# An Overall Linearized Modeling Method and Associated Delay Time Model for the PV System

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- A new method for modeling the overall linearization of the PV system is proposed.
- (2)
- A first attempt is made to study the PV system DTM-VWP by solving for $S$ and $T$.
- (3)
- An SOLM-VWP of the PV system containing a reduced-order model is proposed.
- (4)
- The ${t}_{\mathrm{d}}$ and output characteristic of the PV system can be solved directly using $S$ and $T$.
- (5)
- Through this work, ${v}_{\mathrm{o}}$ of the PV system can be predicted using ${t}_{\mathrm{d}}$ of the PV system.

## 2. Materials and Methods

#### 2.1. The Small-Signal Model for the PV System

#### 2.1.1. Circuit Model of the PV System

#### 2.1.2. The dc-Side linearization Models of the PV System

#### 2.1.3. The Linearization Model of the DC/AC

#### 2.1.4. Linearized Modeling for the PV System Controller’s Delay Time

#### 2.2. The OLM-VWP of the PV System

- (1)
- All circuit components in the circuit are ideal components.
- (2)
- The capacity values of the inductor and capacitor of the DC/DC are set to larger values to ensure that the DC/DC operates in continuous mode.
- (3)
- The PV system is always controlled at the MPP.

#### 2.3. The OLM-VWP of Order Reduction

#### 2.4. The DTM-VWP of the PV System

## 3. Results

#### 3.1. Simulation Experiments

#### 3.1.1. The OLM-VWP Verification on the DC Side of the PV System

#### 3.1.2. SOLM-VWP Verification of the PV System

#### 3.1.3. Linearized Modeling of the PV System for Verification

- (1)
- Validation of the OLM-VWP from input-to-output

- (2)
- Validation of the OLM-VWP from Control-to-Output

#### 3.1.4. Theoretical Verification of Small-Signal Delay in the PV System

#### 3.2. Experimental Validation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

PV | photovoltaic |

MPP | maximum power point |

MPPT | maximum power point tracking |

PWM | pulse width modulation |

VWP | variable weather parameters |

AC | alternating current |

DC | direct current |

DC/AC | DC/AC inverter |

OLM-VWP | overall linearized model with variable weather parameters |

SOLM-VWP | simplified overall linearized model with variable weather parameters |

