A Novel Maximum Power Point Tracking Control Strategy for the Building Integrated Photovoltaic System

: Thin-film photovoltaic technology has begun to be applied in building-integrated photovoltaics (BIPVs), and it is believed that thin-film photovoltaic technology has potential in building-integrated photovoltaic applications. In this paper, a hybrid approach was investigated which combined the maximum power point tracking (MPPT) algorithm of three-stage variable step size with continuous conduction mode (CCM)/discontinuous current mode (DCM). The research contents of this paper include the principle analysis of the maximum power point tracking algorithm, the design of the sampling period, and the design of a double closed-loop control system and correction factor. A system model was built in MATLAB/Simulink, and a comparative simulation was carried out to compare the performance of the proposed method with some traditional methods. The simulation results show that the proposed approach has the ability to fast-track and make the system run stably. Furthermore, it can make the system respond quickly to environmental changes. An experimental platform was built, and the experimental results validated and confirmed the advantages of the proposed


Background and Motivation
Building-integrated photovoltaics (BIPVs) are a promising technology to integrate photovoltaic power generation modules and buildings [1]. It is an economical way to utilize renewable energy and could play an important role in meeting the world's increasing power demand, reducing the consumption of fossil fuels, and protecting the environment [2]. Photovoltaic modules are usually installed on the surface of a protective structure around the building to provide power, while also serving as a functional part of building structure [3,4]. The products can be widely used in sunshades, curtain walls, roofs, doors, and windows. In addition to meeting the requirements of conventional lighting and architectural aesthetics, BIPVs can provide electricity in a clean and environmentfriendly way. BIPVs do not occupy extra land, and they reduce the cost of power transmission and energy consumption, saving on the support structure and reducing the overall cost of the building [5,6]. Therefore, the efficiency of the power generation system is high, and the overall cost can be reduced. At present, many countries in the world are trying to reduce the manufacturing cost and improve the power generation efficiency of BIPVs, by improving the manufacturing techniques and expanding the market size [7,8].
Compared with a silicon module, thin-film photovoltaic modules, as the generation units in a BIPV system, have the advantages of electrical characteristics such as high voltage output and good response to weak light. Moreover, the cell structure of a thin-film module is different from a silicon module in that there is no hot spot. Therefore, when partial shading occurs, the power reduction of a thin-film module is much smaller than that of a silicon module. They also have other advantages, such as low production cost, controllable transparency, and energy conservation when used as building materials. Therefore, thin-film photovoltaic technology is the most commonly preferred technology for BIPVs [9].
Unlike traditional photovoltaic power plants, the operating environment of thin-film modules in BIPVs is complex. For example, as a part of the building, the modules are usually not installed at the optimal elevation angle, and these modules could be subjected to sudden changes of light intensity due to shadows cast by clouds, other architecture, people, vehicles, and so on. These problems can cause power loss. In this regard, research into maximum power point tracking (MPPT) becomes crucial [10][11][12].

