# Improvement of the Maximum Power Point

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1 Improvement of the Maximum Power Point Tracker for Photovoltaic Generators with Particle Swarm Optimization Technique by Adding Repulsive Force among Agents ∗ Department…

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Improvement of the Maximum Power Point Tracker for Photovoltaic Generators with Particle Swarm Optimization Technique by Adding Repulsive Force among Agents
∗ Department
Vanxay Phimmasone∗, Tsugio Endo∗ , Yuta Kondo∗ and Masafumi Miyatake∗ of Engineering & Applied Sciences, Sophia University, Tokyo 102-8554, Japan
Abstract— This paper deals with Maximum Power Point Tracking (MPPT) control of photovoltaic generators. Photovoltaic (PV) generation systems need maximum power point tracker because the PV power output depends on the operating terminal voltage and current. Further, the PV array exhibits two or more MPP’s under partial shading condition and hence ﬁnding the MPP using conventional techniques is a difﬁcult task. To overcome the difﬁculty, ﬁnding the MPP, the authors improve the MPPT with Particle Swarm Optimization (PSO) technique by adding a kind of “repulsion term” to the equation of PSO algorithm. The term enables to improve the response to various types of insolation change. This results in lower cost, higher overall efﬁciency and also the algorithm is simple. The improved PSO-MPPT algorithm is veriﬁed through simulative and experimental studies. It is proved this algorithm is superior to the original PSO-MPPT methods by evaluating generated power and electrical energy. Index Terms— Maximum Power Point Tracker, Multidimensional optimization, Photovoltaic array, Particle Swarm Optimization.
I variation of irradiance maximum area maximum power
V
Fig. 1. I-V characteristics of a solar cell.
shading conditions. If a PV array is partially shaded by the shadow of building, tree etc, realization of MPPT is a difﬁcult task. If the modules with different optimal current, caused by uneven insolation, are connected in series-parallel, local maximum power points (MPPs) often appears in the power -vs- voltage characteristics. This is due to the fact that the optimal current of each PV module is nearly proportional to the insolation falling on it. Under these conditions the conventional MPPT controller may track to a local MPP instead of global MPP. Hence, the generated power may be reduced and PV system efﬁciency will decrease. Several research groups have been made attempts in the global MPPT realization by evolving different algorithms[3][5]. However, most of them use lengthy calculations, on-line sensed data or special circuit conﬁgurations. The authors made an attempt to simplify the MPPT algorithm and to track global MPP under partial shading conditions. The author’s aim is to realize a power-tracking scheme that will have the following salient features: 1) Finding the global MPP to maximize the generated power from the PV source 2) Simplicity in the algorithm and it should use the conventional circuit conﬁguration 3) Applicable to large scale PV system, resulting from series parallel combination of the solar cells. The authors tested the proposed MPPT controller [7]-[8] with
I. I NTRODUCTION Clean and renewable energy source such as photovoltaic (PV) power generation is expected as one of the key technologies to mitigate global warming. It is possible to use the PV power in distributed generation, transportation and mobile applications. Since the PV sources exhibits non-linear v − i characteristics their power output mainly depends on the nature of the connected load. Hence direct load connection to the PV system results in poor overall efﬁciency. As the solar panels are still expensive life cycle cost minimization is essential. To achieve some of these goals direct connected PV systems are replaced by a PV systems having an intermediate maximum power point tracker. The power produced by a PV module depends on the solar irradiance and temperature. It is important to ﬁnd the optimal operating voltage of PV arrays in order to increase the efﬁciency of PV generators. To achieve this, various conventional Maximum Power Point Tracking (MPPT) algorithms [1]-[2] have been proposed and used to extract maximum power from PV arrays under varying atmospheric conditions. However, all the above MPPT schemes are suitable under ideal conditions and are not able to extract true maximum power under partial
I
I
I
+
unshaded module
=
shaded module
V
V P=VI
total
V
V
Fig. 2. Characteristics of PV modules connected in series.
