Islanding detection method in DC microgrids based on MPPT trapezoidal voltage disturbance

Abstract

The invention discloses an islanding detection method in DC microgrids based on MPPT trapezoidal voltage disturbance. The steps are as follows: start the MPPT strategy; set the starting signal threshold of disturbance; measure the output current of PVA at the maximum power; calculate the same environmental factor of PVA with different capacities under the same light intensity and temperature in real time; when the environmental factor is greater than the starting signal threshold of the disturbance, periodic trapezoidal disturbance is carried out to the PVA port voltage reference; if the PCC voltage Upcc exceeds the threshold set by the passive method, it is judged as islanding; otherwise, it is judged whether the change rule of Upcc is consistent with the change rule of the calculated PCC voltage Upccp under the trapezoidal disturbance; If it is consistent, it is judged as islanding; otherwise, it is pseudo islanding.

Claims

1. An islanding detection method in Direct Current (DC) microgrids based on Maximum Power Point Tracking (MPPT) trapezoidal voltage disturbance, wherein, the steps are as follows: start a MPPT strategy; set a starting signal threshold of disturbance Δ.sub.Start; measure an output current of Photovoltaic Array (PVA) at a maximum power; calculate same environmental factor Δ.sub.ST of PVA with different capacities under same light intensity and temperature in real time, ${\Delta }_{\mathrm{ST}}=k_i\frac{I_{\mathrm{pvm}}}{N_p{I}_{\mathrm{sct}}}$ $k_i=\frac{I_{\mathrm{sct}}}{I_{\mathrm{mt}}}$ where, I.sub.pvm is an output current of PVA with different capacities at the maximum power; N.sub.p is a number of parallel branches of PVA with different capacities; k.sub.i is a factor of proportionality, I.sub.sct is a short circuit current and I.sub.mt is a Maximum Power Point output current; ${\Delta }_{\mathrm{Start}}=\frac{S}{S_{\mathrm{ref}}}+\frac{J}{100}\left(T-T_{\mathrm{ref}}\right)$ where, S and Tare a set values of light intensity and temperature at a disturbance starting time, S.sub.ref and T.sub.ref are reference values of light intensity and temperature, and J is a temperature coefficient of short-circuit current; when the environmental factor Δ.sub.ST is greater than the starting signal threshold Δ.sub.start of the disturbance, control all PVAs to start voltage disturbance simultaneously, which means periodic trapezoidal disturbance is carried out to a PVA port voltage reference U.sub.pvref, so that an actual output voltage and power of PVA as well as a Point of Common Coupling (PCC) voltage U.sub.pcc after an islanding are also periodically disturbed; $u_{\mathrm{pvref}}\left(t\right)=\{\begin{array}{cc}\frac{\Delta U_{\mathrm{pv}}}{T_c/2}.Math.\left(t-{\mathrm{nT}}_0\right)+U_{\mathrm{pvm}}& \left({\mathrm{nT}}_0\le t\le \frac{T_c}{2}+{\mathrm{nT}}_0\right)\\ U_{\mathrm{pvm}}+\Delta U_{\mathrm{pv}}& \left(\frac{T_c}{2}+{\mathrm{nT}}_0<t\le T_p-\frac{T_c}{2}+{\mathrm{nT}}_0\right)\\ -\frac{\Delta U_{\mathrm{pv}}}{T_c/2}.Math.\left(t-T_p-{\mathrm{nT}}_0\right)+U_{\mathrm{pvm}}& \left(T_p-\frac{T_c}{2}+{\mathrm{nT}}_0<t\le T_p+{\mathrm{nT}}_0\right)\\ U_{\mathrm{pvm}}& \left(T_p+{\mathrm{nT}}_0<t\le T_0+{\mathrm{nT}}_0\right)\end{array}$ where, T.sub.0 is a period of the trapezoidal disturbance, T is a total duration at two waists of the trapezoidal disturbance in a period, T.sub.p is a duration of the disturbance in a period, n is a non-negative integer, U.sub.pvm is a voltage reference of PVA at the maximum power, and ΔU.sub.pv is an amplitude of the trapezoidal disturbance; and if the PCC voltage U.sub.pcc exceeds the threshold set by the passive method, it is judged as islanding; otherwise, judge whether changing rule of the PCC voltage U.sub.pcc is consistent with changing rule of calculated voltage U.sub.pccp under the trapezoidal disturbance; If it is consistent, it is judged as islanding; otherwise, it is pseudo islanding, and continue to monitor changes in the PCC voltage U.sub.pcc.

