Power Factor at recieving end of wind farm transmission line.

[whitbuzben]

Dear Sirs

I am trying to do a calculation relating to the connection of a 3.6 MW offshore wind-farm to shore via a 9km long subsea cable. The scenario is as follows and is taken from an example in a text book (page 236 Example 10.5 of the attached PDF):

A three phase XLPE subsea cable delivers 3.6MW at power factor 0.8 lagging to a load. The sending end voltage is 33kV. The resistance and reactance of the conductor are 5.31 ohms and 5.54 ohms. I have managed to calculate the receiving end voltage, line current and transmission efficiency as per the example in the attached pdf (please refer to page 236 Example 10.5 of the attached PDF) and it all makes sense.

My question relates to the lagging power factor of 0.8. Lets say for example that the transmission line in the example (see pdf) is a three phase XLPE cable
connecting a 3.6MW wind-farm to shore. The power factor at the sending end is 1 and the voltage is 33kV. When the cable reaches the shore the cable is connected to the onshore grid via a substation where a transformer steps the voltage up from 33kV to 132kV. Under such a scenario how would one know what the receiving end power factor is (and whether it is leading or lagging). Presumably this depends on the nature of the load (which in this case is the 132kV grid)!???

I suppose my question is what determines the power factor at the receiving end of the cable under the scenario described above and what assumptions can be made?

 

[collies99]

Power factor at the receiving end will the phase current relationship to the voltage at the specified location.

since the cable is both resistive and inductive, current flow through the cable for a purely resistive load will result in a lagging PF.

since the cable has shunt capacitive values, it may counteract the cable inductive loading or even overcompensate it resulting in higher that 1pu voltage at the receiving end.

therefore the PF will be dependent on the nature of the load.

if inductive load at the receiving end can be provide with its own var source at the receiving end and in a nut shell you are only sending power down your transmission line, then you will have the optimum PF for the said transmission line.

hope that helps

 

[dpc]

If it's like most wind farms, the cable capacitance will be a major factor. Since the wind farm will normally be producing a small fraction of its rating, excess voltage rise is a common problem. Many windfarm substations incorporate shunt reactors to compensate for the cable capacitance during light load conditions.

 

[collies99]

Possibly requires a STATCOM to be installed at receiving end.

 

[bacon4life]

The example from the book was a radial line; connecting to grid changes which variables are independent.

Example 10.5 is radial line where the pf factor was fixed by the load characteristics and the sending in voltage was fixed at 33 kV by the supply system.

In a wind farm connection there are lots of considerations that go into determining power factor at the interconnection point:
1)inductive losses from current flowing through cables/transformers
2)capacitance from cables
3)inductive losses from many types of wind turbines
4)voltage/power factor control from newer turbines
5)switched capacitor banks
6 STATCOMs or electronic other voltage control devices
7)the interconnection transformer ratio
8)interconnection voltage fluctuations
9)voltage control mode vs power factor mode.

Wind farms can operate in voltage control mode or power factor mode. In power factor mode, they adjust the power factor at the interconnection point by changing the voltage within the wind farm. In voltage control mode, they adjust the voltage at the interconnection point by changing how much reactive power is generated within the wind farm. Which control strategy is used may depend on the time of day/year, the amount of power produced at the moment or the contractual requirements of the Transmission Operator.

In voltage control mode, if the transmission grid voltage goes up, the wind farm would reduce reactive power production to try to lower the wind farm voltage.

In power factor control mode, if the transmission grid voltage goes up, the wind farm voltage would also go up.

In an interconnected system, the power factor of any individual generator does not directly depend on the power factor of the system loads. Rather, the power factor of the individual generator depends on the voltage controls strategy built into that generator and the voltage at the interconnection bus. Of course the reactive power output from each generator does have an influence on the system voltage and on nearby generators.

 

[whitbuzben]

Thanks for the resposes guys. Collies99 your response confirms what I initially though. The PF at the receiving end will essentially depend on the characteristics of the load (though as highlighted by bacon4life the problem is somewhat more complex in the case of a wind farm).

Out of interest if one knows the MVAR rating of the 33 to 132 transformer at the receing end of the cable then it should be possible calculated the inductance and resistance of the load? One could then do a load flow. Is this correct and is it possible to calculate the inductance and resistance values from the MVAR rating of the transformer?


Many Thanks

 

[collies99]

Google "power flow analysis of large wind power plant collector systems with remote voltsge control capability".