Particle Swarm Optimization technique. It worked almost very well, however, in some conditions, it was found that trackability of the global MPP is not enough. In this paper, the authors propose to add a kind of “repulsion term” to the equation of PSO algorithm that determines the magnitude of voltage shift. The term enables to improve the response to various types of insolation change. II. C HARACTERISTICS OF P HOTOVOLTAIC A RRAY A PV module is composed of several solar cells connected in series-parallel to get the desired voltage/ current and shielded with glass to protect against environmental changes. The v − i characteristics of a PV cell is shown in Fig. 1. The current is almost proportional to solar insolation. Most of them also have a by-pass diode and reverse blocking diode. A typical PV generation system is composed of several modules connected in series-parallel to meet the load power demand. Here, a PV system consisting of two modules connected in series is considered. Let us assume that one module is fully illuminated, while the second one is partially shaded. Under this condition the current ﬂowing through the two modules is same, since the modules are connected in series, but current generated by the second module is less than the fully illuminated module. Under this condition the excess current ﬂows through the by-pass diode. The v − i characteristics of individual module as well as the PV total system is shown in Fig. 2. It can be seen that, Fig. 2, there are two MPPs. If the number of modules increases, the characteristics under uneven insolation are complicated and generate two or more MPPs. Under such cases it becomes difﬁcult to realize the MPPT using the conventional methods. Furthermore, if the global MPP can be found, each module is not operated at the optimal condition, because the optimal current is inherently different at different insolations. If the PV system is divided into number of small arrays and each small array is controlled with its own converter then the power loss due to partial shading can be minimized.
MPPT controller DC
sensor
DC DC
sensor
AC
grid / load
DC DC MPPT controller
Fig. 3.
Multiple arrays controlled by multiple controllers.
MPPT controller DC
sensor
DC DC AC
grid / load
DC DC
Fig. 4.
Multiple arrays controlled by a single controller.
However, this scheme requires more number of voltage and current sensors as shown in Fig.3. In order to reduce the cost as well as to have fewer problems with controlling scheme the number of sensors should be less. To this direction authors have proposed a new scheme, shown in Fig.4, where-in a single pair of voltage and current sensors is sufﬁcient to realize the MPPT scheme. The detailed MPPT control technique of this new scheme is discussed in the next section.
pbesti
sk+1 i
k+1 vi
P(V1, V2)
k vi
sk−1 i
Fig. 5.
sk i
gbest
V1
Movement of a PSO agent. Fig. 6.
V2
An image of multidimensional function.
III. PARTICLE S WARM O PTIMIZATION A PPLIED TO MPPT C ONTROL A. Particle Swarm Optimization The authors proposed a Particle Swarm Optimization (PSO)[6] technique to solve the problems involved in the MPPT control discussed in the preceding sections. The PSO method is a simple and effective meta-heuristic approach that can be applied to a multivariable function optimization having many local optimal points. The PSO uses several cooperative agents and each agent shares the information attained by each individual during the search process. In the method, each agent k moves in the search space with a velocity, vi , according to its own previous best solution and its group’s previous best solution. The velocity and position update can be described by the following equations.
k+1 k = wvi + c1 r1 (pbesti − sk ) + c2 r2 (gbest − sk ) vi i i
where N is the size of the row vector and it indicates the number of PV arrays. The velocity variable v can be written as
k−1 k v k = [V1k − V1k−1 , V2k − V2k−1 , · · · , VN − VN ]
(6)
The objective function f is the generated power P , which is the summation of power generated by each array. The output voltage vector s changes in the following order and measures the power P (s). · · · → sk → sk → · · · → sk 1 2 M → sk+1 → sk+1 → · · · → sk+1 → · · · 1 2 M
(7)
(1) (2)
sk+1 i
=
sk i
+
k+1 vi
where w is the momentum factor; c1 and c2 are positive constants; r1 and r2 are the random numbers and their values are in between (0-1). The variable pbesti is used to memorize the best position that the i-th agent has found so far. It is updated like (3) if the condition (4) is satisﬁed, pbesti = sk i f (sk ) > f (pbesti ) i (3) (4)
where M is the number of agents. The authors modiﬁed the PSO algorithm in order to apply it to the MPPT control. In real-time operation, the objective function f often changes due to environmental as well as electrical load changes. Under such cases the agents must be reinitialized so as to search the new MPP again. The agents are reinitialized whenever the following two conditions are satisﬁed. (8) |vi+1 | < Δv |P (si+1 ) − P (si )| > ΔP P (si ) (9)
here f is the objective function that should be maximized. The variable gbest is used to memorize the best position achieved among all the all agents. During the process of optimization the agents’ movement appearance is illustrated in Fig. 5. B. Original Way of Applying PSO to MPPT In case of constant bus voltage applications only one current sensor is sufﬁcient for tracking the maximum power from the several individual PV modules. It can be called a multidimensional MPPT control as shown in Fig. 6. The terminal voltage of the individual PV systems are grouped and represented in the form of N - dimensional row vector as (5).
