## 1 Introduction
Thus, the main novelty of this paper is to define the power expressions that measure the effects of the neutral displacement phenomenon and apply them to the power measurement area. These powers are defined in this paper under the consideration that the neutral-point displacement is able to manifest energies, not only voltages, in powers systems, which were identified in specific components of the source and load instantaneous powers as a result of applying the conservation of energy principle to a three-phase star-configured power system, as described in Section 2 of this paper. The effects of the energies caused by the neutral displacement phenomenon were eliminated in the pass by many commercial power analyzers, using the line-to-line voltages instead of the line-to-neutral (or line-to-earth) voltages in the measurement of the apparent powers, in order to avoid variations derived from the voltage reference point. In our opinion, this solution engenders errors on the values of the apparent powers. Fortunately, this solution is not currently used by the main commercial instrumentation manufacturers, which allow the users to select the point of voltage reference, even including grounded points. Thus, in Section 3, we examined the effects of the neutral displacement phenomenon on the values of the apparent powers of star-configured sources and loads using a proposed power that we refer to as the neutral-displacement power (\(S_{n}\)). In the present work, the square of the neutral-displacement power is defined for each part of a three-phase power system as the difference between the squares of the apparent powers of that part of the system measured using two different voltage reference points. This definition was used to derive expressions of the neutral-displacement power and its components using the well-known power formulation approach proposed by [PERSON] [20], which is the base of a few commercial power analyzers. Hence, the explanation of the different values of apparent powers measured by the power analyzers depending on the selected point of voltage reference can be considered as an application of the neutral displacement phenomenon. Although the proposed power is used in a granted patent [21] and the neutral-point displacement voltage is a well-known phenomenon, the neutral-displacement power is not included in any standard [3; 22; 23] and it is not established by major approaches such as those described in References [24; 25; 26; 27; 28; 29]. The derived neutral-displacement power expressions were experimentally verified in a laboratory and using an actual installation of an electric company, as described in Section 4. The experiments were carried out using the commercial power analyzer Fluke 437 Series II and our prototype power analyzer SIMPELEC [30], which measures the apparent power according to the [PERSON] approach, as well as the proposed neutral-displacement power, more recently incorporated. The conclusions drawn from the present study are finally presented in Section 5. Power Phenomenon Associated with the Voltage Reference Point in a Three-Phase Star-Configured System  
This section demonstrates how the phenomenon of the displacement of the neutral point manifests energies in the power systems, which are finally responsible for the variation of the measured apparent power of a given part of a power system with the voltage reference point.