_{r}{L}_{q}{I}_{qs}}$$Subsequently, ${I}_{ds}^{*}$ is computed such that the following condition is satisfied.$${\Theta}_{s}={\Theta}_{V}-{\Theta}_{I}=0$$The value of ${I}_{ds}^{*}$ is thus:$${I}_{ds}^{*}=\frac{{\Lambda}_{r}-\sqrt{{\Lambda}_{r}^{2}-4{L}_{d}{L}_{q}{I}_{qs}^{2}}}{2{L}_{d}}$$
- ${U}_{dl}^{*}$ is selected to be equal to the grid voltage $({U}_{dl}^{*}=|{U}_{g}\left|\right)$ so that the grid can easily synchronize with the microgrid at the point of common coupling.
- ${U}_{ql}^{*}$ is selected such that the reactive power is very close to zero. It is calculated as follows:Assuming the GSC is ideal, then the active power along the two sides of the GSC are equal.$$\begin{array}{cc}\hfill {I}_{gdc}{V}_{dc}& ={P}_{l}+{P}_{g}^{-}\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& ={U}_{dl}^{*}{I}_{dl}+{U}_{ql}^{*}{I}_{ql}+{P}_{g}^{-}\hfill \end{array}$$
**Remark****4.**Note that ${P}_{g}^{-}$ is the power received by the grid from the GSC as explained in (46) and ${I}_{gdc}$ is the control input of ${V}_{dc}$.From (53), ${U}_{ql}^{*}$ can be derived as follows:$${U}_{ql}^{*}=\frac{{I}_{gdc}{V}_{dc}-{U}_{dl}^{*}{I}_{dl}-{P}_{g}^{-}}{{I}_{ql}}$$ - ${I}_{b}^{*}$ is calculated by dividing ${P}_{net}$ in (47) with ${V}_{b}$ as follows:$$\begin{array}{c}\hfill {I}_{b}^{*}=\frac{{P}_{net}}{{V}_{b}}\end{array}$$
- ${V}_{dc}^{*}$ is set as the MPPT voltage of the PV module (${V}_{dc}^{*}={V}_{pv}^{max}$). However, when the solar irradiance is low, ${V}_{dc}^{*}$ is set as the nominal voltage of the DC-bus. The nominal value of the DC-bus voltage is calculated as [57]:$${V}_{dc}^{*}\ge \frac{1.6\sqrt{2}{U}_{ll}}{\sqrt{3}{m}_{i}}$$

**Proof.**

## 6. Simulation Results

#### 6.1. Case 1: Random Wind and Fixed Solar with Varying Load

^{2}solar irradiance is fixed (Figure 7). Figure 8 depicts the optimal tracking performance of the rotor speed. It can be seen that the proposed controller closely tracks the optimal rotor speed calculated by the MPPT so that maximum power is produced by the PMSG. The response of the d-axis stator current for unity power factor operation is depicted in Figure 9. The DC-bus is receiving contribution from the solar PV, the wind power generator, and the ESS. The response of the DC-bus voltage together with the reference value which is the same as the MPPT voltage of the solar PV is shown in Figure 10. The controller can keep the DC-bus voltage stable and very close to the reference value despite the variation of the wind power, the ESS power, and the load demand.

#### 6.2. Case 2: Step Change in Wind and Solar with Varying Load

^{2}to 965 W/m

^{2}, 933 W/m

^{2}and finally increases to 1000 W/m

^{2}at $t=10$ s, 15 s and 20 s, respectively (Figure 16). The rotor speed follows the desired speed under varying wind conditions (Figure 17), which indicates that the PMSG is rotating at the optimal speed computed by the MPPT algorithm ensuring maximum power generation under variable wind speed. The d-axis stator current tracks the desired current accurately as depicted in Figure 18, that allows wind power transfer with a unity power factor. Furthermore, results obtained using PI controller is also presented in this section. The comparative analysis highlights the performance between the proposed controller and benchmark PI control technique [33] based on the calculated optimal values of ${\omega}_{r}$, ${I}_{ds}$, ${V}_{dc}$, ${I}_{b}$, ${U}_{dl}$, and ${U}_{ql}$.

