High-Power Closed-Loop SMPC-Based Photovoltaic System Characterization under Varying Ambient Conditions

: Photovoltaic energy generation potential can be tapped with maximum efﬁcacy by characterizing the source behaviour. Characterization refers to the systematic terminal measurement-based PV modeling which can further facilitate output prediction and fault detection. Most of the existing PV characterization methods fail for high-power PV array due to increased thermal losses in electronic components. Here, we propose a switched-mode power converter-based PV characterization setup which is designed with input ﬁlter to limit switching ripple entering into PV array under test, thereby enhancing system life and efﬁciency. The high resonant frequency input ﬁlter ensures its compactness with high-speed characterization capability. To further enhance the system performance, a closed-loop current control of the system is designed for high bandwidth and stable phase margins. Variation of the controller parameters under varying ambient conditions of 200–1000 W/m 2 irradiation and 25–70 ◦ C temperature is documented and an adaptive PI controller is proposed. Experimental and simulation results validate the high performance of the closed loop operation of the PV characterization at 1.2 kW range power level in real-time ﬁeld conditions. Compared to the open loop operation, the closed-loop operation eliminates the waveform ringing by 100% during characterization.


Introduction
Photovoltaic characterization is extremely useful in PV research for output prediction, fault diagnosis, and system efficiency estimation. Characterization is defined as the measurement of output voltage and current of a PV panel under given irradiation and temperature conditions. PV characterization finds direct application in performance assessment of different PV technologies [1] based on which the optimization of photovoltaic devices and systems can be achieved [2]. With the onset of new technologies such as renewable energy storage and building integrated photovoltaic system design, high-power characterization-based design and performance evaluation are the need of the hour [3,4]. PV characterization is also being applied for reliability studies of PV systems to map the effect of outdoor soiling and shading [5,6]. Recent examples show the use of PV characterization for important design decisions such as the use of reconfigurable PV systems or the need for distributed maximum power point tracking under shading conditions [7,8].
Based on the terminal measurement of electrical output characteristics, the PV system model is identified using parameter extraction [9], which can further be used to predict the system output under varying ambient conditions [10], along with cell degradation-based aging studies [11] and fault diagnosis [12]. Characterization for low-power solar cells is found extensively both in literature [13][14][15][16] with several low-power single cell/module characterization devices available in industry. The focus of the above-mentioned cell-level characterization is typically in the early design and performance validation stages of the PV device development [17,18]. However, high-power PV array characterization in the range of kilo Watts is not as widely available due to challenges posed by thermal losses in electronic components [19]. It has been noted in [20] that accurate power determination of large area multi-junction modules has been a challenge in recent years.
PV panel characterization requires a light source and an electrical load. To prevent high power handling capability in characterization equipment, dark I-V measurements are sometimes utilized [21] or a controlled single light source is used indoors [22,23]. However, using real-time field-evaluated I-V characteristics helps in classifying the effect of internal and external factors on slow and fast changing terminal response of PV modules [24]. To handle the field challenges such as unpredictable temporal variation in solar insolation and wind-based temperature variation requires fast response of the characterization setup [25,26].
PV characterization is undertaken by subjecting the PV array to a variable load, which can take PV array's rated current and voltage [27]. As the load varies or is varied manually, the terminal current-voltage measurements are noted simultaneously. Rheostat is the simplest variable load whose resistance can be varied manually [28]. However, this simple and cost-effective approach is limited by low sensitivity with extremely sparse data points near the open-circuit and short-circuit regions with slow speed and accuracy for fast changing ambient conditions. Large size of high power variable resistors is another major concern [29] in remote PV applications. Another passive method of PV characterization is discussed in [30,31], wherein a capacitor array is charged to vary the voltage at PV array terminals, which is noted along with terminal current, thereby obtaining the current-voltage characteristics of the PV system [32]. This method is however limited by the response time which is a function of capacitance network's charging and discharging time constant, affecting the time lapse between subsequent current-voltage sweeps [33].
For controllable and faster response times, numerous electronic loads are proposed for PV characterization, some of the most popular ones use transistors whose gate charging is controlled to vary its output resistance [34]. The complete sweep of PV curve from open-circuit to short-circuit, however, requires the operation of transistor in all three modes, causing high energy dissipation in the active region, depending on the maximum irradiation level and PV array ratings. Another similar approach is the use of linearly operated MOSFET in series with a passive resistor which is proposed in [34]. The success of this method lies in proper sizing of MOSFET as per the maximum power dissipation in its active region.
Most of the photovoltaic energy conversion systems consist of switched mode dc-dc converters for power conditioning in various industrial applications [35,36]. Dedicated SMPC systems for PV characterization are proposed in [37]. These SMPC systems are promising to be one of the best methods of characterizing PV arrays owing to their controllable and fast response, designed ability to handle high power and optional power conditioning capability [29]. These converters are further useful in transient characterization of PV panels for dynamic modeling [38] and can therefore be instrumental in fault diagnosis. SMPC systems also work well in fast changing environmental conditions wherein special cautions such as high characterization speeds are needed when irradiation changes fast [26]. IEC standard 60904-1 specifies conditions for PV characterization, namely, within ±1% irradiation variation, within ±2% temperature variation, and at least one point within 0-3% of open circuit voltage for short-circuit interpolation [39]. To satisfy these standard specifications, the developed characterization setup should have a very good dynamic performance, which can be met by a well-designed and well-controlled switched mode power converter.
In this work, we propose a buck-boost converter based PV characterization set up which can sweep the PV array from open circuit to short circuit in a controlled manner with fast response time. To solve the problem of high switching ripple feeding to the source, an input filter with damping is designed for high frequency operation without sacrificing the system bandwidth. To further enhance the system performance, a closed loop controller is designed using an adaptive PI controller for robust operation under varying ambient conditions . Experimental results are produced for both open and closed loop operation of  the converter, where closed loop controller shows smooth transition between operating  conditions with the elimination of the overshoot as compared to the open loop operation.