DC/DC | DC/DC converter circuit |

PLL | phase-locked loop |

DTM-VWP | delay-time model with variable weather parameters |

## Nomenclature

${P}_{\mathrm{max}}(S,T)$ | power of the MPP | $\mathrm{W}$ |

${C}_{1}$ | shunt capacitor of the PV cell | uF |

${C}_{2}$ | filter capacitance of the DC/DC | uF |

${C}_{3}$ | filter capacitance of the DC/AC | uF |

${L}_{1}$ | power inductance of the DC/DC | uH |

${L}_{2}$ | filter inductance of the DC/AC | mH |

${R}_{\mathrm{eq}}$ | equivalent series resistance of the PV cell | Ω |

${R}_{\mathrm{i}}$ | equivalent input resistance of the DC/DC | Ω |

${R}_{1}$ | equivalent resistance at the output end of the DC/DC | Ω |

${R}_{\mathrm{L}}$ | equivalent resistance at the output end of the DC/AC | Ω |

$C(S,T)$ | weather parameters input | |

${D}_{\mathrm{max}}(S,T)$ | duty ratio of the MPP | |

$r$ | internal resistance of filter capacitance of the DC/AC | Ω |

$D$ | modulation duty cycle of the DC/DC | |

$S$ | irradiance | $\mathrm{W}/{\mathrm{m}}^{2}$ |

$T$ | temperature | $\xb0\mathrm{C}$ |

${V}_{\mathrm{m}}$ | reference sine wave signal of the modulator | V |

${V}_{\mathrm{SM}}$ | equivalent input voltage of the photovoltaic cell | V |

${V}_{\mathrm{eq}}$ | equivalent output voltage of the photovoltaic cell | V |

${I}_{\mathrm{eq}}$ | equivalent output current of the photovoltaic cell | A |

${V}_{\mathrm{d}}$ | DC/DC equivalent output voltage | V |

${I}_{\mathrm{d}}$ | DC/DC equivalent output current | A |

${V}_{\mathrm{o}}$ | DC/AC equivalent output voltage | V |

${I}_{\mathrm{o}}$ | DC/AC equivalent output current | V |

${t}_{\mathrm{d}}$ | delay time | s |

${t}_{\mathrm{r}}$ | rise time | s |

${t}_{\mathrm{s}}$ | settling time | s |

${t}_{\mathrm{p}}$ | peak time | s |

$d$ | small-disturbance input duty cycle of the controller of DC/DC | |

${v}_{\mathrm{d}}$ | output voltage of the small-signal input PV system | V |

$c(S,T)$ | small-disturbance input of the DC/DC | |

$d(S,T)$ | control input perturbation | |

${V}_{\mathrm{tri}}$ | the peak value of the triangular carrier wave | V |

${K}_{\mathrm{pwm}}$ | proportionality factor of the inverter control | |

$M$ | modulating ratio |

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**Figure 5.**Global linearized model root locus of the unit negative feedback PV-Buck circuit structure.

**Figure 32.**Comparison of SLOM-VWP and DTM-VWP delay times for PV-Buck systems under inputted disturbance conditions.

**Figure 33.**Comparison of SLOM-VWP and DTM-VWP delay times for PV-Boost systems under inputted disturbance conditions.

**Figure 34.**Comparison of SLOM-VWP and DTM-VWP delay times for PV-Buck–Boost systems under inputted disturbance conditions.

**Figure 35.**Comparison of SLOM-VWP and DTM-VWP delay times for PV-Buck systems under controlled disturbance conditions.

**Figure 36.**Comparison of SLOM-VWP and DTM-VWP delay times for PV-Boost systems under controlled disturbance conditions.

**Figure 37.**Comparison of SLOM-VWP and DTM-VWP delay times for PV-Buck–Boost systems under controlled disturbance conditions.

Structure of Different PV Systems | PV-Buck | PV-Boost | PV-Buck–Boost |
---|---|---|---|

${D}_{\mathrm{M}}$ | $\frac{{P}_{\mathrm{M}}}{C(S,T)}$ | $1-\frac{C(S,T)}{{P}_{\mathrm{M}}}$ | $1-\frac{C(S,T)}{C(S,T)+{P}_{\mathrm{M}}}$ |

${R}_{\mathrm{i}}$ | $\frac{1}{{D}^{2}}\frac{2{R}_{\mathrm{L}}}{{M}^{2}}$ | ${(1-D)}^{2}\frac{2{R}_{\mathrm{L}}}{{M}^{2}}$ | $\frac{{(1-D)}^{2}}{{D}^{2}}\frac{2{R}_{\mathrm{L}}}{{M}^{2}}$ |

${V}_{\mathrm{d}}$ | $D{V}_{\mathrm{eq}}$ | $\frac{{V}_{\mathrm{eq}}}{1-D}$ | $\frac{D{V}_{\mathrm{eq}}}{1-D}$ |

Quantity | Notation | Value |
---|---|---|

Maximal output power | ${P}_{\mathrm{max}}$/$\left(\mathrm{W}\right)$ | 150.15 |

Open-circuit voltage | ${V}_{\mathrm{OC}}$/$\left(\mathrm{V}\right)$ | 22 |

Short-circuit current | ${I}_{\mathrm{SC}}$/$\left(\mathrm{A}\right)$ | 9.19 |

Reference temperature | ${T}_{\mathrm{ref}}/(\xb0\mathrm{C})$ | 25 |

Reference irradiance | ${S}_{\mathrm{ref}}$/${(\mathrm{W}/\mathrm{m}}^{2})$ | 1000 |

Output voltage at maximum power | ${V}_{\mathrm{MPP}}$/(V) | 17.5 |

Output current at maximum power | ${I}_{\mathrm{MPP}}$/(A) | 8.58 |

Number of PV cells | 4 |

Quantity | Notation | Value |
---|---|---|

Filter capacitors for PV cells | ${C}_{1}/(\mathrm{uF})$ | 4.7 $\times {10}^{-3}$ |

