PaperlayerView exact revision on arXiv

Source-linked AI summary

Partial Shading Detection and Smooth Maximum Power Point Tracking of PV Arrays under PSC

Mohammad Amin Ghasemi, Hossein Mohammadian Foroushani, Mostafa Parniani

arXiv:1810.12431v1eess.SP

TL;DR

PV arrays under partial shading develop multiple power peaks, making conventional MPPT unable to reliably reach the global maximum. The paper proposes PSC detection followed by ramp-based voltage control and continuous P-V sampling, with P&O reactivated for small changes. Simulations and experiments validate the proposed approach, which is reported as fast, simple, robust, and minimally disruptive.

  • Problem

    Partial shading creates multiple P-V peaks, while conventional MPPT methods may track local peaks instead of extracting the array’s global maximum power point.

  • Method

    The method detects PSC, then directly controls the array using ramp changes in voltage or duty cycle with continuous voltage-current sampling, without current or voltage feedback control.

  • Results

    The proposed algorithm tracks the GMPP in all simulated cases in less than 70ms and is validated through simulation and experimental results.

  • Takeaways & Limitations

    The proposed method offers cheap implementation, adjustable speed, smooth power changes, minimum negative impact on the connected power system, and efficiency independent of module model.

Abstract

from arXiv · show

One of the most important issues in the operation of a photovoltaic (PV) system is extracting maximum power from the PV array, especially in partial shading condition (PSC). Under PSC, P-V characteristic of PV arrays will have multiple peak points, only one of which is global maximum. Conventional maximum power point tracking (MPPT) methods are not able to extract maximum power in this condition. In this paper, a novel two-stage MPPT method is presented to overcome this drawback. In the first stage, a method is proposed to determine the occurrence of PSC, and in the second stage, using a new algorithm that is based on ramp change of the duty cycle and continuous sampling from the P-V characteristic of the array, global maximum power point of array is reached. P&O algorithm is then re-activated to trace small changes of the new MPP. Open loop operation of the proposed method makes its implementation cheap and simple. The method is robust in the face of changing environmental conditions and array characteristics, and has minimum negative impact on the connected power system. Simulations in Matlab/Simulink and experimental results validate the performance of the proposed methods.

I. INTRODUCTION

The introduction frames partial shading as a key obstacle to maximum-power extraction because conventional MPPT may track local rather than global peaks. It motivates a simple, fast, low-disturbance method that detects PSC and uses ramp-based sampling.

  • Under PSC, bypass diodes can give the array P-V characteristic multiple peak points, while conventional MPPT techniques usually track local peaks instead of the GMPP.
  • Effective MPPT under PSC should track rapidly, remain simple with low computational load, use fewer and cheaper sensors, and disturb the connected grid minimally.
  • Detecting PSC is difficult because no dedicated method had been established, large-power-change thresholds are difficult to set, and changing shading patterns may produce no large power change.
  • The proposed MPPT algorithm uses ramp changes in duty cycle and continuous sampling of the array P-V characteristic.
  • The proposed method is presented as cheap, adjustable in speed, robust across conditions, and minimally disturbing to the connected power system.

A. Uniform Irradiance Condition

The paper models PV modules with a single-diode equivalent circuit and describes voltage-current behavior under uniform irradiance. In this condition, module and array maximum-power points are unique.

  • The paper uses a single-diode model to express the voltage-current relation of a PV module.
  • The module model includes equivalent photocurrent, reverse saturation current, ideal factor, thermal voltage, and equivalent series and shunt resistances.
  • A PV array is represented by parallel strings, each containing series-connected modules, and its uniform-irradiance current-voltage characteristic is derived accordingly.
  • The section presents the single-diode electrical model and the typical module P-V and I-V characteristics used for analysis.
  • Under uniform irradiance, module and array maximum-power points are unique and occur at voltages proportional to their open-circuit voltages.

B. Partially Shaded Condition

Partial shading creates multiple local maximum power points in PV arrays, while the two-stage grid-connected architecture uses a boost converter for PV voltage control and an inverter for grid connection. Open-loop boost-converter control avoids an expensive current sensor, and ramp commands reduce transient effects during MPPT sampling.

