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Dynamic reconfiguration, the monitoring of power production, and the fault diagnosis of photovoltaic arrays, among other applications, require fast and accurate models of photovoltaic arrays. In the literature, some models use the Lambert-W function to represent each module of the array, which increases the calculation time. Other models that use implicit equations to avoid the Lambert-W function do not use the inflection voltages to simplify the system of nonlinear equations that represent the array, increasing the computational burden. Therefore, this paper proposes mathematical models for series-parallel (SP) and total-cross-tied (TCT) photovoltaic arrays based on the implicit equations of the single-diode model and the inflection points of the current–voltage curves. These models decrease the calculation time by reducing the complexity of the nonlinear equation systems that represent each string of SP arrays and the whole TCT. Consequently, the calculation process that solves the model speeds up in comparison with processes that solve traditional explicit models based on the Lambert-W function. The results of several simulation scenarios using the proposed SP model with different array sizes show a reduction in the computation time by 82.97 % in contrast with the traditional solution. Additionally, when the proposed TCT model for arrays larger than 2 × 2 is used, the reduction in the computation time is between 47.71 % and 92.28 % . In dynamic reconfiguration, the results demonstrate that the proposed SP model provides the same optimal configuration but 7 times faster than traditional solutions, and the TCT model is solved at least 4 times faster than classical solutions. [ABSTRACT FROM AUTHOR]

Low-voltage photovoltaic systems are being widely used around the world, including their introduction into the power grid. The development of these systems requires the adaptation of several power converters, their static and dynamic modeling, the design of passive elements, and the design of the controller parameters, among other actions. Today, power converters are key elements in the development of photovoltaic systems, and classical power converters such as buck converters produce discontinuous input and output currents, requiring a high input capacitance and impacting the output power quality of these systems. This paper presents a proposal for a low-voltage photovoltaic system that uses a continuous input/output current buck converter, which enhances the operation of the classical buck converter in photovoltaic systems. The methodology describes the proposed photovoltaic system, including the power converter, its detailed operation, and the analysis of its waveforms. Moreover, the methodology includes a mathematical model of the photovoltaic system's dynamic behavior and the design of a sliding-mode controller for maximum power extraction and perturbation rejection. The photovoltaic system is validated in two ways: first, a comparison with the classical buck converter highlighting the advantages of continuous input/output currents is presented; then, an application example using commercial devices is described in detail. The application example uses a flowchart to design the power converter and the sliding-mode controller, and a circuit simulation confirms the advantages of the continuous input/output current buck converter with its controller. In the circuit simulation, the control strategy is formed by a perturb and observe algorithm that generates the voltage reference for the sliding-mode controller, which guarantees the system stability, tracks the maximum power point, and rejects the double-frequency oscillations generated by an intended microinverter. [ABSTRACT FROM AUTHOR]

The energy consumption estimation of a locomotive for a particular route is important for the selection of a locomotive technology, the improvement of the energy management system, the evaluation of the locomotive's potential energy generation, among others. The methodologies reported in the literature usually assume that the information of the railway track is available; however, in some cases, the track information is incomplete, not available, or the route is still in a planning stage. Therefore, this paper proposes a methodology to estimate the energy consumption and the potential energy generation of a locomotive when the railway track information is not available or incomplete. The methodology begins by extracting the main technical information of the locomotive to be analyzed. Then, the route is traced on Google Earth with steps of 100 m and the obtained information is processed to generate the longitude, latitude, elevation, and distance of the points along the route. From such information, it is possible to generate the slope and curvature profiles, while the speed profile can be obtained from the track operator or the regulations of a specific country. With that information, it is possible to estimate the equivalent power of the locomotive at each point of the route to finally calculate the consumed energy. The proposed methodology is validated with two case studies. The first one compares the results with a methodology available in the literature for the same route and locomotive, while the second case shows the applicability of the proposed methodology for a route without information. [ABSTRACT FROM AUTHOR]

