AIAA 2011-5654

9th Annual International Energy Conversion Engineering Conference 31 July - 03 August 2011, San Diego, California

Newton’s method for fast speed MPPT of solar panel Soichiro Nakamura1 Smart Energy Laboratory.co.,Ltd 33-8 Shimotogari,Sunto,Shizuoka,Japan Minoru Iwasa2 Space Power System Group, Aerospace Research and Development Directorate Japan Aerospace Exploration Agency 2-1-1 Sengen, Tsukuba, Ibaraki, Japan and Masatoshi Nakahara3 Energy Electric Laboratory, Sojo Univercity 4-22-1 Ikeda,Kumamoto,Kumamoto,Japan

Generally in order to achieve the fast MPPT the algorithm must have features of reduced number of repetition and stable operation with high sampling frequency. We propose the new algorithm employing Newton’s Method to satisfy requirements above for the fast MPPT. We also actually implement the proposed method in a MPPT circuit board by using the rapid-control-prototyping (RCP) tool dSPACE. And this paper shows results of the simulation and experiments.

Introduction Maximum Power Point Tracking (MPPT) can be used to get the maximum available power from a Photovoltaic (PV). MPPT is usually embedded in a DCDC converter which inserted between the PV module and the load, battery or another power conditioner. This paper proposes a new method for the MPPT control of PV, which uses Newton’s Method, and compares it to the Hill-Climbing Method which is a conventional way of MPPT. This paper describes the new algorithm, the simulation results and the way of embedding new algorithm in digital controlled boost DCDC converter. The hill-climbing method has been already used in many PV applications since it is a very reliable method. The hill-climbing method is repeating algorithm, which measures output power of a PV and compares it to previously measured power, and this process is repeated many times. Therefore this algorithm essentially has disadvantage of a long tracking time. Moreover, it is not able to operate with 1 American Institute of Aeronautics and Astronautics

Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

high sampling frequency due to the effect of dynamic characteristics of DCDC converter. Consequently the hill-climbing method cannot achieve the fast MPPT. So, we propose the new algorithm employing Newton’s Method to satisfy requirements above for the fast MPPT.

1-1. Generalization of MPPT by Newton’s method. When the voltage of the module is V(V) and the current of the module is I(A), the formula of the power is P = VI (W). Therefore, the equation of the maximum power gives

P’ = I + VI’ = 0

(1)

Here, the symbol dash e.g. P’ denotes the derivative of V. According to Newton’s method, this method approximates x which make f(x) = 0, and the x is determined by below equations

Next, suppose f = P’、x = V then we get the following equation:

Further we get P’’(V) as:

P’’(V) = I’ + I’ + VI’’ = 2I’ + VI’’ (4) As a result, the general difference equation of Newton’s method is determined as:

This equation can find maximum power point any modules which has only one maximum power point.

1-2. Algorithm of solar panel The equation of (5) is applied to solar panel. First, the characteristic of I-V of solar panel is supposed the below characteristic

I: The current of solar panel V: The voltage of solar panel

From this equation

And 2 American Institute of Aeronautics and Astronautics

This equation is substituted for equation (5), and we get the following equation:

Next, suppose aV>>2

Here, it is difficult to use equation (7), because it is an exponent. Therefore following equation is used

1-3. Revision for transient response When the solar panel is connected to the converter, the transient response of the converter influences MPPT. The transient response is caused by L and C, therefore suppose the solar voltage is increased, it will increase afterwards too. So, in order to revise the voltage, the increased voltage is subtracted from the equation (3). As a result, we get following equation:

1-4 Change to duty The duty of converter is changed from the equation of voltage. And the buck converter, for example, is described. According to State Space Averaging Method, we get the duty as:

IL: reactor current Vo: output voltage Vc: it is determined by the on voltage of the switch and the diode r: the loss of the switching elements

This converter is connected a battery.

1-5. Revision for duty In order to revise the difference of the converter’s parameter, according to equation (3)

But, equation (14) is ignored the Rloss or the on voltage of semiconductor. As a result, according to equation (3), the finally equation of duty is determined as:

Here, suppose Dn0 is D0, Newton’s method is used directly the duty. But it is difficult to use, because the transient response influence very strongly. Therefore, in this algorithm, instead of the D 0, Dn0 which is 3 American Institute of Aeronautics and Astronautics

determined from V, which is result of Newton’s method, is used.

2. Simulation on Newton’s method and hill-climbing method. The algorithm is simulated by SCALE which has

PV Model

been developed by one of authors at Energy Electronics Laboratory Sojo Univ. SCALE is intended

Battery Model Load Model

mainly for the simulation for smart grid system, and can analyze the switching operated power circuit with digital control at a very high speed. Fig.1 shows the simulation circuit where the PV module has typical 24W maximum power and

Controller

parameters are given in Table1. The voltage Vo of the

Model

battery as a load of DC-DC converter is 12V. Figure 1. SCALE model.