2. The islanding detection method in DC microgrids according to claim 1, wherein, judge whether the change rule of U.sub.pcc is consistent with that of the calculated PCC voltage U.sub.pccp under the trapezoidal disturbance is to judge whether the PCC voltage meets the following two conditions: 1) The measured value PCC voltage U.sub.pcc of the trapezoidal disturbance at the two waists is equal to a calculated value, U.sub.pccp1, or the measured value PCC voltage U.sub.pcc at an upper base of the trapezoidal disturbance is equal to a calculated value U.sub.pccp2; 2) A change period T.sub.pcc of the PCC voltage U.sub.pcc is equal to the trapezoidal disturbance period, T.sub.0.

3. The islanding detection method in DC microgrids according to claim 2, wherein, the calculation steps of the PCC voltage of the trapezoidal disturbance at the two waists are as follows: $\Delta P_1=\underset{j=2}{\overset{s}{.Math.}}\left[\left(I_{\mathrm{pv}\left(j-1\right)}-\frac{U_{\mathrm{pv}\left(j-1\right)}}{R_s+r_{dj}}\right)\Delta U_{\mathrm{pvj}}-\frac{1}{R_s+r_{\mathrm{dj}}}{\left(\Delta U_{\mathrm{pvj}}\right)}^2\right]r_{\mathrm{dj}}=\frac{\Delta U_{\mathrm{pvj}}}{\Delta I_{\mathrm{pvj}}}\Delta U_{\mathrm{pvj}}=U_{\mathrm{pvj}}-U_{\mathrm{pv}\left(j-1\right)}\Delta I_{\mathrm{pvj}}=I_{\mathrm{pvj}}-I_{\mathrm{pv}\left(j-1\right)}{U}_{\mathrm{pccp}1}=U_{\mathrm{pccm}}\sqrt{1+\frac{\Delta P_1}{P_m}}$ where, ΔP.sub.1 represents a change of PVA output power at two waists of the trapezoidal disturbance, and U.sub.pccm represents a PCC voltage when the PVA port voltage is equal to U.sub.pvm. U.sub.pvj and I.sub.pvj are a sampling values of PVA port voltage and output current in current time, and U.sub.pv(j−1) and I.sub.pv(j−1) are a sampling values at a previous moment respectively, ΔU.sub.pvj represents a change of PVA port voltage after each sampling, ΔU.sub.pv=ΔU.sub.pv2+ΔU.sub.pv3'. . . +ΔU.sub.pvs, s is a number of sampling (s>2), r.sub.dj is a dynamic resistance calculated after each sampling; the calculation steps of the PCC voltage U.sub.pccp2 at the upper base of the trapezoidal disturbance are as follows: $\Delta P_2=\frac{1}{R_{\mathrm{dp}}+R_s}\left[I_{\mathrm{sc}}{R}_{\mathrm{dp}}\left(U_{\mathrm{pvp}}+\Delta U_{\mathrm{pv}}\right)-{\left(U_{\mathrm{pvp}}+\Delta U_{\mathrm{pv}}\right)}^2\right]-P_m{R}_{\mathrm{dp}}=\frac{U_{\mathrm{pvp}}+I_{\mathrm{pvp}}{R}_s}{I_{\mathrm{sc}}-I_{\mathrm{pvp}}}{U}_{\mathrm{pccp}2}=U_{\mathrm{pccm}}\sqrt{1+\frac{\Delta P_2}{P_m}}$ where, ΔP.sub.2 is a change of PVA output power at the upper base of the trapezoidal disturbance, P.sub.m is an output power when the PVA port voltage is U.sub.pvm, U.sub.pvp is a PVA port voltage when the trapezoidal disturbance reaches its maximum value; U.sub.pvp=U.sub.pvm+ΔU.sub.pv, Rap is equivalent static resistance of PVA when PVA port voltage is equal to U.sub.pvp.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) FIG. 1 shows the static equivalent circuit of photovoltaic array.

(2) FIG. 2a is the schematic diagram of photovoltaic array.

(3) FIG. 2b is the schematic diagram of the sub-module (photovoltaic panel) of photovoltaic array.

(4) FIG. 3a shows the Id-Ud characteristic curve of the photovoltaic array equivalent diode.

(5) FIG. 3b shows the P-Upv characteristic curve of photovoltaic array.

(6) FIG. 4 shows the equivalent circuit of the small signal model of photovoltaic array.

(7) FIG. 5 is the schematic diagram of the trapezoidal disturbance of PVA port voltage.

(8) FIG. 6 is the flow chart of the islanding detection method proposed for DC microgrid containing multiple DG.

DESCRIPTION OF THE INVENTION

(9) The technical scheme will be described in detail in combination with reference to the attached drawings.

