Advanced Fuzzy Logic Controller for Tracking the Maximum Power Point of PV Arrays

Advanced Fuzzy Logic Controller for Tracking the Maximum Power Point of PV Arrays

Advanced Fuzzy Logic Controller for Tracking the Maximum Power Point of PV Arrays

1. N. Bhupesh Kumar, Sr. Assistant Professor, Department of EEE, Sir C R Reddy College of Engineering, Eluru

2. Dr. K. Vijaya Kumar Reddy, Professor, Department of ME,JNTUH, Hyderabad

   Abstract With the increasing fossil fuel deficit, global warming

   There is a unique point on the curve, called the maximum

   and damage to the ecosystem the studies on photovoltaic

   power point (MPP), at which the array operates with

   generation are increasing extensively as it is an inexhaustible and

   maximum efficiency and produces maximum output power.

   broadly available energy resource. However, the output power

   As it is well known, the MPP of a PV power generation

   induced in the photovoltaic modules depends on solar radiation and temperature of the solar cells. Therefore, to maximize the

   system depends on array temperature, solar insolation, shading conditions, and PV cells aging, so it is necessary to constantly

   efficiency of the renewable energy system, it is necessary to track

   track the MPP of the solar array. A switch-mode power

   the maximum power point of the PV array. This paper presents a maximum power point tracker using fuzzy set theory to improve

   converter, called a maxi-mum power point tracker (MPPT), can be used to maintain the PV arrays operating point at the

   energy conversion efficiency. An advanced fuzzy controller is

   MPP. The MPPT does this by controlling the PV arrays

   proposed, by using a fuzzy cognitive network, which is in close

   voltage or current independently of those of the load. If

   cooperation with the presented fuzzy controller. This new method gives a very good maximum power operation of any PV array under different climatic conditions such as changing insolation and temperature. The simulation studies show the effectiveness of the proposed algorithm.

   properly controlled by an MPPT algorithm, the MPPT can locate and track the MPP of the PV array. How-ever, the location of the MPP in the IV plane is not known a priori. It must be located, either through model calculations or by a search algorithm. Fig. 2 shows a family of PV IV curves

   1. INTRODUCTION

      under increasing irradiance, but at constant temperature.

      With the increasing fossil fuel deficit, global warming

      Needless to say there is a change in the array voltage at which

      and damage to the ecosystem, renewable energy sources

      the MPP occurs. For years, research has focused on various

      (solar, wind, tidal, and geothermal, etc.) are attracting more

      MPP control algorithms to draw the maximum power of the solar array. These techniques include look-up table methods,

      attention as alternative energy sources. Among the

      using neural networks [1], [2], perturbation and observation

      renewable energy sources solar photovoltaic (PV) energy has

      (P&O) methods [3][6], and computational methods [7]. For

      been widely utilized in small-sized applications. It is also the

      example, Hiyama et al. [1] presented a neural network

      most promising candidate for research and development for large-scale uses as the fabrication of less costly photovoltaic

      application to the identification of the optimal operating point of PV modules and designed a PI-type controller for real-time

      devices becomes a reality.

      maximum power tracking. Optimal operating voltages are

      Photovoltaic system as a number of applications such as

      identified through the proposed neural network by using the

      water pumping, domestic and street lighting, electric

      open-circuit voltages measured from monitoring cells and

      vehicles, hybrid systems, military and space applications,

      optimal operating currents are calculated from the measured

      refrigeration and vaccine storage, power plants, etc., all in either stand-alone or grid-connected configurations. A PV array is by nature a nonlinear power source, which under

      short-circuit currents

      constant

      uniform

      irradiance

      has a

      currentvoltage

      (IV)

      characteristic like that shown in Fig. 1.

      Figure 2: PV array (I V) characteristics at various insolation levels

      The output of the neural network goes through the PI

      Figure 1: PV array (I V) and PV characteristics

      controller

      to the

      voltage

      control

      loop

      of the

      inverter to

      change

      the

      terminal

      voltage of

      the

      PV system

      to the

      Moreover, during the operation

      of the PV array the FCN

      identified optimal one.

      weights are continuously updated

      based on data from

      the

      Fuzzy-based MPPT

      technique [8],

      [9] is one of the

      encountered operating conditions. The performance of the

      computational methods, which have

      demonstrated fine

      method is tested using climatic data for a specific PV system

      performances under different environmental operating conditions.

      of the market, which reaches its MPP with great accuracy for various operational conditions, such as changing insolation

