Blondel’s Theorem

Blondel’s Theorem is used to help meter technicians decide what type of metering installation is needed to meter a particular service. So, what does Blondel’s Theorem say and what does it do for us.

What Does Blondel’s Theorem Say?

Blondel’s Theorem really is more simple than many people think. Blondel figured out what was needed to accurately meter different types of services. Blondel’s Theorem basically says that you need one less element in your watthour meter than the number of wires in the service to accurately meter the service.

Blondel’s Theorem states that in an electrical system of N conductors (wires), accurate power or energy measurement requires at least N-1 meter elements (stators), provided all voltage coils are connected to a common reference conductor.

N-1 Formula

• N = number of conductors in service
• N – 1 = number of elements required
• 1 element contains 1 potential coil and 1 current coil

What does that mean?

That is all well and good, but what does it mean? Inside the watthour meters are stators, or elements. In this case we interchange the two. A stator inside the watthour meter is made up of one current coil and one voltage coil. So for example, to meter a single phase two-wire service accurately according to Blondel’s Theorem we would need a watthour meter with one stator because we have two wires. This meter is referred to as a 1s meter.

Putting Blondel’s Theorem into Practice

Let’s say that we now want to meter a three-phase, three-wire service typically referred to as a three-wire delta service. What would we need to use? According to Blondel’s Theorem we would need go down our list of meter forms and find out that we need to use a form 5s meter which has two elements in it.

Understanding Blondel’s Theorem using CTs

I think that now you have the idea. But I think it is actually easier to explain with CT’s. Let’s restate Blondel’s Theorem and instead of saying elements let’s say CT’s. So, to accurately meter a particular service we need to make sure that we have one less CT than the number of wires in the service. For example, let’s say that we have a Form 9s meter installed on a three-phase, 4-wire wye service. How many CT’s will we need? If you came up with three then you are correct.

Non-Blondel Compliant Meters

Now, I do want to post a disclaimer here and the reason is that there are non Blondel compliant meters and metering installations out there. The thing that we have to remember when we see these things is that Blondel’s Theorem is just that, a theorem and it is possible to meter services accurately without complying to Blondel’s Theorem. However, it is my opinion that it is much easier to attempt to use Blondel’s Theorem in your system and have uniformity across all of your installations than to say that you figured out a way that it would work without it. When Blondel calculated his theorem I bet he did not have metering for Electric Vehicles (EVs) in mind!

The most common example of a intentionally non-compliant setup is the standard Form 2S single-phase meter used on residential 3-wire service 120/240V. A single-phase 3-wire service has 3 conductors (Line 1, Line 2, and Neutral). According to Blondel’s Theorem, N-1, a strictly compliant measurement requires 2 full elements—meaning 2 separate potential coils and 2 separate current coils. However, Form 2S meters utilize a single potential coil connected across the 240V hot legs alongside 2 current coils (or a split coil). Because the meter measures voltage only across Line 1 to Line 2, it relies on the assumption that the line-to-neutral voltages are perfectly balanced at 120V each.

If line-to-neutral voltages become unbalanced due to heavy single-pole loads, the meter’s internal voltage reference no longer reflects true line-to-neutral conditions, resulting in minor metering errors. Despite violating Blondel, utilities widely accept the Form 2S because the cost savings of manufacturing a single potential coil meter far outweigh the negligible energy registration errors in balanced residential settings. This, however, is starting to change in the industry as utilities and meter manufacturers, along with ANSI committees, are making a push towards Blondel compliant meter forms, like the Form 12S meter.

Other classic examples of non-compliant meters include “2.5-element” forms, such as the Form 6S (socket) and Form 14S (self-contained) used on 3-phase 4-wire Wye services. A 4-wire Wye system has 4 conductors (A, B, C phases, plus Neutral), requiring 3 full elements N-1 = 3, as seen in a Form 9S or 16S meter for 100% mathematical accuracy under all conditions. A 2.5-element meter cuts hardware costs by using only 2 potential coils instead of 3, relying on delta-connected potential windings and shared current coils to approximate the third phase.

While a 2.5-element meter registers accurately when system voltages are perfectly symmetrical, any phase voltage unbalance causes the meter to over- or under-register total energy consumption. Today, while legacy 2.5-element meters remain in the field, modern solid-state metering setups almost universally opt for full 3-element (Form 9S/16S) configurations to ensure absolute Blondel compliance and eliminate voltage unbalance errors on high-revenue commercial and industrial customers.

If you want to learn about another more advanced topic, visit Hall Effect.

Phasors and Blondel’s Theorem

Blondel’s Theorem and the concept of phasors are closely intertwined in the realm of electrical metering, as both are essential for understanding and designing accurate metering systems. Blondel’s Theorem provides the foundational rule for determining the number of elements or CTs required to meter a service accurately. Phasors, on the other hand, enable the precise representation and analysis of the voltage and current waveforms within these services. Together, they ensure that metering devices accurately measure not just the magnitude of electrical quantities but also their phase relationships, which is crucial for effective energy management.

For instance, phasor diagrams are a valuable tool for visualizing the angular relationships between voltage and current in a system. These relationships directly influence how metering devices, designed according to Blondel’s Theorem, operate. Understanding phasors allows technicians to troubleshoot metering installations more effectively by identifying issues such as incorrect wiring or phase imbalances. By mastering both concepts, technicians and engineers can ensure that metering systems provide the accuracy and reliability needed for modern energy management and billing.

Curious about how phasors simplify the complex world of AC circuits and power measurement? Meter technicians rely on this essential knowledge to enhance their skills—don’t miss out! Click here to uncover the key to mastering phasor diagrams today.

Quick Reference Table

Conclusion

Blondel’s Theorem is a cornerstone of accurate and efficient metering in the electrical industry. By understanding its principles, technicians can determine the correct metering installation for any service, ensuring precision and uniformity. When combined with the knowledge of phasors and their role in AC systems, Blondel’s Theorem becomes even more powerful, enabling technicians to address complex challenges in energy measurement and management like understanding demand metering. Whether you’re troubleshooting a system or designing a new installation, mastering these concepts is essential for success in modern metering applications.