(10) Through appropriate modification of MPPT strategy, the output power of PVA is made to fluctuate in accordance with periodic trapezoid signal near the maximum power, thus leading to periodic fluctuation of PCC voltage after the islanding. If the change rule of PCC voltage after islanding occurs conforms to the theoretical analysis, then it is judged that islanding occurs in DC microgrid. Moreover, when multiple photovoltaic arrays supply power to the load simultaneously in the same area, given that the disturbances imposed by different PVAs may cancel each other out and thus reduce the accuracy of islanding detection, the present invention provides a scheme of disturbance synchronization, which ensures the reliability of islanding detection.

(11) An islanding detection method in DC microgrids based on MPPT trapezoidal voltage disturbance, wherein, the steps are as follows:

(12) Step 1, start the MPPT strategy; set the starting signal threshold of disturbance Δ.sub.start; measure the output current of PVA at the maximum power; calculate the same environmental factor Δ.sub.ST of PVA with different capacities under the same light intensity and temperature in real time.

(13) In order to accurately reflect the change of external light intensity and temperature without relying on sensor equipment, by analyzing the correlation between PVA output current and light intensity and temperature, the environmental factor Δ.sub.ST can be obtained to reflect the change of environmental parameters by PVA output current, so that the same environmental factor Δ.sub.ST can be calculated under the same light intensity and temperature for PVA with different capacities.

(14) In order to improve the calculation accuracy of environmental factor Δ.sub.ST, the PVA used in this method should all be composed of photovoltaic panels of the same type, and the number of photovoltaic panels in series on different PVA parallel branches should be the same.

(15) The active method of AC islanding detection is more reliable and accurate than the passive method. However, since most of these methods need to inject disturbance signals into PCC, when multiple photovoltaic arrays supply power to the load simultaneously, how to keep different disturbance signals synchronized is a problem that must be faced. Similarly, the active method in the DC islanding detection also needs to ensure the synchronization between different disturbance signals.

(16) To solve this problem, a disturbance voltage synchronization strategy based on environmental factor Δ.sub.ST is proposed, where the same environmental factor Δ.sub.ST can be calculated for different PVAs without relying on communication, and can be used as the starting signal of disturbance, so as to ensure the synchronization of disturbance.

(17) The output of PVA fluctuates because the output current of photovoltaic cells composing PVA will change with the external light intensity and temperature. However, when sudden changes in light intensity and temperature due to abrupt weather changes or obstructions are ignored, light intensity and temperature vary uniformly throughout the day and can be regarded as approximately unchanged in a short time. Since the changing speed of light intensity and temperature is far less than the tracking speed of MPPT strategy for PVA maximum power point, it can be considered that PVA has been operating at maximum power. When PVA operates stably at the maximum power point, all electric quantities in the system remain unchanged. At this time, the diode in the PVA equivalent circuit can be regarded as a static resistor R.sub.d with constant resistance, as shown in the static equivalent circuit of photovoltaic array in FIG. 1.

(18) $\begin{array}{cc}P=\frac{1}{R_d+R_s}\left(I_{\mathrm{sc}}{R}_d{U}_{\mathrm{pv}}-U_{\mathrm{pv}}^2\right)& \left(1\right)\end{array}$$\begin{array}{cc}{R}_d=\frac{U_{\mathrm{pv}}+I_{\mathrm{pv}}{R}_s}{I_{\mathrm{sc}}-I_{\mathrm{pv}}}& \left(2\right)\end{array}$

(19) The output current I.sub.pv of PVA, port voltage U.sub.pv and static resistance R.sub.d change with the light intensity and temperature. Therefore, Equation (1) represents the relationship between the output power and the port voltage when PVA operates stably under different lighting intensities and temperatures. R.sub.s is the equivalent series resistance of PVA. When PVA outputs the maximum power, its port voltage, output current and power are U.sub.pvm, I.sub.pvm and P.sub.m respectively. The following equations can be obtained according to Equations (1) and (2):

(20) $\begin{array}{cc}{P}_m=\frac{1}{R_{\mathrm{dm}}+R_s}\left(I_{\mathrm{sc}}{R}_{\mathrm{dm}}{U}_{\mathrm{pvm}}-U_{\mathrm{pvm}}^2\right)& \left(3\right)\end{array}$$\begin{array}{cc}{R}_{\mathrm{dm}}=\frac{U_{\mathrm{pvm}}+I_{\mathrm{pvm}}{R}_s}{I_{\mathrm{sc}}-I_{\mathrm{pvm}}}& \left(4\right)\end{array}$

(21) F(U.sub.pv)=I.sub.scR.sub.dmU.sub.pv−U.sub.pv.sup.2, According to Equation (3), (U.sub.pvm, F(U.sub.pvm)) is a point on the quadratic function F(U.sub.pvc). The horizontal coordinate of the symmetry axis of the quadratic function curve is R.sub.dmI.sub.sc/2. Let the factor of proportionality between it and U.sub.pvm be k, then the relationship between them can be expressed as:

(22) $\begin{array}{cc}k{U}_{\mathrm{pvm}}=\frac{I_{\mathrm{sc}}{R}_{\mathrm{dm}}}{2}& \left(5\right)\end{array}$

(23) The relationship between PVA short circuit current I.sub.sc and port voltage and output current can be obtained by combining Equation (4) and Equation (5).