      The fuzzy controller introduced in [8] uses dP/dI and its

      and temperature and seasonal variations.

      variations

      (dP/dI), as the

      inputs and

      computes MPPT

      Organization of the paper is as follows. In Section II,

      converter duty cycle. The fuzzy tracker of [9] considers

      mathematical relations between the essential variables of a

      variation of duty cycle, but replaces dP/dI by the variation of

      PV system are presented. These relations are necessary for

      panel power. An online search algorithm that does not

      simulating its operation under different insolation and

      require the measurement of temperature and solar irradiation

      temperature levels. In Section III, an MPPT method, which

      level is proposed in reference [10]. Other researchers

      is based on a fuzzy controller methodology, is analysed.

      analysed and coared the various MPPT techniques [7], [11],

      Section IV makes a brief introduction in FCMs and presents

      [12]. Besides that, in [11] a simple DSP-based MPPT

      the graph of the proposed FCN, which will be used in close

      algorithm is proposed, while in [12] a combination of the

      cooperation with the fuzzy controller, in order to track the

      modified constant voltage control and the incremental

      MPP of a PV system. Simulated experimental results, based

      conductance method is introduced, showing good efficiency

      on climatic data of one year and on the operation of a typical

      (especially in lower insolation intensity). Finally, in [13],

      PV array of the market are given in Section V. Finally,

      [14] efforts have been made to model the dynamic behaviour of a PV system in order to study its interaction with the pertinent MPPT system, while in [15], MPPT assessment and testing methods were presented in order to identify the accuracy, error and efficiency of the MPPTs.

      This paper presents an advanced fuzzy logic controller, which uses fuzzy sets theory [8] in close cooperation with fuzzy cognitive networks (FCNs). FCNs [16], [17] constitute

      Section VI concludes the work.

   2. SIMULATION OF THE PV SYSTEM

      an extension

      of the

      well

      known

      fuzzy

      cognitive

      maps

      (FCMs) [18], so that they are able to operate in continuous interaction with the physical system they represent, while at the same time they keep track of the various operational

      Figure 3 : Equivalent circuit of a solar cell

      equilibrium points met by the system. FCNs can model

      Using the equivalent circuit of a solar cell (Fig. 3) and

      dynamical complex systems that change with time following

      the pertinent equations [11] the nonlinear (IV)

      nonlinear laws. They use a symbolic representation for the

      characteristics of a solar array are extracted, neglecting the

      description and modelling of the system. In order to

      series resistance

      illustrate different aspects in the behaviour of the system, an

      I I I exp[qV / kTA) 1] Vi

      (1)

      FCN is consisted of nodes with each node representing a

      i ph rs i R

      characteristic of the system, including possible control sh

      actions. These nodes interact with each other showing the dynamics of the system under study. Moreover, the FCN has the ability of continuous interaction with the physical system

      Where Ii is the PV array output current (A); Vi is the PV array output voltage (V); q is the charge of an electron; k is Boltzmanns constant in J/K; A is the pn junction ideality

      it represents, sending control actions and receiving feedback

      factor; T is the cell temperature (K); and Irs is the cell

      from the system. The FCN integrates the accumulated

      reverse saturation current. The factor A in (1) determines the

      experience and knowledge on the operation of the system, as

      cell deviation from the ideal pn junction characteristics.

      a result of the method by which it is constructed, i.e., using human experts who know the operation of system and its

      The ideal value ranges between 1 and 5, according to [11] and to the commercially available software package for PV

      behaviour, but most significantly, it can adapt this

      systems PVSYST V3.1 (see Table I).

      knowledge based on the feedback from the physical system or by using appropriate training data.

      The photocurrent Iph depends on the solar radiation and the cell temperature as stated in the following:

      The

      nodes

      of the

      FCN represent essential

      operational S

      (Voltage,

      Current,

      Insolation,

      Temperature)

      and

      control

      I ph I scr Ki T Tr

      (2)

      (Current)

      variables

      of the

      PV system.

      The

      node

      100

      interconnection weights are determined using data, which are

      Where

      Iscr

      is the

      PV array

      short

      circuit

      current at

      constructed so that they cover the operation of a PV system under a wide range of different climatic conditions. Once the

      reference

      temperature

      and

      radiation

      (A);

      ki is

      the

      short

      FCN

      is trained it

      can be

      mounted

      on any PV

      system.

      circuit current temperature coefficient (A/K) and S is the solar radiation (mW/cm2).