Contributions of This Work
The main contributions of this work are as follows.
1. A switched-mode power conversion-based PV characterization setup is introduced in this work which not only reduces system losses, but also prevents high frequency noise injection in the PV source. 2. Design and development of the high frequency damped input filter providing highspeed characterization without affecting closed-loop controller performance and system stability, while ensuring compact size. documented for system operation under closed-loop operation with changing ambient conditions. 6. The system is shown to remain stable under 200-1000 W/m 2 irradiation variation and 25-70 • C temperature with a high characterization speed within tens of milliseconds. 7. This study presents a 1.2 kW range high power PV system characterization based on high performance converter with scalability owing to low loss and stable operation under varying ambient conditions. Switched mode power converter provides greater than 80% efficiency, unlike linear electronic loads. 8. The results show superior performance in terms of fast variable characterization speed and tunable sensitivity of the converter: the features which are absent in the commercially available I-V tracers. 9. The developed PV characterization method is ten times more cost effective compared to commercial PV equipment with comparable speed. 10. Compared to commercial PV characterization equipment the proposed method offers at least three times higher power level with comparable accuracy. 11. It lays the foundation for PV parameter extraction, fault diagnosis, shading studies, accelerated life, and reliability testing of PV systems.
This paper is organized into five sections: Following introduction, the theory of a damped input filter design is discussed in Section 2. Section 3 discusses the design of the closed loop controller along with simulation results. Experimental results constitute Section 4, and Section 5 concludes the paper followed by Appendix A and references.

