Load capability estimation of dry-type transformers used in PV-systems by employing field measurements

Abstract

Transformer insulation aging is a critical issue for both reliable and economic operations, and for planning of electrical systems. As insulation aging depends on the hottest-spot temperature, transformer management can be improved with a suitable model for temperature estimation and prediction. However, the temperature inside transformers varies dynamically because of changes in both the cooling conditions and the load cycles. Hence, this paper presents an algorithm to estimate and predict the hottest-spot in dry-type distribution transformers, so that their capability and insulation life can be assessed. This procedure is focused on transformers used to directly connect PV-inverters to the grid in order to consider the uncontrolled power generation of distribution PV-systems. To implement the algorithm, it is assumed that records of ambient temperature, PV-system power generation cycle and winding temperature are available. With these data, the parameters of an equivalent thermal circuit are fitted in order to dynamically model the transformer hottest-spot. The method was validated using twelve-day records of a $70\,\hbox { kW}_{\mathrm{p}}$ PV-generation system connected to a ${75}\,\hbox {kVA}$ dry-type transformer. Results show that an enhancement in the hot-spot estimation is reached, and an assessment of the performance in real-time monitoring of the transformer capacity is achieved employing the proposed algorithm.

Appendix

In order to implement the proposed EKF, the following set of equations were derived, where the subscript R is related to the rated condition.

$$\begin{aligned}&\frac{\mathrm{d}\varTheta _{\mathrm{HS}}}{\mathrm{d}t} = \frac{n \left( P_{\mathrm{C}}+L^2 \left( P_{i^2 R,R} K_T+\frac{P_{\mathrm{eddy},R}}{K_T}\right) -\frac{\varTheta _{\mathrm{HS}}-\varTheta _{a}}{R_{0,R} \left( \frac{\rho \left( \varTheta _{\mathrm{HS}}\right) }{\rho \left( \varTheta _{\mathrm{HS},R}\right) } \right) ^{m}}\right) }{m_p C_{p}} \end{aligned}$$

(8)

$$\begin{aligned}&\frac{\mathrm{d} f}{\mathrm{d}\varTheta _{\mathrm{HS}}} = \frac{n}{m_p C_{p}} \left( L^2 \left( \frac{P_{i^2 R,R}}{T_k+\varTheta _{\mathrm{HS},R}} -\frac{P_{\mathrm{eddy},R}}{K_T \left( T_k+\varTheta _{\mathrm{HS}} \right) }\right) \nonumber \right. \\&\quad \left. -\frac{1}{R_{0,R} \left( \frac{\rho \left( \varTheta _{\mathrm{HS}}\right) }{\rho \left( \varTheta _{\mathrm{HS},R}\right) } \right) ^{m}}\right. \nonumber \\&\quad +\left. \frac{m\left( \varTheta _{\mathrm{HS}}-\varTheta _{a}\right) \left( 1.07\cdot 10^{-5}\varTheta _{\mathrm{HS}}-3.78\cdot 10^{-3}\right) }{ \rho \left( \varTheta _{\mathrm{HS}}\right) R_{0,R} \left( \frac{\rho \left( \varTheta _{\mathrm{HS}}\right) }{\rho \left( \varTheta _{\mathrm{HS},R}\right) } \right) ^{m}}\right) \end{aligned}$$

(9)

$$\begin{aligned}&\frac{\mathrm{d} f}{\mathrm{d}n} = \frac{P_{\mathrm{C}}+L^2 \left( P_{i^2 R,R} K_T+\frac{P_{\mathrm{eddy},R}}{K_T}\right) -\frac{\varTheta _{\mathrm{HS}}-\varTheta _{a}}{ R_{0,R} \left( \frac{\rho \left( \varTheta _{\mathrm{HS}}\right) }{\rho \left( \varTheta _{\mathrm{HS},R}\right) } \right) ^{m}}}{m_p C_{p}} \end{aligned}$$

(10)

$$\begin{aligned}&\frac{\mathrm{d} f}{\mathrm{d}m} = \frac{\left( \varTheta _{\mathrm{HS}}-\varTheta _{a}\right) n \ln \left( \frac{\rho \left( \varTheta _{\mathrm{HS}}\right) }{\rho \left( \varTheta _{\mathrm{HS},R}\right) } \right) }{R_{0,R} \left( \frac{\rho \left( \varTheta _{\mathrm{HS}}\right) }{\rho \left( \varTheta _{\mathrm{HS},R}\right) } \right) ^{m} m_p C_{p}} \end{aligned}$$

(11)

$$\begin{aligned}&\frac{\mathrm{d} f}{\mathrm{d}L} = \frac{n 2L \left( P_{i^2 R,R} K_T+\frac{P_{\mathrm{eddy},R}}{K_T}\right) }{R_{0,R} \left( \frac{\rho \left( \varTheta _{\mathrm{HS}}\right) }{\rho \left( \varTheta _{\mathrm{HS},R}\right) } \right) ^{m}m_p C_{p}} \end{aligned}$$

(12)

$$\begin{aligned}&\frac{\mathrm{d} f}{\mathrm{d} \varTheta _a} = \frac{n}{R_{0,R} \left( \frac{\rho \left( \varTheta _{\mathrm{HS}}\right) }{\rho \left( \varTheta _{\mathrm{HS},R}\right) } \right) ^{m}m_p C_p} \end{aligned}$$

(13)