CN103092249A - Tracing method of solar battery maximum power point - Google Patents

Abstract

The invention discloses a tracing method of a solar battery maximum power point. A part of curve which is nearby the maximum power point of a solar battery output characteristic power/ voltage curve 1 is approximated to a parabola 2, a parabolic equation is solved by using three groups of power/ voltage data 3, 4 and 5 on the part of the curve, and an extreme point 6 of the parabolic equation is the maximum power point 7 output by the solar battery.

Description

A kind of solar cell maximum power point tracing method

Technical field

The present invention relates to a kind of solar cell maximum power point tracing method.

Background technology

That solar energy power generating has is pollution-free, noiseless, the advantage such as inexhaustible, nexhaustible, and need not to produce material except sunlight, is a kind of green energy resource with bright prospects, occupies an important position in system in future.

Solar cell output power and illumination, the gentle loading condition of ring are relevant, and have unique maximum power point (MPP) certain under illumination, the gentle loading condition of ring.In order to improve generating efficiency, need to follow the tracks of maximum power point.At present solar cell battery maximum power point tracing method is a lot, and the most frequently used have constant voltage-tracing method (CVT), a disturbance observation (P﹠amp; Q) and increment conductance method (INC) etc.

The principle of constant voltage tracing (CVT) is in temperature one regularly, under different light intensity, the maximum power point corresponding voltage of solar cell almost drops on same point, make solar cell working on this fixed voltage, can realize the MPPT maximum power point tracking of solar cell.Disturbance observation (P﹠amp; Q) principle is the MPPT maximum power point tracking that realizes solar cell by output power and the operating voltage of relatively coming to determine increase or minimizing solar cell of last time with this solar cell.The principle of increment conductance method (INC) is (I/V) relatively, to regulate a kind of maximum power point tracing method of solar cell output voltage direction with judgement by solar cell the dynamic conductivity value (dI/dV) of exporting and the negative that Static Electro is led.

In said method, constant voltage tracing (CVT) is a kind of approximate maximum power point tracing method, when temperature changes, can not follow the tracks of exactly.And disturbance observation (P﹠amp; Q) and increment conductance method (INC) be all to calculate by loop iteration to approach maximum power point, the time of tracking and precision are affected by step-length, step-length is larger, tracking time is shorter, precision is lower, step-length is less, tracking time is longer, precision is higher.

Summary of the invention

The present invention's purpose is: propose a kind of solar cell maximum power point tracing method, realize MPPT maximum power point tracking rapidly and accurately, overcome deficiency of the prior art.In order to realize the present invention's purpose, intend by the following technical solutions:

A kind of solar cell maximum power point tracing method, output power/the voltage curve that it is characterized in that solar cell is symmetrical unimodal curve near the maximum power point place, can be approximately take maximum power point as the summit, maximum power point place voltage is the parabolic curve of axis of symmetry, by detecting three groups of power/voltage data on this part curve, find the solution parabolic equation, the extreme point of parabolic equation is the maximum power point of solar cell, and the method step is as follows:

Step 1, definite method of three groups of power/voltage Data Detection points

Under the illumination state, the output characteristics of solar cell can be approximately diode characteristic, and electric current changes with voltage index.If solar cell is considered as constant current source, semiconductor material bulk resistor, electrode and semiconductor material contact resistance, electrode conductor resistance and metallic conductor resistance are considered as resistance in series, be parallel resistance with battery edge leakage current and the equivalence of battery metal bridge leakage current, can obtain the solar cell equivalent electrical circuit, between the electric current of its output characteristics and voltage, relation is suc as formula (1):

$I=I_{\mathrm{ph}}-I_o[e^{\frac{q(U+{\mathrm{IR}}_s)}{\mathrm{AKT}}}-1]-\frac{(U+{\mathrm{IR}}_s)}{R_p}---\left(1\right)$

Wherein, I output current (A), U output voltage (V), I _phPhotogenerated current (A), R _sResistance in series (Ω), R _pParallel resistance (Ω), the desirable constant of A diode, I _oDiode reverse drain saturation current (A), the q quantity of electric charge 1.6 * 10 ^-19C, K Boltzmann constant 1.38 * 10 ^-23J/K; The T environment temperature (℃);