   3. MPPT BY FUZZY LOGIC CONTROLLER [8]

      TABLE 1

      The

      objective

      of the

      controller

      is to

      track

      and

      Factor A Dependence on PV Technology

      Technology A

      extract maximum power from the PV arrays for a given solar insolation level. The maximum power corresponding to the optimum operating point is determined for a different solar

      Si-mono

      1.2

      insolation level. Normally a dc dc converter is utilized

      Si-poly a-Si:H

      a-Si:H tandem a-Si:H triple CdTe

      CIS

      1.3

      1.8

      3.3

      5

      1.5

      1.5

      between the input source and the load for the purpose of MPPT.

      1. Fuzzification

         In [8], the authors focused on single inputsingle

         AsGa 1.3

         output plant, in which control is determined on the basis of satisfaction of two criteria relating to two input variables of

         The reverse saturation current Irs varies with temperature,

         the presented controller, namely error (E) and

         change of

         according to the following:

         error (CE), at a sampling instant k.

         The variable E and CE are expressed as follows:

         T 3

         1.115 1

         1

         P (k ) P (k 1)

         Irs Irr T exp k1 A T

         T

         (3)

         Ek pv pv

         (7)

         r

         r

         I pv (k ) I pv (k 1)

         Where Tr is the cell reference temperature, Irr is the

         CE(k)

         = E(k)

         – E(l-1)

         (8)

         reverse saturation current at Tr, k is the Boltzmanns

         constant in eV/K and the band gap energy of

         the

         Where Ppv(k) and Ipv(k) are the power and current of the

         semiconductor used in the cell is equal to 1.115.

         PV array, respectively. Therefore, E(k) is zero at the

         Finally, the next equation was used in the computer

         maximum power point of a PV array. In Fig. 4(a), the fuzzy

         simulations to obtain the open circuit voltage of the PV array Equations

         set of input E(k) is presented, while in Fig. 4(b), the fuzzy set of input CE(k) is shown. Finally, Fig. 4(c) shows the

         AkT I ph I rs

         respective fuzzy set of the output dD, which represents the

         Voc q

         ln

         I rs

         (4)

         change of the on/off duty ratio of the switch S of a step-up boost converter similar to the one shown in Fig. 5.

         From (2) to (4), we get

         I k T T s 3

         scr i

         r

         100

         Tr

         1.115 1

         1

         I rr

         exp

         1

         (5)

         exp

         Vocq / AkT 1

         T

         k A Tr

         T

         and from (1)

         Rsh

         Voc

         (6)

         • I rs exp qVoc / kTA 1

         The

         required

         data

         for

         identifying

         the

         maximum

         operating point at any insolation level and temperature are the following:

         1. ki ;

         2. Open circuit voltage Voc (for initial conditions Tr = 25 C, S = 100 mW/cm2);

         3. Short circuit current Iscr (for initial conditions Tr = 25 C, S = 100 mW/cm2);

         4. Maximum power voltage Vmp (for initial conditions Tr =25 C, S = 100 mW/cm2);

         5. Maximum power point current Imp(for initial conditions Tr = 25 C, S = 100 mW/cm2);

         Figure. 5. Step-up boost converter for MPPT.

         Table – II

         Figure. 4. Membership function for (a) input E(k); (b) input CE(k); (c) output dD.

      2. Inference Method

      Table II shows the rule table of the fuzzy controller where all the entries of the matrix are fuzzy sets of error E(k) change of error CE(k), and change of duty ratio dD to the boost converter. In the case of fuzzy control, the control rule must be designed in order that input variable E(k) has to always be zero.

      As an example control rule in Table II: IF E is PB AND CE is ZO THEN dD is PB

      FUZZY RULE TABLE

      Figure. 6. Sample versus power of PV array using P&O method. At point A, the P&O method reaches the MPP for first time after iteration (27)

      Figure. 7. Sample versus power of PV array, using fuzzy controller method. At point B, the fuzzy controllers method reaches MPP after iteration (24).

