Embodiment
1 local shades place an order string array output characteristics
1.1 local shades place an order string array mathematical modeling
In order to analyze the output characteristics of single string array, it is necessary first to establish the mathematical modeling of single string array exactly.In reality
In the application of border, photovoltaic cell manufacturer can provide the user open-circuit voltage V of the product under standard test conditionoc, short circuit electricity
Flow Isc, maximum power point voltage VmWith maximum power point electric current Im.In view of analyzing the convenience with calculating, standard ginseng can be established
Contacting between number and output characteristics, so selecting solar cell engineering mathematical modeling herein:
I=Isc-C1Isc[exp(V/C2Voc)-1] (1)
I:Photovoltaic cell output current;
Isc:Photovoltaic cell short circuit current;
C1:Parametric equation, see formula (2);
V:Photovoltaic cell output voltage;
C2:Parametric equation, see formula (3);
Voc:Photovoltaic cell open-circuit voltage.
Wherein,
C1=(1-Im/Isc)exp(-Vm/C2Voc) (2)
C1:In parametric equation, generation, return formula (1);
Im:Maximum power of photovoltaic cell point electric current;
Isc:Photovoltaic cell short circuit current;
Vm:Maximum power of photovoltaic cell point voltage;
C2:Parametric equation, see formula (3);
Voc:Photovoltaic cell open-circuit voltage.
C2=(Vm/Voc-1)[ln(1-Im/Isc)]-1 (3)
C2:In parametric equation, generation, return formula (1);
Vm:Maximum power of photovoltaic cell point voltage;
Voc:Photovoltaic cell open-circuit voltage;
Im:Maximum power of photovoltaic cell point electric current;
Isc:Photovoltaic cell short circuit current.
When battery temperature and intensity of illumination change, the formula that may be referred to document offer recalculates Isc、Voc、
Im、VmEtc. parameter, it is possible to obtain the output characteristics under New Terms.
In order to obtain sufficiently large output voltage, monomer photovoltaic cell is generally passed through into series-parallel mode in practical application
It is combined into large-sized photovoltaic array.Assuming that a photovoltaic array battery strings quantity in parallel is Np, the electricity connected in each battery strings
Pond plate quantity is Ns, then according to formula (1), the mathematical modeling of the photovoltaic array can be described with equation below under uniform illumination:
Ia=IscNp{1-C1[exp(Va/C2NsVoc)-1]} (4)
Ia:Photovoltaic array output current;
Isc:Photovoltaic cell short circuit current;
Np:Photovoltaic array battery strings quantity in parallel;
C1:Parametric equation, see formula (2);
Va:Photovoltaic array output voltage;
C2:Parametric equation, see formula (3);
Ns:The photovoltaic cell quantity connected in battery strings;
Voc:Photovoltaic cell open-circuit voltage.
By the N in equation (4)pTake 1, that is, obtain uniform illumination place an order string array mathematical modeling.But when array because
Blocking for a variety of causes and when forming local shades, the illumination of array received is no longer uniform, and now the mathematical modeling of equation (4) is just
It is no longer applicable.
From simplest circumstance of occlusion analysis establish local shades place an order string array mathematical modeling.An assuming that single string battle array
Row are by Ns1Individual unblanketed photovoltaic cell and Ns2Individual hypographous photovoltaic cell two parts are composed in series, Isc1And Isc2It is right respectively
Answer the short circuit current of two parts battery strings.In order to prevent hot spot effect, each photovoltaic cell will bypass diode in parallel.When
Array output current I>Isc2When, more than Isc2Electric current flowed through from hypographous photovoltaic cell bypass diode in parallel, now
The only unblanketed external power output of photovoltaic cell, hypographous photovoltaic cell and its bypass diode all turn into consumption power
Load, now C-V characteristic be shadow-free battery C-V characteristic;As array output current I≤Isc2When, corresponding bypass two
Pole pipe forms reverse biased, and now C-V characteristic is the C-V characteristic for having shade battery.Analyzed based on more than, the list string array
Mathematical modeling can represent [12] by following piecewise function:
I:Single string array output current;
Isc1:Shadow-free blocks the short circuit current of substring in single string array;
C1:Parametric equation, see formula (2);
V:Single string array output voltage;
C2:Parametric equation, see formula (3);
Ns1The photovoltaic cell quantity that shadow-free blocks in individual single string array;
Voc1:Shadow-free blocks the open-circuit voltage of substring in single string array;
Isc2:There is the short circuit current of shadow occlusion substring in single string array;
Ns2There is the photovoltaic cell quantity of shadow occlusion in individual single string array;
Voc2:There is the open-circuit voltage of shadow occlusion substring in single string array.