Under short circuit condition, U=0, I=I _sc, because output voltage fails to reach diode turn-on voltage, the minimum I of the electric current of flowing through on diode _o≈ 0, has

I _sc＝I _ph-I _scR _s/R _p (2)

Under open-circuit condition, U=U _oc, I=0 has

$I_o=(I_{\mathrm{ph}}-U_{\mathrm{oc}}/R_p)/(e^{\frac{{\mathrm{qU}}_{\mathrm{oc}}}{\mathrm{AKT}}}-1)---\left(3\right)$

Can solve I according to short circuit and open-circuit condition _phAnd I _oFollowing formula (4)-(5):

I _ph＝I _sc(1+R _s/R _P) (4)

$I_o=(I_{\mathrm{sc}}-\frac{U_{\mathrm{oc}}-I_{\mathrm{sc}}{R}_s}{R_p})e^{\frac{-q{U}_{\mathrm{oc}}}{\mathrm{AKT}}}---\left(5\right)$

Output voltage be multiply by simultaneously with equation both sides in arrangement formula (1)-(5), can get solar cell power/voltage equation suc as formula (6):

$P=\frac{I_{\mathrm{sc}}(R_s+R_p)U{-U}^2-{\mathrm{PR}}_s}{R_p}+\frac{U_{\mathrm{oc}}U-I_{\mathrm{sc}}(R_s+R_p)U}{R_p}{e}^{\frac{q({\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DEST\_PATH\_HSB00001046366400011.png"\; state="\{\{state\}\}">U</figure-callout>}}^2+{\mathrm{PR}}_s-U_{\mathrm{oc}}U)}{\mathrm{AKTU}}}---\left(6\right)$

Equation (6) is the implicit equation of power corresponding voltage, utilizes the Lambert function that the demonstration equation that formula (6) is converted into the power corresponding voltage is got formula (7):

$P=\frac{[{\mathrm{UI}}_{\mathrm{sc}}(R_s+R_p)-U^2]}{R_s+R_p}-\frac{\mathrm{AKTU}}{{\mathrm{qR}}_s}W\left(Y\right)---\left(7\right)$

Wherein,

$Y=\frac{{\mathrm{qR}}_s[I_{\mathrm{sc}}(R_s+R_p)-U_{\mathrm{oc}}]}{\mathrm{AKT}(R_s+R_p)}\exp \left\{\frac{q(R_s+R_p)(U-U_{\mathrm{oc}})-{\mathrm{qR}}_s[U-I_{\mathrm{sc}}(R_s+R_p)]}{\mathrm{AKT}(R_s+R_p)}\right\}$

The place has at maximum power point

Thereby solve maximum power point voltage suc as formula (8);

$U_m=\frac{[{\mathrm{qR}}_s{I}_{\mathrm{sc}}-\mathrm{AKT}](R_s+R_p)[1+W\left(Y_m\right)]}{2q{R}_s[1+W\left(Y_m\right)]+q{R}_{p}W\left(Y_m\right)}---\left(8\right)$

Due to open-circuit voltage U _ocWith short-circuit current I _scCan detect acquisition, so formula (7) only contains parameter A, R _sAnd R _pFor different solar cells, parameter A ∈ [1,2] is arranged, R _s∈ [0, ∞], R _P∈ [∞, 0] utilizes parameter A, R _sAnd R _PDullness on solar cell power/voltage curve affects rule, can obtain parameter A=1, R _s=0, R _pCoboundary curve and the A=2 of=∞, R _s=∞, R _p=0 lower boundary curve can get maximum power point corresponding voltage U on coboundary curve and lower boundary curve in substitution formula (7)-(8) respectively with upper and lower boundary curve parameter _QAnd U _O ^*And maximum power point P and P ^*Other arbitrary parameters A, R _sAnd R _pThe power/voltage curve on maximum power point must be at P and P ^*Between, maximum power point place corresponding voltage is at U _QAnd U _O ^*Between;