Design of Damped Input Filter for SMPC-Based PV Characterization System
In order to characterize a 1.2 kW PV array of series and parallel connected PV panels, a buck-boost converter is operated as an electronic load. This converter causes high input current ripple at the PV terminals, which can be prevented by the introduction of an input filter. To ensure that the introduction of an input filter does not affect the control of the system in any way, Middlebrook's extra element theorem is used in its dual form [40]. The transfer function G(s) of the system with an extra element (input filter with transfer function Z o (s) in this case) can be written in terms of the original transfer function as where the driving point impedance Z D (s) of the system is computed with zero variation in control input (duty ratio d): Z D (s) = Z i (s)|d =0 (2) and the null point impedance Z N is computed as the input impedance of converter which makes the output null. It can be expressed as To ensure that the new transfer function is not significantly different than the original transfer function in the frequency range of interest, the following conditions need to be satisfied [40]: The driving point impedance for the buck-boost converter can be derived from its small signal ac equivalent circuit as shown in Figure 1 [40]. Note that the Z N in PV characterization is computed unlike the case of conventional output voltage nulling as the input current is to be controlled, for which case Z N needs to be computed differently. To make the input current null, an impedance Z N needs to be introduced such that the value ofĩ g due tod is nullified by introduction of Z N . This is possible only when the currentĩ b flows through Z N and does not enter PV. Equivalently, a voltage sourceṽ b is introduced across Z N to produce a counter currentĩ b . When the transfer functionṽ b i b , in the small signal ac equivalent circuit of the buck-boost converter, as given in Figure 1 is computed, this ratio comes out to be the driving point impedance of the converter Z D . Therefore, to control the PV input current for characterization using the buck-boost converter, Z N = −Z D is obtained, making the comparison of ||Z o || and ||Z D || sufficient to satisfy the Middlebrook's Extra Element Theorem.
For an LC input filter, the transfer function can be written as Introducing a damping factor of ζ = 0.36 ensures (4) conditions are satisfied in the frequency range of interest. The circuit of the damped input filter is shown in Figure 2. With damping, the input filter transfer function modifies to (7).
Following the damped filter design procedure of [40], C b and R f are designed.

Closed Loop Control Design
To control the PV terminal current or voltage for characterization, there are two approaches: One is to control the system in open loop and other is the closed-loop operation. Under open-loop operation, the duty ratio command to the buck boost converter is given, which leads to a certain operating point on the current-voltage characteristic. This operating point on the PV module characteristic depends on the net resistance posed by the DC-DC converter, which in steady state is a function of output load and duty ratio. The block diagram of the open loop operation is shown in Figure 3a, wherein by periodically updating duty ratio in predefined steps, complete open-circuit to short-circuit operation of the PV module under test can be captured. This method however suffers from high waveform ringing and oscillations in the measured terminal characteristics [19]. Limitations of the open-loop operation in terms of waveform ringing can be overcome with the help of a well-designed closed-loop controller whose block diagram is given in Figure 3b. Figure 3b depicts the reference PV source currentĩ * g compared with the sensed source currentĩ g , and the error e is fed to the controller to produce the control parameter duty ratiod which controls the plant operation. Small signal transfer function from the duty cycle to the source current is the product of (7) and (8), the values of which are computed at standard test conditions (STC) of 1000 W/m 2 , 25 • C with rated open circuit V g = 45 V and short circuit current of I g = 9 A for each 300 W PV module, scaled up as per series/parallel connection. Values for this plant transfer function can be obtained using the detailed analysis presented in the Appendix A, where a look-up table is developed which connects the varying ambient conditions in terms of irradiation and temperature to varying PV module voltage values from open-circuit operation to short-circuit operation as quantified by the duty ratio variation.
To control this system in closed loop, a proportional integral (PI) controller is used. A PI controller ensures negligible steady state error while ensuring fast dynamic response compared to an integral control [19]. In order to evaluate the performance and stability of a closed loop system, one approach is to analyze the frequency response of its open loop transfer function (OLTF). In the present analysis, this approach is followed by creating MATLAB script files by coding the plant transfer functions using lookup tables as described in the Appendix A. Further, the bode function of the MATLAB toolbox is used to plot the frequency response of the combined controller-plant transfer function. Based on the control theory, a closed-loop system is considered stable when the gain margin (GM) and phase margin (PM) are positive for its open-loop transfer function. To apply this approach in our analysis, we use the frequency response of the OLTF which is the product of the PI controller transfer function along with plant transfer function as described above. In this analysis, the GM and PM are determined for stability and bandwidth is determined for performance or the time response of the closed loop system. Note that in open loop operation, the controller transfer function is not involved. To design the PI controller parameters, the stability and performance are both taken into account here. A K p = 1/24 is chosen to give nearly 40 • phase margin at STC and K I = 26.2 gives a zero at 100 Hz, which ensures complete phase recovery of 90 • at gain cross over. The bode plots of the open loop transfer function at varying duty ratios are plotted in Figure 4.
From the frequency response of the OLTF in Figure 4, for a given operating condition given by the duty ratio, the gain margin is obtained from the bode plot by evaluating the OLTF magnitude below zero dB when the phase crosses −180 • . Further, the phase margin is determined by noting the phase and adding 180 • to it when the magnitude crosses zero dB. From this analysis, it can be seen that minimum phase margin of 45 • is seen across entire duty ratio variation and gain margins are infinite except for 5% duty ratio, for which a 40 dB gain margin is obtained. Therefore the designed controller will lead to a stable operation under real-time field conditions. Bandwidth is seen to be in kHz range for a majority of operating conditions except for near open circuit condition, thereby ensuring high characterization speed and lower response time under closed loop operation.
The designed controller is seen to perform well except for lower duty ratio range, where the controller bandwidth becomes low. This calls for an adaptive gain PI controller as the plant itself varies with the point of operation.