Problems and Solution
In the literature, there are many reported control strategies for MPPT. Generally, there are three perturbing methods: the current perturbation method, the duty cycle perturbation method, and the voltage perturbation method. The current perturbation method has low control accuracy and large oscillations around the maximum power point, so it is not common either in theoretical research or engineering applications. The duty cycle perturbation method (also called the perturbation-andobservation method) has been widely studied [13]. However, power oscillations exist near the maximum power point. The perturbation value affects the tracking speed and the oscillation amplitude [14]. The voltage perturbation method (also known as the hill-climbing method) is also commonly used in engineering applications. The key of this method is the closed-loop control of the DC-DC converter. In terms of the control effect or control accuracy, the voltage perturbation method performs better than the former two methods [15,16].
There are many control strategies based on the voltage perturbation method to achieve the maximum power point. Among these control strategies, the most commonly used method is the use of traditional proportion integral differential (PID) controllers because they are simple and easy to implement [17,18]. Usually, most of the PID controllers are designed under a continuous conduction mode (CCM) condition; however, when the environment changes rapidly, the DC-DC converter may work in discontinuous conduction mode (DCM) [19]. The PID controllers designed for CCM cannot be employed in DCM directly; otherwise, the performance of the power generation is reduced. The fuzzy control strategy is simple in design and easy to understand, and it has strong robustness. However, the simple fuzzy processing of information can reduce the control accuracy and dynamic performance of the system [20,21]. The sliding mode control strategy is independent of the control object model, and its system response is fast. However, due to the existence of a sliding surface, there is chattering near the control target (i.e., the maximum power point), and this behavior affects the stability of the system [22]. The artificial neural network control strategy has self-learning and selfadaptive ability, but the algorithm is complex and difficult to realize [23].
In order to address the issues of the above controllers, based on the two-stage variable step size method (improved traditional hill-climbing algorithm), this paper proposes an MPPT algorithm called the three-stage variable step size (3SVSS) method. According to the inherent characteristics of the boost converter, an appropriate selection method of the sampling period is introduced that reduces the system power loss. Based on the traditional double closed-loop (DCL) controllers in CCM and DCM, this paper proposes a CCM/DCM hybrid control strategy where two correction factors are introduced. With the proposed hybrid control strategy, the control accuracy of the system is not reduced when the irradiance changes continuously, especially in an environment with weak light [24,25]. The control strategy proposed in this paper was verified by simulation and experimental work, and the proposed method was also compared to other methods in order to confirm its advantages.

Characteristics of the Thin-Film Photovoltaic Modules
In Jain's work [26], the mathematical equation of the thin-film photovoltaic module is expressed as: where npIL is the photocurrent; npI0 is the reverse saturation current; q is the electron charge; K is the Boltzmann constant; T is the absolute temperature; A is the diode factor; Rs is the series resistance; and Rsh is the parallel resistance. Its equivalent circuit is shown in Figure 1. In engineering applications, considering some specific factors, the two-point method and its improved method are generally used to simplify Equation (1) to a certain extent. That is, parallel resistance is very large, so the part with 1/Rsh can be neglected. Since the series resistance is generally much smaller than the forward-conducting resistance of the diode, the photocurrent is assumed to be equal to the short-circuit current. Then the voltage and current in the open-circuit state and the maximum power point state are substituted into Equation (1) to obtain an approximated model.
In Equations (5)-(7), Sref = 1000 W/m 2 , a is the current temperature coefficient, and b is the voltage temperature coefficient.
According to Equations (2)-(7), the P-V and I-V curves under different light intensities were obtained, as shown in Figure 2.

Proposed MPPT Algorithm
As shown in Figure 2, the different illumination intensities hardly affected the shift of the maximum power point. The working temperature generally changed slightly; hence, its effect was not considered in this paper. The maximum power point roughly corresponded to 75% of the opencircuit voltage of the module. In the proposed MPPT algorithm, there are three stages. According to Figure 3, in stage 1, the output voltage of the module is controlled to 75% of the open-circuit voltage without detecting the voltage and current of the module. The following two stages, when approaching the maximum power point, are determination of the disturbing direction and step size by comparing with a smaller set value; hence, the step sizes are smaller than one of the traditional two-stage variable step-size control strategies. The flow chart of the proposed algorithm is shown in Figure 4. The power was calculated using the sampled voltage and current. The change in direction of the voltage was determined by comparing the voltage change with a set value.