For guaranteeing check point near maximum power point, according to reference voltage U _Q, can provide step-length definition algorithm as follows: had by the triangle correspondence theorem $U_Q-U_O=\frac{P-P_Q}{P-P^{*}}(U_Q-{U_O}^{*}),$ Therefore getting the point voltage step-length is defined as:

$U_{\mathrm{step}}=U_Q-\left[\frac{n-m}{n}(U_Q-U_O)\right]---\left(9\right)$

m＝0，±1，±2，±3

In formula, n is the interval division number, can rule of thumb determine; M counts for intend gathering power, due to the maximum power point of all kinds of power/voltage curves might

Therefore both sides are set when m is zero, get a little to exist

On line segment, when m be on the occasion of the time, get a little and exist The line segment right side, otherwise The line segment left side;

Step 2 is utilized three groups of power/voltage data, finds the solution parabolic equation P=aU ²+ bU+c, and calculate para-curve extreme point (U _m, P _m), required result is the solar cell maximum power point.

Step 3 when intensity of illumination or environment temperature change, only needs to repeat a said process and gets final product.

Characteristics of the present invention:

Calculated by model due to the maximum power point of solar cell and get, so stable output power; Because the working point of detecting is relatively less, so shortened tracking time, improved generating efficiency.

Description of drawings

Fig. 1 has illustrated solar cell power/voltage curve of the present invention to meet parabolic characteristic.

Fig. 2 has illustrated the solar cell equivalent electrical circuit.

Fig. 3 has illustrated the non-crystal silicon solar cell check point to determine method.

Fig. 4 has illustrated the crystal silicon solar batteries check point to determine method.

Fig. 5 has illustrated control flow chart of the present invention.

1 is solar cell output power/voltage curve; 2 is para-curve; 3 is check point (U _m1, P _m1); 4 is check point (U _m2, P _m2); 5 is check point (U _m3, P _m3); 6 is the extreme point of parabolic equation; 7 is the solar cell maximum power point; 8 is solar cell power/voltage coboundary curve; 9 is solar cell power/voltage lower boundary curve; 10 is the solar array voltage/powertrace of arbitrary parameter.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described further.

Referring to Fig. 1, solar cell output power/voltage curve 1 is symmetrical unimodal curve near the maximum power point place, can be approximately take maximum power point as the summit, maximum power point place voltage is the parabolic curve of axis of symmetry, by detecting three groups of power/voltage Data Detection point (U on this part curve _m1, P _m1) 3, check point (U _m2, P _m2) 4 and check point (U _m3, P _m3) 5, find the solution parabolic equation, the extreme point 6 of parabolic equation is solar cell maximum power point 7, when concrete operations, comprises following step:

Step 1, definite method of three groups of power/voltage Data Detection points

Under the illumination state, the output characteristics of solar cell can be approximately diode characteristic, and electric current changes with voltage index.If solar cell is considered as constant current source, semiconductor material bulk resistor, electrode and semiconductor material contact resistance, electrode conductor resistance and metallic conductor resistance are considered as resistance in series, be parallel resistance with battery edge leakage current and the equivalence of battery metal bridge leakage current, can obtain the solar cell equivalent electrical circuit as shown in Figure 2, between the electric current of its output characteristics and voltage, relation is suc as formula (1):

$I=I_{\mathrm{ph}}-I_o[e^{\frac{q(U+{\mathrm{IR}}_s)}{\mathrm{AKT}}}-1]-\frac{(U+{\mathrm{IR}}_s)}{R_p}---\left(1\right)$

Wherein, I output current (A), U output voltage (V), I _pgPhotogenerated current (A), R _sResistance in series (Ω), R _pParallel resistance (Ω), the desirable constant of A diode, I _oDiode reverse drain saturation current (A), the q quantity of electric charge 1.6 * 10 ^-19C, K Boltzmann constant 1.38 * 10 ^-23J/K; The T environment temperature (℃);

Under short circuit condition, U=0, I=I _sc, because output voltage fails to reach diode turn-on voltage, the minimum I of the electric current of flowing through on diode _o≈ 0, has