Filter capacitors for DC/DC | ${C}_{2}/(\mathrm{uF})$ | 4.7 $\times {10}^{-3}$ |

Filter capacitor for DC/AC | ${C}_{3}/(\mathrm{uF})$ | $2.2\times {10}^{-7}$ |

Power inductors for DC/DC | ${L}_{1}/(\mathrm{mH})$ | 4.7 $\times {10}^{-3}$ |

Filter inductor for DC/AC | ${L}_{2}/(\mathrm{mH})$ | 5 $\times {10}^{-5}$ |

Load resistance | ${R}_{\mathrm{L}}/(\mathrm{\Omega})$ | 500 |

Switching frequency | ${f}_{\mathrm{PWM}}/(\mathrm{kHz})$ | 20 |

Modulation ratio | M | 0.5 |

MOSFET | Internal resistance/$\left(\mathrm{m}\mathrm{\Omega}\right)$ | 1 |

MOSFET | Buffer resistance/$\left(\mathrm{k}\mathrm{\Omega}\right)$ | 500 |

Diode | Internal resistance/$\left(\mathrm{m}\mathrm{\Omega}\right)$ | 1 |

Diode | Buffer resistance/$\left(\mathrm{\Omega}\right)$ | 500 |

Input small disturbance | $c(S,T)$ | |

Control small disturbances | $d(S,T)$ |

Difference Structure DC/DC | Initial Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | Perturbation Value Status $(\mathit{S},\mathit{T})/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | $\mathit{c}\left(\mathit{S},\mathit{T}\right)$ | ${\mathit{D}}_{\mathbf{max}}\left(\mathit{S},\mathit{T}\right)$ | ${\mathit{t}}_{\mathbf{d}}/\left(\mathbf{s}\right)$ | ${\mathit{t}}_{\mathbf{p}}/\left(\mathbf{s}\right)$ | ${\mathit{t}}_{\mathbf{r}}/\left(\mathbf{s}\right)$ | ${\mathit{t}}_{\mathbf{s}}/\left(\mathbf{s}\right)$ |
---|---|---|---|---|---|---|---|---|

Buck | 400,10 | 1000,40 | 4.74 | 0.425 | 0.242 | 0.837 | 0.483 | 0.552 |

800,30 | 1000,40 | 0.78 | 0.627 | 0.109 | 0.449 | 0.219 | 0.301 | |

1000,40 | 800,10 | 4.19 | 0.722 | 0.071 | 0.194 | 0.142 | 0.155 | |

Boost | 400,10 | 1000,40 | 4.74 | 0.256 | 0.176 | 0.393 | 0.351 | 1.073 |

800,30 | 1000,40 | 0.78 | 0.496 | 0.071 | 0.214 | 0.141 | 1.418 | |

1000,40 | 800,10 | 4.19 | 0.562 | 0.074 | 0.232 | 0.147 | 1.586 | |

Buck–Boost | 400,10 | 1000,40 | 4.74 | 0.573 | 0.112 | 0.288 | 0.223 | 1.299 |

800,30 | 1000,40 | 0.78 | 0.665 | 0.099 | 0.306 | 0.199 | 1.597 | |

1000,40 | 800,10 | 4.19 | 0.695 | 0.102 | 0.322 | 0.203 | 1.518 |

Difference Structure DC/DC | Initial Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | Perturbation Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | $\mathit{C}\left(\mathit{S},\mathit{T}\right)$ | $\mathit{d}\left(\mathit{S},\mathit{T}\right)$ | ${\mathit{t}}_{\mathbf{d}}/\left(\mathbf{s}\right)$ | ${\mathit{t}}_{\mathbf{p}}/\left(\mathbf{s}\right)$ | ${\mathit{t}}_{\mathbf{r}}/\left(\mathbf{s}\right)$ | ${\mathit{t}}_{\mathbf{s}}/\left(\mathbf{s}\right)$ |
---|---|---|---|---|---|---|---|---|

Buck | 400,10 | 1000,40 | 73.26 | 0.297 | 0.207 | 0.836 | 0.414 | 0.537 |

800,30 | 1000,40 | 70.72 | 0.070 | 0.100 | 0.449 | 0.200 | 0.273 | |

1000,40 | 800,10 | 68.52 | 0.104 | 0.071 | 0.194 | 0.142 | 0.159 | |

Boost | 400,10 | 1000,40 | 73.26 | 0.306 | 0.181 | 0.393 | 0.361 | 1.083 |

800,30 | 1000,40 | 70.72 | 0.053 | 0.078 | 0.224 | 0.156 | 1.433 | |

1000,40 | 800,10 | 68.52 | 0.074 | 0.081 | 0.246 | 0.162 | 1.614 | |

Buck–Boost | 400,10 | 1000,40 | 73.26 | 0.122 | 0.112 | 0.298 | 0.224 | 1.311 |

800,30 | 1000,40 | 70.72 | 0.024 | 0.107 | 0.326 | 0.214 | 1.621 | |

1000,40 | 800,10 | 68.52 | 0.033 | 0.113 | 0.344 | 0.225 | 1.544 |

Initial Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | Perturbation Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | $\mathit{c}\left(\mathit{S},\mathit{T}\right)$ | ${\mathit{D}}_{\mathbf{max}}\left(\mathit{S},\mathit{T}\right)$ | ${\mathit{t}}_{\mathbf{d}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{p}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{r}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{s}}/(\mathbf{s})$ |
---|---|---|---|---|---|---|---|