(24) 0$\begin{array}{cc}{I}_{\mathrm{sc}}=\frac{2{\mathrm{kU}}_{\mathrm{pvm}}}{\left(2k-1\right)\frac{U_{\mathrm{pvm}}}{I_{\mathrm{pvm}}}-R_s}& \left(6\right)\end{array}$

(25) Since the equivalent series resistance R.sub.s of PVA is much smaller than U.sub.pvm/I.sub.pvm, and k is greater than 1, it can be ignored and simplified to Equation (7).

(26) $\begin{array}{cc}{I}_{\mathrm{sc}}=\frac{2k}{\left(2k-1\right)}{I}_{\mathrm{pvm}}=k_i{I}_{\mathrm{pvm}})& \left(7\right)\end{array}$$\begin{array}{cc}{I}_{\mathrm{sc}}=I_{\mathrm{scref}}.Math.{\Delta }_{\mathrm{ST}}& \left(8\right)\end{array}$$\begin{array}{cc}{\Delta }_{\mathrm{ST}}=\left(\frac{S}{S_{\mathrm{ref}}}+\frac{J}{100}\left(T-T_{\mathrm{ref}}\right)\right)& \left(9\right)\end{array}$

(27) According to Equation (7), there is a proportional relationship between the short circuit current I.sub.sc of PVA and the output current I.sub.pvm at the maximum power, and the proportional coefficient is k.sub.i (k.sub.i>1). According to Equation (7), the short-circuit current I.sub.sc can be obtained directly from I.sub.pvm. Equation (8) is PVA's correction equation for the reference value I.sub.scref of short-circuit current considering the actual light and temperature changes. I.sub.scref is the PVA's short-circuit current under standard conditions (S=1000 W/m.sup.2, T=25° C.). The following equation can be obtained from the equations (7) and (8):

(28) $\begin{array}{cc}{\Delta }_{\mathrm{ST}}=k_i\frac{I_{\mathrm{pvm}}}{I_{\mathrm{scref}}}& \left(10\right)\end{array}$

(29) According to Equation (10), if I.sub.scref and k.sub.i are known, PVA can calculate the environmental factor Δ.sub.ST in real time.

(30) FIG. 2a-2b shows the schematic diagram of PVA and its sub-modules. The sub-modules are equivalent to the actual photovoltaic panels, and a number of photovoltaic panels constitute PVA through series and parallel. The sum of the current of each parallel branch of PVA is equal to the total output current of PVA, and the voltage at both ends of any parallel branch is equal to the port voltage of PVA. PVA is composed of different photovoltaic panels in different series and parallel modes, and the output characteristics of PVA are also different.

(31) As shown in the right figure in FIG. 2a, multiple photovoltaic cells are connected in series to form a single photovoltaic panel. The output current of the photovoltaic panel is equal to the output current of each photovoltaic cell I.sub.pvc, I.sub.pvc1, . . . , I.sub.pVCNs. And when the output current of the photovoltaic cell is less than its short-circuit current, the current I.sub.Db flowing through the bypass diode can be ignored. If PVA has N.sub.p parallel branches and each parallel branch has N.sub.sp photovoltaic panels in series, the equivalent series resistance of the whole PVA is equal to 1/N.sub.p of the series resistance of a single photovoltaic cell. The relationship between PVA output current I.sub.pv and port voltage U.sub.pv is as follows:

(32) $\begin{array}{cc}{I}_{\mathrm{pv}}=N_p\left[I_{\mathrm{sc}\_\mathrm{pvc}}-I_{0\_\mathrm{pvc}}\left(e^{\frac{q}{\mathrm{NKT}}\left(U_{\mathrm{pv}}/N_{\mathrm{sp}}{N}_s+I_{\mathrm{pvc}}{R}_{s\_\mathrm{pvc}}/N_p\right)}-1\right)\right]& \left(11\right)\end{array}$

(33) I.sub.sc_pvc, I.sub.0_pvc and R.sub.s_pvc are short circuit current of photovoltaic cells, diode reverse saturation current and equivalent series resistance of photovoltaic cells respectively. According to Equation (11), when the number N.sub.sp of photovoltaic panels in series on each parallel branch is the same, the ratio of output current of different PVA is approximately equal to the ratio of the number of parallel branches, since the series resistance R.sub.s_PVC of photovoltaic cell is very small.

