Physical models used > Batteries - General model description

Model choice justification

We have developed a non conventional battery model, trying to avoid the pitfalls which arise in a number of existing PV software: either an extreme simplification, which can only lead to rough evaluations of the system behavior, or adjusted models based on numerous (often interrelated) parameters whose physical meaning is often not clear to the user, and practically necessitate a complete measurement of each battery used. We have therefore tried to fulfill the following criteria :

-	On the one hand, the model should be presented to the user in a rather simple manner, involving à priori only "explicit" parameters specific to each battery: type of technology, voltage, number of elements, nominal capacity, possible internal resistance and Faradic efficiency, ageing properties.

-	Most of these parameters should be available from the detailed datasheets. Others are predefined, specific to each technology.

But on the other hand, it should be sufficiently detailed to satisfy the needs of the simulation of the PV system, where the charging current is practically imposed by the solar generator. In particular, its behavior in voltage, not critical in the intermediary zones, should be realistic enough at the end of charge and discharge to make the controller operating correctly. Further, it will be important to be able to estimate the ageing and the possible maintenance imposed by the conditions of use.

Voltage model

The model should evaluate the battery voltage at any time, as a function of the State of charge (SOC), the current, the temperature, eventually the ageing.

An accurate operating voltage determination is essential when the system control decisions are based on voltage thresholds (as involved in most practical systems). SOC-based controls are less used, as the SOC is not directly accessible to measurement.

For Lead-acid batteries PVsyst lets the choice of the control mode to the user, either working with the voltages, or on the SOC calculation (see Controller operating thresholds) . And therefore the voltage is essential.

With Li-Ion batteries, where for some technologies the voltage variations are very low, and the begin/end of charge are not always well defined before attaining a dangerous region, in the present time we have only allowed using the SOC.

Therefore at current date PVSyst provides 2 distinct models :

othe lead-acid model

othe lithium-ion model

Capacity, State of charge (SOC)

The capacity is defined as the current [Ah] that you can draw from the fully charged battery. It is normally the main characteristics (with the nominal voltage) defining a Battery.

However the capacity is not a well-defined property: it depends on:

oThe charging / discharging current rate

oThe battery temperature

oThe ageing.

This variability - along with other current losses - is the main reason why the "State of charge" (SOC) is not well defined in the reality. Even if the controller performs an accurate balance of the charging and discharging currents, the SOC variation will depend on these operating conditions. For a controller operating with SOC criteria, the error will increase along the charging / discharging periods. The "recalibration" of the SOC will only occur when attaining the overcharging or discharging voltage thresholds.

Notation for the Capacity:

With Lead-acid batteries, the nominal capacity is usually specified as C10 or C100 [Ah]. This means the capacity when discharging in 10 hours, or 100 hours, i.e with a current of C10/10 or C100/100 [A].

There may be a difference of up to 25 to 40% between these 2 values !

Therefore be careful when comparing L_A batteries: a usual car battery will usually be specified as C10, when some providers of batteries for solar use will specify C100. This is "justified" as the usual operating conditions for PV systems (storage of 2-4 days) will be most of the time at C50 or higher.

Now on the Li-Ion datasheets, the nominal capacity is usually specified for C2 or C5 (a discharge in 2 or 5 hours). Because in many applications (electric cars, mobility, computers, etc) this corresponds to usual conditions. This is possible because the internal resistance of the Li-Ion batteries is very low.

On these datasheets, the curves are often labelled as 0.2C, or 0.5C. 0.2 C means a discharge rate of 0.2 * capacity [A], i.e. C5, or 0.5 * capacity [A], i.e. C2.

Curves are often specified for 2C, 5C etc... (discharge in 0.2 or 0.5 hours) which would be a prohibitive discharge rate for lead-acid !

In PVsyst, we adopted the convention of always defining the nominal capacity as C10.