^{2}and 933 W/m

^{2}at $10\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}<t\le 20\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$. During this interval, the PV MPPT voltage also falls, and thus the reference DC-bus voltage is set as the nominal value instead of the PV MPPT voltage to maintain a constant DC-bus voltage. It can be observed that the proposed controller keeps the DC-bus voltage stable and constant value under varying PV power, wind power, and load demand as depicted in Figure 19. The load demand profile is similar to case 1 as shown in Figure 20. The utility grid is receiving power at $0<t\le 9\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ and sending power at $9\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}<t\le 20\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ and $30\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}<t\le 40\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$. The HRES is off-grid at $20\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}<t\le 30\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$. When $0\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}<t\le 9\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$ and $20\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}<t\le 30\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$, the surplus power is transferred to the battery. When $9\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}<t\le 20\phantom{\rule{3.33333pt}{0ex}}\mathrm{s}$, the battery is unable to cover the power deficit as the maximum power it can safely deliver is 1 MW. As a result, 0.9 MW of the load demand is shedded for protecting the battery and maintain the power balance of the HRES.

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

A | P-N junction factor |

${B}_{mode}$ | Operational mode of the bi-directional converter of battery |

B2B | Back-to-back |

$\beta $ | Pitch angle |

${C}_{dc}$ | DC-bus capacitance |

${C}_{p}$ | Power coefficient |

${D}_{1}$ | Duty cycle of the battery converter during charge mode |

${D}_{2}$ | Duty cycle of the battery converter during discharge mode |

DFIG | Doubly-fed induction generator |

ESS | Energy storage system |

${E}_{g}$ | Band gap energy of the semiconductor material |

${E}_{th}$ | Thevenin’s voltage |

${\eta}_{b}$ | Efficiency of the battery |

FLC | Fuzzy logic control |

GSC | Grid-side converter |

HRES | Hybrid renewable energy system |

${I}_{b}$ | Battery current |

${I}_{di}$ | GSC d-axis output AC current |

${I}_{dl}$ | d-axis load current |

${I}_{ds}$ | d-axis stator current |

${I}_{g}$ | Grid current |

${I}_{gdc}$ | GSC DC current |

${I}_{pv}$ | PV output current |

${I}_{qi}$ | GSC q-axis output AC current |

${I}_{ql}$ | q-axis load current |

${I}_{qs}$ | q-axis stator current |

${I}_{sc}$ | PV short circuit current |

J | Inertia of the mechanical shaft |

${K}_{B}$ | Boltzman’s constant |

${L}_{b}$ | Battery inductance |

${L}_{d}$ | d-axis self-inductance |

${L}_{f}$ | Grid-side filter inductance |

${L}_{l}$ | Load inductance |

${L}_{g}$ | Line inductance |

Li-ion | Lithium-ion |

$\lambda $ | Tip speed ratio |

${I}_{l}$ | Load current |

${L}_{q}$ | q-axis self-inductance |

${L}_{th}$ | Thevenin’s inductance |

${\Lambda}_{r}$ | Rotor flux |

MIMO | Multi-input-multi-output |

MPPT | Maximum power point tracking |

${N}_{p}$ | Number of parallel connected modules |

${N}_{s}$ | Number of series connected modules |

${\omega}_{g}$ | Electrical angular speed |

${\omega}_{r}$ | Angular speed of wind turbine |

${P}_{b}$ | Battery power |

${P}_{g}$ | Grid power |

${P}_{g}^{-}$ | Power received by the grid |

${P}_{g}^{+}$ | Power transferred by the grid |

${P}_{l}$ | Load demand active power |

${P}_{net}$ | Net power |

${P}_{pv}$ | Solar power |

${P}_{w}$ | Wind power |

P&O | Perturb and Observe |

PMSG | Permanent magnet synchronous generator |

PV | Photo-voltaic |

${\psi}_{i}$ | Temperature coefficient |

q | Electron charge |