Proposed Control Strategy
The DCL control system is shown in Figure 5 as the boost converter works in CCM mode; that is, the output of the voltage loop is the input of the current loop, which is used to generate the pulse width modulation (PWM) signal. The state-space average modeling of the equivalent circuit of the boost converter is given by: where d is duty cycle of the switch. The small-signal model of the boost converter is: Substituting Equation (10) into Equation (9) and (8) results in: The open-loop transfer function of the voltage control loop is derived as: The open-loop transfer function of the current control loop is derived and expressed by Equation (14): When the irradiance decreases dramatically or the load increases abruptly, it is likely that the boost converter works in the DCM. The control mechanism in the DCM is different from that in the CCM because of different state-space average models and transfer functions. In order to achieve seamless transition between the two modes, a correction factor is introduced into the system. When the converter is working in CCM, the correction factor is 1, and it has no effect on the system. When the converter is working in DCM, the correction factor can compensate for the output of the CCM feedback. Therefore, the corresponding controller can be modified accordingly. As shown in Figure  6, based on the traditional closed-loop control, the correction factors αDCM(z) and βDCM(z) are introduced into the voltage loop and the current loop, respectively, which leads to the proposed CCM/DCM hybrid control. With this control strategy, the boost converter can be regarded as a hybrid automata model. This model includes the continuous process (CP) and the discrete process (DP). According to the continuous state signals of CP, that is the inductor current and output voltage, DP can control the transition of the discrete state as a finite state machine. The correction factors can be calculated as follows. When the boost converter works in DCM, the state-space average model of the equivalent circuit of the boost converter is given by: The voltage ratio M in DCM is: where K0 = 2L/R0Ts, Ts is the switching period. The transfer function of the voltage loop is: The transfer function of the current loop is: The transformation from the S-domain to Z-domain is performed to obtain the following discretized system.

Design of the Sampling Period
According to the small signal equivalent circuit of the boost converter shown in Figure 7, the transfer function of v pv to d is: in mpp where Cin and L are the input capacitance and inductance, respectively, and C0 and R0 the output capacitance and resistance, respectively. V0 is the steady-state output voltage. According to Equation (26), the response of v pv to the amplitude Δd of duty cycle disturbance d can be deduced as follows: The response of P to small signal disturbance amplitude Δd can be expressed as which is a typical second-order system. The disturbance of output power satisfies the following inequality: In Equation (30), ΔPτ is the peak of the maximum overshoot of the system in the adjustment time.
According to feedback control theory, when the system has been adjusted for time Tτ, the output of the system is basically stable, and the expression of Tτ is: where τ is usually taken as a reference index for the end of the transient process. When τ < 0.03, the transient process ends. In order to prevent the MPPT algorithm from the effect caused by the inherent transient oscillation characteristics, the sampling period Tc needs to meet the following requirements: It should be emphasized that Equation (34) is the constraint of the sampling period of the system output power.
According to Equations (26) and (29), the power output of the photovoltaic system is subject to an oscillation process, and the oscillation time is restricted by two factors: the inherent parameters of the system L, Cin and the resistance Rmpp corresponding to the maximum power point. In order to ensure the reliability of the MPPT algorithm and the dynamic response of the system, it is necessary to ensure that the sampling time meets Equation (34). On the basis of meeting Equation (34), the sampling period cannot be too large. The sampling time should be selected appropriately, and in this paper, it was obtained by

Simulation Parameters and Models
In MATLAB/Simulink, for meeting the needs of our research work in the future, two First Solar FS-4112 thin-film modules connected in series were used; their parameters are tabulated in Table 1. The simulation model of the module adopts the engineering mathematical model derived by the twopoint method and its improved method. The overall system is shown in Figure 8, and the parameters are shown in Table 2.    Figure 9a shows the results for the perturbation-and-observation (P&O) method. Because of the strict linear relationship between the output power and duty ratio of the DC-DC converter, it is difficult for the whole system to maintain a good performance in terms of the dynamic response and stability at the same time, at any step size. If the step size is too large, the tracking accuracy is reduced. If the step size is too small, it takes a long time to reach the maximum power point, especially when the light intensity changes. The time for modules to recover to the maximum power point will be very short. The vibration is also severe during the power rise. When the steady state is reached, the oscillation amplitude of the power output is larger than under the other three methods. Figure 9b shows the results for the two-stage variable step size control strategy. Both the dynamic response and the stability at the maximum power point are obviously improved, but there is power fluctuation in the rising stage. At the same time, because the two-stage variable step control method simply uses two different steps from zero to maximum power point, it cannot meet the inherent characteristics of the system, which will lead to a large energy loss. Figure 9c,d shows the results for the DCL control method and the proposed CCM/DCM hybrid control strategy. They adopt the same 3SVSS-MPPT algorithm but different voltage control strategies. The speed of maximum power tracking is guaranteed, because in the first stage, the voltage corresponding to the maximum power point of the module is achieved by the closed-loop control. Then a two-stage variable step-size control method is adopted near the maximum power point. When the module is working near the maximum power point, the step size of the 2nd and 3rd stage of the methods, shown in Figure 9c,d, is relatively small, the voltage at the maximum power point is stable, and the power oscillation is decreased. That is to say, the performances of these two methods are significantly improved. It should be mentioned that under fixed irradiance, the performance of the DCL control strategy is a little better than the CCM/DCM hybrid control strategy, but in other circumstances, the CCM/DCM hybrid control strategy has more advantages.

