Quote of the Day

In my many years I have come to a conclusion that one useless man is a shame, two is a law firm, and three or more is a congress.

— John Adams

## Introduction

A salesman called today and asked how to estimate the cost of running an ONT for a year. This post documents how I answered his question.

## Background

### Power Conversion Setup

Figure 1 shows how the power conversion for this particular ONT is performed. There actually are two power conversion stages involved: (1) 120 V AC to -48 V, and (2) -48 V to 12 V. Two conversion stages were required because no off-the-shelf, 12 V UPS exists that had sufficient battery capacity to meet the customer's backup time requirements. However, a -48 V UPS is available with a large enough battery to meet their needs. This type of problem is common in real-world deployments.

### Power Costs

Figure 2 shows how power costs vary around the United States. Most customers know how much they pay for power, but the map makes it easy to see how ONT operating costs vary around the country. I explained how this map is created in this blog post.

The salesman who asked the question on power costs really liked this chart.

### Power Cost Model

Equation 1 shows the formula that relates load power to the power drawn from the AC power system.

Eq. 1 |

where

*η*is the efficiency of the 120 V_{1}_{AC}to -48 V_{DC}conversion (80%).*η*is the efficiency of the -48 V_{2}_{DC}to 12 V_{DC}conversion (85%).*P*is the power drawn from a 120 V_{AC}_{RMS}AC outlet ( W ).*P*is power drawn by the 12 V load, which in this case is an optical network terminal that uses 50 W._{Load}*N*is the number of hours per year.

The annual operating cost of an ONT is determined by the amount of energy drawn from the AC power system. Equation 2 allows us to compute the cost of running an ONT for one year.

Eq. 2 |

where

*λ*is the cost of a kilowatt-hour of electrical energy (kW-hr)*C*is the yearly cost, which is what our customer wants to know.

Equation 2 contains the variable *P _{AC}*, whose value I do not know because it depends on the efficiency of the power conversion process. However, I can find out the efficiencies of the power converters from their manufacturers. I can then use these efficiencies and

*P*to compute

_{Load}*P*.

_{AC}Specifically, I can solve Equation 1 for *P _{AC}* and substitute the result into Equation 2, which give Equation 3. I now have an expression for the annual operating cost and I know all the value of all the variables.

Eq. 3 |

## Analysis

Figure 3 shows my calculations using Equation 3.

## Conclusion

This post illustrates how to estimate the cost of running a piece of network gear. Calculations like these are done every day by network service providers.

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