Rectifiers with power factor correction are key devices to supply DC loads from AC sources, guaranteeing a power factor close to one and low total harmonic distortion. Boost-based power factor correction rectifiers are the most widely used topology and they are formed by a power stage (diode bridge and Boost converter) and a control system. However, there is a relevant control problem, because controllers are designed with linearized models of the converters for a specific operating point; consequently, the required dynamic performance and stability of the whole system for different operating points are not guaranteed. Another weak and common practice is to design the power and control stages independently. This paper proposes a co-design procedure for both the power stage and the control system of a Boost-based PFC rectifier, which is focused on guaranteeing the system's stability in any operating conditions. Moreover, the design procedure assures a maximum switching frequency and the fulfillment of different design requirements for the output voltage: maximum overshoot and settling time before load disturbances, maximum ripple, and the desired damping ratio. The proposed control has a cascade structure, where the inner loop is a sliding-mode controller (SMC) to track the inductor current reference, and the outer loop is an adaptive PI regulator of the output voltage, which manipulates the amplitude of the inductor current reference. The paper includes the stability analysis of the SMC, the design procedure of the inductor to guarantee the system stability, and the design of the adaptive PI controller parameters and the capacitor to achieve the desired dynamic performance of the output voltage. The proposed rectifier is simulated in PSIM and the results validate the co-design procedures and show that the proposed system is stable for any operating conditions and satisfies the design requirements. [ABSTRACT FROM AUTHOR]

DC microgrids are composed of loads, renewable sources, and storage devices that require control and protection to operate safely. The flyback converter is an alternative to connect paralleled batteries with nominal voltage DC buses; however, until now, complex controllers have been proposed, making difficult their implementation. On the other hand, when the voltage of a DC microgrid is not properly controlled, the loads may be damaged due to the voltage outside of the safe range. Therefore, proposed in this paper are two adaptive PI-structures to control a battery charger based on a flyback converter to be used in DC microgrids. The first adaptive current controller regulates the magnetizing current for stabilizing the system, and the second adaptive voltage controller regulates the voltage of the DC bus to protect the elements of the microgrid. The methodology to design the adaptive parameters of the PI-structures is developed as follows: first, the power stage of the flyback converter is introduced to derive a control-oriented model. The battery and the DC bus of the microgrid, which are interfaced by the flyback converter, are represented with widely accepted approaches. The second step is focused on modeling the system. The flyback converter, which includes a capacitance to model the DC microgrid, is represented by a dynamic model. The differential equations are averaged, and several transfer functions of the main variables are obtained. In the third step, the transfer functions are used to design the PI adaptive current controller and the PI adaptive voltage controller. In the last step, several recommendations are made to implement the power and control stages in low-cost hardware. An application example with realistic parameters is carried out in PSIM to validate the controller loops design. A battery of 12 V is connected to a DC microgrid of 48 V through a flyback converter with a switching frequency of 50 kHz. The settling time and deviation of the DC microgrid voltage, after a perturbation, are 0.845 ms and 2.04 V respectively, while the maximum values are adjusted to be 1 ms and 2.4 V. The simulation results validate the proposed procedure and the effectiveness of the PI-structures in regulating the magnetizing current and the DC bus voltage. [ABSTRACT FROM AUTHOR]

Featured Application: Improve the dynamic response and perturbation rejection of two-stage flyback-based microinverters or flyback-based photovoltaic power optimizers. A method to design a sliding-mode control of a photovoltaic system based on a flyback converter is proposed. First, the photovoltaic system is modeled to design the sliding-mode controller and to select the parameters of a maximum power point tracking algorithm. Then, the detailed design of the sliding-mode controller is presented, which includes the establishment of the sliding surface. The transversality, reachability, and equivalent control tests are also developed. Because the power extraction of the PV system is carried out through a P&O MPPT algorithm, the selection of the perturbation magnitude, the perturbation period, and the maximum switching frequency is integrated into the control design. Additionally, since the derivative of the MPPT output could prevent the achievement of the reachability test, a filter to limit that derivative is also integrated into the design process. The whole method is illustrated in an application example where the data of a BP585 PV module and a real flyback converter are used. Once the parameters were obtained, circuital simulations performed in PSIM validated the intended operation of a PV system composed of a PV module and a flyback converter, which is connected to a source that produces the perturbations of an AC grid. [ABSTRACT FROM AUTHOR]