Introduction of Adaptive Gain PI Controller
As seen from Figure 4 the controller performance is not satisfactory at low duty ratios, therefore an adaptive gain PI controller is introduced here. At low duty ratios, the gain is enhanced for higher bandwidth. The resulting open loop transfer functions for the open circuit operation of the system is shown in Figure 5.   With the introduction of the adaptive gain PI controller: at low duty ratio of 0.05, a bandwidth of 237 rad/s is achieved showing a seventeen time improvement compared to the fixed gain PI controller. On further analysis it is seen that the performance near 0.25 duty ratio can also be enhanced with a gain of 4, as higher gain at this condition reduces the phase margin. Based on the theoretical analysis of the plant transfer function, for duty ratios of less than 25% a gain of 2 4 is used, and for duty ratios of more than 25% but less than 45%, a gain of 2 2 is used in this algorithm. Choosing gains as the multiples of 2 comes in handy while digital programming. The adaptive gain scheduling with specific transition values are given in the complete algorithm flowchart in Figure 6.

Algorithm for Complete Curve Tracing
For controlling the input current from zero to short circuit value, its upper limit needs to be evaluated. To get that value in real-time, at the start of the characterization a high duty ratio (d) command is given to the controller and the sensed input current (i sns ) is noted as reference (i re f ). For complete curve tracing, this reference value is reduced in predefined current steps (∆i) to trace the compete curve. The gain of the PI controller is decided as per the duty ratio value. PI controller proportionality (K p ) and integral gains (K I ) remain fixed. The switch PWM duty ratio (d) is determined as the product of the controller gain and the error signal (i err ), which is further scaled down by the sawtooth carrier amplitude (V m ). This entire procedure as represented in the flowchart of Figure 6, sequentially measures the i sns and v sns as the real-time sensed current and voltage of the PV array terminals for complete i-v characterization.

Comparison of Open Loop and Closed Loop System Response
To quantify the performance comparison of PV array characterization in closed and open loop operations, the PV current and voltage characteristics are simulated for near open circuit condition, near short-circuit condition, and maximum power point conditions, respectively. These results are quantified in terms of percentage overshoot above its steady state value and 5% settling time as shown in Table 1. Percentage overshoot for open loop condition is denoted by PO OL , and settling times are denoted with ST OL and ST CL for open and closed loop conditions, respectively. Overshoot for closed loop response is seen to reduce significantly with comparable settling time in closed and open loops except for near short circuit condition which has lower bandwidth. Note that overshoot was not observed for closed loop response and is therefore not reported in Table 1, showing achieved desired performance.