k sk = [V1k , V2k , · · · , VN ]
The equations (8) and (9) represents agents convergence detection and sudden change of insolation, respectively. As already reported in [7], the experimental result of the original PSO-MPPT showed that the global MPP on the 2 dimensional searching plane could be tracked within one second even under partially shaded conditions. The typical waveform of the response is shown in Fig.7. However, the original PSO-MPPT had a shortcoming of inappropriate response in gradual change of insolation. Therefore, the authors intended to improve the original PSO-MPPT. C. Improvement of PSO by Adding Repulsion Term In the proposed method that is an improvement of the original PSO method, the magnitude of voltage shift for each
(5)
500 375 250 125 0 1 0.5 0 1 0.5 0
P[W]
D1
D2 1
unshaded partially shaded
2
3
4 t [s]
5
Fig. 7.
Transient response of output power and duty cycles of two boost choppers for two PV arrays.
TABLE I PARAMETERS OF THE PSO. PSO agents 3 N 2 PSO coefﬁcients w 0.4 c1 0.8 c2 1.2 conditions of initialization Δv [V] 0.8 ΔP 0.15 M
gate signal gate controller D1 MPPT controller D2 I 3 φ IPM
Electronic Load
current sensor
agent is determined by the following equation that repulsive term is added as the 4th term,
k+1 vi
PV1 PV2
= −
k wvi
+ c1 r1 (pbesti − sk ) + c2 r2 (gbest i k k c3 r3 (cent − si )/(|centk − sk | + d)3 , i
−
sk ) i (10)
Fig. 8.
where c3 and r3 are a positive constant and a random number whose value is in between (0-1). The function “cent” is the center of all agents described as the following equation, centk =
M i=1
Circuit conﬁguration of the experimental system. TABLE II I NITIAL POSITION OF AGENTS . agent V1 [V] V2 [V] 1 0.2Vop 0.2Vop 2 0.8Vop 0.5Vop 3 0.5Vop 0.8Vop : open circuit voltage of the array
sk i . M
(11)
The constant d is a small number and needed to avoid the 4th term divided by zero in centk = sk . If the 3 agents converge i to around the center of the agents, the 4th term is getting large to diverge the agents. It is effective especially in frequent and gradual insolation changes, e.g. cloudy conditions. IV. E XPERIMENTAL S YSTEMS The PSO algorithm parameters used in this paper are tabulated in Table I which were determined by trial and error method using simulations. They were re-tuned after the previous paper[7]. The appropriate number of agents M was already discussed in [9]. Fixed values were used for the agents’ initial positions and they are given in Table II. The conﬁguration of the experimental system is shown in Figs 8 and 9. Two PV arrays, which consist of six PV modules
Vop
(Fuji Electric Co. ELR-615-160Z) connected in series-parallel, connected to an electronic load via two boost choppers. The terminal voltages of the individual PV arrays were to be controlled by their respective choppers. Rated output power and voltage of each PV array was about 300 W and 50 V respectively. Actually, two legs of a three phase Intelligent Power Module (IPM) was used to realize the two boost choppers. Digital Signal Processor (DSP TMS320C32) based data acquisition was used to generate the PWM gate signals and to realize the proposed MPPT control scheme. A current sensor was inserted in the load circuit. It measures the total power generated by the two arrays including converter loss.
