There are two voltage specifications that need to be matched. The first is the component itself: most manufacturers specify the maximum system voltage on the data sheet. The voltage of the photovoltaic array must not exceed the maximum system voltage of the photovoltaic modules used.

The second voltage is not allowed to exceed the maximum input voltage of the inverter: this number is generally lower than the maximum system voltage of the component, so it has received more attention. This number is highlighted in the following data extracted from the inverter data sheet (see Figure 2).

The maximum input voltage of the inverter refers to the maximum DC voltage that the inverter can safely handle. If the open circuit voltage of the photovoltaic array exceeds the maximum input voltage of the inverter, the inverter electronics may be damaged.

Most grid-interactive inverters also have a maximum power point tracking (MPPT) range, which specifies the minimum voltage and the maximum voltage. Within this range, the inverter can track the maximum power point to ensure system performance as much as possible; beyond this range, system performance may be reduced. The upper limit of the MPPT range may be the same as the maximum input voltage, or it may be a lower voltage (that is, the inverter can handle a voltage higher than the highest voltage of the MPPT range, but cannot track the maximum power point of the array at a higher voltage. ).

A typical photovoltaic array consists of several modules connected in series to form a branch, or several branches are connected in parallel to form an array. Assuming that all components are identical, the output voltage of the array is the voltage of a single branch. The branch voltage depends on the number of PV modules in the branch, and it will show how to calculate the maximum number of modules allowed in a branch. It is important that the branch voltage is lower than the maximum voltage of the system and lower than the maximum input voltage of the inverter; in addition, the branch voltage should also be within the MPPT range-these characteristics are marked in the inverter data sheet . The importance of the MPPT range is easy to understand, but the maximum and minimum input voltages of the inverter are more important to system designers, because the minimum input voltage affects the system performance, and the maximum input voltage affects the safety of the inverter.

The first step is to obtain the highest and lowest temperature of the installation site, called the highest and lowest ambient temperature. Using these data, the battery temperature of the photovoltaic module can be calculated. The working temperature of photovoltaic cells is much higher than the air temperature in the weather report. The designer must first consult the national specifications, which may specify the ambient temperature or battery temperature in the capacity configuration calculation. The following examples quote the temperature in Berlin, Germany and Sydney, Australia. These cases are used to illustrate the capacity allocation requirements in hot climates and cold climates. In Australia, national standards mandate that the maximum operating temperature of the battery should not be higher than the ambient temperature of 25°C. This number is also often used in the United States, but it is not used as a standard. The minimum operating temperature of the battery is the same as the minimum ambient temperature, because when the photovoltaic module starts to generate electricity in the morning, the module has not yet heated up.

Case 1: Sydney, Australia

The ambient temperature in Sydney varies from 0-50°C (32-122F), so the highest and lowest battery temperatures are as follows:

Environment temperature 0℃ | Minimum battery temperature = minimum ambient temperature | =0℃ |

Ambient temperature 50℃ | Maximum battery temperature=50℃ +25℃ | =75°C |

Case 2: Berlin, Germany

The ambient temperature in Berlin is -10-40°C. (14~104F), so the highest and lowest battery temperatures are as follows:

Ambient temperature -10℃ | Minimum battery temperature = minimum ambient temperature | =-10℃ |

Ambient temperature 40℃ | Maximum battery temperature=40℃+25℃ | =65℃ |

The temperature of the photovoltaic array will affect its performance. The next step will be to solve how the expected operating temperature of the battery affects the array output voltage. In order to do this, the data sheet information of the photovoltaic module is required. Photovoltaic module data sheets generally provide at least one voltage temperature coefficient, which is a special rating used to describe the effect of temperature on battery voltage, usually expressed as a percentage or V/℃. However, some manufacturers only provide the temperature coefficient of the maximum power P, which can be used to approximate the temperature coefficient of voltage.

Using the voltage temperature coefficient, the annual maximum and minimum output voltages of the photovoltaic array can be calculated to ensure that these voltages are within the operating voltage range required by the inverter. The maximum power point voltage (V_{mp}) of the array should not be lower than the minimum working voltage of the inverter. If the component branch circuit voltage is lower than the minimum working voltage of the inverter, the inverter will shut down(Thus the array stops generating power), or it will not work at the maximum output power of the array.

The photovoltaic modules used in these cases are monocrystalline silicon modules produced by Sharp, and the inverter is SMA Sunny Boy 3000.

In order to calculate the component voltage at a specific temperature, one of the following formulas needs to be used:

If the temperature is higher than 25°C :

U_{X℃}=U_{STC}﹣[γ_{v}×(T_{X℃}﹣T_{STC})]

If the temperature is lower than 25°C:

U_{X℃}=U_{STC}＋[γ_{v}×(T_{X℃}﹣T_{STC})]

In the formula, U_{X℃} is the voltage (V) at a specific temperature; U_{STC} is the voltage under standard test conditions, that is, the rated voltage (V); γ_{v} is the voltage temperature coefficient (absolute value) (V/℃); T_{X℃} is Battery temperature (℃); Tsrc is the temperature (℃) under standard test conditions (ie 25℃)

Note: The second formula is not strict, it is just a simplified representation of the concept. However, it can get the correct answer for specific working conditions.