      As a fuzzy inference method, Mamdanis method is

      So far the fuzzy controller is performing better

      used with max-min operation fuzzy combination law. For the

      compared to the classic P&O one by adjusting appropriately

      defuzzification the centre of area (COA) and the max

      the voltage of the dcdc converter, in order to reach the MPP

      criterion method (MCM) is used [19].

      of a PV array, faster and with no fluctuation. Some

      The characteristics of the simulated dcdc boost

      disadvantages of the fuzzy controllers method are

      converter ae given in the Appendix A.

      eliminated using FCN. As it is well known, the MPP of a PV

      The fuzzy controller method is used as MPPT instead of

      array varies according to temperature and/or insolation

      the simple P&O method [20], because by doing so there is a

      variations; thus, the fuzzy controller starts its search for this

      reduction not only in the time required to track the MPP but

      new MPP, by using as starting point the previous MPP

      also in the fluctuation of power, as it is clearly presented in Figs. 6 and 7.

      (corresponding to the previous temperature and insolation levels). This devolvement demands a considerable number

      of iterations, especially if this new MPP is located far away from the previous one, which means that the wasted energy

      influences other nodes and in which degree. The weight of the interconnection between node Ci and node Cj denoted by

      is significant.

      1. faster

         devolvement

         from

         one

         MPP to

         Wij,

         could be

         positive

         (Wij

         >0)

         for

         positive

         causality or

         another is ensured with the use of an FCN, just like the

         negative

         (Wij

         <0)

         for

         negative

         causality or

         there is no

         proposed one presented in the next section. It will be shown in the following results that FCN, in close cooperation with the presented fuzzy controller, will become a robust MPPT

         relationship between node Ci , and node Cj , thus Wij = 0.

         The causal knowledge of the dynamic behaviour of the

         method, in order to minimize the wasted energy.

         system is

         stored

         in the

         structure

         of the

         map

         and in

         the

         interconnections

         that

         summarize

         the

         correlation

         between

   4. FCN APPROACH FOR THE PHOTOVOLTAIC PROJECT

      This section presents an FCN designed to represent the operation of a photovoltaic system. Our aim is to use the

      cause and effect. The value of each node is influenced by the values of the connected nodes with the corresponding causal weights and by its previous value. So, the value Aj for each node Cj is calculated by the following rule [21]:

      FCNs, which are extensions

      of FCMs, for estimating the

      N

      s s1

      s1

      maximum power point of the photovoltaic system.

      Aj

      f Ai

      i1,i j

      Wij Aj

      (9)

      1. FCMs

         FCMs

         approach is a hybrid

         modelling methodology,

         where

         Asj , is the value of node Cj at step s,

         Asi 1 is the value of node Ci , at step s 1,

         exploiting characteristics of both fuzzy logic and neural

         Asj1 is the value of node Cj at step s 1, and

         networks theories, and it may play an important role in the

         Wij is the weight of the interconnection between

         development of intelligent manufacturing systems. The

         nodes Ci and Cj ·

         utilization of existing knowledge and experience on the

         f is a squashing function: f = 1/[1 + ecx ].

         operation of complex systems is the core of this modelling approach.

         The graphical illustration of an FCM is a signed directed graph with feedback, consisting of nodes and weighted inter- connections. Nodes of the graph stand for the nodes that are used to describe the behaviour of the system and they are

         By using c = 1, we convert the nodes values in the range [0,1].

         To account for the existence of steady nodes, (9) has to be slightly modified so that it does not provide with erroneous results. Steady value nodes are the nodes that influence the remaining graph but they are not influenced by any other

         connected by signed and weighted arcs representing the

         node of the graph. In this case, nodes values are now

         causal relationships that exist among nodes (Fig. 8).

         computed through equations [16]

         s,FCM

         N s1,FCM

         s1,FCM

         Aj

         f Ai

         i1,i j

         Wij Aj

         (10)

         And for the steady-state nodes the correction equation is

         A

         A

         s,FCM

         j

         system

         A

         A

         j

         (11)

         where Asystemj is the nodes value, derived from the physical system.

      2. Cognitive Graph for the PV Project

         The

         graph shown in

         Fig. 9

         represents a photovoltaic

         Figure. 8. Simple fuzzy cognitive map

         Each node represents a characteristic of the system. In general it stands for states, variables, events, actions, goals, values, trends of the system, which is modelled as an FCM

         system, for a MPPT use. The graph have six nodes, where nodes C1, C2, and C6 are steady value nodes and nodes C3, C4, C5 could be control nodes. In this approach, node C4 is the control node whose value is used to regulate the current of the system. The regulation of the current of the system means that a different power is now the output power of the

         [18]. Each node is characterized by a number Aj , which

         photovoltaic.