PSO-B energy extracted ratio [%]
1Ax 1Ay 1Az
1Bx 1By 1Bz
2Ax 2Ay 2Az
2Bx 2By 2Bz
HIL PSO-A PSO-C
PV1
Fig. 9.
250 200 power [W] 150 100 50 0 0 10 20 30 40
PV2
PSO-B PSO-A PSO-C HIL
Connection of PV modules and numbering.
frequency of sinusoidal insolation change [Hz]
Fig. 11.
Frequency characteristics.
PSO-B ideal value 50 60 time [s] 70 80 90 100
Fig. 10.
An example of simulation waveform.
The control program was developed in C/C++ environment, which will be compiled and downloaded on to the DSP platform. An electronic load was set for constant battery voltage of 100 V. Inductance of the smoothing reactor was 60 [mH]. The output voltage vector s changed after every 0.05 seconds and followed the sequence of control as described by (7). The relation between array voltage V and duty ratio of the chopper D is written as (12) because the output voltage was kept 100 V constant by the electronic load in this system. V (12) D =1− 100 In this paper, only one array PV1 was used because the proposed method was compared with the simple Hill Climbing method which can control only one array. V. R ESULTS AND D ISCUSSION A. Several Types of MPPT Controllers to be Compared In order to discuss the effectiveness of the proposed method, the following MPPT controllers were assumed. HIL: The simplest hill climbing method was used. The method involves moving the operating voltage by one step and then examining the change in generated power. If the power increases, the operating point moves in the same direction, else it is moves in the opposite direction. The step size of voltage was set to 1.2 V and the required control cycle time is 0.1 s. PSO-A: The original PSO method was used. It has the initializing function shown in (8)-(9). Repulsive term is NOT implemented. The method will respond to stepwise insolation change quickly.
PSO-B: One of the proposed PSO method was used. Repulsive term was used, but initialization was NOT fully implemented in order to reduce the loss in gradual and frequent insolation change. If the condition of initialization was satisﬁed, the method only reset the recorded values of output power at pbest , without initializing agents’ positions. In this case only, the value of ΔP was 0.05. PSO-C: The other proposed PSO method was used. Both repulsive term and initialization are implemented. The method will have both advantage of PSO-A and B. B. Simulation It is not easy to generate identical gradual insolation change in each experiment. Therefore, as the ﬁrst step, the MPPT controllers was compared with simulations. The I − V characteristic of an array used in the simulations is I = −8.66 × 10−5 exp(0.18V ) + 4.92pins , (13)
where the units of I and v are [A] and [V] respectively and pins [kW/m2 ] shows the power of insolation. The equation is based on the measured characteristic. The other conditions in simulations are the same as that in experiments shown in the previous section. In the simulations, uniform solar insolation was assumed. The insolated power pins was changed like sinusoidal wave shown in Fig. 10, pins (t) = 0.75 + 0.25 cos(2πf t)[kW/m2 ], (14)
where f was the frequency of insolation change. The value f is changed to scan the characteristic of frequency response. Since the response time constant is 1 second and more as shown in Fig. 7, the range of f is set between 0.0001 [s] and 1 [s]. Each MPPT was evaluated with extracted energy divided by theoretically maximum energy. It is named “energy extracted ratio.” The frequency responses calculated with simulation results were plotted in Fig. 11. From the results, the original PSOA is not suitable for gradual insolation change, because the
60 50 voltage [V] 40 30 20 10 0 0 100 200 300 time [s] 400 500 600
to adapt gradual insolation change and initialize the position of agents in some points to respond faster insolation change. On the other hand, PSO-A could not move the operating point because the conditions of initialization shown in (8) and (9) was not satisﬁed against gradual change of insolation. VI. C ONCLUSIONS The novel MPPT algorithm using PSO technique was improved to control operating point appropriately under conditions of gradual and frequent insolation change. It is proved from simulation and experiments that the added term of repulsion force was working well. The authors are still improving the proposed method and intend to apply the method in this paper to multidimensional array voltage control.
