Modelling and Parameter Identification Using Reduced I-V Data

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A linear method to extract diode model parameters of solar panels from a single I–V curve

The I-V characteristic curve is very important for solar cells/modules being a direct indicator of performance. But the reverse derivation of the diode model parameters from the I-V curve is a big challenge due to the strong nonlinear relationship between the model parameters. It seems impossible to solve such a nonlinear problem accurately using linear identification methods, which is proved wrong in this paper. By changing the viewpoint from conventional static curve fitting to dynamic system identification, the integral-based linear least square identification method is proposed to extract all diode model parameters simultaneously from a single I-V curve. No iterative searching or approximation is required in the proposed method. Examples illustrating the accuracy and effectiveness of the proposed method, as compared to the existing approaches, are presented in this paper. The possibility of real-time monitoring of model parameters versus environmental factors (irradiance and/or temperatures) is also discussed

Very short term irradiance forecasting using the lasso

We find an application of the lasso (least absolute shrinkage and selection operator) in sub-5-min solar irradiance forecasting using a monitoring network. Lasso is a variable shrinkage and selection method for linear regression. In addition to the sum of squares error minimization, it considers the sum of ℓ1-norms of the regression coefficients as penalty. This bias–variance trade-off very often leads to better predictions.<p></p> One second irradiance time series data are collected using a dense monitoring network in Oahu, Hawaii. As clouds propagate over the network, highly correlated lagged time series can be observed among station pairs. Lasso is used to automatically shrink and select the most appropriate lagged time series for regression. Since only lagged time series are used as predictors, the regression provides true out-of-sample forecasts. It is found that the proposed model outperforms univariate time series models and ordinary least squares regression significantly, especially when training data are few and predictors are many. Very short-term irradiance forecasting is useful in managing the variability within a central PV power plant.<p></p&gt

Time Dependent Saddle Node Bifurcation: Breaking Time and the Point of No Return in a Non-Autonomous Model of Critical Transitions

There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle-node bifurcations. In particular, the term `tipping', or critical transition has in recent years entered the discourse of the general public in relation to ecology, medicine, and public health. The saddle-node bifurcation and its associated theory of catastrophe as put forth by Thom and Zeeman has seen applications in a wide range of fields including molecular biophysics, mesoscopic physics, and climate science. In this paper, we investigate a simple model of a non-autonomous system with a time-dependent parameter $p(\tau)$ and its corresponding `dynamic' (time-dependent) saddle-node bifurcation by the modern theory of non-autonomous dynamical systems. We show that the actual point of no return for a system undergoing tipping can be significantly delayed in comparison to the {\em breaking time} $\hat{\tau}$ at which the corresponding autonomous system with a time-independent parameter $p_{a}= p(\hat{\tau})$ undergoes a bifurcation. A dimensionless parameter $\alpha=\lambda p_0^3V^{-2}$ is introduced, in which $\lambda$ is the curvature of the autonomous saddle-node bifurcation according to parameter $p(\tau)$, which has an initial value of $p_{0}$ and a constant rate of change $V$. We find that the breaking time $\hat{\tau}$ is always less than the actual point of no return $\tau^*$ after which the critical transition is irreversible; specifically, the relation $\tau^*-\hat{\tau}\simeq 2.338(\lambda V)^{-\frac{1}{3}}$ is analytically obtained. For a system with a small $\lambda V$, there exists a significant window of opportunity $(\hat{\tau},\tau^*)$ during which rapid reversal of the environment can save the system from catastrophe