Simulation Results under Drastic Changes in Irradiance
In order to reflect the change of light intensity in the BIPV system, in Figure 10, the change of irradiance was set as follows. Within the first 0.5 s, the irradiance was 1000 W/m 2 , and it decreased by 200 W/m 2 every 0.5 s until 2 s was reached. After 2 s, the irradiance increased by 200 W/m 2 every 0.5 s until 3.5 s. Figure 11 presents the simulation results of the output power of thin-film modules under the abrupt irradiance change. According to the characteristics of the module, when the irradiance changes, the current at the maximum power point of the module changes obviously, and the changing trend is almost the same as that of power, while the voltage is almost unchanged. As observed in Tables 3 and 4, when the irradiance changed from 1000 W/m 2 to 400 W/m 2 , the regulated powers by the three conventional methods were obviously lower than the theoretical value. This also means that the average powers and deviations were larger than under the CCM/DCM hybrid control strategy, especially when the irradiance was low. Compared with the three conventional methods, the most significant advantage of the CCM/DCM hybrid control strategy is high accuracy even when the irradiance is low or changes dramatically. When the irradiance changed from 400 W/m 2 to 1000 W/m 2 , the CCM/DCM hybrid control strategy also had a much better performance in terms of recovering the original stable state than other methods. Among the four exhibited methods, the CCM/DCM hybrid control strategy is the only one that had good reproducibility with a deviation of no more than 1 W, as the irradiance was leaping up and down. Additionally, the CCM/DCM method delivered the most power among the four methods at a low irradiance, such as 600 and 400 W/m 2 . This led to the highest average power being achieved by the CCM/DCM method both when the irradiance was decreasing and increasing, as exhibited in Table 3. In the whole process of irradiances change, the average power of the proposed method was the highest among the four methods. Therefore, the proposed control strategy caused less power loss than the other three methods. In another words, the control strategy proposed in this paper has a relative deviation below 2.2%, which is much lower than the other three methods, as shown in Figure 12. The relative deviation is defined as the power deviation divided by the theoretical maximum power.   Moreover, the proposed control strategy works at a higher efficiency under low irradiance, such as 400 W/m 2 . It is the only method that could deliver the theoretical maximum power. This is particularly important for BIPVs, since the mounting angles of thin-film BIPV modules are likely perpendicular, with large deviation from the optimal elevation angle. The CCM/DCM hybrid control method could deliver more power from the thin-film modules under such conditions.

Description of the Experimental Setup
The overall experimental system is shown in Figure 13. In order to realize the rapid and continuous change of irradiance and maintain consistency in the simulation, a PV1000 photovoltaic simulator was utilized during debugging to substitute for the output of thin-film PV modules working under an actual light source. The parameters of the thin film in PV1000 are set the same as in Matlab. Three scenarios were simulated: working under fixed irradiance (S = 1000 W/m 2 ), various sampling times (Ts = Tc = 100 μs, Ts = 50 μs < Tc, Ts = 200 μs), and sudden change of irradiance (the same as the condition of simulation). Other experimental parameters were the same as the simulation parameters tabulated in Table 2. The control algorithm was implemented in the TMS320F28335 control board. The data logger statement was used to obtain the experimental waveforms.  When the irradiance is fixed, the experimental results confirm the simulation results and verify the advantages of the proposed CCM/DCM hybrid control strategy. As exhibited in Figure 14 c,d, the rising time of the output power of the module was 3 s, which was shorter than under the other two methods, and the power oscillations within the rising time and at the maximum power point were also smaller. In terms of the P&O algorithm, the output power of the module did not reach the maximum within the test time. For the two-stage variable step method, when the modules reached the maximum power within 4 s, there were obvious oscillations and some power loss.