  • Partially Shaded Condition: Under partial shading, insolated modules can force shaded modules to consume power, producing multiple local maxima on the string P-V characteristic.The described example has two irradiance levels and two shaded among four series modules.
  • Partially Shaded Condition: The partially shaded string’s local-MPP voltage varies with irradiance ratio and shaded-to-insolated module ratio, while the minimum separation between local-MPP voltages exceeds V_mpp-mod.The voltage moves between bounds as the irradiance ratio changes.
  • System Structure: The grid-connected system separates PV-side voltage control by a DC/DC boost converter from grid connection by an inverter, with a DC-link capacitor reducing coupling.The boost converter absorbs array power by controlling voltage; the inverter generates AC voltage for the grid.
  • Open-Loop Control: Open-loop control generates the required converter input voltage from the input-output voltage relation and eliminates the boost-converter inductor-current sensor.Compared with two-loop closed-loop control, it may have more steady-state error and transients.
  • Open-Loop Control: Ramp commands produce negligible converter transients, whereas step commands cause oscillation, overshoot, switching stress, and losses, especially in the constant-current region.The simulated step response settles in about 15 ms, so MPPT sampling must occur after that interval.

IV. PARTIAL SHADING CONDITION DETECTION

The paper presents a partial-shading-condition detection algorithm based on three criteria and evaluates it across various partial-shading patterns.

  • IV. PARTIAL SHADING CONDITION DETECTION: The PSC detection algorithm uses three criteria and is evaluated under various partial-shading patterns.The passage introduces both the detection method and its performance evaluation scope.

A. PSI index as Partial Shading Condition Detection Criterion

The PSI index uses normalized power-derivative behavior to distinguish partial shading from uniform conditions and identify the relevant local-maximum region. Although detection can fail in extreme shading-ratio cases, conventional P&O still reaches the global maximum in those cases.

  • PSI index: The first criterion defines PSI as a normalized derivative of PV-array power for detecting partial shading.Its sign and magnitude differ between shaded and uniform-irradiance operating regions.
  • PSI index: Positive PSI indicates a local string maximum above V*44)QPP, whereas negative PSI indicates a local maximum below V™§§)•¨¨.The two cases correspond respectively to shaded modules producing a characteristic derivative response and shaded modules being bypassed.
  • PSI index: Fig. 5 compares I-V and P-V characteristics of a PV string across different partial-shading patterns.The curves provide the operating-characteristic context for multiple local maxima and PSI behavior.
  • Detection boundary: When K is too high or IR is too low, PSI may approach zero and fail to detect partial shading.These conditions correspond to the second local maximum being near V*44)=MP.
  • Detection boundary: If PSI misses such a case, conventional P&O tracks the second maximum because its power is much greater than the first local maximum.The second maximum is therefore the global maximum under the stated extreme-ratio conditions.

B. Updating 𝑉*44)QPP and Final PS Detection Criteria

The method updates V*44)QPP using temperature-dependent module parameters and applies three criteria through a flow-charted detection procedure. PSI is extended from series strings to arrays using a weighted-average relation.

  • Updating V*44)QPP: Under partial shading, V*44)QPP is unavailable directly because the array operating voltage is no longer V**4)QPP.The method therefore estimates the reference using temperature information rather than measuring every module temperature.
  • Updating V*44)QPP: The proposed update uses one sample-module temperature with the temperature coefficients ρQPP and ρ*'+ to estimate V**4)QPP and V**4)*'+.The sample module may be either shaded or insolated, so the method considers three cases.
  • Final PS detection criteria: The three detection criteria are combined so that the array is classified as partially shaded when at least one threshold condition is met.Thresholds were selected from simulations of many partial-shading scenarios and array structures.
  • Final PS detection criteria: Fig. 6 presents the flow chart of the proposed algorithms for partial-shading detection.The flow chart summarizes the sequence implementing the combined criteria.
  • Array extension: For an array, PSI is the weighted average of the PSI values of individual strings, so PSI and the two other criteria suffice for array-level detection.This extends the criterion beyond the previously analyzed series string.

C. Effectiveness of proposed algorithm for PSC detection

The proposed detector was evaluated through simulations of five partial-shading patterns using a configured PV array. Combining all three criteria detected every simulated pattern and avoided the threshold and disturbance issues identified for comparison methods.

  • Simulation setup: The simulations used a 3x5 PV array composed of ND195R1S modules under three irradiance-temperature combinations.The simulated conditions were Sc = 0.9 kW/m^2 at 35 C, Sf = 0.6 kW/m^2 at 30 C, and SÇ = 0.3 kW/m^2 at 25 C.
  • Simulation setup: Five different partial-shading patterns were evaluated, with ternary digits representing the module counts at the three irradiance-temperature levels in each string.Temperature and voltage of the marked module were assumed measured.
  • Detection results: Using all criteria in (9) detected all simulated partial-shading cases, whereas PSI alone missed PSC5 and the third criterion alone missed PSC2.The combined criteria provided robustness across the tested patterns.
  • Comparison: Compared with big-power-change detection, the proposed method avoids sensitivity to an arbitrary threshold for distinguishing partial shading from uniform irradiance.Compared with the method in, it also does not impose a big disturbance on the system.

