Improved adaptive segmented droop control method for photovoltaic direct current microgrid

Abstract

The application discloses an improved adaptive segmented droop control method of a photovoltaic direct-current microgrid, and belongs to the technical field of direct-current distribution network operation and control. In view of the problem that segmented droop control cannot achieve good control effect due to random output of each photovoltaic power supply, and the problem that adaptive segmented droop control has sudden change of droop coefficients when photovoltaic output continuously changes, a nonlinear function is adopted to make the droop characteristic curve smoothly transit at the rated working point. Secondly, an improved adaptive segmented droop control system is designed, then an output impedance model of a photovoltaic side converter is established by using a small signal analysis method, and it is analyzed that the improved control method can effectively suppress system circulating current. Finally, simulation analysis is carried out in MATLAB / Simulink, and it is verified that the method has better control effect, can not only improve the offset rate of bus voltage in a light load state and improve the power distribution accuracy in a heavy load state, but also can make the transition process of the system more stable when the photovoltaic output continuously changes.

Description

Technical Field

[0001] This invention belongs to the field of DC distribution network operation and control technology, specifically relating to an improved adaptive segmented droop control method for photovoltaic DC microgrids. Background Technology

[0002] With the widespread adoption of new energy sources and continuous breakthroughs in power electronics technology, the development of DC microgrids has been driven, enabling large-scale photovoltaic power sources to be efficiently connected to the grid. In DC microgrids, DC-DC converters integrate photovoltaic power sources into the DC bus, which then supplies power to DC loads or transmits electrical energy to the AC grid via DC-AC inverters. Droop control, with its advantages of not requiring communication interconnections and high reliability, has become a common method for voltage regulation in DC microgrids. However, traditional droop control methods struggle to determine the droop coefficient.

[0003] For the selection of droop coefficient, Zhang Guorong, Bi Kangjun, Xie Runsheng, et al. Coordinated control of multiple interleaved parallel voltage balancers in bipolar DC microgrids [J]. Acta Energiae Solaris Sinica, 2021, 42(07):44-50. Based on parallel interleaved voltage balancers, an improved droop control strategy with secondary regulation is proposed using the indirect current sharing method, which realizes the reasonable distribution of load current of parallel converters. Peng Qiao, Liu Tianqi, Zhang Yingmin, et al. Adaptive droop control of DC grid considering power margin and system stability [J]. Proceedings of the CSEE, 2018, 38(12): 3498-3506. For DC grid systems containing wind power, a two-stage droop control method is proposed, which enables each converter to adjust voltage and power according to real-time power margin. Prabhakaran P, Goyal Y, Agarwal V. Novel Nonlinear Droop Control Techniques to Overcome the Load Sharing and Voltage Regulation Issues in DC Microgrid[J]. IEEE Transactions on Power Electronics, 2018, 33(5):4477-4487. The effects of linear and nonlinear droop control methods on voltage regulation, power distribution and stability were compared, and it was verified that the appropriate nonlinear droop control has a better regulation effect. Wang YZ, Wen WJ, Wang CS, et al. Adaptive voltage droop method of multiterminal VSC-HVDC systems for DC voltage deviation and power sharing[J]. IEEE Transactions on Power Delivery, 2019, 34(1):169-176. In order to solve the problem that the DC voltage and output power of each converter reach the limit value in transient state, a control strategy of adjusting the droop coefficient by using power distribution factor and voltage deviation factor is proposed. Zhi Na, Ding Ke, Huang Qinghui, et al. Virtual DC Motor Control Strategy Based on PU Droop Characteristics [J]. Journal of Electrical Engineering, 2021, 36(06):1238-1248. To solve the problem of bus voltage fluctuation in DC microgrid systems, a virtual DC motor control strategy based on PU droop characteristics is proposed by equating the electromechanical transient process of DC motor with the droop control characteristics. Droop control has limited ability to solve voltage and power fluctuations caused by changes in photovoltaic output by changing the system inertia, and the uncertainty of photovoltaic output will also cause problems such as increased system circulating current.

[0004] Under the same system load, when the output power allocated by the photovoltaic power source does not exceed the rated operating point, the system load is light; when the output power allocated by the photovoltaic power source exceeds the rated operating point, the system load is heavy. Selecting different values ​​for the droop coefficient in segmented droop control under light and heavy load conditions will lead to unreasonable system power distribution and ineffective control of the bus voltage deviation rate as the output of each photovoltaic power source changes continuously. Summary of the Invention

[0005] To address the problem of abrupt changes in the droop coefficient in adaptive segmented droop control when photovoltaic power output changes continuously, this invention provides an improved adaptive segmented droop control method for photovoltaic DC microgrids.

