Wave digital adapters for reciprocal second-order sections

IEEE Trans. Circuits Syst. I

Maffezzoni

Daniel

et al. 2018

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.

“…, Z N ] is a diagonal matrix, whose non-zero entries are the reference port resistances. In [43], [44], it is proved that the scattering matrix S such that b = Sa…”

Section: A Wave Digital Scattering Matrix Derivationmentioning

confidence: 99%

Wave-Based Analysis of Large Nonlinear Photovoltaic Arrays

IEEE Trans. Circuits Syst. I

Maffezzoni

Daniel

et al. 2018

“…The derived blocks are then connected together through port connections and the WD structure is derived. In this Section, we briefly review how to compute the scattering matrices representing arbitrary reciprocal connection networks, i.e., topological interconnections possibly incorporating ideal transformers, in the WD domain [8], [39], [56], [57]. The reader who might be interested in the WD modeling of connection networks embedding both reciprocal and non-reciprocal linear elements, e.g., controlled sources, nullors or gyrators, is referred to [58].…”

Section: Background On Wave Digital Structuresmentioning

confidence: 99%

“…, j N ] T is the column vector of all port currents, v t is a column vector of size q, 1  q < N, collecting independent port voltages, j l is a column vector of size p, p = N q, collecting independent port currents. Matrices Q and B are generalizations of the fundamental cut-set matrix and fundamental loop matrix, respectively, as explained in [8], [56], [57], and they satisfy the orthogonality property BQ T = 0, where 0 is a zero matrix of proper size. According to (1), each port voltage in v is expressed as a linear combination of the q independent port voltages collected in v t , while each port current in j is expressed as a linear combination of the p independent port currents collected in j l [57].…”

Section: A Modeling Connection Networkmentioning

confidence: 99%

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Linear Multistep Discretization Methods With Variable Step-Size in Nonlinear Wave Digital Structures for Virtual Analog Modeling

IEEE/ACM Trans. Audio Speech Lang. Process.

Maffezzoni

Sarti

2019

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.

“…This method represents a reciprocal multiport on the graph-theoretic links and twigs basis and uses the orthogonality of the circuit and cutset matrices to derive voltage wave scattering behavior. This has been used for particular network synthesis reciprocal multiports sections including bridged-T [27], twin-T [28], Brune / Darlington C, and Darlington D [29]. A technique for efficient implementation is proposed in [30].…”

Section: B Scattering Of Reciprocal Junctionsmentioning

confidence: 99%

Modeling Circuits With Arbitrary Topologies and Active Linear Multiports Using Wave Digital Filters

Werner

IEEE Trans. Circuits Syst. I

Smith

et al. 2018

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.