(34) $\begin{array}{cc}\frac{I_{\mathrm{pv}2}}{I_{\mathrm{pv}1}}=\frac{N_{p1}\left[I_{\mathrm{sc}\_\mathrm{pvc}}-I_{0\_\mathrm{pvc}}\left(e^{\frac{q}{\mathrm{NKT}}\left(U_{\mathrm{pv}1}/N_{\mathrm{sp}}{N}_s+I_{\mathrm{pvc}}{R}_{s\_\mathrm{pvc}}/N_p\right)}-1\right)\right]}{N_{p2}\left[I_{\mathrm{sc}\_\mathrm{pvc}}-I_{0\_\mathrm{pvc}}\left(e^{\frac{q}{\mathrm{NKT}}\left(U_{\mathrm{pv}2}/N_{\mathrm{sp}}{N}_s+I_{\mathrm{pvc}}{R}_{s\_\mathrm{pvc}}/N_{p2}\right)}-1\right)\right]}\approx \frac{N_{p1}}{N_{p2}}& \left(12\right)\end{array}$

(35) To sum up, when different PVA meet the following two conditions: 1) They are composed of photovoltaic panels of the same type; 2) The number Nsp of photovoltaic panels in series on each parallel branch is the same. Then the ratio of the output current I.sub.pv of different PVA is equal to the ratio of the number N.sub.p of parallel branches of different PVA, that is, the parallel branch current of different PVA is approximately equal.

(36) The reference value of the photovoltaic panel short-circuit current I.sub.sct is put into Equation (10) to obtain the equation of output current I.sub.pvm and environmental factor Δ.sub.ST when PVA operates at the maximum power.

(37) $$\begin{gathered} \begin{array}{cc}{\Delta }_{\mathrm{ST}}=k_i\frac{I_{\mathrm{pvm}}}{N_p{I}_{\mathrm{sct}}} \\ {k}_i=\frac{I_{\mathrm{sct}}}{I_{\mathrm{mt}}}& \left(13\right)\end{array} \end{gathered}$$

(38) I.sub.pvm is the output current of PVA at the maximum power; N.sub.p is the number of parallel branches of PVA. k.sub.i will not change with light and temperature, and can be obtained directly from the short circuit current I.sub.sct and maximum power point output current I.sub.mt in the factory parameters of photovoltaic panels.

(39) Equation (13) can be used to calculate the same environmental coefficient Δ.sub.ST for different PVA. The environmental coefficient can be calculated in real time for each PVA. Set the threshold Δ.sub.Start of starting disturbance so that different PVA can start the disturbance at the same time, thus ensuring the synchronization of the disturbance.

(40) FIG. 3b shows the P-U.sub.pv characteristic curve of PVA. The output power P will change with the PVA port voltage U.sub.pv. Therefore, MPPT strategy can keep PVA running at the maximum power point by adjusting the size of U.sub.pv, as shown in Point Q in FIG. 3b. If the MPPT strategy is slightly modified so that it no longer tracks the maximum power point Q but makes small fluctuations around the Point Q, such as Point A and Point B in FIG. 3b, the purpose of power disturbance can be achieved. According to the P-U.sub.pv characteristic curve of PVA, the slope of the curve on the right side of the maximum power point Q changes faster than the slope of the curve on the left. This means that the voltage change required for the disturbance to Point B is smaller than the disturbance to point A under the same power disturbance effect. Therefore, the present invention adopts the disturbance to the right of the maximum power point.

(41) To sum up, the change of PVA output power is realized by changing its port voltage. When U.sub.pv fluctuates near the voltage U.sub.pvm at the maximum power point, the voltage U.sub.d at both ends of the diode in the equivalent circuit of PVA will also change accordingly. At this point, the positions of the three points A, Q and B on the P-U.sub.pv characteristic curve on the diode I.sub.d-U.sub.d characteristic curve are shown in FIG. 3a. The Point Q on the curve in FIG. 3a is the working point where the diode is located when PVA is operating at the maximum power point, and the horizontal coordinate is the voltage U.sub.dm at both ends of the diode at the maximum power. When the PVA port voltage changes very little near U.sub.m, the voltage at both ends of the diode also changes very small, then the three points A, Q and B on the diode I.sub.d-U.sub.d characteristic curve can be approximately regarded as in a straight line. At this point, the diode exhibits linear characteristics under a small voltage disturbance. The resistance is a fixed value, and is the reciprocal of the slope of the line AQB. This analysis method is called small signal model analysis method. The equivalent circuit of the photovoltaic array small signal model is shown in FIG. 4. The dynamic resistance r.sub.d is the equivalent resistance of the diode under small voltage disturbance. At this point, the relationship between PVA output current change ΔI.sub.pv and voltage change ΔU.sub.pv is shown as follows:

(42) $$\begin{gathered} \begin{array}{cc}\Delta I_{\mathrm{pv}}=\Delta I_{\mathrm{sc}}-\frac{\Delta U_{\mathrm{pv}}+\Delta I_{\mathrm{pv}}{R}_s}{r_d} \\ {r}_d=\frac{{\mathrm{dU}}_d}{{\mathrm{dI}}_d}& \left(14\right)\end{array} \end{gathered}$$

(43) R.sub.s is the equivalent series resistance of PVA, where PVA short circuit current I.sub.sc is unchanged before and after disturbance, so its variation ΔI.sub.sc is zero. So:

(44) $\begin{array}{cc}\Delta I_{\mathrm{pv}}=-\frac{\Delta U_{\mathrm{pv}}}{r_d+R_s}& \left(15\right)\end{array}$

(45) The idea of the present invention is to carry out periodic disturbance near the PVA maximum power point. The output current I.sub.pvm and port voltage U.sub.pvm of PVA at the maximum power point are known. Suppose the variation of voltage and current are:
ΔU.sub.pv=U.sub.pvp−U.sub.pvm  (16)
ΔI.sub.pv=I.sub.pvp−I.sub.pvm  (17)

(46) U.sub.pvp and I.sub.pvp are the port voltage and output current of PVA when the power decreases to a stable level after disturbances are applied respectively. According to Equation (16) and Equation (17), U.sub.pvm, I.sub.pvm, ΔI.sub.pv and ΔU.sub.pv can represent the change of PVA output power ΔP.sub.1:
ΔP.sub.1=ΔU.sub.pvI.sub.pvm+ΔI.sub.pvU.sub.pvm+ΔU.sub.pvΔI.sub.pv  (18)

(47) According to Equations (15)-(18), the relationship between variation ΔU.sub.pv of PVA port voltage and output power variation ΔP of photovoltaic cell can be obtained.

(48) $\begin{array}{cc}\left(I_{\mathrm{pvm}}-\frac{U_{\mathrm{pvm}}}{R_s+r_{\mathrm{dm}}}\right)\Delta U_{pv}-\frac{1}{R_s+r_{\mathrm{dm}}}{\left(\Delta U_{\mathrm{pv}}\right)}^2=\Delta P_1& \left(19\right)\end{array}$

(49) With small voltage disturbance, the dynamic resistance of the diode is a fixed value r.sub.dm, which can be obtained by taking the derivative of the U.sub.dm and inverting according to the diode I.sub.d−U.sub.d characteristic curve. According to the analysis of the diode I.sub.d−U.sub.d characteristic curve in the FIG. 3a, the voltage variation at both ends of the diode is small when the variation ΔU.sub.pv of PVA port voltage is very small (less than 1V). At this point, the dynamic resistance r.sub.d is approximately unchanged at ΔU.sub.pv. However, for PVA, the variation of port voltage around 1V will not lead to the fluctuation of PVA output power, which cannot achieve the purpose of power disturbance.

(50) However, the ΔU.sub.pv sufficient to cause PVA output power fluctuation can be divided into several cells by the definite integral method, and the dynamic resistance corresponding to each cell can be regarded as a fixed value, satisfying the conditions required in Equation (19). The sum of all the inter-cell power variations is the total power variation ΔP.sub.1.

(51) $\begin{array}{cc}\Delta P_1=\underset{j=2}{\overset{s}{.Math.}}\left[\left(I_{\mathrm{pv}\left(j-1\right)}-\frac{U_{\mathrm{pv}\left(j-1\right)}}{R_s+r_{\mathrm{dj}}}\right)\Delta U_{\mathrm{pvj}}-\frac{1}{R_s+r_{\mathrm{dj}}}{\left(\Delta U_{\mathrm{pvj}}\right)}^2\right]& \left(20\right)\end{array}$$\begin{array}{cc}{r}_{\mathrm{dj}}=\frac{\Delta U_{\mathrm{pvj}}}{\Delta I_{\mathrm{pvj}}}& \left(21\right)\end{array}$$\begin{array}{cc}\Delta U_{\mathrm{pvj}}=U_{\mathrm{pvj}}-U_{\mathrm{pv}\left(j-1\right)}& \left(22\right)\end{array}$$\begin{array}{cc}\Delta I_{\mathrm{pvj}}=I_{\mathrm{pvj}}-I_{\mathrm{pv}\left(j-1\right)}& \left(23\right)\end{array}$