Case 1: Sydney, Australia

Environment temperature 0℃ | Corresponding component battery temperature=0℃ | =0℃ |

Ambient temperature 50℃ | Corresponding component battery temperature=50℃ +25℃ | =75°C |

Calculate the highest voltage

The highest component voltage (V_{oc}) occurs at the lowest temperature of the battery, which is 0°C in this example. Therefore, when calculating the maximum voltage, the open circuit voltage V_{oc} should be used and the value should be adjusted according to the temperature coefficient. It can be seen from the data sheet that the open circuit voltage under standard test conditions is 30.2v, so:

Calculate the difference between battery temperature and 25℃ | 0℃-25℃=-25℃ |

Then multiply by the temperature coefficient to get the voltage rise value | -25°C x (-0.104)V/°C =2.60V |

Finally calculate the highest voltage | 30.2V +2.60V =32.80V |

Calculate the lowest voltage

The lowest component voltage occurs when the battery temperature is the highest, that is, the battery temperature is 75°C. This data is calculated using the maximum power point voltage (V_{pm} or V_{mp}) and the corresponding temperature coefficient. Since the temperature coefficient of the maximum power voltage is not given, an approximate formula can be used to estimate the temperature coefficient of the maximum power-given in the form of %/℃ on the data sheet, it must be converted to V/℃:

The temperature coefficient should be converted to decimal | -0.485%=-0.00485 |

The temperature coefficient (V/℃) is calculated from the component or V. | -0.00485 x 24V=-0.1164V/℃ |

Use this information to calculate the minimum voltage as follows: | |

Calculate the difference between battery temperature and STC | 75℃-25℃=50℃ |

Multiply by V_{mp} or V_{mp} temperature coefficient | 50℃ x (-0.1164V/℃)=-5.82V |

V_{mp} minus voltage derating factor = lowest voltage of the array | 24V-5.82V =18.18V |

Therefore, the lowest component voltage is 18.18V, and the highest voltage (ie 32.8V) and the lowest voltage (ie 18.18V) are used to calculate the number of components allowed for each branch. Usually these data have to add a safety margin, generally the minimum voltage is increased by 10%, and the maximum input voltage is reduced by 5%.

Calculate the minimum number of components in the branch

The voltage drop on the DC cable should be introduced in the calculation: the voltage drop is estimated to be 1%, so the lowest voltage should be minus 1% voltage drop (so the voltage data should be multiplied by a factor of 0.99) | 18.18V x0.99 =17.99V |

The minimum input voltage of the inverter (see data sheet) should be increased by 10% as a safety margin (So the voltage data should be multiplied by 1.1) | 268Vx1.1=294.8V |

Finally, the minimum number of components in the branch is obtained by dividing the above data by the minimum voltage of the components | 294.8V/17.99V=16.39 modules |

At least 17 modules are connected in series on a branch |

Technical data | Sunny Boy 3000 |

Maximum DC power | 3200 W |

Maximum DC voltage | 600V |

MPP voltage range | 268~480V |

DC rated voltage | 350V |

Minimum DC voltage/starting voltage | 268V/330V |

Calculate the maximum number of components in the branch

First, the maximum input voltage of the inverter is reduced by 5% as a safety margin (so the maximum voltage data is multiplied by 0.95) | 600V x0.95 =570V |

The maximum voltage of the inverter divided by the maximum voltage of the components (as calculated above, determine the maximum number of components allowed in a branch) | 570V/32.8V=17.38 modules |

For safety reasons, this data should be rounded down, so each branch must have 17 components.

Case 2: Berlin, Germany

Now we apply the same method to locations where the temperature range (-10-40°C) is very different. The maximum voltage will appear at the lowest operating temperature of the battery -10°C, and the open circuit voltage coefficient (-0.104V/°C) is calculated as follows:

Calculate the highest voltage

Calculate the difference between battery temperature and 25℃ | -10℃-25℃=-35℃ |

Then multiply by the temperature coefficient to get the voltage rise value | -35℃ x (-0.104)V/℃ =3.64V |

Finally calculate the highest voltage | 30.2V +3.64V =33.84V |

Calculate the maximum number of components in the branch

First, the maximum input voltage of the inverter is reduced by 5% | 600V x0.95 =570v |

The maximum voltage of the inverter divided by the maximum voltage of the components (as calculated above, determine the maximum number of components allowed in a branch) | 570V/33.84V = 16.84 modules |

For security reasons, this data should be rounded down, so each branch must have 16 components.

Calculate the lowest voltage

The lowest voltage appears when the battery temperature is 65°C, calculated as follows: | |

Calculate the temperature coefficient of PV module V_{mp}/V_{pm} (V/C) | -0.00485 x 24V=-0.1164V/℃ |

Calculate the difference between battery operating temperature and STC | 65℃-25℃=40℃ |

Then multiply by the temperature coefficient of V_{mp} | 40℃ x (-0.1164V/℃)=-4, 66V |

Subtract the last data from the rated V_{mp} (calculate the minimum voltage data under the highest temperature condition) | 24V-4.66V =19.34V |

Calculate the minimum number of components in the branch

The lowest component voltage multiplied by the voltage drop factor on the DC cable (1%) | 19.34V x0.99 = 19.15V |

The minimum input voltage of the inverter should be multiplied by 1.1 times, taking into account the 10% safety margin | 268V x1.1 =294.8V |

Finally, the minimum number of components in the branch is obtained by dividing the previous data by the lowest voltage of the component | 294.8V/19.15V=15.39 modules |

This data should be rounded up (because this is the minimum value), so a branch has at least 16 modules connected in series.