         Control

         nodes

         are

         the

         nodes

         the

         values of

         represents its value and it results from the transformation of the real value of the systems variable, for which this node

         which will be used to the real system as control actions. Node C4 is used to calculate the optimum current needed to

         stands, in the interval [0, 1]. It must be mentioned that all the

         regulate

         the

         output

         power

         of the

         photovoltaic

         in the

         values

         in the

         graph

         are

         fuzzy,

         and

         so weights

         of the

         maximum point. The nodes of the graph are related to the

         interconnections

         belong

         to the

         interval

         [1,

         1].

         With

         the

         following physical quantities of the photovoltaic system.

         graphical

         representation of

         the

         behavioral

         model

         of the

         system,

         it becomes

         clear

         which

         node

         of the

         system

         Figure. 9 FCN Designed for the photovoltaic project

         Node C1 represents the irradiation with range in the interval [0, 1], 0 is the minimum point of the irradiation

         For example the value of weight W63 is allowed to be updated when the weights that affect node C3 (W13, W43, and W53) are going to take values larger from the absolute value 1. In this situation, weight is activated and its value is no longer set to zero. By using equilibrium node C6 and the weights connecting this node with nodes C3, C4, and C5, we manage to regulate the values of nodes C3, C4, and C5, by always keeping values of the graph weights below absolute value 1.

      3. FCN Approach for the Photovoltaic Project

      FCN [16], [17], constitute an extension of FCMs. Unlike FCMs, which rely only on the use of the initially acquired experts knowledge about the operation of the system and which is represented by the weights values of the map, FCNs may use these values only as a starting point or may not use them at all. The operation of FCNs is tightly connected with

      (usually 0

      mW/cm2)

      and

      one

      is the

      maximum

      point,

      the operation of the physical system providing control values

      corresponding to 100 mW/cm2.

      and taking feed-back from the system. Moreover, during its initial training or its subsequent interaction with the physical

      Node C2 represents the temperature that also must be in

      system,

      the

      FCN

      keeps

      track of

      its

      previous

      equilibrium

      the

      interval

      [0,

      1].

      Zero is

      the

      minimum

      point

      of the

      points by means of a collection of fuzzy if-then rules. Using

      temperature

      (usually 30

      C)

      and

      one

      is the

      maximum

      these characteristics, the FCN becomes a dynamic control

      point, usualy 70C. system. In this paper we use the FCN in close cooperation

      with a

      fuzzy MPPT controller

      and

      with

      a PV system as

      Node

      C3 represents

      the

      optimum

      voltage

      of the

      shown in

      Fig.

      10.

      The

      FCN

      is first

      off-line

      trained by

      photovoltaic system for the climatologic data obtained at the specific point of time, which also must be in the interval [0, 1], 0 is the minimum point of the voltage (usually 0 V) and one is the maximum point Vmax, where Vmax is calculated, according to (4) by setting

      T = Tmin and S = Smax.

      appropriately constructed data and then it is connected to any PV system to get feedback and send control values to regulate its output. Once the FCN is trained its knowledge can be updated and the FCN acts as an adaptive controller of the PV system.

      1. Initial

         Off-Line

         Training of

         the

         FCN:

         The

         off-line

         Node

         C4 represents

         the

         optimum

         current of

         the

         training is being performed in an incremental manner. This

         photovoltaic system for the climatologic data obtained at the means that for each training data vector that contains PV

         specific point of time, which also must be in the interval [0,

         value

         variables

         corresponding to

         different

         operation

         1]. Here 0 is the minimum point of the current (usually 0 A) and 1 is the maximum point Imax, where Imax is calculated, according to(2) by setting T = Tmax and S = Smax.

         Node C5 expresses the optimum output power of the

         conditions, the FCN weights are updated to comply with the data vector. Moreover, this new acquired knowledge is been stored in a fuzzy-rule data base. We can divide the training into two cooperating stages.

         photo-voltaic system for the climatologic data obtained at 2) Stage 1Weight Updating Using New Data: This

         the specific point of time, which also must be in the interval

         stage

         is concerned

         with

         the

         method

         of updating

         the

         [0, 1]. Here 0 is the minimum point of the power (usually 0

         interconnections

         weights

         of FCN

         taking

         into

         account

         W) and 1 is the maximum point Wmax, where Wmax is a

         training

         data.

