2622 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 7, JULY 2008 A Variable Step Size INC MPPT Method for PV Systems Fangrui Liu, Shanxu Duan, Fei Liu, Bangyin Liu, and Yong Kang Abstract—Maximum power point tracking (MPPT) techniques are employed in photovoltaic (PV) systems to make full utilization of PV array output power which depends on solar irradiation and ambient temperature. Among all the MPPT strategies, the incremental conductance (INC) algorithm is widely used due to the high tracking accuracy at steady state and good adaptability to the rapidly changing atmospheric conditions. In this paper, a modiﬁed variable step size INC MPPT algorithm is proposed, which automatically adjusts the step size to track the PV array maximum power point. Compared with the conventional ﬁxed step size method, the proposed approach can effectively improve the MPPT speed and accuracy simultaneously. Furthermore, it is simple and can be easily implemented in digital signal processors. A theoretical analysis and the design principle of the proposed method are provided and its feasibility is also veriﬁed by simu- lation and experimental results. Index Terms—Incremental conductance (INC), maximum power point tracking (MPPT), variable step size. I. I NTRODUCTION P HOTOVOLTAIC (PV) generation is becoming increas- ingly important as a renewable source since it exhibits many merits such as cleanness, little maintenance and no noise. The output power of PV arrays is always changing with weather conditions, i.e., solar irradiation and atmospheric temperature. Therefore, a maximum power point tracking (MPPT) control to extract maximum power from the PV arrays at real time becomes indispensable in PV generation systems. In recent years, a large number of techniques have been proposed for tracking the maximum power point (MPP) [1]–[12]. Fractional open-circuit voltage and short-circuit cur- rent [1], [2] strategies provide a simple and effective way to acquire the maximum power. However, they require periodical disconnection or short-circuit of the PV modules to measure the open-circuit voltage or short-circuit current for reference, resulting in more power loss. Hill climbing and perturb and observe (P&O) methods are widely applied in the MPPT con- trollers due to their simplicity and easy implementation [3]–[5]. The P&O method involves a perturbation in the operating volt- age of the PV array, while the hill climbing strategy introduces Manuscript received July 13, 2007; revised February 18, 2008. This work was supported in part by the Delta Power Electronics Science and Education Development Fund under Grant DREK200501 and in part by the National Natural Science Foundation of China under Grant 50777025. The authors are with the College of Electrical and Electronic Engi- neering, Huazhong University of Science and Technology, Wuhan 430074, China (e-mail: fangruihust@163.com; dshanxu@263.com; dyj_lf@163.com; lby@smail.hust.edu.cn; ykang@mail.hust.edu.cn). Color versions of one or more of the ﬁgures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identiﬁer 10.1109/TIE.2008.920550 a perturbation in the duty ratio of the power converter [5] and is more attractive due to the simpliﬁed control structure [6]. Nevertheless, steady-state oscillations always appear in both methods due to the perturbation. Thus, the power loss may be increased. Incremental conductance (INC) method, which is based on the fact that the slope of the PV array power versus voltage curve is zero at the MPP, has been proposed to improve the tracking accuracy and dynamic performance under rapidly varying conditions [7], [8]. The steady state oscillations would be eliminated in theory since the derivative of the power with respect to the voltage vanishes at MPP. However, null value of the slope of the PV array power versus voltage curve seldom oc- curs due to the resolution of digital implementation. Although the INC method is a little more complicated compared with the P&O/hill climbing strategy, it can be easily implemented due to the advancements of digital signal processors (DSPs) [9]. Moreover, fuzzy and neural network methods [10], [11] that focus on the nonlinear characteristics of PV array provide a good alternative for the MPPT control. Since the output charac- teristics of the PV array should be well ascertained to create the MPPT control rules, the versatility of these methods is limited. The INC MPTT algorithm usually uses a ﬁxed iteration step size, which is determined by the accuracy and tracking speed re- quirement. Thus, the corresponding design should satisfactorily address the tradeoff between the dynamics and steady state os- cillations. To solve these problems, a modiﬁed INC MPPT with variable step size is proposed in this paper. The step size is auto- matically tuned according to the inherent PV array characteris- tics. If the operating point is far from MPP, it increases the step size which enables a fast tracking ability. If the operating point is near to the MPP, the step size becomes very small that the oscillation is well reduced contributing to a higher efﬁciency. In the following, the design principle of the modiﬁed variable step size INC MPPT is presented on the basis of uniform irradiance for PV array. Both simulation and experimental design exam- ples are then provided, and the corresponding results conﬁrm that the proposed method can effectively improve the dynamic performance and steady state performance simultaneously. II. PV ARRAY MPPT A. PV Array Characteristics Generally, a PV module comprises of a number of PV cells connected in either series or parallel and its mathematical model can be simply expressed as [12]–[14] I o = n p I ph − n p I rs  exp  K o V n s  − 1  (1) 0278-0046/$25.00 © 2008 IEEE Authorized licensed use limited to: S. Abbas Taher. Downloaded on December 28, 2008 at 03:41 from IEEE Xplore. Restrictions apply.