${Q}_{b}$ | Battery capacity |

${Q}_{l}$ | Load demand reactive power |

R | Radius of wind turbine |

RES | Renewable energy source |

RSC | Rotor-side converter |

${R}_{b}$ | Battery internal resistance |

${R}_{l}$ | Load resistance |

${R}_{s}$ | Stator resistance |

${R}_{se}$ | Equivalent series resistors |

${R}_{sh}$ | Equivalent shunt resistors |

${R}_{th}$ | Thevenin’s resistance |

$\rho $ | Density of air |

S | Solar irradiance level |

SMC | Sliding mode control |

$SoC$ | State-of-charge of battery |

$So{C}^{max}$ | Upper limit of SoC |

$So{C}^{min}$ | Lower limit of SoC |

T | Ambient temperature |

${T}_{e}$ | Electrical torque |

${T}_{m}$ | Mechanical torque |

${T}_{r}$ | Operating temperature of the PV module |

${\Theta}_{I}$ | Stator current angle |

${\Theta}_{s}$ | Stator power factor angle |

${\Theta}_{V}$ | Stator voltage angle |

${U}_{dl}$ | d-axis load voltage |

${U}_{g}$ | Grid voltage |

${U}_{ll}$ | Line-to-line RMS voltage |

${U}_{ql}$ | q-axis load voltage |

${V}_{b}$ | Battery voltage |

${V}_{D}$ | Diode voltage in the PV circuit |

${V}_{dc}$ | DC-bus voltage |

${V}_{ds}$ | d-axis stator voltage |

${V}_{pv}$ | PV output voltage |

${V}_{qi}$ | GSC q-axis output voltage |

${V}_{qs}$ | q-axis stator voltage |

${V}_{w}$ | Wind speed |

WECS | Wind energy conversion system |

${Z}_{l}$ | Load impedance |

${Z}_{th}$ | Thevenin’s impedance |

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Wind Turbine Generator | Solar PV Generator (KC200GH-2p) | ||||
---|---|---|---|---|---|

Parameter | Symbol | Value | Parameter | Symbol | Value |

Air denisty (kg/m ^{3}) | $\rho $ | 1.25 | Ambient Temperature (°C) | T | 25 |

Radius of wind turbine (m) | R | 28.2 | Maximum power at MPP (W) | ${P}_{max}^{MPP}$ | 200 |

Maximum Voltage at MPP (V) | ${V}_{max}^{MPP}$ | 26.3 | |||

d-axis stator current (mH) | ${L}_{ds}$ | 9.8 | P-N junction factor | A | 1.8 |

Temperature coefficient (mA/°C) | ${\psi}_{i}$ | 4.79 | |||

q-axis stator current (mH) | ${L}_{qs}$ | 9.8 | Equivalent shunt resistor ($\Omega $) | ${R}_{sh}$ | 313.33 |

Rotor flux (Wb) | ${\Lambda}_{r}$ | 28 | Equivalent series resistor ($\Omega $) | ${R}_{se}$ | 0.193 |

Inertia of Mechanical Shaft (kg·m ^{2}) | J | 4000 | Short circuit current (A) | ${I}_{sc}$ | 8.21 |

Maximum current at MPP (A) | ${I}_{max}^{MPP}$ | 7.61 | |||

Number of pole pairs | P | 8 | Number of parallel modules | ${N}_{s}$ | 68 |

Optimum tip speed ratio | ${\lambda}_{opt}$ | 8.1 | Number of series modules | ${N}_{p}$ | 95 |

Power coefficient | ${C}_{p}^{max}$ | 0.48 | Open-circuit voltage (V) | ${V}_{oc}$ | 32.9 |

Battery Energy Storage System | Grid Parameter | ||||
---|---|---|---|---|---|

Parameter | Symbol | Value | Parameter | Symbol | Value |

Battery efficiency | ${\eta}_{b}$ | 0.9 | Filter inductance ($\mathrm{mH}$) | ${L}_{f}$ | 16.9 |

Battery capacity (AH) | ${Q}_{b}$ | 100 | Line inductance (mH) | ${L}_{g}$ | 1.69 |

Battery power (MW) | ${P}_{b}$ | 1 | Load demand (MW) | ${P}_{l}$ | 2 |

Battery voltage (V) | ${V}_{b}$ | 500 | Line-to-line voltage (V) | ${U}_{ll}$ | 4000 |

Upper SoC limit (%) | $So{C}^{max}$ | 90 | DC-bus | ${C}_{dc}$ | 1670 |

Lower SoC limit (%) | $So{C}^{min}$ | 10 | capacitance ($\mathsf{\mu}F$) |

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**MDPI and ACS Style**

Maaruf, M.; Khan, K.; Khalid, M.
Robust Control for Optimized Islanded and Grid-Connected Operation of Solar/Wind/Battery Hybrid Energy. *Sustainability* **2022**, *14*, 5673.
https://doi.org/10.3390/su14095673

**AMA Style**

Maaruf M, Khan K, Khalid M.
Robust Control for Optimized Islanded and Grid-Connected Operation of Solar/Wind/Battery Hybrid Energy. *Sustainability*. 2022; 14(9):5673.
https://doi.org/10.3390/su14095673

**Chicago/Turabian Style**

Maaruf, Muhammad, Khalid Khan, and Muhammad Khalid.
2022. "Robust Control for Optimized Islanded and Grid-Connected Operation of Solar/Wind/Battery Hybrid Energy" *Sustainability* 14, no. 9: 5673.
https://doi.org/10.3390/su14095673