I _sc＝I _ph-I _scR _s/R _p (2)

Under open-circuit condition, U=U _oc, I=0 has

$I_o=(I_{\mathrm{ph}}-U_{\mathrm{oc}}/R_p)/(e^{\frac{{\mathrm{qU}}_{\mathrm{oc}}}{\mathrm{AKT}}}-1)---\left(3\right)$

Can solve I according to short circuit and open-circuit condition _phAnd I _oFollowing formula (4)-(5):

I _ph＝I _sc(1+R _s/R _P) (4)

$I_o=(I_{\mathrm{sc}}-\frac{U_{\mathrm{oc}}-I_{\mathrm{sc}}{R}_s}{R_p})e^{\frac{-q{U}_{\mathrm{oc}}}{\mathrm{AKT}}}---\left(5\right)$

Output voltage be multiply by simultaneously with equation both sides in arrangement formula (1)-(5), can get solar cell power/voltage equation suc as formula (6):

$P=\frac{I_{\mathrm{sc}}(R_s+R_p)U{-U}^2-{\mathrm{PR}}_s}{R_p}+\frac{U_{\mathrm{oc}}U-I_{\mathrm{sc}}(R_s+R_p)U}{R_p}{e}^{\frac{q({\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DEST\_PATH\_HSB00001046366400011.png"\; state="\{\{state\}\}">U</figure-callout>}}^2+{\mathrm{PR}}_s-U_{\mathrm{oc}}U)}{\mathrm{AKTU}}}---\left(6\right)$

Equation (6) is the implicit equation of power corresponding voltage, utilizes the Lambert function that the demonstration equation that formula (6) is converted into the power corresponding voltage is got formula (7):

$P=\frac{[{\mathrm{UI}}_{\mathrm{sc}}(R_s+R_p)-U^2]}{R_s+R_p}-\frac{\mathrm{AKTU}}{{\mathrm{qR}}_s}W\left(Y\right)---\left(7\right)$

Wherein,

$Y=\frac{{\mathrm{qR}}_s[I_{\mathrm{sc}}(R_s+R_p)-U_{\mathrm{oc}}]}{\mathrm{AKT}(R_s+R_p)}\exp \left\{\frac{q(R_s+R_p)(U-U_{\mathrm{oc}})-{\mathrm{qR}}_s[U-I_{\mathrm{sc}}(R_s+R_p)]}{\mathrm{AKT}(R_s+R_p)}\right\}$

The place has at maximum power point

Thereby solve maximum power point voltage suc as formula (8);

$U_m=\frac{[{\mathrm{qR}}_s{I}_{\mathrm{sc}}-\mathrm{AKT}](R_s+R_p)[1+W\left(Y_m\right)]}{2q{R}_s[1+W\left(Y_m\right)]+q{R}_{p}W\left(Y_m\right)}---\left(8\right)$

Due to open-circuit voltage U _ocWith short-circuit current I _scCan detect acquisition, so formula (7) only contains parameter A, R _sAnd R _pFor different solar cells, parameter A ∈ [1,2] is arranged, R _s∈ [0, ∞], R _P∈ [∞, 0] utilizes parameter A, R _sAnd R _PDullness on solar cell power/voltage curve affects rule, can obtain parameter A=1, R _s=0, R _pSolar cell power/voltage coboundary curve 8 and the A=2 of=∞, R _s=∞, R _p=0 solar cell power/voltage lower boundary curve 9.Upper and lower boundary curve parameter can be got maximum power point corresponding voltage U on solar cell power/voltage coboundary curve 8 and solar cell power/voltage lower boundary curve 9 in substitution formula (7)-(8) respectively _QAnd U _O ^*And maximum power point P and P ^*, on the solar array voltage/powertrace 10 of other arbitrary parameters, maximum power point must be at P and P ^*Between, maximum power point place corresponding voltage is at U _QAnd U _O ^*Between;

