Transformer load losses cause various adverse effects, such as derating, a decreased lifetime, and greenhouse gas emissions. In this paper, the load losses caused by non-linear loads on distribution transformers are analyzed. For this study, the load loss expressions provided by the IEEE Standard C57.110 and ANSI/UL 1561-1562 were adapted to the usual case where the transformer currents differ in each phase. The novel load loss expressions adapted from the IEEE Standard C57.110 were applied using the software known as the “Transformer Loss Calculator” (TLC), implemented with LabVIEW. For the application of new load loss expressions, carbon dioxide (CO₂) emissions were determined by multiplying the load losses by the emission factors of each country. The experimental results are based on the recordings made by a FLUKE 435 Series II analyzer on the second of two 1000 kVA transformers, feeding real residential distribution networks with very differently distorted loads. An analysis of these transformers shows that the annual energy losses and CO₂ emissions obtained from the adapted load loss expressions could be more than 5% of those determined by the original IEEE and ANSI Standard expressions. Due to these percentage loss and emission differences, it is advisable to use the TLC software in transformer monitoring instruments.

Reactive power is a very important quantity in electric power systems since it affects the efficiency of these systems. Also, capacitive loads can produce over-voltages in electric transformers by Ferranti effect, which produces bad power quality, so it is necessary to measure the reactive power correctly. In this paper reactive phenomena in three-phase power systems with unbalanced voltages are expressed and measured in the light of the IEEE Std 1459-2000. For analyzing the reactive phenomena the positive-sequence fundamental frequency instantaneous reactive power is used. By comparing the expressions of this instantaneous power in three-phase systems with unbalanced voltages with those corresponding to balanced voltages, the reactive phenomenon due to the unbalances is obtained by separating of the traditional reactive power yield by the reactive loads in electric power systems. These reactive phenomena in three-phase power systems are formulated in the same way as Steinmetz defined reactive power in single-phase systems, by adding the amplitudes of each phase of its respective instantaneous reactive power. In the paper, this new formulation of the reactive phenomena has been applied on actual industrial and urban electric installations to obtain values of these reactive powers. Data registered express the following conclusions: a) reactive power is divided into two components: due to the reactive loads and caused by the unbalances, b) both reactive components can be inductive or capacitive quantities and, therefore, can be added or compensated, c) reactive power caused by the unbalances can exist even though in resistive systems, when there are unbalances at sources and at loads in the same time and, generally, when there is not any symmetry in the system.

Similarly to how Steinmetz developed his theory of alternating current in single-phase sinusoidal systems, a few formal relationships between expressions of the instantaneous and Buchholz’s apparent power in three-phase systems were identified in this paper. Based on these relationships, a methodology to express Buchholz’s apparent power and its components in any three-phase, wye-configured system—sinusoidal or non-sinusoidal, balanced or unbalanced—through instantaneous power expressions was established. The application of the proposed method to the entire system allowed the determination of a novel quantity referred to as neutral-displacement power, which measured the impacts of the phenomena caused by the neutral path operation on the values of the source and load apparent power. These impacts were analyzed using a real-world urban installation with a neutral conductor deterioration simulation via an Excel platform as an application example.

This paper describes constitution, design and operation of a passive unbalance compensator for variable loads in three-phase industrial installations. Compensator is integrated by three-phase connections of variable coils and capacitors. Values of those elements, and thus unbalance power delivered by the compensator, can be changed by switches commanded by an electronic control circuit. An important compensator design parameter introduced in this paper is the “power of the unbalance step” since it defines composition and values of the elements of the “unbalance step”, which is the basic three-phase connection of inductances and capacitances in the compensator. Because unbalances in power systems are caused by active and reactive loads, two unbalance steps have been defined: active and reactive; however, power of the unbalance compensator does not depend on the total active and reactive powers, but the differences between their values in each phase of the load.