         Since

         the

         training is

         being

         performed

         characteristic given from PV operational data under Tmin and Smax.

         incrementally, during stage 1, only one data vector is used. The FCN converges to its new weights values after a number

         of iterations. In each training iteration the FCN uses the

         Node C6 is an artificial design node, the value of which is used to regulate the equilibrium point in the nodes C3, C4,

         updated weights to reach new equilibrium node values by means of (10) and (11). These values are compared to the

         and C5. The value of C6 is steady and equals 1. The weights

         given

         training

         values

         and

         the

         error

         is given

         for

         the

         new

         W63, W64, and W65, respectively, are originally set to 0 and are allowed to change only, when one or more weights affecting nodes 3, 4, and 5 exceed the value of absolute 1.

         updating iteration.

         Rij

         in

         i1

         Wij

         Wij

         if Wij

         0 and

         Rij 0if Wij 0

         (14)

         where constant value is used to drive values Rij in the range [0, 1]. In most practical situations, = 0.1.

         1. Stage 2Storage of the New Knowledge in a Fuzzy Rule

            Database:

            The

            procedure

            described

            in the

            previous

            stage

            modifies our knowledge about the system by continuously modifying the weight interconnections and consequently, the node values. After the weight updating is taking place, the FCN reaches a new equilibrium point using (10) and (11). Since a new training vector might produce different weights and different equilibrium point we have to keep track of the current knowledge (weights and equilibrium points) to be used after the training phase. We do that by producing fuzzy ifthen rules, according to the following procedure [17].

            Suppose, for example, that the FCN after being trained by a data vector converges to the following weight matrix:

            W=

            and concludes to an equilibrium point, which is

            A = [A1 A2

            A3 A4

            A5 A6].

            Suppose also that for a new training data vector, it concludes to a new equilibrium point

            B = [B1 B2

            B3 B4

            B5 B6]

            Figure10: simplified flowchart of the proposed method

            With weight matrix

            W=

            W=

            K=

            The

            off-line

            training

            and

            the

            subsequent

            operation

            are

            The

            fuzzy

            rule

            database,

            which is

            obtained

            using

            the

            described bellow.

            information

            from

            the

            two

            previous

            equilibrium

            points, is

            The weight updating is used by the following extended delta rule [16]

            depicted in Figures. 11 and 12 and is resolved as follows:

            j

            j

            p Asystem

            N

            1

            A system W A system

            There are two rules related to the above two different equilibrium situations

            1 e

            A system A FCN

            i 1,i j i

            (12)

            ij j

            Rule 1

            j j and node 4 is mf1 and node 5 is mf1 and node 6 is mf1

            W k W k 1 R ap(1 p)A FCN

            (13)

            ij ij ij i

            where p is the error, k is the number of iteration, a is the

            w23 is mf1 and w24 is mf1 and w25 is mf1 and w34 is mf1

            learning rate (usually a = 0.1) and Rij is a calibration

            and w35 is mf1 and w43 is mf1 and w45 is mf1 and w53 is

            variable, which prevents the FCN node and weight values

            mf1 and w54 is mf1 and w63 is mf1 and w64 is mf1 and

            from being driven in their saturation point. Rij can be

            w65 is mf1

            computed by the following [16]:

            Rule 2

            Figure. 11. Left-hand side (if part).

            The

            number

            and

            shape

            of the

            fuzzy

            membership

            functions of

            the

            variables of

            both

            sides

            of the

            rules

            are

            gradually modified as new desired equilibrium points appear to the system during its training. To add a new triangular membership function in the fuzzy description of a variable, the new value of the variable must differ from one already

            encountered

            value

            more

            than a

            specified

            threshold.

            The

            threshold

            comes

            usually as

            a compromise

            between

            the

            maximum number of allowable rules and the detail in fuzzy representation of each variable.

            Figure. 12. Right-hand side (then part).

            Once

            the

            new

            knowledge

            has

            been

            stored

            using

            the

            above procedure we run again stage 1 using a new training vector. The procedure stops after all data vectors have been

            If there is a change in the values of temperature and

            presented.