1000,25 | 800,25 | 1.95 | 0.702 | 0.077 | 0.3582 | 0.14 | 0.155 |

800,25 | 600,25 | 0.35 | 0.633 | 0.142 | 0.4405 | 0.239 | 0.283 |

600,25 | 400,25 | 1.02 | 0.539 | 0.153 | 0.416 | 0.282 | 0.305 |

1000,10 | 1000,40 | 6.14 | 0.684 | 0.105 | 0.305 | 0.166 | 0.209 |

800,10 | 600,40 | 6.15 | 0.618 | 0.141 | 0.462 | 0.224 | 0.281 |

400,10 | 400,40 | 6.09 | 0.425 | 0.293 | 0.836 | 0.500 | 0.597 |

400,10 | 1000,40 | 4.74 | 0.425 | 0.265 | 0.836 | 0.447 | 0.529 |

800,20 | 1000,25 | 0.78 | 0.627 | 0.134 | 0.449 | 0.209 | 0.279 |

1000,40 | 800,10 | 4.19 | 0.722 | 0.076 | 0.193 | 0.14 | 0.152 |

Initial Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | Perturbation Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | $\mathit{c}\left(\mathit{S},\mathit{T}\right)$ | ${\mathit{D}}_{\mathbf{max}}\left(\mathit{S},\mathit{T}\right)$ | ${\mathit{t}}_{\mathbf{d}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{p}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{r}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{s}}/(\mathbf{s})$ |
---|---|---|---|---|---|---|---|

1000,25 | 800,25 | 1.95 | 0.549 | 0.073 | 0.226 | 0.144 | 1.557 |

800,25 | 600,25 | 0.35 | 0.500 | 0.071 | 0.215 | 0.143 | 1.429 |

600,25 | 400,25 | 1.02 | 0.414 | 0.070 | 0.198 | 0.449 | 1.357 |

1000,10 | 1000,40 | 6.14 | 0.537 | 0.071 | 0.222 | 0.144 | 1.525 |

800,10 | 600,40 | 6.15 | 0.488 | 0.070 | 0.211 | 0.141 | 1.398 |

400,10 | 400,40 | 6.094 | 0.256 | 0.175 | 0.293 | 0.351 | 1.072 |

400,10 | 1000,40 | 4.74 | 0.256 | 0.174 | 0.393 | 0.351 | 1.072 |

800,20 | 1000,25 | 0.78 | 0.496 | 0.069 | 0.214 | 0.141 | 1.418 |

1000,40 | 800,10 | 4.19 | 0.562 | 0.073 | 0.232 | 0.147 | 1.586 |

Initial Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | Perturbation Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | $\mathit{c}\left(\mathit{S},\mathit{T}\right)$ | ${\mathit{D}}_{\mathbf{max}}\left(\mathit{S},\mathit{T}\right)$ | ${\mathit{t}}_{\mathbf{d}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{p}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{r}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{s}}/(\mathbf{s})$ |
---|---|---|---|---|---|---|---|