Effect of Ambient Conditions on Controller Performance
Variation of closed loop controller performance with change in ambient conditions can be gauged by plotting the bode plots of the open loop transfer function, wherein solar irradiance variation from 200 to 1000 W/m 2 is shown along with the temperature variation from 25 to 70 • C. The impact of ambient conditions on the plant transfer function is evaluated in terms of the PV terminal voltage and duty ratio correlation which varies with irradiation and temperature. These correlated data are produced in the Appendix A for reference. Figure 7 shows the variation of the controller bandwidth and phase margin with ambient conditions for maximum power point operation near the converter duty ratio d = 0.6. It can be seen that as the irradiation increases the bandwidth improves but phase margin reduces. The effect of temperature occurs only at higher irradiation levels above 600 W/m 2 as seen from Figure 7. As temperature increases the phase margin improves but the bandwidth reduces for the system under consideration.
To study the performance of the designed adaptive gain PI controller across a range of operating points with changing ambient conditions, Table 2 is produced. It gives the worst case and best case controller performance parameters such as the bandwidth and stability parameters namely the gain and phase margins. Here, ω BW min marks the minimum bandwidth and ω BW max marks the maximum bandwidth. Table 2 also marks the point of operation of the converter in terms of duty ratio denoted in parentheses for every maximum and minimum condition. Phase margins are indicated as PM min and PM max for minimum and maximum values. As far as gain margins are concerned, the system holds an infinite value for other than very low duty ratios, for which case a minimum gain margin of nearly 40 dB is observed at d = 0.05 with a constant phase cross over frequency of 58.3 krad/s, thereby ensuring system stability.
This analysis shows that with the designed controller, the system remains stable with a high bandwidth despite the changes in the ambient conditions of varying irradiance and temperature.   Table 1 shows the time domain performance which can further be correlated to the frequency domain analysis as quantified in Table 2. The bandwidth of the controller as shown in columns 2 and 3 of Table 2 is inversely related to the settling time of the systems, which is quantified in columns 4 and 5 of Table 1. It can be seen that under higher values of duty ratio, which correspond to the short circuit condition in a buck-boost converter, the bandwidth is low. This leads to larger values of settling times. Similarly, at low duty ratio values, corresponding to the open circuit operation, the system bandwidth is higher in Table 2, due to the adaptive gain of the controller, leading to lower settling times in Table 1. Time-domain and frequency-domains are also related in terms of stability. When the gain and phase margins are higher, system is stable with lower overshoots observed in the time-response. It can be seen that throughout the operating ranges of varying ambient conditions, a phase margin of more than 45 • and a gain margin of more than 40 dB in Table 2, helps in complete elimination of overshoot in Table 1 for closed loop operation as compared to the open loop operation.

Experimental Validation
In this section, the complete experimental setup along with the obtained experimental results under real-field characterization are presented followed by the bench-marking of the quantified results with existing PV characterization methods.  The assembled hardware for the buck-boost SMPC-based PV characterization setup is shown in Figure 9. This system consists of several subsystems, namely, input filter, IGBT (insulated-gate bipolar transistor) based dc-dc converter, gate-drive card, current and voltage protection card, current and voltage sensor cards, FPGA controller board, and converter status display card. The adaptive-gain duty ratio variation control algorithm is coded in VHDL (very high speed integrated circuit hardware description language) and fed to the FPGA (field-programmable gate array) controller for generating PWM (pulse width modulation) signal for the buck-boost converter. The dc-dc converter is designed to work at 20 kHz switching frequency and PV terminal voltage and current signals are sampled at 20 Hz rate. The circuit diagram of the buck-boost converter is shown in Figure 10.
The ratings of the passive components and switches are as follows, with more details on the experimental setup design being given in [19].   Comparison between the open-loop and closed-loop performance of the characterization setup can be gauged by the experimental step response of the system. When the PV module is connected to the converter, under open-loop operation, the system response shows waveform ringing and oscillations. The percentage overshoot in the open-loop operation is observed to be as high as 100% of its steady state value as seen in Figure 11a. When the response of the closed-loop controller is captured, it is seen to achieve its desired performance as shown in Figure 11b, where PV voltage, current, and output voltage are seen to transition smoothly without any overshoot or ringing unlike open loop operation, as expected from Table 1. An improvement of 100% is observed in PV current overshoot prevention in Figure 11b [41] and current is seen to be linearly proportional to irradiation level [42] which changes with the time of the day and the cloud cover.

