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# Reactive power definition

We need to better define terms, here. What exactly are you calling "losses"? Is that a real energy loss, measured in Joules or kWh? If we limit the meaning of "losses" to Joules or kWh, then such losses cannot be represented as X.I^2.

Basically, I really think it is misleading to talk about reactive power losses (although it is done so frequently).

For instance, let's take a transformer for an example. You test a transformer and you get short-circuit and open-circuit impedances and losses. Then, the most basic model for such transformer is a T circuit, with series RL impedances (R and X) for each winding, with a central magnetizing shunt branch usually represented by parallel-connected R and L (G and B for their conductance and susceptance, respectively).

Furthermore, we often "lump" the series impedance in just one "side" of the transformer.

Then, in the most simplistic way, we calculate the series resistance to match the losses from the short-circuit test (assuming voltages are really low across the magnetizing branch, so the current across the shunt-connected resistance is low, thus the losses introduced by the shunt resistance can be neglected in these results). The reactance of the series impedance (leakage reactance X) is calculated from the measured impedance (test result) and the calculated value for the series resistance.

Conversely, the magnetizing branch (the parallel RL branch) is calculated from the open-circuit test results. Once again, G is calculated to match the losses measured in that test (assuming very low currents, therefore the R.I^2 losses can be neglected). And B is then calculated from the measured impedance for the open-circuit test and the calculated value of G.

Long story short: the test results show all losses in the transformer, hysteresis, eddy currents, copper, etc. The equivalent model "lumps" these losses in a resistance.

Why? Because there are no losses (in Joules) in a capacitance or an inductance, in a RLC circuit (circuit theory, ideal capacitors/reactors. In real life, capacitors and inductors have resistances and losses that can be measured as Joules, or we can detect an increase in temperature when in service).

What is X.I^2? That is a "sink" of reactive power, if this is an inductance, but it is a "source" of reactive power if this is a capacitance. You might call these reactive power losses, but then you might end up with negative losses, if you have more capacitance than inductance in a given example (for instance, the pi-model of a long transmission line in open circuit or light load).

Again, you have properly identified these terms as reactive power losses. So far we are in agreement. The problem is that thinking about reactive power as "losses" might give the impression we are talking Joules. We are not.

Finally, if you don't have enough reactive power to "supply" all these X.I^2 "losses" voltages will drop. If you have excess "negative losses" from capacitors (cables, lines, etc.) voltages will rise.

My point: if you control voltages properly, you don't have to worry about reactive power. If you struggle to control voltages, you don't have enough reactive "sources" to sustain the necessary energization/magnetization of the AC system.

Basically, I really think it is misleading to talk about reactive power losses (although it is done so frequently).

For instance, let's take a transformer for an example. You test a transformer and you get short-circuit and open-circuit impedances and losses. Then, the most basic model for such transformer is a T circuit, with series RL impedances (R and X) for each winding, with a central magnetizing shunt branch usually represented by parallel-connected R and L (G and B for their conductance and susceptance, respectively).

Furthermore, we often "lump" the series impedance in just one "side" of the transformer.

Then, in the most simplistic way, we calculate the series resistance to match the losses from the short-circuit test (assuming voltages are really low across the magnetizing branch, so the current across the shunt-connected resistance is low, thus the losses introduced by the shunt resistance can be neglected in these results). The reactance of the series impedance (leakage reactance X) is calculated from the measured impedance (test result) and the calculated value for the series resistance.

Conversely, the magnetizing branch (the parallel RL branch) is calculated from the open-circuit test results. Once again, G is calculated to match the losses measured in that test (assuming very low currents, therefore the R.I^2 losses can be neglected). And B is then calculated from the measured impedance for the open-circuit test and the calculated value of G.

Long story short: the test results show all losses in the transformer, hysteresis, eddy currents, copper, etc. The equivalent model "lumps" these losses in a resistance.

Why? Because there are no losses (in Joules) in a capacitance or an inductance, in a RLC circuit (circuit theory, ideal capacitors/reactors. In real life, capacitors and inductors have resistances and losses that can be measured as Joules, or we can detect an increase in temperature when in service).

What is X.I^2? That is a "sink" of reactive power, if this is an inductance, but it is a "source" of reactive power if this is a capacitance. You might call these reactive power losses, but then you might end up with negative losses, if you have more capacitance than inductance in a given example (for instance, the pi-model of a long transmission line in open circuit or light load).

Again, you have properly identified these terms as reactive power losses. So far we are in agreement. The problem is that thinking about reactive power as "losses" might give the impression we are talking Joules. We are not.

Finally, if you don't have enough reactive power to "supply" all these X.I^2 "losses" voltages will drop. If you have excess "negative losses" from capacitors (cables, lines, etc.) voltages will rise.

My point: if you control voltages properly, you don't have to worry about reactive power. If you struggle to control voltages, you don't have enough reactive "sources" to sustain the necessary energization/magnetization of the AC system.

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