1000,25 | 800,25 | 1.95 | 0.689 | 0.118 | 0.388 | 0.249 | 1.515 |

800,25 | 600,25 | 0.35 | 0.666 | 0.115 | 0.383 | 0.249 | 1.515 |

600,25 | 400,25 | 1.02 | 0.630 | 0.119 | 0.383 | 0.246 | 1.516 |

1000,10 | 1000,40 | 6.14 | 0.683 | 0.119 | 0.383 | 0.249 | 1.514 |

800,10 | 600,40 | 6.15 | 0.661 | 0.117 | 0.383 | 0.247 | 1.515 |

400,10 | 400,40 | 6.09 | 0.573 | 0.123 | 0.386 | 0.248 | 1.536 |

400,10 | 1000,40 | 4.74 | 0.573 | 0.112 | 0.386 | 0.224 | 1.536 |

800,20 | 1000,25 | 0.78 | 0.665 | 0.118 | 0.383 | 0.249 | 1.516 |

1000,40 | 800,10 | 4.19 | 0.695 | 0.117 | 0.383 | 0.230 | 1.516 |

Initial Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | Perturbation Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | $\mathit{C}\left(\mathit{S},\mathit{T}\right)$ | $\mathit{d}\left(\mathit{S},\mathit{T}\right)$ | ${\mathit{t}}_{\mathbf{d}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{p}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{r}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{s}}/(\mathbf{s})$ |
---|---|---|---|---|---|---|---|

1000,25 | 800,25 | 71.50 | 0.049 | 0.079 | 0.242 | 0.160 | 1.576 |

800,25 | 600,25 | 69.55 | 0.086 | 0.076 | 0.225 | 0.154 | 1.444 |

600,25 | 400,25 | 69.20 | 0.157 | 0.075 | 0.204 | 0.152 | 1.370 |

1000,10 | 1000,40 | 74.66 | 0.025 | 0.081 | 0.239 | 0.160 | 1.546 |

800,10 | 600,40 | 72.71 | 0.065 | 0.076 | 0.221 | 0.155 | 1.413 |

400,10 | 400,40 | 73.26 | 0.001 | 0.176 | 0.393 | 0.361 | 1.083 |

400,10 | 1000,40 | 73.26 | 0.306 | 0.175 | 0.393 | 0.361 | 1.083 |

800,20 | 1000,25 | 70.72 | 0.053 | 0.076 | 0.224 | 0.156 | 1.433 |

1000,40 | 800,10 | 68.52 | 0.074 | 0.081 | 0.246 | 0.162 | 1.614 |

Initial Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | Perturbation Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | $\mathit{C}\left(\mathit{S},\mathit{T}\right)$ | $\mathit{d}\left(\mathit{S},\mathit{T}\right)$ | ${\mathit{t}}_{\mathbf{d}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{p}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{r}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{s}}/(\mathbf{s})$ |
---|---|---|---|---|---|---|---|

1000,25 | 800,25 | 71.50 | 0.049 | 0.079 | 0.242 | 0.160 | 1.576 |

800,25 | 600,25 | 69.55 | 0.086 | 0.076 | 0.225 | 0.154 | 1.444 |

600,25 | 400,25 | 69.20 | 0.157 | 0.075 | 0.204 | 0.152 | 1.370 |

1000,10 | 1000,40 | 74.66 | 0.025 | 0.081 | 0.239 | 0.160 | 1.546 |

800,10 | 600,40 | 72.71 | 0.065 | 0.076 | 0.221 | 0.155 | 1.413 |

400,10 | 400,40 | 73.26 | 0.001 | 0.176 | 0.393 | 0.361 | 1.083 |

400,10 | 1000,40 | 73.26 | 0.306 | 0.175 | 0.393 | 0.361 | 1.083 |

800,20 | 1000,25 | 70.72 | 0.053 | 0.076 | 0.224 | 0.156 | 1.433 |

1000,40 | 800,10 | 68.52 | 0.074 | 0.081 | 0.246 | 0.162 | 1.614 |

Initial Value Status $(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | $\mathbf{Perturbation}\mathbf{Value}\mathbf{Status}(\mathit{S},\mathit{T})$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | $\mathit{C}\left(\mathit{S},\mathit{T}\right)$ | $\mathit{d}\left(\mathit{S},\mathit{T}\right)$ | ${\mathit{t}}_{\mathbf{d}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{p}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{r}}/(\mathbf{s})$ | ${\mathit{t}}_{\mathbf{s}}/(\mathbf{s})$ |
---|---|---|---|---|---|---|---|