Experimental Results
Here, 55 • C is observed as the average PV module surface temperature under Bengaluru weather, where these experiments are conducted. However, under varying ambient conditions including solar irradiation and PV module temperature, the expected voltage and current can be computed using the developed PV steady-state models in [43] which gives a direct relation between the linear scaling of current with irradiance and logarithmic relation of voltage with temperature. Under such conditions also, the developed method remains applicable as the controller is stable with high performance under wide variation of irradiance from 200-1000 W/m 2 and wide variation of temperature from 25 to 70 • C.  Figure 13. Measured current-voltage characteristics as obtained from the developed characterization system for (a) cloudy sky irradiating three PV panels connected in series, (b) bright sky irradiating three PV panels in connected in series, (c) cloudy sky irradiating four series connected PV panels (d) bright sky irradiating four series connected panels. Each polycrystalline PV panel under test is rated at 300 W. Scale: (a) current on y-axis is 2 A/div, voltage on x-axis is 50 V/div; (b) current on y-axis is 5 A/div, voltage on x-axis is 50 V/div; (c) current on y-axis is 2 A/div, voltage on x-axis is 50 V/div; (d) current on y-axis is 5 A/div, voltage on x-axis is 50 V/div. Some open questions that have evolved as next steps to this study but beyond the scope of present article include dynamic impedance estimation of PV modules using small signal ac characterization with the present SMPC closed loop controller. Another challenging yet exciting application of this work is the accelerated lifetime, aging and reliability study of PV modules using the developed PV characterization setup.

Performance Comparison with Other Characterization Methods
From the experimental results, the dynamic performance of the proposed characterization method is quantified and benchmarked against existing methods in terms of speed, accuracy, efficiency, power level, and cost effectiveness.
• From Figures 11 and 12, the settling time of the SMPC-based closed loop characterization is seen to be in tens of milliseconds, which is comparable to the best performing commercial PV electronic loads [44]. A measurement time of 20 ms is reported in [45] and 50-100 ms is reported in [34]. • The proposed method has a high accuracy which is at par with 0.1% or less characterization error in commercial electronic loads for PV characterization [45]. The accuracy of the proposed method is based on the resolution and accuracy of the voltage and current sensors [46] and data logging equipments [47].
• The developed switched mode power converter (SMPC) has an accuracy in the range of 85-90% which is much higher than the linear electronic loads which use linear operation of MOSFET [34] or BJT [48]. The efficiency of linear power supplies is typically noted in the range of 40 to 60%, whereas that of SMPC is in the upwards of 80% [49]. • The power level of the proposed method is in kW range whereas the maximum power level of the commercial equipment and setups developed in PV literature varies from tens of watts [48] to 100 W [34] and goes to a maximum of 300 W [44]. These commercial equipments are also limited by voltage and current ratings and prevent the characterization of series and parallel connected PV modules in an array. • The proposed equipment can be developed in a few hundred dollars whereas the price range of equivalent commercial equipment is above thousand US dollars [44]. Therefore, the developed equipment is at least ten times more cost effective.

Conclusions
In this work, the design, development, and implementation of a high-power closedloop photovoltaic characterization setup based on switched mode power converter is presented. The developed buck-boost converter is seen to be efficient, accurate, and fast when applied to the electrical output measurement of PV arrays. The present system is operated up to 1.2 kW and can be directly scaled up for higher power PV system characterization owing to lower operational losses and compact size. Performance of the system is optimized using a proposed adaptive gain PI controller. This closed loop controller is designed for high bandwidth and stable phase margin under varying ambient conditions of 200-1000 W/m 2 irradiance and 25-70 • C temperature. The proposed controller is validated with simulation and experimental results showing its superior performance in terms of lower overshoot and ringing for step change in the point of operation near maximum power point and initial startup transient with respect to the open loop operation where a 100% reduction in the PV current's overshoot is observed. The motivation for a SMPS-based PV load follows from desirable attributes of variable capture speed and tunable sensitivity, which help in partial shading analysis and global maximum power point tracking. This lays the foundation for a PV energy conversion system which not only processes the solar energy, but can also be used for system modeling through high-performance characterization, which further helps in output prediction and fault diagnosis, and can be instrumental in accelerated life testing of PV arrays.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A
To understand the impact of ambient conditions on plant parameters, the PV source voltage and the duty ratio correlation is produced here as shown in Table A1. It can be seen that as the irradiation increases voltages for same duty ratios increase and as temperature increases voltages for same duty ratios decrease. This data correlation is used in evaluation of the controller performance in varying ambient conditions and is obtained by simulation of PV characteristics based on datasheet model of the 300 W polycrystalline PV module [43]