Featured Application: Interface low-voltage battery packs with medium-voltage or high-voltage DC buses, e.g., DC buses in microgrids or electric vehicles. Devices connected to microgrids require safe conditions during their connection, disconnection and operation. The required safety is achieved through the design and control of the converters that interface elements with the microgrid. Therefore, the design of both power and control stages of a battery charger/discharger based on a flyback is proposed in this paper. First, the structure of a battery charger/discharger is proposed, including the battery, the flyback, the DC bus, and the control scheme. Then, three models to represent the battery charger/discharger are developed in this work; a switched model, an averaged model, and a steady-state model, which are used to obtain the static and dynamic behavior of the system, and also to obtain the design equations. Based on those models, a sliding-mode controller is designed, which includes the adaptive calculation of one parameter. Subsequently, a procedure to select the flyback HFT, the output capacitor, and the K v parameter based on operation requirements of the battery charger/discharger is presented in detail. Five tests developed in PSIM demonstrate the global stability of the system, the correct design of the circuit and controller parameters, the satisfactory regulation of the bus voltage, and the correct operation of the system for charge, discharge and stand-by conditions. Furthermore, a contrast with a classical PI structure confirms the performance of the proposed sliding-mode controller. [ABSTRACT FROM AUTHOR]

In Photovoltaic (PV) systems with Distributed Maximum Power Point Tracking (DMPPT) architecture each panel is connected to a DC/DC converter, whose outputs are connected in series to feed a grid-connected inverter. The series-connection forces the output voltage of those converters to be proportional to the converter' output power; therefore, under mismatched conditions, the output voltage of a highly-irradiated converter may exceed the rating (safe) value, causing an overvoltage condition that could damage the converter. This paper proposes a sliding-mode controller (SMC) acting on each converter to regulate both the input and output voltages, hence avoiding the overvoltage condition under partial shading. The proposed control strategy has two operation modes: maximum power point tracking (MPPT) and Protection. In MPPT mode the SMC imposes to the PV panel the voltage reference defined by an MPPT technique. The Protection mode is activated when the output voltage reaches the safety limit, and the SMC regulates the converter' output voltage to avoid overvoltage condition. The SMC has a bilinear sliding surface designed to provide a soft transition between both MPPT and Protection modes. The SMC analysis, parameters design and implementation are presented in detail. Moreover, simulation and experimental results illustrate the performance and applicability of the proposed solution. [ABSTRACT FROM AUTHOR]

Photovoltaic (PV) arrays can be connected following regular or irregular connection patterns to form regular configurations (e.g., series-parallel, total cross-tied, bridge-linked, etc.) or irregular configurations, respectively. Several reported works propose models for a single configuration; hence, making the evaluation of arrays with different configuration is a considerable time-consuming task. Moreover, if the PV array adopts an irregular configuration, the classical models cannot be used for its analysis. This paper proposes a modeling procedure for PV arrays connected in any configuration and operating under uniform or partial shading conditions. The procedure divides the array into smaller arrays, named sub-arrays, which can be independently solved. The modeling procedure selects the mesh current solution or the node voltage solution depending on the topology of each sub-array. Therefore, the proposed approach analyzes the PV array using the least number of nonlinear equations. The proposed solution is validated through simulation and experimental results, which demonstrate the proposed model capacity to reproduce the electrical behavior of PV arrays connected in any configuration. [ABSTRACT FROM AUTHOR]