V. PROPOSED ALGORITHM FOR MPPT UNDER PSC

The proposed MPPT method scans the array’s P-V characteristic continuously with a ramp command, after detecting partial shading, to locate the GMPP. It bounds the search region, then resumes P&O for small operating changes.

  • Motivation: Heuristic PSC methods sample multiple voltages and can be slow because each measurement must wait for boost-converter settling.The cited converter’s maximum settling time is about 20 ms.
  • Scanning strategy: Continuous sampling during a ramp command scans the array characteristic rather than evaluating only selected voltage points.The ramp can be implemented with an analog rate limiter or digitally through small duty-cycle changes.
  • Algorithm sequence: The method detects PSC, activates GMPPT when shading is confirmed, and otherwise calls P&O.For changing shading patterns, it first ramps the array voltage to the specified detection point before checking the PSC criteria.
  • Search bounds: The search region is bounded using voltage and power inequalities, stopping the positive ramp when higher voltages cannot exceed the current MPP estimate.After shading follows uniform irradiance, the negative search bound is also restricted using the estimated MPP current.
  • Convergence: The method samples the complete relevant voltage region and therefore guarantees convergence to the GMPP under any partial shading condition.It requires no PV electrical characteristics beyond an approximate maximum array voltage used to define the search region.
  • Implementation: A 4000 V/s ramp reaches a 200 V GMPP voltage in about 50 ms, while sampling must be coordinated with ramp rate and converter dynamics.The paper states that existing microcontrollers provide sufficient sampling capability and that imperfect boost-converter response does not limit the method.
  • Grid interaction: Excessive ramp rates can increase dP_array/dt and disturb the grid, although 4000 V/s is reported to provide fast tracking with sufficiently low disturbance.The concern is tied to grid interaction during GMPPT rather than to convergence itself.

VI. SIMULATION AND EXPERIMENTAL RESULTS

The paper evaluates the proposed GMPPT method across multiple aspects using both Matlab/Simulink simulations and experiments.

  • Evaluation scope: Performance is evaluated in various aspects using simulations and experiments.The evaluation section introduces both simulation and experimental validation of GMPPT under PSC.

A. Simulation Results

Simulations compare the proposed method with PSO-based and intelligent MPPT alternatives under uniform irradiance and two partial-shading patterns. The proposed method tracks the GMPP rapidly while reducing grid transients and avoiding dependence on module make or model.

  • Simulation setup: The proposed method is compared against a three-particle PSO-based algorithm and another frequently referenced intelligent MPPT method.The simulated PV array is a 5x6 array of ND195R1S modules evaluated under uniform irradiance and two partial-shading patterns.
  • Tracking performance: The proposed algorithm tracks the GMPP in all simulated cases in less than 70 ms.The simulation uses 0.5 ms voltage-current conversion time and a 4000 V/s search ramp.
  • Grid interaction: Ramp-based voltage changes increase tracking speed and reduce converter transients and stress compared with step-based changes.Lower injected-power changes produce lower point-of-common-coupling voltage transients and better power quality.
  • Method comparison: The proposed method is independent of PV module make and model, whereas a comparison method’s efficiency depends on module uniformity and model-dependent sampling intervals.The paper presents these characteristics in a comparison of three MPPT methods.

B. Experimental Results

Experiments apply the proposed MPPT method to a boost-converter setup with a shaded PV array. The tested partial-shading pattern produces three local maxima, creating a GMPP-tracking challenge.

  • Experimental setup: The experimental setup uses a boost converter paralleled with eight batteries totaling 96 V to maintain a constant output voltage.The setup includes the converter and PV array used for experimental validation.

VII. CONCLUSION

The paper presents a simple, fast GMPPT method for partial shading that uses smooth power changes and is validated by simulation and experiments. Its implementation is inexpensive, adjustable in speed, minimally disruptive, and independent of module model.

  • The proposed GMPPT method is simple enough for implementation on a cheap AVR microcontroller.
  • Its adjustable speed and smooth power changes enable rapid tracking with minimal negative impact on the connected power system.
  • The method’s efficiency is guaranteed and does not depend on the module model.
Loading 1810.12431v1…