Capacity as function of the discharge rate model

This correction is the main one used for the estimation of the SOC during the simulation.

oWith Lead-acid batteries, the datasheets usually specify the capacity at different rates, and PVsyst applies an interpolation function.

oWith Li-ion batteries, we apply a parametrization proposed by Peukert. (this could also be used for Lead-acid in the lack of explicit values).

NB: with Li-ion batteries, the capacity variation is much lower than for the Lead-acid: we usually adopted a Peukert coefficient of 1.02, which corresponds to a C100/C10 ratio of 1.05.

Capacity as function of the Temperature

The capacity is reducing when the temperature decreases.

For Lead-acid, the lower possible temperature is related to the freezing of the electrolyte, which depends on the state of charge (acid concentration). An empty battery is more sensitive to extreme temperatures.

For the lead-acid batteries, PVsyst proposes a default capacity derate function which should not be so different from battery to battery.

For the Li-Ion, this dependency may usually be determined from the usual discharge curves specified on the datasheets, as function of the temperature.

NB: For a solar static system, the battery temperature is usually not very significant: the battery bank is indoor at a rather constant temperature. This would not be the case, for example for an electric vehicle, which is charged indoor, and discharged at external temperature.

Capacity function of the battery age

This property was not known when developing the model for Lead-acid batteries. Therefore PVsyst doesn't take it into account

The capacity decrease is now mentioned on some Li-Ion datasheets. However we have not yet included this in the model, so that PVsyst doesn't take this effect into account when studying the ageing of stand-alone systems. A model should be developed in the future.

Ageing and wear and tear

One of the advantages of the program is also to evaluate the wear and tear of the battery depending on the running conditions, and therefore the investment to be planned for its replacement. Please also see "Battery Ageing, Nb of cycles"

Ageing is governed by two phenomena:

-a "static" longevity, characteristic of the battery, whether it is used or not. This value is often given by the manufacturer at a reference temperature (20°C). But it strongly varies with temperature, and we will agree with most manufacturers that it reduces by a factor of 2 for a temperature increase of 10°C !

-a deterioration due to use, depending on the number of cycles and the depth of the discharge at each cycle. This is usually given by manufacturers as a number of cycles as function of the depth of discharge. If the ageing degradation effect is identical whatever the depth of discharge, this curve becomes an hyperbola: for each point the total stored energy during the battery life is the DOD * Nb. of cycles !

State of wear (SOW)

During the simulation, for each discharging step, we evaluate a wear and tear increment proportional to the current, but weighted by the actual depth of the state of discharge. The global wearing out of the time step is considered as the sum of these two evaluations.

This is also the reason why on the final report, the total energy stored during the simulation is mentioned on the loss diagram. A good design should aim at decreasing the stored energy (for example by a better load management during the day).

The simulation involves 2 kinds of ageing evolution, varying from 1 or 100% (new battery) to 0 (battery to be replaced): the variables involved are:

- SOWCycl : dynaminc wear due to the number of cycles

- SOWStat : static wear due to the age of the battery.

At a given time, the global state of wear (SOW) is the minimum of these 2 values.

Model used in simulations

During the simulation, the battery voltage is computed as function of the actual current and temperature.

For the evaluation of the SOC, the capacity is evaluated during the discharge as function of the current rate and the temperature, and memorized for being reused during the next charging period.

Additional current losses (Gassing in case of overcharging in Lead-acid, self-discharge, coulombic efficiency) are also accounted for the evaluation of the SOC. The balance of the input and output energies over a long period - taking all these effects into account, and especially the voltages - will give the real energetic efficiency of the battery during the operation.

The ageing is also evaluated over the simulation period.

The simulation may help for exploring the effect of the control thresholds adjustments, either on the performances of the PV system, or on the aging conditions of the battery.

We can note that for "normally sized" systems, the battery capacity is not a crucial point in the system performance. A little difference may act on the overcharging or PLOL losses, without affecting significantly the global performance.