When singly a variety of different local shades on string array be present and block, the short circuit of the battery strings under different illumination intensity
Electric current also differs.Now the mathematical modeling of single string array is similar to the piecewise function of formula (5), and segmentation limit still depends on battle array
Row output current I and each short circuit current IscnThe magnitude relationship of (n is the quantity of the different illumination intensity received on single string array).
Placed an order the most basic mathematical modeling of string array so formula (5) is local shades.For the accuracy of formula (5) model, there is document
Prove that the model can accurately emulate local shades and place an order the output characteristics of string array by measured data of experiment, this section point
Analysis local shades place an order the output characteristics of string array, mainly improve compound MPPT algorithm to draw and provide theoretical foundation, therefore
The experimental verification process to the model is not discussed herein.
Influence of 1.2 local shades to single string array output characteristics
According to the segmentation thought of formula (5) model, simulated program is write using MATLAB language, can be emulated any local cloudy
Shadow blocks the output characteristics for the string array that places an order.For the ease of analyzing, the concept of the shading factor is firstly introduced into[12-13]:
E:The shading factor;
Esh:Intensity of illumination under shadowed condition;
Eref:With reference to intensity of illumination (1000W/m2)。
In formula, EshFor the intensity of illumination under shadowed condition, ErefWith reference to intensity of illumination, generally to take 1000W/m2.Therefore,
The span of the shading factor is between 0~1.
Choose a series of different single string arrays of pattern that block to be emulated, per strip array series-connected cell plate number Ns=10,
Batteries in parallel connection string number Np=1, Ns1~Ns3Partial intensity of illumination is respectively 1000W/m2、500W/m2、200W/m2, specifically block
Pattern is as shown in table 1:
The emulation of table 1 blocks pattern with single string array
P1~P5:The label of the single string array of 5 of emulation;
Ns1~Ns3:The photovoltaic cell quantity that single string array is connected under 3 kinds of intensities of illumination respectively;
E:The shading factor.
From the canonical parameter of the STP150S-24/Ac type solar panels of STP company:Voc=43.3V, Isc
=4.72A, Vm=34.5V, Im=4.35A, temperature are set to 25 DEG C.
The I-U characteristics that P1 under uniform illumination is can be seen that with reference to table 1 and Fig. 1, Fig. 2 are in single knee shape, and P-U characteristics exist single
Peak value;
There are 2 kinds of different intensities of illumination in P2, its I-U characteristic is in 2 stairsteppings, and P-U characteristics have 2 peak values;P3
Rule as similarly meeting.When singly string array or wherein one section have more a kind of intensity of illumination because of shadow occlusion when, the moon
The output characteristics of shadow part has the process of one section of decline, i.e. power output reduces, so as to cause I-U characteristics to have more a ladder
Shape, P-U characteristics have more a local peaking.Therefore, several intensities of illumination are received on single string array, its I-U characteristic is just in several
Individual stairstepping, P-U characteristics there is several peak values.
P2, P4, P5 in Fig. 3,4 are irradiated by two kinds of intensities of illumination, shading factor E=0.5, carefully contrast P2,
P4, P5 two peak values, position and size are influenceed by the cell panel quantity that is blocked.When blocking cell panel number Ns2>E×NsWhen,
Maximum power point is located at right side, that is, tends to voltage source region, and the cell panel for now having shield portions is in maximum power point, such as schemes
Shown in P4 in 4;When blocking cell panel number Ns2<E×NsWhen, maximum power point is located at left side, that is, tends to current source region, now
The cell panel of unobstructed part is in maximum power point, as shown in the P5 in Fig. 4;If Ns2=E × Ns, then two-part maximum work
Rate is almost equal, and as shown in P2 in Fig. 4, the now selection of maximum power point depends on external loading size.