Experiment Results
As shown in Figure 14 c,d, the output power of the modules reached a steady state after 3 s. When the output power of the modules reaches the maximum, the oscillation state should be altered by changing the sampling period of the system, according to Equation (18). This is shown in Figure 15. It can be seen in Figure 15 that the sampling time significantly affects the output power of the module and the stability of the MPPT algorithm. As shown Figure 15a, when the sampling period is appropriately designed, the output power of the modules is close to the theoretical value, and the oscillation near the maximum power point is about 1 W, which is relatively small. This indicates low power loss and high conversion efficiency. When the sampling time is short, there are too many transitions in the MPPT algorithm, although the oscillation of the system at the maximum power point is not more than 2 W, as shown in Figure 15b. In this case, the actual output power is slightly lower than the theoretical value, and the system efficiency is reduced. As shown in Figure 15c, if the sampling period of the system is large, the oscillation of the system at the maximum power point is nearly 3 W, and the output power is also lower than the theoretical value. The overall efficiency of the system is reduced as well. Figure 16 shows the comparative test results for the output power of the four methods under dramatic irradiance change. These results are consistent to the simulation. When the light intensity changes dramatically, such as from 1000 W/m 2 to 800 W/m 2 , only the CCM/DCM hybrid control strategy can control the output power of the modules at close to the theoretical power output value in Table 5. When the irradiance decreases dramatically in a short period of time (from 800 W/m 2 to 600 W/m 2 to 400 W/m 2 ), it can be seen from Table 5 that the average power of the first three methods is lower than that of the proposed method. It also means that the first three control algorithms lead the output power to deviate significantly from the theoretical value, as shown in Table 6. The maximum deviation during the irradiance decreasing is 55 W. That is, their control accuracy is even worse in real applications than in the simulation, causing deterioration of the system energy efficiency. However, as shown in Figure 17, the proposed method has a relative deviation as low as 5%, which is much lower than the other three methods. What is more, the relative deviation of the CCM/DCM method remains stable between 3% and 5% for all four irradiances. When the irradiance suddenly rises again, the results are similar to those in the simulation; the proposed method has a good ability to recover the original steady state. In short, the proposed method shows a much better performance than the first three methods.   Conclusively, the experimental data in Tables 5 and 6 indicate a high tracking accuracy and energy efficiency of the CCM/DCM hybrid control strategy, compared to the other three methods. Therefore, the proposed control strategy will ensure PV system energy efficiency. Since BIPV systems operate under an irradiance lower than 1 sun and encounter in most circumstances dramatic irradiance changes, the proposed CCM/DCM hybrid control strategy is particularly suitable for BIPVs and will deliver more energy than the other three methods.

Conclusions
In this paper, considering the special working environment of BIPV systems and the characteristics of thin-film photovoltaic modules, a 3SVSS MPPT algorithm was proposed. This algorithm was realized by disturbing the voltage of thin-film modules. After the MPPT algorithm was introduced, a reasonable design of sampling period was introduced in this paper, so that the energy loss of the system was reduced. Lastly, a CCM/DCM hybrid control strategy based on CCM and DCM of the DC-DC converter was proposed to realize perturbing the voltage of the modules. The proposed method simplified the design of the control parameters in two modes to a certain extent and could fully guarantee the respective control performances. What is more, the proposed control strategy can be used for other DC-DC converters as well, although only the boost converter was used in this paper.
In order to reflect the advantages of the MPPT control strategy proposed in this paper, by setting a fixed light intensity in the simulation and comparing with other control algorithms (P&O, two-stage variable step size, and DCL control), the MPPT control strategy proposed in this paper demonstrated a good performance in two basic indicators of MPPT performance, namely, rapidity and stability. In order to better reflect its application advantages in BIPV systems, different irradiance conditions were considered in the simulation. The simulation results showed that the proposed algorithm has high tracking accuracy and is promising for applications in BIPVs. The experimental work further verified the proposed scheme and proved that the proposed controller is suitable for BIPV applications.

Conflicts of Interest:
The authors declare no conflict of interest. The output current of the Boost converter