Power Factor
Basic definitions
In an AC circuit, the Power (or Energy when integraed in the time) may be described by:
- Active Power: this is a real power, able to create movement or heat.
- Reactive power: virtual "power", created or absorbed by devices like inductors (motors) or capacitors.
- Apparent power: is the combination of these contributions.
In a sinusoïdal evolution, these contributions are a result of the phase shift of the current with respect to the voltage.
These quantities are usually represented on a vector diagram:
In an AC circuit, the apparent power is defined as the product of the voltage by the current, when these are measured independently (i.e. the effective value of the voltage and the effective value of the current); Papparent = Ueff * Ieff, expressed in [kVA].
The active power is the power obtained along one sinus period, when we integrate the product of the instantaneous Voltage by the Instantaneous Current at each time step. This results in a multiplication by the cosine of the phase shift:
Pactive = Ueff * Ieff * Cos(phi) expressed in [kW].
The reactive power is the vectorial difference of these contributions:
Preactive = Ueff * Ieff * Sin(phi) expressed in [kVAr].
We name "Power factor" the ratio between active and apparent power, i.e. Cos(phi).
It is very important to observe that the "Reactive power" is not a real power (not an energy): it cannot produce any movement nor heat nor any other effect.
Reciprocally, you can create Reactive power without consuming any "real" (active) power. This is what happens in capacitors or inductors.
NB: The Cos(Phi) value defines indistinctly the Leading and Lagging situations. People sometimes use the Tan(Phi) quantity for distinguishing between these situations.This is not really significant in PVsyst, as we only deal with the active energy.
Reactive power produced by an inverter
The active energy produced by an inverter is always a result of the input DC energy provided by the PV array. Any "real" energy difference between the output and the input of the inverter would be transformed into heat (this is the case of the inverter's inefficiency).
Now with the new technologies (Pulse Width Modulation, PWM) it is possible to create voltage and current signals with any phase shift, at no additional energetic cost. This is just a question of programming in the PWM control.
This is the reason why the grid manager may ask the PV systems for producing Reactive energy, in order to compensate the reactive energy consumed by the motors (and other devices like switching power supplies). Otherwise this is ordinary done with big sets of capacitors.
This phase shift production results of an explicit control within the inverter, i.e. a parameter specified by the control system. In PVsyst we consider fixing a constant Power factor along the year, or possibly in monthly values. Specifying this in hourly values is foreseen, but not yet implemented.
In the simulation results
When defining a Power Factor, the results will define two new quantities, the reactive and apparent energy exchanged to the grid. They will appear at the bottom of the loss diagram.
The reactive energy is computed at the inverter level as
EReGrid [kVAh] = E_Avail [kWh] * Tan(Phi),
according to a Power Factor value (=cos(phi)) required from the grid that is either fixed for the entire year or given in monthly values (set through the Energy Management tab). Note that in System you should use an inverter whose limits can reach this cos(phi) value.
The apparent energy is then computed from the energy delivered to the grid at the injection point (i.e. from the active (or real) energy fed to the grid) as
EApGrid [kVAh]^2 = E_Grid [kWh] ^2 + EReGrid^2.
The apparent energy is obviously always superior to the active energy.
Note that, as the reactive component is set at the inverter level (the inverter doesn't have knowledge of what happens downstream), those two energies are computed at different points in the system, i.e. at the inverter output and at the injection point. Therefore, if some active energy is consumed or produced in between (e.g. from self-consumption or from battery storage), the effective angle between the active and apparent energy at the injection point might be modified with respect to the requested power factor set at the inverter. This is illustrated in more details in the figure and sections below. Note how the apparent power is the vector sum of active and reactive power at a given point of the system.
An average cos(phi) value effectively delivered to the grid is also given in the loss diagram along the reactive energy.
Power Factor and Self-Consumption
In PVsyst the load consumes only active power. Since the power factor does not change at inverter level, the power factor is increasing at the injection point.
Power Factor and Grid limitation
The grid manager may ask for a limitation in apparent or in active power. In the presence of a grid limitation: the grid injection limitations act as inverter clipping. The reactive power is therefore following the clipped active power according to cos(phi) ⇒ cos(phi) at the injection point does not change.
NB: some grid limitation requirements are based on a specific state of the Grid (especially the grid voltage). Taking such requirements into account is not possible in a PVsyst simulation, as it would require knowing the Grid voltage at each time step, as an input parameter.
Power Factor and AC losses
Some of the active power is lost in the AC circuit.
When applying a power factor, for keeping the same active power, the current has to increase:
Ieff (apparent) = Ieff (active) / Cos(phi)
Therefore the wiring ohmic losses - proportional to I² - will increase, either in the wires, and in the transformers.
However, in the present time, PVsyst doesn't evaluate the impedance losses, especially in the transformers. Therefore the reactive energy is identical at the inverter output and the injection point. i.e. the cos(phi) specified in the inverter is equal to the value required at the grid level as defined in the Energy Management tab.
Therefore only the active energy injected into the grid is reduced by the AC ohmic losses, and similarly to the self-consumption case, the cos(phi) value will be reduced.
Power Factor and storage
The battery stores and delivers only active power. Therefore the power factor can increase or decrease at the injection point momentarily. However, averaged on the battery cycle, the power factor can only decrease as the charge/decharge steps add additional losses of active energy.
Procedure
The operating power factor is specified for the whole system. You define it using the Energy Management button.
The power factor may be specified in yearly or monthly values.
For grid limitation, you should choose whether the limit is in active or in apparent power.
NB: The derogation options "Force as apparent/active power" will force all inverters to operate under this conditions. This has been kept here for compatibility with old versions < 7.3.3, and for possible tests. It is not recommended.
Effect on PNom
The inverter production is basically independent on the Power factor.
However there may be an effect on the overload conditions, according to the inverter's specifications.
- either the nominal power PNom is specified in active power [kW]. In this case the simulation is not dependent on the Power factor.
- or the nominal power PNom is specified as apparent power [kVA], so that the power limitation will occur for an active power
PNom(act)[kW] = PNom(app)[kVA] * Cos(Phi). As thePnom(act)is lower, the overload loss will be higher, and depends on the specified cos(Phi). Be attentive that in the "System" tab, this is not taken into account for the dimensioning of the DC / AC ratio and one might need to adapt the dimensioning of the inverter power once a given Power factor has been chosen.
NB: Since the version 7.3.3, each inverter operates according to its own Pnom mode specification. There is a possibility of forcing all the inverters in one or the other mode, but this is not recommended. This should only be used for tests.