         2. Control of a PV System Using the Trained FCN and the Fuzzy Controller:

         Once the FCN is off-line trained, it can be connected to

         insolation before the fuzzy controller drives the duty ratio of the switch S to the proper value corresponding to the MPP then the FCN interferes to the procedure and sends a new proper value for MPP voltage for the new insolation and

         the PV system according to Fig. 10. The FCN receives

         temperature

         feedback from the fuzzy controller and from the PV array also. Once the error E(k) of the fuzzy controller is set to zero, it means that the duty ratio of the switch S of the boost converter is set to the proper value, so that the PV array is in

   5. RESULTS

      It is quite evident that irradiation and temperature play

      its maximum power point. This new maimum power point

      the most significant role on the maximum power that is

      gives a new equilibrium point to the FCN. The new

      drawn from a PV module. In order to measure these two

      equilibrium point is used to train further the FCN.

      quantities a pyranometer and a thermocouple is often used, although the output from these two measuring devices is not

      always

      the

      most

      adequate

      information

      to identify

      the

      the calculated by only the fuzzy controller method [8]. It is

      operating point yielding the maximum power, which is of course a drawback of this methodology. The short circuit

      clearly depicted that by using the FCN + fuzzy controller MPPT system, we have a significant energy gain. Actually,

      current

      from

      the

      PV array

      gives

      the

      most

      adequate

      the combined method needs only five iterations, in order to

      information of the effective insolation and temperature using (1)(6).

      reach the new MPP, while the fuzzy controller method alone needs 12 iterations, in order to reach the same MPP. Each

      We construct

      training

      data

      for

      the

      FCN

      using

      the

      iteration

      corresponds

      to one

      second,

      following

      the

      same

      following

      procedure: We

      use

      some

      typical

      climatic

      data.

      sampling procedure with [8].

      These data are chosen to be Irradiation (S-node 1). We select

      values

      in the

      range

      0100

      mW/cm2

      using a

      step

      of 5

      mW/cm2. Temperature (T-node 2). We select values in the range 30 C70 C, using a step of 5 C.

      By using all the possible combinations of these data and

      by using

      the

      simulation

      of the

      photovoltaic

      array, we

      calculate the values of the optimum voltage (node 3), current (node 4), and output power (node 5) from (1) to (4). Using these node values for nodes 15, we update the weights of the FCN according to stage 1 of the training procedure and

      Figure. 13. Sample versus power of PV-array. (A) Theoretical, (B) proposed method, and (C) fuzzy controller

      for

      the

      equilibrium

      point

      derived

      for

      any

      possible

      combination, we store the knowledge according to stage 2.

      The possible combinations of the climatic data are 441 and the FCN creates 21 triangular fuzzy numbers for nodes 1 and 2, 24 for node 3, 48 for node 4, 43 for node 5, 5 for node

      6. Also,

      287

      fuzzy ifthen

      rules

      are created

      to store

      the

      knowledge. The number of rules appears to be large because they account for all possible combinations of climatic data, even for those which are unlikely ever to occur. This number could be significantly reduced if we exclude this kind of combinations.

      When we connect the FCN system to the PV array, if the

      Figure. 14. Sample versus power of PV-array. (A) Theoretical, (B) proposed method, and (C) fuzzy controller

      In Fig. 14, a similar comparison among the performance

      error E(k) is zero, fuzzy MPPT controller sends the values of

      of the three methods but in different temperature and

      nodes 1 and 2 to the training part of the algorithm and

      insolation conditions than those of Fig. 13 is given. We can

      through the fuzzy rule database, the system decides, which

      see that the new MPP was exactly the point that the FCN

      weights values are appropriate to express the values of nodes

      instantly returned to the dcdc converter for the new

      3, 4, and 5. Executing (10) and (11) and by using the weights derived above, we calculate the new equilibrium point which expresses the values of the optimum current, voltage and output power of the PV array for the climatic data obtained at the specific time instant. In the next step the FCN sends the values of the control nodes to the dcdc boost converter, thus determining the optimum current, which corresponds to the maximum output power for the climatic data obtained at the specific time instant.

      In order to evaluate the effectiveness of the proposed

      insolation and temperature levels. That is why the proposed method (B) does not need to use the fuzzy controller, in order to reach the MPP. In this case by using the proposed method we reach the MPP after only one iteration, while by using only the fuzzy controller the system reached the MPP after 18 iterations.

      algorithm,

      we used

      the

      trained

      FCN

      for

      controlling

      the

      operation of the BP270L PV array. The parameters of the PV array are given in Appendix B, where a sample of the weight

      matrix

      and

      the

      corresponding

      equilibrium

      points

      is also

      given. Fig. 13 presents a comparison between (A) the

      Figure. 15. Sample versus power of PV-array. (A) Theoretical, (B) proposed

      theoretical (computed by (1)(4)) MPP, (B) the calculated by the proposed FCN and fuzzy controller method and (C)

      method (off-line trained FCN), (C) fuzzy controller, and (D) proposed method (only on-line trained FCN).