Emulated more than and analysis, the presence of local shades can produce very big shadow to single output characteristics for going here and there array really
Ring, more complicated especially as shadow condition, caused local peaking is also more, and this easily causes conventional MPPT algorithm to photovoltaic
The tracking error of system maximum power point, influence the delivery efficiency of photovoltaic generating system, it is therefore desirable to adopt for local shades problem
Appropriate solution is taken, to mitigate influence of the local shades to photovoltaic system.
The improvement of 2 compound MPPT algorithms
Mitigate local shades mainly has two kinds to the method that photovoltaic system influences:The first is the structure of change system, will
The structure of centralization is changed to the structure of string data or more string datas, or even directly uses DC Module structure, so can be simultaneously
Solve the problems, such as that global peak declines and local peak interference.But, transform controller in system can be caused using such method
Quantity rolls up, and increases system complexity, system Construction cost is improved, so should not use, the light of current practice
Volt system still uses the structure of photovoltaic cell connection in series-parallel substantially;Second is reservation system centralized configuration, and research possesses the overall situation
The MPPT algorithm of peak value decision-making function, Research Challenges essentially consist in the interference problem for overcoming local peaking, rapidly and accurately tracked
To real maximum power point.Photovoltaic system multi-peak MPPT algorithm common at present is slightly introduced in preface part, according to it
Advantage and disadvantage, select compound MPPT algorithm to do photovoltaic system multi-peak MPPT maximum power point tracking research herein, and for wherein
Some problems are slightly improved.
The principle of conventional composite MPPT algorithm is divided into two steps:The first step is it needs to be determined that the neck of a real maximum power point
Domain, system operating voltage is moved on to the rapidity for herein, ensureing tracking.Equivalent resistive conductor R under known uniform illuminationpm=Vpm/Ipm
Intersection point with photovoltaic array VA characteristic curve is maximum power point, it is possible to utilizes photovoltaic battle array under this line and local shades
The intersection point of row VA characteristic curve determines the operating voltage at the end of the first step;Second step is to utilize traditional perturbation observation method
The operating voltage determined from the first step proceeds by MPPT maximum power point tracking.Conventional composite MPPT algorithm is in algorithm design and program
In compiling procedure, easily there is following Railway Project:
1) when the operating voltage that the first step determines falls on local minimum point, now dP/dI=0 is also set up, algorithm meeting
Therefore it is real maximum power point to be mistakenly considered current local minimum point, causes tracking error;
2), may be by pseudo- maximum power point as true when the operating voltage that the first step determines falls on pseudo- maximum power point
Positive maximum power point, causes tracking error;
3) although second step is higher using perturbation observation method tracking efficiency and easy realization, near maximum power point
Fluctuation it is larger, certain required precision can not be met, and because external environment is mutated algorithm may be caused to fail.
It is for problem above, it is necessary to slightly modified to conventional composite MPPT algorithm:
1) in order to prevent local minimum point and pseudo- maximum power point from causing tracking error to algorithm, need to record in the first step
The extreme point that is traced into scanning process is simultaneously compared;
2) second step avoids using perturbation observation method, selects tracking accuracy of a relatively high and less conductance affected by environment
Method of addition.