The solar model P-V curve is shown in Figure 2. Firstly, the simulation result of hill-climbing

Voc

30(V)

Vmp

24(V)

(Constant Voltage mode ) to MPPT mode. The condition is shown

Isc

1.25(A)

below sampling frequency is 100Hz, and the switching frequency

Imp

1(A)

is 40kHz. In this case it took about 500msec to converge on

Table 1. PV parameters.

method is shown in Figure 3. In this simulation, it is mode transient from CV mode

maximum power point. Next, in order to improve the response of hill-climbing method, the operating frequency is increased and the result is shown in Figure 3. As can be seen form Figure 4, if the operation frequency increased, the response of converter become unstable or cannot find maximum power point. Therefore, in order to increase the operating frequency, it is necessary to use different algorithm. Secondly, the simulation result of Newton’s

the sampling frequency is 5kHz. It is very high speed

compared

to

HILL-CLIMING

METHOD. Therefore the response of this algorithm is

PV Power (W)

method is shown in Figure 5. In this simulation,

very fast, and the speed of convergence is about 5msec.

PV Voltage (V) Figure 2. P-V curve.

As a result, this method is able to achieve operation of MPPT at high speed. 4 American Institute of Aeronautics and Astronautics

V(V)

Vs

Is

About 500ms

T (msec) MPPT mode CV mode

Figure 3. Hill-climbing method response. Vs

V(V)

Is T (msec)

Figure 4. Hill-climbing method response (20kHz). V (V)

Vs

Is

About 5ms

T (msec) MPPT mode CV mode Figure 5. Newton’s method response.

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3. Implementation of the algorithm. Boost DCDC converter

RCP board

PWM output

Analog input dSPACE

dSPACE DS1103

interface Figure 6. DCDC converter board and dSPACE RCP system.

This section roughly describes the whole system used to confirm the proposed method.

The

controller models are constructed by using MATLAB/Simulink and are implemented directly to the target system. This way of implementation is called RCP (Rapid Control Prototyping), which is one of ways called MBD (Model Base Development). These controller models are downloaded automatically to the prototyping system which is provided by dSPACE. In this system a solar allay simulator (SAS) is used instead of solar panels. A main power circuit (buck DC-DC converter) board has interface for dSPACE tools, and this board can be operated easily with RCP strategy. (Figure 6)

Experiment The experiment of hill climbing method and

Vs

Newton's method was done with experimental environment which was described in section 3.

Vo

First, Steady state response of Newton's method is shown in Figure 7.

The Vs is output voltage of SAS(Solar Array

24.6V

Simulator) and the Vo is output voltage of

14.5V

DCDC converter. Each state can be confirmed that converges Figure 7. Steady State Response of newton’s

to a constant value. And, according to 1 sec average of the

method.

measured waveform, the maximum power point tracking rate was 99 percent. Second, the transient waveform of hill-climbing method is shown in Figure 8, which is mode transition of CV mode to MPPT mode.

In this case, the solar voltage is 29V, and it is controlled 5 volts to transient MPPT. And in ideal case 6 American Institute of Aeronautics and Astronautics

of simulation, the duty changes 0.45 to 0.6. Now, the duty width of hill-climbing method is 0.002 and operation frequency is 100Hz, this algorithm is needed to repeat 75

3s

times and it takes more than 750ms in ideal

MPPTmode

condition.

In the measured waveforms, it took more than

3s

because

of

the

influence

CVmode

of

measurement error.

Figure 8. Mode transition of hill-climbing method.

Third, the transient waveform of the newton's method is shown in Figure 9, which is mode transition of CV mode to MPPT mode.

In this case, mode transition took 5ms. 5ms

This result is almost same with the simulation waveform.

MPPTmode

24V

Finally, the results show that the response of

CVmode

newton's method operates more than 100 times faster than the hill-climbing method.

Figure 9. Mode transition of Newton’s method.

Conclusion Compared with hill-climbing method, Newton’s method is better way to operate at quite high speed, and it achieves much faster MPPT. One of applications for Newton’s method MPPT, for example, is Electric Vehicle (EV) because maximum power point of such solar panel changes very easily and suddenly. High speed MPPT can catch up with that fast change of characteristics of the solar panel. Eventually the battery in the EV spends less energy, and it can be expected to extend the distance of driving. Also, it can be used for small satellite. Because it is always rolling its body in order to stabilize itself, therefore the maximum power point will change easily too. But, the Newton’s method MPPT has some demerits. First, the performance of MPPT depends on the accuracy of the AD converters. Second, comparing the equation of the Newton’s method with the Hill-climbing method, the Newton’s method is more complex than the other one. So, we have to solve these problems for practical use.

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References 1

Gelff Walker ”Evaluating MPPT converter topologies using a MATLAB PV model”

2

Hitoshi Kidokoro ”The development of controller for DC-DC converter using Model Based Design”

IEICE Technical Report

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