TRAFOFLEX - advanced concept of efficient use of transformers leveraging the DTR technology

The Slovenian low-voltage distribution grid is facing a rapid peak load growth, mainly due to the massive transition to electric heating and the increasing integration of electric vehicle charging infrastructure. The pace of emerging problems – given the massive integration of renewables - is greater than the ability of the DSOs to reinforce the grid. That’s why it’s important to utilize the existing distribution power system infrastructure as much as possible. Dynamic Thermal Rating (DTR) technology, together with the utilization of flexibility, can gain an extra load band while leaving operational safety intact. DTR is a power system operation concept aiming at maximizing utilization of the equipment (power lines, transformers) when weather conditions allow it, without compromising the safety of operation and without a negative impact on the life expectancy of the equipment.

TR calculation concept for distribution transformers (left). Temperature measurements of pylon mounted Kolektor-Etra transformer (right).

Power transformers are designed to operate throughout their lifetime at pre-defined ambient conditions in line with international standard requirements. At 40 °C ambient temperature and nominal loading, a typical actual transformer’s loading capability, or shorter - loadability, can be considered a static value, as defined on the naming plate. If the transformer is cooled down due to cooler ambient conditions (e.g., during colder seasonal periods) or during periods when loading is below the nominal, transformer operation above rated power is possible without exceeding the specified temperature limits and without compromising the transformer’s operational reliability and normal life expectancy.

Our job was to devise a physical model that adequately describe thermal state of the transformer, implement its numerical solution and deploy the model in operational use. Conventional models described in standards and their further developments attempt to capture the entirety of non-linear heat transfer dynamics with a single exponent parameter. This is a reasonable approach for modelling a wide spectrum of transformers with the simplest applicable model and a set of predetermined parameters. Our ambitions of simulating various types of transformer enclosures with generalized parameters force us to take a more granular approach and separately account for each physical mechanism of heat transfer. We construct a general multi-mass model that allows us to simulate heat transfer between N sequential bodies using different mechanisms of heat generation/transfer. We settled on the model shown with two inner mass bodies for the transformer and an outer mass body for the enclosure. The latter is not included when simulating pole-mounted transformers.

A schematic representation of the multi-mass model used to simulate the enclosed transformers.

We implemented numerical solution of the model in C++ for compatibility with the DSO’s backend system. Optimization and analysis were performed in Python through bindings for the C++ backend. Due to weather data availability limitations, we only use the modelled terms that rely on measured temperature. The ambient temperature is measured outside the transformer enclosure and used as input for our model. We minimize the mean average error between the modelled and measured top liquid and internal enclosure temperatures with Powell minimization method. Due to the high number of parameters and the model’s nonlinearity, we are presented with a difficult optimization problem that has many local minima. This problem is resolved by using a stochastic approach to minimization where we use the known relations between physical characteristics and parameter values to determine reasonable boundary values that we then use to randomly generate initial values for the optimization method. The spectra of thus obtained optimization results are then analysed to determine when enough runs have been performed to be reasonably certain that we found or are at least close to the global minimum.