Thought is improved based on more than, the compound MPPT algorithm flow chart after improvement is as shown in figure 8, specific steps:
The first step:Initialize the electric parameter of photovoltaic array cell panel and block pattern;
Second step:Calculate photovoltaic array resistance:Rpv=V/I;Wherein V is photovoltaic array voltage, and I is photovoltaic array electric current;
3rd step:Calculate the equivalent resistance of photovoltaic cell under uniform illumination:Rpm=Vpm/Ipm;VpmFor equivalent voltage;IpmFor
Equivalent current;
4th step:Compare equivalent resistance RpmWith photovoltaic array resistance RpvSize, if Rpm<Rpv, then it is maximum to preserve local
Value, and second step is returned, otherwise, perform the 5th step;
5th step:MPPT maximum power point tracking is carried out using conductance increment method;
6th step:Judge whether photovoltaic array power output changes, if changing, obtain opening for photovoltaic array
Road voltage VocWith short circuit current Isc, and the 7th step is performed, otherwise, perform the 8th step;
7th step:Judge photovoltaic array short circuit current IscWhether change, if changing, return to the 5th step, it is no
Then, second step is returned;
8th step:Judge whether tracked power points is maximum power point, if so, then performing the 9th step, otherwise, return
Maximum power point, and return to the 5th step;
9th step:Lock maximum power point.
3 artificial circuits design to be calculated with component parameters
Fig. 9 is artificial circuit master-plan block diagram, mainly includes PV modules, DC-DC conversion circuit and pwm control circuit three
It is most of.The effect of DC-DC conversion circuit is the output voltage for adjusting photovoltaic system to be preferably tracked.Herein with PV
Input voltage of the output voltage of module as DC-DC conversion circuit, because the output voltage of PV modules is less than normal, it is necessary to be risen
Pressure, so this paper DC-DC conversion circuit selection Boost circuit;The effect of pwm control circuit is then to produce to have different duties
The square wave of ratio, the break-make of FET in translation circuit is controlled, makes output voltage values size adjustable.
The Simulink emulation modules of 3.1 single string arrays
The Simulink emulation modules of single string array are as shown in Figure 7.Wherein, V is an externally input voltage, it is possible thereby to calculate
Go out the output current of single string array, then foreign current is converted into by controllable current source, be output to from output interface 2
External circuit.S-Function in figure is the S function write using MATLAB language, be local shades place an order string array mathematics
The Simulink package module that the m files of model are represented with non-patterned mode.Because photovoltaic cell is typical non-thread
Property element, its output characteristic curve is nonlinear curve, so in artificial circuit, makes m files and Simulink using S function
Module relation gets up.4 output valve Isc_new、Voc_new、Im_newIt is with the new ginseng that is calculated of external environment change with Vm_new
Number, calculated for participating in the tracking of MPPT modules.
3.2MPPT Simulink emulation modules
MPPT Simulink emulation modules are as shown in Figure 8.Here according to the compound MPPT algorithm stream of improvement shown in Fig. 5
Journey, the same S function write using MATLAB language, the m Document encapsulations of compound MPPT algorithm will be improved into Simulink modules,
Make m files associated with Simulink.Because the carrier of this paper algorithms is generally PC or single-chip microcomputer, if using sinusoidal pulsewidth
Modulation system controls inverter, then also needs to build sine-wave generator in addition, algorithm is become complicated.Therefore directly make herein
The control signal exported with MPPT modules is compared with the triangular wave of certain frequency, so as to construct the side of suitable duty ratio
Ripple.
The Simulink emulation modules of 3.3 Boost circuits calculate with parameter
The Simulink emulation modules of Boost circuit are as shown in figure 9, for adjusting the output voltage of single string array to meet
The demand of MPPT maximum power point tracking, wherein there is three main component parameters to need to calculate, i.e. switching tube frequency f, energy storage inductor
Value L and filtering capacitance C.
3.3.1 switching tube frequency f calculating
Switching tube frequency is smaller, and the time that system reaches stable state is longer, it is necessary to which the inductance chosen is also bigger, and big inductance increases
The volume and weight of system is added, system is become heavy, but at the same time had the advantage that the loss of switching tube diminishes, made
Increased with the life-span;Switching tube frequency is bigger, and the operating efficiency of system can be obviously improved, and the inductance value of selection is also smaller, and system is small
Skilful light and flexible, but the at the same time loss of switching tube is also clearly, caloric value aggravation.So consider system effectiveness,
The factor of each side such as volume, weight, cost, loss, this paper switching tube frequency f selections 50kHZ.
