In this paper, a novel analysis method based on Wave Digital (WD) principles is presented. The method is employed for modeling and efficiently simulating large PhotoVoltaic (PV) arrays under partial shading conditions. The WD method allows rapid exploration of the current-voltage curve at the load of the PV array, given: the irradiation pattern, the nonlinear PV unit model (e.g. exponential junction model with bypass diode) and the corresponding parameters. The Maximum Power Point can therefore easily be deduced. The main features of the proposed method are the use of a scattering matrix that is able to incorporate any PV array topology and the adoption of independent one-dimensional nonlinear solvers to handle the constitutive equations of PV units. It is shown that the WD method can be considered as an iterative relaxation method that always converges to the PV array solution. Rigorous proof of convergence and results about the speed of convergence are provided. Compared to standard Spice-like simulators, the WD method results to be 35 times faster for PV arrays made of some thousands elements. This paves the way to possible implementations of the method in specialized hardware/software for the real time control and optimization of complex PV plants.

Abstract-The Wave Digital Filter (WDF) technique derives digital filters from analog prototypes which classically have been restricted to passive circuits with series/parallel topologies. Since most audio circuits contain active elements (e.g., opamps) and complex topologies, WDFs have only had limited use in Virtual Analog modeling. In this article we extend the WDF approach to accommodate the unbounded class of nonseries/parallel junctions which may absorb linear multiports. We present four Modified-Nodal-Analysis-based scattering matrix derivations for these junctions, using parametric waves with voltage, power, and current waves as particular cases. Three derivations afford implementations whose cost in multiplies are lower than multiplying by the scattering matrix. Negative port resistances may be needed in WDF modeling of active circuits, restricting the WDF to voltage or current waves. We propose two techniques for localizing this restriction. Case studies on the Baxandall tone circuit and a "Frequency Booster" guitar pedal demonstrate the proposed techniques in action.

There is a growing interest in Virtual Analog modeling algorithms for musical audio processing designed in the Wave Digital (WD) domain. Such algorithms typically employ a discretization strategy based on the trapezoidal rule with fixed sampling step, though this is not the only option. In fact, alternative discretization strategies (possibly with an adaptive sampling step) can be quite advantageous, particularly when dealing with nonlinear systems characterized by stiff equations. In this article, we propose a unified approach for modeling capacitors and inductors in the WD domain using generic linear multi-step discretization methods with variable time-step size, and provide generalized adaptation conditions. We also show that the proposed approach for implementing dynamic (energystoring) elements in the WD domain is particularly suitable to be combined with a recently developed technique for efficiently solving a class of circuits with multiple one-port nonlinearities, called Scattering Iterative Method. Finally, as examples of application, we develop WD models for a Van Der Pol oscillator and a dynamic diode-based ring modulator, which use different discretization methods.

In this paper, an existing approach for modeling and efficiently implementing arbitrary reciprocal connection networks using Wave Digital scattering junctions based on voltage waves is extended to be used in a broader class of Wave Digital Filters based on different kinds of waves. A generalized wave definition which includes traditional voltage waves, current waves and power-normalized waves as particular cases is employed. Closed-form formulas for computing the scattering matrices of the junctions are provided. Moreover, the approach is also extended to the family of Biparametric Wave Digital Filters, which have been recently introduced in the literature.

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A large class of transcendental equations involving exponentials can be made explicit using the Lambert W function. In the last fifteen years, this powerful mathematical tool has been extensively used to find closed-form expressions for currents or voltages in circuits containing diodes. Until now almost all the studies about the W function in circuit analysis concern the Kirchhoff (K) domain, while only few works in the literature describe explicit models for diode circuits in the Wave Digital (WD) domain. However explicit models of NonLinear Elements (NLEs) in the WD domain are particularly desirable, especially in order to avoid the use of iterative algorithms. This paper explores the range of action of the W function in the WD domain; it describes a procedure to search for explicit wave mappings, for both one-port and multi-port NLEs containing diodes. WD models, describing an arbitrary number of different parallel and anti-parallel diodes, a transformerless ring modulator and some BJT amplifier configurations, are derived. In particular, an extended version of the BJT Ebers-Moll model, suitable for implementing feedback between terminals, is introduced

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