(52) Equation (20) is the PVA power variation equation of trapezoidal disturbance at the two waists. Where, I.sub.pvj and U.sub.pvj are the sampling values of PVA port voltage at the current moment, U.sub.pv(j-1) and I.sub.pv(j-1) are the sampling values of PVA port voltage and output current at the previous moment, and ΔU.sub.pvj is the variation of PVA port voltage after each sampling. ΔU.sub.pv=ΔU.sub.pv2±ΔU.sub.pv3+ . . . +ΔU.sub.pvs. s is the number of sampling (s>2), r.sub.dj is the dynamic resistance calculated after each sampling;

(53) When the PVA port voltage gradually increases from U.sub.pvm to U.sub.pvp and becomes stable, the output power of PVA will no longer decrease, reaching a new stable operating point. At this point, the circuit satisfies the equivalent condition of static resistance. According to Equation (3), the following equations can be obtained:

(54) 0$\begin{array}{cc}\Delta P_2=\frac{1}{R_{\mathrm{dp}}+R_s}\left[I_{sc}{R}_{\mathrm{dm}}\left(U_{\mathrm{pvm}}+\Delta U_{\mathrm{pv}}\right)-{\left(U_{\mathrm{pvm}}+\Delta U_{\mathrm{pv}}\right)}^2\right]-P_m& \left(24\right)\end{array}$$\begin{array}{cc}{R}_{\mathrm{dp}}=\frac{U_{\mathrm{pvp}}+I_{\mathrm{pvp}}{R}_s}{I_{sc}-I_{\mathrm{pvp}}}& \left(25\right)\end{array}$

(55) Where, ΔP.sub.2 is the variation of PVA output power at the upper base of the trapezoidal disturbance, P.sub.m is the output power when the PVA port voltage is U.sub.pvm, U.sub.pvp is the PVA port voltage when the trapezoidal disturbance reaches its maximum value; U.sub.pvp=U.sub.pvm+ΔU.sub.pv, R.sub.dp is equivalent static resistance of PVA when PVA port voltage is equal to U.sub.pvp.

(56) If the power P.sub.L consumed by DC load during grid-connected operation differs greatly from the output power P of PVA, according to the following equations, the PCC voltage U.sub.pcc will change significantly after islanding occurs.

(57) $$\begin{gathered} \begin{array}{cc}{P}_L=\frac{U_N^2}{R} \\ P=\frac{U_{\mathrm{pcc}}^2}{R}& \left(26\right)\end{array} \end{gathered}$$

(58) Where, U.sub.N is the rated voltage of DC bus. When the DC power grid is in normal operation, the allowable deviation range of DC bus voltage varies according to the DC voltage level. It is stipulated in the Chinese National Standard GB/T 35727-2017 that the allowable voltage deviation range of low-voltage DC distribution network below 1500V is −20%−+5% of U.sub.N.

(59) Therefore, the threshold of the passive method in the present invention is set as 0.8 U.sub.N and 1.05 U.sub.N. When it is detected in the system that the U.sub.pcc is less than 0.8 U.sub.N or greater than 1.05 U.sub.N, it will be judged as islanding. According to the standard, the variation range of PVA output power P can be calculated from the above equation, which is 0.64 P.sub.L˜1.1025 P.sub.L. In other words, when P<0.64 P.sub.L or P>1.1025 P.sub.L, the PCC voltage will exceed the threshold of passive method after the islanding occurs.

(60) If the output power of PVA matches the load power or changes little, the U.sub.pcc will not exceed the threshold of the passive method after the islanding occurs. According to equations (20) and (27), equations (24) and (27), the calculated U.sub.pcc1 and U.sub.pcc2 of PCC voltage at the two waists and the upper base of trapezoidal disturbance can be obtained respectively.

(61) $\begin{array}{cc}\Delta P=\frac{U_{\mathrm{pccp}}^2-U_{\mathrm{pccm}}^2}{R}& \left(27\right)\end{array}$$\begin{array}{cc}{U}_{\mathrm{pccp}1}=\sqrt{U_{\mathrm{pccm}}^2+\Delta P_1.Math.R}& \left(28\right)\end{array}$$\begin{array}{cc}{U}_{\mathrm{pccp}2}=\sqrt{U_{\mathrm{pccm}}^2+\Delta P_2.Math.R}& \left(29\right)\end{array}$

(62) In the actual situation, the load resistance is usually unknown. After the islanding occurs, the load resistance R can be calculated according to the output power of the PVA array and the PCC voltage. Therefore, equations (28) and (29) can be expressed as:

(63) $\begin{array}{cc}{U}_{\mathrm{pccp}1}=U_{\mathrm{pccm}}\sqrt{1+\frac{\Delta P_1}{P_m}}& \left(30\right)\end{array}$$\begin{array}{cc}{U}_{\mathrm{pccp}2}=U_{\mathrm{pccm}}\sqrt{1+\frac{\Delta P_2}{P_m}}& \left(31\right)\end{array}$

(64) Specifically, judge whether the PCC voltage meets the following two conditions: 1) The measured U.sub.pcc at the two waists of the trapezoidal disturbance is equal to the calculated U.sub.pccp1, or the measured U.sub.pcc at the upper base of the trapezoidal disturbance is equal to the calculated U.sub.pccp2; 2) The change period, T.sub.pcc, of measured U.sub.pcc, is equal to the trapezoidal disturbance period, T.sub.0. If the conditions are met, it will be judged as islanding; otherwise, it will be pseudo islanding, and the change of U.sub.pcc will continue to be monitored.