3.3.2 energy storage inductor L selection
When gate-controlled switch is in on-state, energy storage inductor obtains energy from power end and puts aside;At gate-controlled switch
When off-state, energy storage inductor charges to electric capacity and provides energy to load simultaneously with power supply.Pass through theory analysis, Boost
The step-up formula of circuit is:
Wherein UoAnd UiRespectively output voltage and input voltage, D are dutycycle.Ignore the loss of circuit, input power with
Power output is equal, i.e. Pi=Po, UiIi=UoIo, so having
Wherein IiAnd IoRespectively input current and output current.The standard that energy storage inductor is chosen is can to ensure circuit work
Make that electric current is continuous, now the ripple component of inductive current should meet relational expression:
ΔiL:Inductive current ripple component;
ton:Switching tube service time;
Ui:Input voltage;
L:Energy storage inductor value;
D:Dutycycle;
T:Work period;
Ii:Input current.
Wherein tonIt is switching tube service time, T is the work period, so, inductance value should meet:
L:Energy storage inductor value;
Ui:Input voltage;
Ii:Input current;
D:Dutycycle;
T:Work period;
Uo:Output voltage;
f:Switching tube frequency;
Io:Output current.
The STP150S-24/Ac type solar panel strings of STP company during 10 pieces of characteristic Simulations of selection herein
The single string array of connection composition is as research object, maximum open circuit voltage 433V, output voltage 500V, and generally array reaches most
Voltage at high-power is about the 78% of open-circuit voltage, so it is about 30% that can calculate dutycycle D by formula (7), switch
Pipe frequency selects 50kHZ, and above numerical value is brought into formula (10) and considers certain allowance, and the selection of this paper energy storage inductors value is
800μH。
3.3.3 filter capacitor C selection
When gate-controlled switch is in on-state, the voltage on electric capacity powers to the load;When gate-controlled switch is in off-state, energy storage
Inductance charges to electric capacity simultaneously with power supply[20].Assuming that the quantity of electric charge of electric capacity is Q, then only when switching tube turns off in a cycle
(toff) when just have Q>0, the output ripple voltage formed by Q is:
ΔUo:The output ripple voltage formed by the quantity of electric charge;
Q:The quantity of electric charge;
C:Filtering capacitance;
Io:Output current;
toff:The switching tube turn-off time;
D:Dutycycle;
T:Work period.
C:Filtering capacitance;
Io:Output current;
D:Dutycycle;
T:Work period;
ΔUo:The output ripple voltage formed by the quantity of electric charge.
Each variable value is all constant, and output ripple voltage takes the 0.2% of output voltage, brings into formula (12) and considers certain
Allowance, this paper filtering capacitances selection be 10 μ F.
4 simulation results
With reference to Section 1 local shades place an order the string analysis of array output characteristics, the improved compound MPPT algorithm of Section 2 and
The photovoltaic system multi-peak MPPT artificial circuits of Section 3 design, to two kinds of different offices of single string array P-U characteristic curves bimodal
Portion's shadow occlusion situation carries out MPPT emulation, the compound MPPT algorithm after checking improvement.
4.1 maximum power points tend to voltage source region
The STP150S-24/Ac type solar panels of 10 pieces of STP companies of selection, which are together in series, forms single string battle array
Row, the canonical parameter of cell panel is Voc=43.3V, Isc=4.72A, Vm=34.5V, Im=4.35A, temperature are set to 25 DEG C, its
In 2 pieces of cell panels be in 1000W/m2Uniform illumination under, 8 pieces of cell panels are influenceed by shadow occlusion, intensity of illumination 500W/m2,
Draw its theoretical output characteristic curve as shown in the P4 in Fig. 3,4 by model emulation.Utilize the photovoltaic system designed in Section 3
Multi-peak MPPT artificial circuits are improved the maximal power tracing emulation of compound MPPT algorithm, and the tracking obtained from oscillograph is bent
Line is as shown in figs. 10-12:
When system working stability, the fluctuation of power output, operating voltage and operating current is as illustrated in figs. 13-15:
It was found from Fig. 3,4 simulation curve P4, the pattern of blocking place an order string array theoretical power output be about
720.68W, quiescent potential 328V, operating point electric current are 2.197A.Improvement is can be seen that from Figure 10-15 aircraft pursuit course
Compound MPPT algorithm analogue system can lock maximum power point in 0.52s or so, and the maximum power point traced into is about 719.9W,
Power swing amplitude is about 1.9W, and quiescent potential is stable in 328V or so, and voltage pulsation amplitude is about 12V, operating point electric current
Stabilization is about 0.080A in 2.195A or so, current fluctuation amplitude.