      Fig. 15 demonstrates the reason why it is better to use

      1. Based

         on these

         parameters

         the

         training

         data

         are

         off-line training. As we can see the system is in an MPP,

         produced

         using

         the

         various

         combinations

         of the

         corresponding to a specific insolation and temperature level. climatic data and (1)(4).

         The

         next

         MPP,

         corresponding

         to another

         insolation

         and

      2. The FCN is being off-line trained using the above data

         temperature level, is a point with which the FCN has already been trained off-line. Using, as feedback from the PV array, the values of current, voltage and sort circuit current and by using (1)(4) the control system calculates the insolation and the temperature corresponding to the feedback values. The so computed insolation and temperature values are in this

         and according to the procedure described in Section IV.

      3. Once the FCN is off-line trained, it is left to operate with the specific PV array in close cooperation with the fuzzy controller.

It is evident that this procedure can be applied to any

case values with which FCN has already been trained off- PV array of the market.

line.

Thus,

the

proposed

method

re-turns

the

optimum

control law instantly to the dcdc converter, as it is shown in Fig. 15 (plot B). If there was no off-line training, then the values of insolation and temperature, corresponding to the

1. CONCLUSION

A novel method for maximum power point tracking was presented in this paper. The method combines a fuzzy MPPT

new

MPP,

would

not be

values

for

insolation

and

with

an appropriately

designed

FCN

to speed-up

the

temperature, with which the FCN has already been trained. procedure of reaching the accurate maximum power point of

In this case the FCN returns initially an MPP value, which is

a photovoltaic

array

under

changing

environmental

far

away

from

the

actual

one.

Therefore,

the

proposed

conditions. The method presents very good results, i.e., only

method

will

need a

number of

steps

before

reaching the

0.78% error in energy production when compared with the

actual

MPP

(plot

D).

It has

to be

mentioned

that

this

theoretical expected production of a commercially available

phenomenon

appears

mainly

in the

be-ginning of

the

photovoltaic array, simulated n climatic data of a whole

operation of the method, when the FCN is totally untrained. year. The methodology can be applied on any photovoltaic

After

a sufficient

time of

operation

the

FCN

gains

array of the market. Due to the existence of the FCN the

experience and therefore it acts as if it was initially off-line trained

method could track and adapt to any physical variations of the photovoltaic array through time. Therefore, the method is

guaranteed

to present

its

very

good

performance

TABLE III

COMPARISON OF VARIOUS MPPT METHODS

independently of these variations.

APPENDIX A

The dcdc boost converter has been simulated, according to characteristics described below:

Array: BP270L PV array;

1. dcdc converter input voltage (Vi): 13.724.7 V;

2. dcdc converter output voltage (Vo): 48 V;

3. Switching frequency (f s): 33 kHz.

Finally, in order to estimate the energy gain of the new method (FCN + fuzzy controller MPPT) in comparison to

Below are shown the basic equations necessary for the dcdc boost converter design [22]

the method which uses fuzzy controller only we performed the following experiment. Using data from the year 2002 we ran both methods to give us the maximum power points and

Vo

Vi

1

1 D

t

, I i I o

1

1 D

1

calculated

the

energy

acquired

from

the

PV array.

Both

where

D on

and T

methods are compared to the optimal one [theoretical MPP values, computed by using (1) – (4) and the results are shown in Table III. It can be observed that the proposed method

T f s

APPENDIX B

PV system data:

(both

cases

1. and D)

outperforms

method C

(fuzzy

1. ki

   = 2.8 mA/ C;

   controller only). Actually, when the off-line trained FCN is used the proposed method provides with only a 0.78% less energy production than the optimal (theoretical) case.

   ii) iii) iv)

   Open circuit voltage Voc = 21.4 V; Short circuit current Iscr = 4.48 A; Maximum power voltage Vmp = 17.1 V;

   A typical

   real

   life

   application

   of the

   proposed

   1. Maximum power current Imp = 4.15 A.

      methodology would require the following steps. Based on the node description presented in Section IV and

      1. Once a specific PV array is selected its parameters, as by using the PV system data given by the manufacturer we

those

indicated

in Appendix B,

are

entered

to the

can see, as an example, an equilibrium point with weight

controller. matrix

W =

And A vector is A = [0.247

0.5762

0.6288

0.2179

0.1837

1]

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   S = 24.7mW/cm2, W = 16.048W.

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