1000,25 | 800,25 | 71.50 | 0.023 | 0.111 | 0.340 | 0.223 | 1.520 |

800,25 | 600,25 | 69.55 | 0.036 | 0.106 | 0.326 | 0.219 | 1.621 |

600,25 | 400,25 | 69.20 | 0.056 | 0.106 | 0.305 | 0.217 | 1.487 |

1000,10 | 1000,40 | 74.66 | 0.012 | 0.111 | 0.335 | 0.219 | 1.496 |

800,10 | 600,40 | 72.71 | 0.02 | 0.107 | 0.321 | 0.215 | 1.609 |

400,10 | 400,40 | 73.26 | 0.001 | 0.111 | 0.298 | 0.223 | 1.310 |

400,10 | 1000,40 | 73.26 | 0.122 | 0.114 | 0.298 | 0.223 | 1.310 |

800,20 | 1000,25 | 70.72 | 0.024 | 0.111 | 0.326 | 0.219 | 1.621 |

1000,40 | 800,10 | 68.52 | 0.033 | 0.115 | 0.343 | 0.225 | 1.545 |

Different Conditions of Input | Different Circuit Structures | SEE | RMSR (%) |
---|---|---|---|

Inputted disturbance | Buck | 1.598 | 1.264% |

Boost | 0.969 | 0.984% | |

Buck–Boost | 1.716 | 1.196% | |

Controlled disturbance | Buck | 3.071 | 1.615% |

Boost | 4.065 | 1.842% | |

Buck–Boost | 5.029 | 2.041% |

PV-Buck Generation System Circuit Parameters | ||||||||
---|---|---|---|---|---|---|---|---|

Initial value status $(S,T)$$/(\mathrm{W}/{\mathrm{m}}^{2},\xb0\mathrm{C})$ | Perturbation value status $(S,T)$$/(\mathrm{W}/{\mathrm{m}}^{2},\xb0\mathrm{C})$ | Modulation ratio $M$ | ${R}_{\mathrm{L}}$ | ${C}_{1}$ | ${C}_{2}$ | ${C}_{3}$ | ${L}_{1}$ | ${L}_{2}$ |

400,10 | 1000,40 | 0.95 | 5Ω | 470 uF | 1000 uF | 1 uF | 500 uH | 3 mH |

PV-Boost generation system circuit parameters | ||||||||

Initial value status $(S,T)$$/(\mathrm{W}/{\mathrm{m}}^{2},\xb0\mathrm{C})$ | Perturbation value status $(S,T)$$/(\mathrm{W}/{\mathrm{m}}^{2},\xb0\mathrm{C})$ | Modulation ratio $M$ | ${R}_{\mathrm{L}}$ | ${C}_{1}$ | ${C}_{2}$ | ${C}_{3}$ | ${L}_{1}$ | ${L}_{2}$ |

400,10 | 1000,40 | 0.95 | $53.3\mathrm{\Omega}$ | 1000 uF | 470 uF | 1 uH | 500 uF | 3 mH |

System Type | Initial Value Status $\left(\mathit{S},\mathit{T}\right)$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | Perturbation Value Status $\left(\mathit{S},\mathit{T}\right)$$/(\mathbf{W}/{\mathbf{m}}^{2},\xb0\mathbf{C})$ | Output Voltage Variation | System Delay Time |
---|---|---|---|---|

PV-Buck | 400,25 | 1000,25 | 2.60 V | 12.82 ms |

600,10 | 100,45 | 0.384 V | 12.5 ms | |

PV-Boost | 1000,25 | 400,25 | 10 V | 73 ms |

800,20 | 1000,40 | 1.57 V | 21.75 ms |

System Type | Duty Cycle | Input Steady-State Voltage | Input Perturbation | Nonideal Condition Output Value | Ideal Condition Output Value | Nonideal Condition Output Value | Ideal Condition Output Value |
---|---|---|---|---|---|---|---|

PV-Buck | 0.423 | 51.2 V | 34.7 V | 20.4 V | 21.65 V | 16.0 V | 14.67 V |

PV-Boost | 0.256 | 13.13 V | 18.32 V | 16.4 V | 17.64 V | 23.2 V | 24.62 V |

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## Share and Cite

**MDPI and ACS Style**

Zhu, X.; Li, S.; Fan, J.
An Overall Linearized Modeling Method and Associated Delay Time Model for the PV System. *Energies* **2023**, *16*, 4202.
https://doi.org/10.3390/en16104202

**AMA Style**

Zhu X, Li S, Fan J.
An Overall Linearized Modeling Method and Associated Delay Time Model for the PV System. *Energies*. 2023; 16(10):4202.
https://doi.org/10.3390/en16104202

**Chicago/Turabian Style**

Zhu, Xianping, Shaowu Li, and Jingxun Fan.
2023. "An Overall Linearized Modeling Method and Associated Delay Time Model for the PV System" *Energies* 16, no. 10: 4202.
https://doi.org/10.3390/en16104202