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I am trying to understand the difference between active and reactive power. Reactive power is said to be "wasted" because it is constantly alternating between a source and load in AC power system. What is confusing to me is that, this isn't some ontologically distinct form of energy. These are still electrons oscillating in a circuit. Why does active power not also oscillate between source and load? I assume this oscillation is because the polarity is switching back and forth rapidly from the AC generator source, so there shouldn't be any special distinction to how the electrons respond?

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Apply an alternating voltage to a capacitor. The capacitor will charge with one polarity on the rising quarter-cycle, discharge on the following quarter-cycle, charge with the opposite polarity, and discharge again. Assuming the capacitor is ideal, there is no energy lost in the capacitor; all the charge that went in at one voltage comes out at the same voltage. This "sloshing" of energy back and forth is reactive power.

Now apply that same alternating voltage to a resistor. The resistor will dissipate energy at V^2/R on both half-cycles. All the energy that goes into the resistor is turned into heat that dissipates into the environment. This is active power.

Reactive power isn't "wasted" per se, but it doesn't perform any useful work. And while it is conserved for the most part, all the lines and devices (transformers etc) from the generating station to the point of use need to be sized to accommodate it. There's also the extra losses incurred in resistive heating in the transmission chain that drive designers to power factor correct their devices to something closer to 1 (active power only).

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The difference between pushing electrons through a resistive load, and pushing them through a capacitor/inductor is easier to understand when you consider what happens when you stop pushing, rather than as you push.

If, as you push, the force-times-distance energy you expend to move each individual charge is immediately removed from system by some environmental "energy sink", then as soon as you stop pushing, the electrons stop moving. The energy you gave them is lost to that sink.

If however, as you push charges, the environment does not steal away the force-times-distance energy you expended when moving them, but rather causes the electrons to somehow "push back" like a spring pushes back as you deform it, then when you release or relax the potential difference that delivered energy to the charges, the charges can return that energy. Under the force of whatever "spring mechanism" that got "wound up" when you displaced them, those charges can now deliver the same force-times-distance energy back to the source, returning to their initial locations.

In the case of a capacitive load, the energy you give to charges by injecting them onto a plate, and ejecting equal charge from the opposite plate, results in an imbalance of charge on either side, manifesting an electric field. It is that electric field that now pushes the charges in a direction back from whence they came. Thus the energy delivered to the charges to get them into this situation in the first place is not leaked or lost to the environment, it is simply stored, ready to impart force-times-distance energy to whatever is connected across the capacitor some time later.

For inductors, the "wind up spring" energy storage mechanism is magnetic rather than electric, but the same principle applies. When the force that imparts energy to charges (to eventually become a magnetic field) is relaxed, the magnetic field begins to collapse and that same energy causes the charges to push, rather than be pushed. A better analogy is perhaps a moving mass with momentum, rather than a spring, but the important concept is that energy delivered to accelerate charges isn't lost, just stored in some manner.

Active loads do not "wind up" like this. You can turn an inductor into an active load by causing its magnetic field to make something metallic/magnetic nearby move, which is what happens in a motor. Instead of allowing the magnetic field's energy to return to the electrical source, you can drain it away by accelerating a mass instead.

Resistors are the exact opposite of springs, in this analogy. It's as if charges are being dragged across a surface with friction. Things get hot, and when the potential difference that pushes those charges is removed, there's no energy stored in such a way that can cause the charges to "spring" back.

This isn't just about "electrons oscillating", because you are right, that's essentially what's happening. However, movement alone is not sufficient to explain the energy exchanges and mutations that are going on. In addition to position and velocity, you must also consider the forces at work, and the distances that charges are travelling, and the coulombs of charge.

In the same way that mechanical systems have "springiness", so do electrical systems. Some elements are springs, some aren't. Some springs are more springy than others. It's all about springs. Reactive systems are springy, resistive systems are not.

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To say reactive power is wasted is wrong. Without it ac electric motors, generators or transformers do not work.

Actve power or real power (P in W) is something we get out of the circuit. In a resistor, real power is given off as heat. In an ac electric motor, real power produces torque to drive a load.

Current (red) and Voltage (blue) are in phase and multiplying the instantaneous values at every instance in time gives an instantaneous power (green) that goes from 0 to \$P_{Max}\$, with source providing \$P_{Avg} = \frac {P_{Max}}{2}\$. Positive average so power creates heat in a resistor.

R Series circuit

With a pure inductor [or capacitor], the voltage and current waveforms are out of phase. I lags \$V_S\$ by 90° [I leads \$V_S\$ by 90° for capacitor]. The inductor consumes power to form a magnetic field, but returns it to the source the next quarter cycle. Similarily, the capacitor consumes power to form an electric field, but returns it to the source the next quarter cycle.

Current (red) lags Voltage (blue) by 90° and multiplying gives an instantaneous power (green) that has a positive and negative component. When both waveforms are positive, power is consumed. When one is negative, power is returned.

L Series circuit

\$P_{Avg}\$ is 0, so no real power.

But the source is providing power to the circuit. This power is reactive power, inductive reactive power \$Q_L\$ in VAR [or capacitive reactive power \$Q_C\$ for capacitors].

Up to this point, you may wonder why I bring up capacitors. Capacitors provide power factor correction for inductors, providing leading reactive power to meet needs of lagging reactive power.

If \$Q_C\$ = \$Q_L\$, then all power from source goes to resistor. I is in phase \$V_S\$. Essentially, the capacitor acts as a source for the inductor. The collapsing electric field in capacitor forms a magnetic field in the inductor and vice versa.

Current (red) and Source Voltage (blue) are in phase. \$V_C\$ (purple) is opposite in polarity to \$V_C\$ (brown) and cancel each other out. All power (green) from source goes to resistor.

RLC Series circuit

Graph source: Waveforms for Series AC Circuits

Referenced app allows you to explore different waveforms for different series circuits.

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