We've found that many people struggle to understand how Power Factor (PF) impacts demand charges. Frequently, end use customers pay a significant premium each month in demand charges because their PF is below a threshold set by the utility in the rate tariff. Oftentimes its not obvious to the untrained eye when there are extra charges associated with a bad PF on the customer bill. In this blog post, we are going to walk through PF and hopefully make it more understandable to the average commercial and industrial consumer.

First, what is PF? We've heard all kinds of analogies that sort of make sense (e.g., head on the beer, raised wheelbarrow, etc.), but most people just sort of accept that PF exists and over thinking it is just too much work. PF is a dimensionless number, often expressed as a percentage, that reflects the relationship between kilowatts (kW) and kilovolt-amperes (kVA). A PF of one (sometimes referred to as unity) reflects a perfect PF where kW and kVA are equal. Many people find it helpful to disaggregate kW and kVA into their building block components to better understand them. We've done this below.

**k = **abbreviation for 1,000. 1 kW = 1,000 Watts

1 Watt = 1 Joule / sec. - (this is a measure of work done, referred to as Real Power) **A = Ampere - (1 Coloumbe per second, this is a measure of electric current)**

**V = Volt - (difference in electric potential across a wire found by A * Ω where Ω is resistance in ohms)**

**Volt-Ampere (VA) = Apparent Power -**(This is the total power supplied to the circuit. It's found by multiplying together the Root Mean Squares (RMS) of the voltage and the current. Since AC power is sinusoidal, it can also be found with this equation, VA = (

**V**peak/√2) * (

**I**peak/√2), but the best way to explain this concept is visually.

On AC systems, both the current and voltage are sinusoidal. If loads are reactive, then voltage and current will be out of phase and the Apparent Power (S) will need to be greater to accomplish the same work (in Watts) as a non-reactive load. The graphic above shows this clearly. The hypotenuse shows the total Apparent Power (S) given a certain combination of real (P) and reactive power (Q). The bottom side of the triangle shows the amount of power (P) available to do Work which decreases as reactive power (Q) increases. If Q was zero, then S and P in the triangle would be equal to each other and the PF would be 1. The cosine of the interior angle in this triangle will give you the PF since the cosine of an angle is equal to the length of the adjacent side divided by the hypotenuse (remember SOH, CAH, TOA from high school geometry?). To put this triangle in real world terms, think of a reactive load like an old heavy-duty electric motor that is just starting up. The motor will dissipate a lot of energy as heat while getting up to speed and the energy dissipated as heat won't result in actual Work (in Watts). This energy lost as heat represents the reactive power (Q). The real power (P) is the kinetic energy that the motor is able to impart to do Work. The apparent power (S) is the total power that must be delivered and is determined based on the amount of the useful real power (P) and the reactive power (Q) that is lost as heat.

We've found that the water analogy is often a good way to explain electricity concepts to non-technical people. In thinking about reactive loads, the water wheel is probably the best illustration of the concept. Like an old heavy-duty motor, a water wheel requires a lot of energy to get going but once its moving at the same speed as the current it requires much less energy to maintain. Customer commonly ask what they can do about reactive loads and associated demand charge penalties. The answer is "it depends", but it could involve any of the following: replace the offending equipment with more modern equipment; institute behavioral changes so reactive loads are used during off-peak hours; or install capacitors. Some utilities will even help subsidize the cost of capacitors for customers with very reactive loads. The graphic below explains a bit more about inductors and capacitors.

Now that we've fully explained PF and reactive loads, its time to talk about money and why we should care about this stuff. There are many utilities out there that charge commercial and industrial customers a penalty for having a poor PF. Anytime you see demand charges billed in units of kVA, you should know that PF is baked into the demand charge and any drop in PF below 1 results in additional billed units of demand. The graphic to the right shows a bill from Connecticut Light and Power (CL&P). In the CL&P service territory, demand is billed in kVA for large commercial and industrial customers.

Some utilities are more subtle in how they penalize customers for a poor PF. NStar's Boston Edison tariff is a great example of this. The excerpt from the tariff for the B7 commercial/industrial rate shown below illustrates how this rate charges customers the greater of their demand in kW or 90% of their kVA demand. In essence, this results in additional demand charges for all customers with a PF of less than 90%. A customer with a PF of 85% and a peak demand of (850 kW / 1,000 kVA) would pay for 900 kVA of demand, or 50 extra units of demand relative to a customer with a PF of 90% or better. For customers in areas where demand charges are high, extra units of billed demand can result in significant costs. The good thing is that most utilities draw the line around 90% PF so to make excess charges due to poor PF go away, you don't have to be perfect, just better than 90%.

West Penn Power (a First Energy Company) provides another example of how utilities bill customers for low PF. The excerpts from the tariff below show that the utility charges for units of reactive demand which are measured in kVars. Charges for kVars don't kick in until the measured reactive demand exceeds 35% of the kW demand. Excess reactive demand, in kVars, is charged to the customer at a rate of $0.40/kVar for all kVars greater than 35% of the kW demand. This type of billing structure is hard to follow, but customers with a good PF typically won't have reactive demands high enough to trigger these charges. Its a bit more convoluted than the NStar example shown above, but has the same effect of charging a penalty to customers with low PFs.

This stuff can be complicated, if you are struggling to understand a PF billing issue, call us. We can probably help.