For guaranteeing check point near maximum power point, according to reference voltage U _Q, can provide step-length definition algorithm as follows: had by the triangle correspondence theorem $U_Q-U_O=\frac{P-P_Q}{P-P^{*}}(U_Q-{U_O}^{*}),$ Therefore getting the point voltage step-length is defined as:

$U_{\mathrm{step}}=U_Q-\left[\frac{n-m}{n}(U_Q-U_O)\right]---\left(9\right)$

m＝0，±1，±2，±3

In formula, n is the interval division number, can rule of thumb determine; M counts for intend gathering power, due to the maximum power point of all kinds of power/voltage curves might

Both sides as shown in Figure 3 and Figure 4, are therefore set when m is zero, get a little to exist On line segment, when m be on the occasion of the time, get a little and exist

The line segment right side, otherwise

The line segment left side;

Step 2 is utilized three groups of power/voltage Data Detection point (U _m1, P _m1) 3, check point (U _m2, P _m2) 4 and check point (U _m3, P _m3) 5, find the solution parabolic equation P=aU ²+ bU+c, and the extreme point 6 of calculating parabolic equation, required result is solar cell maximum power point 7;

Step 3 when intensity of illumination or environment temperature change, only needs to repeat a said process and gets final product.

Claims (1)

1. solar cell maximum power point tracing method, it is characterized in that solar cell output power/voltage curve (1) is symmetrical unimodal curve near the maximum power point place, can be approximately take maximum power point as the summit, maximum power point place voltage is the parabolic curve of axis of symmetry, by detecting three groups of power/voltage Data Detection point (U on this part curve _m1, P _m1) (3), check point (U _m2, P _m2) (4) and check point (U _m3, P _m3) (5), find the solution parabolic equation, the extreme point of parabolic equation (6) is the maximum power point (7) of solar cell, when concrete operations, comprises following step:

Step 1, definite method of three groups of power/voltage Data Detection points

Under the illumination state, the output characteristics of solar cell can be approximately diode characteristic, electric current changes with voltage index, if solar cell is considered as constant current source, semiconductor material bulk resistor, electrode and semiconductor material contact resistance, electrode conductor resistance and metallic conductor resistance are considered as resistance in series, be parallel resistance with battery edge leakage current and the equivalence of battery metal bridge leakage current, can obtain the solar cell equivalent electrical circuit as shown in Figure 2, between the electric current of its output characteristics and voltage, relation is suc as formula (1):

$I=I_{\mathrm{ph}}-I_o[e^{\frac{q(U+{\mathrm{IR}}_s)}{\mathrm{AKT}}}-1]-\frac{(U+{\mathrm{IR}}_s)}{R_p}---\left(1\right)$

Wherein, I output current (A), U output voltage (V), I _phPhotogenerated current (A), R _sResistance in series (Ω), R _pParallel resistance (Ω), the desirable constant of A diode, I _oDiode reverse drain saturation current (A), the q quantity of electric charge 1.6 * 10 ^-19C, K Boltzmann constant 1.38 * 10 ^-23J/K; The T environment temperature (℃);

Under short circuit condition, U=0, I=I _sc, because output voltage fails to reach diode turn-on voltage, the minimum I of the electric current of flowing through on diode _o≈ 0, has

I _sc＝I _ph-I _scR _s/R _p(2)

Under open-circuit condition, U=U _oc, I=0 has

$I_o=(I_{\mathrm{ph}}-U_{\mathrm{oc}}/R_p)/(e^{\frac{{\mathrm{qU}}_{\mathrm{oc}}}{\mathrm{AKT}}}-1)---\left(3\right)$

Can solve I according to short circuit and open-circuit condition _phAnd I _oFollowing formula (4)-(5):

I _ph＝I _sc(1+R _s/R _P) (4)

$I_o=(I_{\mathrm{sc}}-\frac{U_{\mathrm{oc}}-I_{\mathrm{sc}}{R}_s}{R_p})e^{\frac{-q{U}_{\mathrm{oc}}}{\mathrm{AKT}}}---\left(5\right)$

Output voltage be multiply by simultaneously with equation both sides in arrangement formula (1)-(5), can get solar cell power/voltage equation suc as formula (6):