400 500 600
200 180 160 140 120 100 80 60 40 20 0 0 100 200 300 time [s]
power [W]
R EFERENCES
[1] T. Esram, P. L. Chapman: “Comparison of Photovoltaic Array Maximum Power Point Tracking Techniques” IEEE Transaction on Energy Conversion, Vol. 22, No. 2, pp.439-449, 2007. [2] N. A. Ahmed and M. Miyatake: “A Novel Maximum Power Point Tracking for Photovoltaic Applications Under Partially Shaded Insolation Conditions” Electric Power System Research, Vol.78, No.5, pp.777-784, 2008. [3] K. Kobayashi, I. Takano and Y. Sawada: “A Study on a Two Stage Maximum Power Point Tracking Control of a Photovoltaic System under Partially Shaded Insolation Conditions” in Proc. of IEEE Power Engineering Society General Meeting, pp.2612-2617, 2003. [4] A. M. Bazzi, S. H. Karaki: “Simulation of a New Maximum Power Point Tracking Technique for Multiple Photovoltaic Arrays” in Proc. of IEEE International Conference on Electro/Information Technology, pp.175-178, 2008. [5] H. Patel and V. Agarwal: “Maximum Power Point Tracking Scheme for PV Systems Operating Under Partially Shaded Conditions” IEEE Transactions on Industrial Electronics, Vol.55, No.4, pp.1689-1698, 2008 [6] J. Kennedy and R. Eberhart : “Particle Swarm Optimization” in Proc. of IEEE International Conference on Neural Networks, Vol. IV, pp.19421948, Perth, 1995. [7] M. Miyatake, M. Veerachary, N. Fujii, F. Toriumi and N. A. Ahmed: “Multidimensional Maximum Power Point Tracking Control for Converters Connected to Photovoltaic Arrays with Particle Swarm Optimization Technique” in Proceedings of ICEMS 2006, Nagasaki, Japan, 2006. [8] M. Miyatake, F. Toriumi, T. Endo and N. Fujii : ”A Novel Maximum Power Point Tracker Controlling Several Converters Connected to Photovoltaic Arrays with Particle Swarm Optimization Technique” in Proc. of EPE 2007, No.700, Aalborg, Denmark, 2007. [9] T. Inada, I. Hiratsuka, C. Mizuochi, H. Ko and M. Miyatake : “The relation between the number of agents of Particle Swarm Optimization method and the efﬁciency of MPPT for photovoltaic generators” in Proc. of Japan Industry Applications Society Conference IEE of Japan, Vol.1, No.69, pp.I-285-286, Fukui, Japan, 2005. (in Japanese)
Fig. 12.
70 60 50 40 30 20 10 0
Array voltage and power of PSO-A in the experiment.
voltage [V]
0
100
200
300 time [s]
400
500
600
180 160 140 120 100 80 60 40 20 0
power [W]
0
100
200
300 time [s]
400
500
600
Fig. 13.
Array voltage and power of PSO-C in the experiment.
energy extracted ratio is the lowest between f = 0.01[Hz] and 1[Hz]. One of the proposed method PSO-B is the best in the simulations, but it should be noted that PSO-B cannot respond to stepwise insolation change because of omitting initialization. The other proposed method PSO-C is more improved than PSO-A and can also respond to stepwise insolation change. But, from Fig. 11, it is found that there may be still more room to raise energy extracted ratio as PSO-B and HIL methods. C. Behavior of Operating Point in Experiments The improved PSO-MPPT algorithm was also veriﬁed through experimental studies. A cloudy day was chosen to prove the behavior of operating point under gradual and frequent change of insolation. Waveforms of the experimental results in gradual and frequent insolation changes for PSO-A and C are shown in Figs 12 and 13, respectively. It is proved that the proposed method PSO-C could keep small ﬂuctuation