# How Should Measurement Uncertainties Be Expressed in a Smart Grid Scenario?

- Details
- Written by Lorenzo Peretto, Mihaela Albu and Alessandro Ferrero

*The estimation of measurement uncertainties in power flow analysis is not merely a challenging and interesting theoretical problem; it has important consequences for power system stability. Depending on which standardized procedures are followed, estimation of combined uncertainties can vary by a factor of almost two.*

When the inaugural workshop on Applied Measurements for Power Systems was held last fall in Aachen, Germany, two critically important problems immediately surfaced: disagreement about how power grid measurement uncertainties are best expressed and what procedures need to be adopted to assure stability on the grid.

The workshop, held at the E.ON Energy Research Center of RWTH Aachen University and organized by a section of IEEE's Instrumentation and Measurement Society, reviewed the most recent findings about sensors, instrumentation and measurement methods in power systems, with a view toward highlighting present-day issues. It brought together in the main people from industry and academia.

Specific topics included power system monitoring, current transducers, state estimation, measurement methods and power electronics. But the subject that most engaged the audience was the expression of uncertainty in the power flow analysis, especially when the quantities described from the measurements are used in control algorithms as well as for billing purposes.

This topic is closely related to what is known in the business as "legal metrology"—that is, the rules established by power system regulators for measurement of grid dynamics. It is an essential subject for working power engineers to understand, encompassing how to apply correct methods to account for the uncertainty contributed by each element of a measurement system; how to combine the contributions due to all sources; how to propagate those contributions through the measurement algorithms; how to define the "target uncertainty" before performing any given measurement; and how to select the proper instrumentation for reaching the defined goal.

All standards pertinent to the power engineering area must contain terms and procedures relevant to uncertainty that are mutually consistent and in agreement with reference standards in this field. For example, the IEC's 61000-4-30, "Electromagnetic Compatibility—Testing and Measurement Techniques, Power Quality Measurement Methods," defines the measurement uncertainty affecting a measurement result as the maximum expected deviation of a measured value from its actual value.

But the standard ISO/IEC Guide 98-3, "Uncertainty of Measurement—Part 3: Guide to the Expression of Uncertainty in Measurement," has a definition of uncertainty that is significantly different from that given in the IEC 61000-4-30. Most notably, it distinguishes between "uncertainty" and "error."

In ISO/IEC Guide 98-3, a measurement error is defined as a measurement "minus a true value of the measurand." Given that the true value of a measurand cannot be known, a conventional value of a measurand is assumed in the definition. Furthermore, "uncertainty of measurement" is defined as a parameter associated with the result of a measurement, which characterizes the dispersion of the values that could reasonably be attributed to the measurand. It is stated that this definition must not be inconsistent with other definitions, like an estimate characterizing the range of values within which the true value of a measurand lies.

ISO/IEC 98-3, however, relies on the earlier definition representing measurement uncertainty by the standard deviation of a random variable associated with the measurement results. This implies that uncertainty expresses an interval around a central value in which the measurand value can fall within a given probability. This probabilistic approach is not considered in the IEC 61000-4-30. So while the uncertainty is treated as a deterministic parameter in IEC 61000-4-30, in IOS/IEC 98-3, it is defined as a confidence interval.

Moreover, in ISO/IEC 98-3, uncertainty is given by the standard deviation of the random variable representing the measured value or multiples of it. From all this, it can be inferred that if measurement uncertainty is evaluated according to the ISO/IEC standard, it will be assigned completely different values than those obtained if the IEC 61000-4-30 definition is applied.

To take an example, if a rectangular distribution is assumed for the random variable representing the measurement result, the difference in quantitative terms between the values of uncertainty according to the two definitions above is equal to the sqrt(3). This means that the uncertainty as defined in the IEC 61000-4-30 is roughly 1.7 times the uncertainty evaluated according to ISO/IEC 98- 3. In other words, the IEC 61000-4-30 uncertainty is 70 percent larger!

The discussion initiated during the panel session at AMPS 2010 has certainly raised a very important, unresolved issue that could easily sew confusion and even misunderstandings among people involved in both control systems and legal metrology. The above example comparing definitions between two standards highlights a general problem that arises when more than one standard employs the same terms and definitions.

In electric power, if different definitions are used to evaluate the error or uncertainty in measurements, then how are the calibration results of power or energy meters to be expressed? How do we certify that a Power Measurement Unit (PMU) is working within its rated accuracy? Moreover, how do we calibrate potential and current sensors for measurements and even billing purposes?

If a product manufacturer brings a measurement device to a test laboratory to obtain certification—and if that laboratory relies, per regulation, on the ISO/IEC 98-3 definition of uncertainty—then the vendor might find later on that it cannot sell its device because the power company or utility that wants to buy it refers to a different standard with a different definition of uncertainty. The manufacturer or vendor would have to test its device again, losing money and lengthening the time-to-market for that device.

So how do we get beyond this impasse? The expression of uncertainty is a critical topic in many applications in smart grids, where utilities with distributed generation in their networks require that power flowing in the network is monitored with accuracy for a faster and correct state estimation or control. A uniformity and harmonization between different standards is becoming ever more urgent and mandatory. The risk is that in a few years we could experience a new Tower of Babel, with a multiplicity of mutually unintelligible standards.