$P=\frac{I_{\mathrm{sc}}(R_s+R_p)U{-U}^2-{\mathrm{PR}}_s}{R_p}+\frac{U_{\mathrm{oc}}U-I_{\mathrm{sc}}(R_s+R_p)U}{R_p}{e}^{\frac{q(U^2+{\mathrm{PR}}_s-U_{\mathrm{oc}}U)}{\mathrm{AKTU}}}---\left(6\right)$

Equation (6) is the implicit equation of power corresponding voltage, utilizes the Lambert function that the demonstration equation that formula (6) is converted into the power corresponding voltage is got formula (7):

$P=\frac{[{\mathrm{UI}}_{\mathrm{sc}}(R_s+R_p)-U^2]}{R_s+R_p}-\frac{\mathrm{AKTU}}{{\mathrm{qR}}_s}W\left(Y\right)---\left(7\right)$

Wherein,

$Y=\frac{{\mathrm{qR}}_s[I_{\mathrm{sc}}(R_s+R_p)-U_{\mathrm{oc}}]}{\mathrm{AKT}(R_s+R_p)}\exp \left\{\frac{q(R_s+R_p)(U-U_{\mathrm{oc}})-{\mathrm{qR}}_s[U-I_{\mathrm{sc}}(R_s+R_p)]}{\mathrm{AKT}(R_s+R_p)}\right\}$

The place has at maximum power point

Thereby solve maximum power point voltage suc as formula (8);

$U_m=\frac{[{\mathrm{qR}}_s{I}_{\mathrm{sc}}-\mathrm{AKT}](R_s+R_p)[1+W\left(Y_m\right)]}{2q{R}_s[1+W\left(Y_m\right)]+q{R}_{p}W\left(Y_m\right)}---\left(8\right)$

Due to open-circuit voltage U _ocWith short-circuit current I _scCan detect acquisition, so formula (7) only contains parameter A, R _sAnd R _pFor different solar cells, parameter A ∈ [1,2] is arranged, R _s∈ [0, ∞], R _P∈ [∞, 0] utilizes parameter A, R _sAnd R _PDullness on solar cell power/voltage curve affects rule, can obtain parameter A=1, R _s=0, R _pSolar cell power/voltage coboundary curve (8) and the A=2 of=∞, R _s=∞, R _p=0 solar cell power/voltage lower boundary curve (9) can get solar cell power/voltage coboundary curve (8) and the upper maximum power point corresponding voltage U of solar cell power/voltage lower boundary curve (9) in substitution formula (7)-(8) respectively with upper and lower boundary curve parameter _QAnd U _O ^*And maximum power point P and P ^*, the upper maximum power point of the solar array voltage/powertrace of other arbitrary parameters (10) must be at P and P ^*Between, maximum power point place corresponding voltage is at U _QAnd U _O ^*Between;

For guaranteeing check point near maximum power point, according to reference voltage U _Q, can provide step-length definition algorithm as follows: had by the triangle correspondence theorem $U_Q-U_O=\frac{P-P_Q}{P-P^{*}}(U_Q-{U_O}^{*}),$ Therefore getting the point voltage step-length is defined as:

$U_{\mathrm{step}}=U_Q-\left[\frac{n-m}{n}(U_Q-U_O)\right]---\left(9\right)$

m＝0，±1，±2，±3

In formula, n is the interval division number, can rule of thumb determine; M counts for intend gathering power, due to the maximum power point of all kinds of power/voltage curves might

Both sides, as shown in Figure 3.Therefore set as m when being zero, get a little and exist

On line segment, when m be on the occasion of the time, get a little and exist

The line segment right side, otherwise

The line segment left side;

Step 2 is utilized three groups of power/voltage Data Detection point (U _m1, P _m1) (3), check point (U _m2, P _m2) (4) and check point (U _m3, P _m3) (5), find the solution parabolic equation P=aU ²+ bU+c, and the extreme point of parabolic equation (6), required result is solar cell maximum power point (7);

Step 3 when intensity of illumination or environment temperature change, only needs to repeat a said process and gets final product.

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