4.2 maximum power points tend to current source region
Single string array of selection is identical with 4.1 sections, and cell panel canonical parameter is constant, temperature-resistant, and the pattern of blocking is changed to it
In 8 pieces of cell panels be in 1000W/m2Uniform illumination under, 2 pieces of cell panels are influenceed by shadow occlusion, intensity of illumination 500W/m2,
Draw its theoretical output characteristic curve as shown in the P5 in Fig. 3,4 by model emulation.Obtained from the oscillograph of MPPT analogue systems
The aircraft pursuit course arrived is as shown in figs. 16-18;
When system working stability, the fluctuation of power output, operating voltage and operating current is as shown in figs. 19-21;
It was found from Fig. 3,4 simulation curve P5, the pattern of blocking place an order string array theoretical power output be about
1201.88W, quiescent potential 279V, operating point electric current are 4.295A.From aircraft pursuit course as can be seen that improving compound MPPT
Algorithm simulating system can lock maximum power point in 0.5s or so, and the maximum power point traced into is about 1197W, power swing width
Degree is about 13W, and quiescent potential is stable in 280V or so, and voltage pulsation amplitude is about 22V, and operating point electric current is stable in 4.275A
Left and right, current fluctuation amplitude are about 0.350A.
Contrast improves peak power of the compound MPPT algorithm to single string array under two kinds of different local shades circumstance of occlusion
Point tracking emulation, no matter maximum power point tends to voltage source region or tends to current source region, the algorithm have it is good with
Track performance, it can rapidly and accurately trace into actual maximum power point and lock maximum power point, not by local minimum
The interference of point and pseudo- maximum power point, tracking error is in the range of 6% that engineering allows.
MPPT:MPPT maximum power point tracking (Maximum Power Point Tracking);
Voc:Photovoltaic cell open-circuit voltage;
Isc:Photovoltaic cell short circuit current;
Vm:Maximum power of photovoltaic cell point voltage;
Im:Maximum power of photovoltaic cell point electric current;
I-U characteristics:I-E characteristic (C-V characteristic);
P-U characteristics:Power-voltage characteristic;
Rpv:Photovoltaic cell resistance;
Rpm:Equivalent resistance.
Vpm:Equivalent voltage;
Ipm:Equivalent current;
PV:Photovoltaic (battery);
DC-DC:DC-to-dc;
PWM:Pulse width modulation ((Pulse Width Modulation);
Boost circuit:Booster circuit.
5 summarize
Asked herein for what conventional composite MPPT algorithm was likely to occur in tracking photovoltaic system multi-peak maximum power point
Topic, it is proposed that follow-on compound MPPT algorithm, i.e., added during scanning maximum power point field and preserve local most
The big link for being worth and comparing, it is of a relatively high using precision during maximum power point is locked and influenceed by environmental change smaller
Conductance increment method substitute traditional perturbation observation method.By building artificial circuit in MATLAB/Simulink, using changing
Compound MPPT algorithm after entering, the string maximum power point of photovoltaic array that placed an order respectively to local shades tend to voltage source region and electric current
Two kinds of different situations of source region are tracked emulation.Simulation results show, no matter actual maximum power point falls within where, changes
Compound MPPT algorithm after entering rapidly and accurately can be tracked and locked, and will not be maximum by local minimum point and puppet
The interference of power points.