Power management of variable capacitors in electrical grid systems according to the criterion of mini-mum energy loss

The aim is to manage the transmitted reactive power in electrical grids using variable capacitor batteries according to the criterion of minimum energy loss under different annual reactive load schedules and different numbers of variable capacitor sections. The main theoretical relations were obtained by the methods of mathematical modelling and integral calculus using the theory of optimal control. The influence of the power and number of sections in a capacitor battery on energy losses in the grid was estimated using computational experiments. Dependencies for energy losses in a capacitor battery, as well as for reducing energy losses in the grid, were obtained. These expressions are valid for linearized load schedules. It is shown that the dependences of energy losses in a capacitor battery and the reduction of losses in the grid on the section power have inflection points and pass through a maximum. The presence of inflection points is associated with a change in the number of capacitor sections operating throughout the year. The presence of a maximum is explained by the fact that, with an increase in the power of the capacitor battery, its operating time decreases under the complete number of variable sections. It is established that the batteries of static capacitors with two variable sections can reduce energy losses when transmitting reactive power by over 90%. For three- and four-section static capacitors, the loss reduction is close to 100%. The reduction in energy losses increases when approaching maximal levels of annual reactive load. Energy losses in electrical grid systems can be reduced by capacitor batteries with no more than three or four variable sections. In most cases, this can be achieved by two-section capacitor batteries.

Integration of a soft dielectric composite into a cantilever beam for mechanical energy harvesting, comparison between capacitive and triboelectric transducers

Flexible dielectrics that harvest mechanical energy via electrostatic effects are excellent candidates as power sources for wearable electronics or autonomous sensors. The integration of a soft dielectric composite (polydimethylsiloxane PDMS-carbon black CB) into two mechanical energy harvesters is here presented. Both are based on a similar cantilever beam but work on different harvesting principles: variable capacitor and triboelectricity. We show that without an external bias the triboelectric beam harvests a net density power of 0.3 $$\upmu \mathrm{W}/{\mathrm{cm}}^{2}$$ μ W / cm 2 under a sinusoidal acceleration of 3.9g at 40 Hz. In a variable capacitor configuration, a bias of 0.15 $$\mathrm{V}/\upmu \mathrm{m}$$ V / μ m is required to get the same energy harvesting performance under the same working conditions. As variable capacitors’ harvesting performance are quadratically dependent on the applied bias, increasing the bias allows the system to harvest energy much more efficiently than the triboelectric one. The present results make CB/PDMS composites promising for autonomous portable multifunctional systems and intelligent sensors.