Sunday, August 14, 2011

Maximum Demand Tariff and its relationship with power factor and load factor

In this write-up, I summarize my findings of energy billing in Hong Kong and its relationship with Maximum Demand, Power Factor and Loading.

There are only 2 power utilities company in Hong Kong:

  • Hong Kong Electric (HKE)
  • China Light and Power (CLP)
They each have their own monopoly in their respective area. HKE takes Hong Kong Island, and CLP gets the Kowloon Peninsula, Lantau Islands the Northern Territories.
Image courtesy of CLP Power
Below are links to HKE and CLP's commercial and industrial tariffs 
HKE and CLP both provide this concept of "Maximum Demand Tariff" or MDT which has the potential to lower energy cost for high energy consumer. In the investigation summarized below, I focused on HKE because they provide a simpler MDT scheme (not necessary cheaper or better).

Hong Kong Electric provides an excellent explanation on how a customer will be billed if they opted for the "Maximum Demand Tariff"

As their example showed, opting for the Maximum Demand Tariff may not be beneficial for all customer. As HKE has pointed out on their website:
Maximum Demand Tariff consists of two parts, i.e. demand charge and energy charge. The demand charge is based on the maximum demand in kVA, while the energy charge depends on the energy consumption in Unit (kWh) of the month. Tariff charges are subject to a minimum of 100 kVA of the chargeable demand.
Maximum Demand Tariff is only beneficial to electrical installations with a high load factor. This applies to accounts of considerably high electricity consumption over a long period of time with a steady load. If these conditions are not satisfied, it is possible that the electricity charge could be higher under Maximum Demand Tariff than Commercial, Industrial & Miscellaneous Tariff.
Looking into the concept of Maximum Demand and the calculations, it will be most beneficial to customers with a more constant load over time and a high power factor. This is because the maximum demand charge, at least in the HKE's case, is calculated using the peak average apparent power in a 30 minutes period within the billing period (1 month).  

The observation where a customer with a more constant load will benefit by using the Maximum Demand Tariff billing method is pretty straightforward.  Since the peak usage is close to the average energy usage, the demand charge will be small relative to the energy charge.

Power factor plays a role in the calculation is due to the fact that Demand Charge in the "Maximum Demand Tariff" is measured in VA (Apparent Power) vs. W (Real Power) as in Energy Charge.

I did some Goolging around trying to look for the formula which HKE use to calculate their "Maximum Demand Tariff", but was unable to find it (Anyone with that information please drop me a note!).  I did some analyzing of HKE's Comparison Between Maximum Demand Tariff and Commercial, Industrial & Miscellaneous Tariff and played around a bit with their Maximum Demand Tariff Calculator, I deduced/guesstimate the billing formula/logic to be something like this:
maxdemand = consumption/1440/lf/pf

demandcharge = maxdemand * 44.2
if (maxdemand > 400) then
	demandcharge = 400*44.2 + (maxdemand - 400)*43.2
end

basiccharge = consumption * 0.861
if (maxdemand*200 < consumption) then
	basiccharge = (maxdemand*200)*0.861 + (consumption-maxdemand*200)*0.801
end

fueladj = consumption * 0.302

mdt = demandcharge + basiccharge + fueladj
Using the above function, I was able to plot a graph to visualized the costing under the maximum demand tariff billing method against the power factor and "load factor".
I define the loading factor as the following:
Maximum Demand = Consumption / 1440 / Load Factor / Power Factor
Load Factor is a ratio (unit-less) number between 0 and 1 which indicates how "well" distributed the load is across time.  
  • A load factor of 1 indicates the power consumption is perfectly constant across time (at least all 30 minutes sample frame consume the same amount of energy during the billing period)
  • A load factor of 0 indicates all power within the billing period is consume in 30 minutes time frame which the maximum demand is calculated
Here I plot a graph of the above formula in scilab for the power factor range 0.5-1.0, load factor 0.1-0.3 and power consumption at 120,000 kWh

I chose the range and values above to ensure the HKE's maximum demand tariff calculation examples were included in the plot. The two example are:
  • MDT = HK$153,716.00 where load factor ~= 0.21929824..., power factor = 1
  • MDT = HK$163,120.00 where load factor ~= 0.15151515..., power factor = 1
If we also make the assumption which typical loading factor is around 0.1 - 0.3 range, from the above plot we can see that we can reduce the energy consumption bill under the MDT scheme by:
  • Improving the load factor: spreading the load across time especially during peak energy consumption
  • Improving the power factor of the loading during the maximum demand period.
For the next step, it is probably worth quantifying the cost of improving the power factor of the entire loading of the energy consumer vs shifting loads from peak time to other times. Combined with the information in this post, we will be able to calculate the ROI on projects aimed at improving either the load factor and/or power factor.