From Engle & Granger model to Johansen model for a more accurate photovoltaic power output forecast - Ramenah, Harry (Annals of Mathematics and Physics, 2022)
The French government has recently decided to increase the Photovoltaic (PV) capacities to reach 35GW by 2028 in all french territories, the European territory, and overseas territories such as Reunion Island in the Indian Ocean. However, integrating growing numbers of PV power installations and microgrids onto the grid can result in larger-than-expected fluctuations in grid frequency. This is due to PV power output that is not only a function of the operating temperature and solar irradiation but also of other environmental parameters. In this paper, only two environmental parameters are considered in the European zone and when the Engle & Granger statistical method is used, a relationship between variables such as photovoltaic power output and solar irradiation at a different level is obtained. The final relationship without suspicious heteroscedasticity is determined. The model is formulated on the basis of photovoltaic real conditions statistical approach and is more realistic than steady approach models. The Engle & Granger method does not distinguish several cointegration relationships when more variables are considered. For the overseas zone, we added other measured environmental variables and applied a more robust statistical method known as the Johansen vector error correction model (VECM) cointegration approach. In the VECM model, for N explanatory variables and for N > 2, we established a long-run equilibrium relationship that has been tested and the outcome is more than reliable when comparing the model to measured data.