(65) The power disturbance in the invention is realized by changing the voltage reference value u.sub.pvref of MPPT strategy, and the piecewise function of u.sub.pvref that changes with time is shown in Equation (32):

(66) $\begin{array}{cc}{u}_{\mathrm{pvref}}\left(t\right)=\{\begin{array}{cc}\frac{\Delta U_{\mathrm{pv}}}{T_c/2}.Math.\left(t-{\mathrm{nT}}_0\right)+U_m& \left({\mathrm{nT}}_0\le t\le \frac{T_c}{2}+{\mathrm{nT}}_0\right)\\ U_{\mathrm{pvm}}+\Delta U_{\mathrm{pv}}& \left(\frac{T_c}{2}+{\mathrm{nT}}_0<t\le T_p-\frac{T_c}{2}+{\mathrm{nT}}_0\right)\\ -\frac{\Delta U_{\mathrm{pv}}}{T_c/2}.Math.\left(t-T_p-{\mathrm{nT}}_0\right)+U_m& \left(T_p-\frac{T_c}{2}+{\mathrm{nT}}_0<t\le T_p+{\mathrm{nT}}_0\right)\\ U_{\mathrm{pvm}}& \left(T_p+{\mathrm{nT}}_0<t\le T_0+{\mathrm{nT}}_0\right)\end{array}& \left(32\right)\end{array}$

(67) Where, T.sub.0 is the period of trapezoidal wave, T.sub.c is the duration of two waists of trapezoidal wave, T.sub.p is the duration of disturbance, and n is an integer greater than zero. ΔU.sub.pv is the variation of port voltage, and U.sub.pvm is the voltage reference value at the maximum power point.

(68) When unplanned islanding occurs in the DC system, the mismatch between supply and demand of DG and load will cause the voltage change at PCC. Although over-voltage/under-voltage passive method has a large non-detection zone, it can still quickly realize islanding detection in the case of mismatch between supply and demand. Therefore, according to the passive method, an islanding detection method based on the PCC voltage change rule in the disturbance period and applicable to the DC microgrid containing multiple DG is formed, as shown in the FIG. 6. As shown in FIG. 6, the detailed steps of the scheme are as follows:

(69) Step 1: First, start MPPT strategy to track the maximum power of photovoltaic array, and measure the output current at maximum power I.sub.pvm in real time. Then, set the threshold of environmental parameters for starting disturbance as A.sub.Start according to the change of actual light intensity and temperature.

(70) Step 2: The value of Δ.sub.ST is calculated in real time by the I.sub.pvm measured in the previous step and the known factory parameters of photovoltaic panel I.sub.mt, I.sub.sct and the number of parallel branches of photovoltaic array N.sub.p.

(71) Step 3: When Δ.sub.ST is greater than the set threshold Δ.sub.Start, the photovoltaic array will start trapezoidal disturbance with a period of T.sub.0 and duration of T.sub.p.

(72) Step 4: Calculate the theoretical values of U.sub.pccp1 and U.sub.pccp2 of PCC voltage at the two waists and the upper base of the trapezoidal disturbance respectively, and detect the change of PCC voltage U.sub.pcc and the change period T.sub.pcc of PCC voltage in real time. If U.sub.pcc<0.8 U.sub.N or U.sub.pcc>1.05 U.sub.N, the passive method will directly detect it as islanding. Go to step 5 if the threshold of passive method is not exceeded.

(73) Step 5: Judge whether U.sub.pcc is equal to the calculated value of PCC voltage U.sub.pccp1 or U.sub.pccp2, at the time of disturbance. If one of the conditions is met, go to Step 6; otherwise, return to the previous step.

(74) Step 6: Judge whether the PCC voltage variation period T.sub.pcc is equal to T.sub.0. If the conditions are met, it will be judged as islanding; otherwise, it will be judged as pseudo islanding, and return to Step 4.

(75) The above are only the preferred embodiments of the present invention, and are not intended to limit the scope of the invention. The claims define the scope of the protection of the present invention.

(76) It will be appreciated by one skilled in the art that numerous changes and additions could be made thereto without deviating from the spirit or scope of the invention.