[0006] To achieve the above objectives, the present invention employs the following technical solutions:

[0007] An improved adaptive piecewise droop control method for photovoltaic DC microgrids is proposed. First, a DC microgrid containing multiple photovoltaic power sources is established. Second, based on the piecewise droop control strategy, a photovoltaic output coefficient determined by ambient temperature and light intensity is introduced. Then, a nonlinear function is used to improve the piecewise droop characteristic curve, mitigating the problem of abrupt changes in the droop coefficient at the rated operating point. An improved adaptive piecewise droop control system is designed. Next, a small-signal analysis method is used to establish an output impedance model for the photovoltaic-side converter, analyzing the impact of the improved control method on the system circulating current. Finally, a simulation model is built to verify the effectiveness of the improved control strategy.

[0008] Furthermore, the specific method for establishing a DC microgrid containing multiple photovoltaic power sources is as follows:

[0009] A DC microgrid consists of photovoltaic (PV) power sources, DC-DC converters, energy storage devices, DC loads, grid-side inverters, and an AC grid. Each PV power source comprises several PV arrays with equal parameters and equal rated capacity. The PV-side DC-DC converter uses an LLC resonant bidirectional full-bridge converter. Besides providing current isolation, the LLC resonant bidirectional full-bridge converter offers advantages such as a wide input voltage range, high power conversion efficiency, and the ability to achieve zero-voltage start-up across all loads. The energy storage-side DC-DC converter uses a Buck-Boost structure. In the DC microgrid, the DC-DC converter integrates the power generated by the PV power sources into the DC bus, which then supplies power to the DC loads or transmits the power to the AC grid via the grid-side inverter.

[0010] When the AC grid has no power dispatch requirements for the DC microgrid, the grid-side inverter stops operating, and the DC microgrid is in islanded mode. When the AC grid has power dispatch requirements for the DC microgrid, the grid-side inverter adopts PQ control. At this time, the AC grid is equivalent to a constant power load of the DC microgrid, and the system is equivalent to an islanded mode. This islanded mode has an additional constant power load compared to the islanded mode when the AC grid has no power dispatch requirements for the DC microgrid.

[0011] Based on the different requirements of the system for the photovoltaic unit, the photovoltaic unit is divided into three operating modes according to the bus voltage signal: Mode 1: When the bus voltage U dc ≥1.05U oiref In mode one, the photovoltaic power supply is controlled by segmented drooping, and the energy storage device operates in constant power charging mode; in mode two, when the bus voltage is 0.95U... oiref dc <1.05U oiref At this time, the photovoltaic power supply is controlled by MPPT, and the energy storage device is under droop control; Mode 3: when the bus voltage U dc ≤0.95U oiref At that time, the photovoltaic power supply is controlled by MPPT, and the energy storage device operates in constant power discharge mode; where U dc U represents the DC bus voltage. oiref This indicates the reference value of the DC bus voltage. When the system is operating in mode one, the output power of the photovoltaic unit (composed of all photovoltaic power sources) is greater than the power required by the system, and the photovoltaic power sources operate at reduced load to maintain the stability of the bus voltage. When the system is operating in other modes, in order to make full use of photovoltaic energy, the photovoltaic power sources do not undertake the function of bus voltage regulation.

[0012] Furthermore, the segmented droop control strategy is specifically as follows:

[0013] The droop control of the photovoltaic-side converter in a DC microgrid is expressed as follows:

[0014]

[0015] The droop coefficient for droop control is expressed as:

[0016]

[0017] Among them: U oi For the input DC bus voltage; U oiref K is the reference value for the DC bus voltage. i P is the droop factor of the photovoltaic converter. oi This refers to the output power of the photovoltaic-side converter. This is a reference value for the output power of the photovoltaic-side converter under standard conditions; U represents the maximum output power of the photovoltaic power source under standard conditions.​oimax U oimin P represents the maximum and minimum values ​​of the input DC bus voltage. oimax P oimin P represents the maximum and minimum output power of the photovoltaic converter. oimax It equals the maximum output power of the photovoltaic power source under standard conditions.

[0018] The reference value for the output power of the droop-controlled photovoltaic power supply is:

[0019]

[0020] Where: α is the proportional constant for reduced load operation, α<1, and its value is usually in the range of 0.6 to 0.8, and is taken as 0.6;

[0021] Under the same system load, when the output power allocated by the photovoltaic power source does not exceed the rated operating point, the system load is light; when the output power allocated by the photovoltaic power source exceeds the rated operating point, the system load is heavy. After the photovoltaic power source reduces its load, the system's regulation performance differs under light and heavy load conditions. Segmented droop control is adopted to meet the requirements of the DC microgrid under different conditions.

[0022] The sagging coefficient for segmented sagging control is expressed as:

[0023]

[0024] Photovoltaic power output power and temperature T i and light intensity S i The relationship between them is:

[0025]

[0026] ΔS i =S i / S ref -1

[0027] ΔT i =T i -T ref

[0028] Where: P imppt The maximum output power of the photovoltaic power source under any conditions; S represents the maximum output power of the photovoltaic power source under standard conditions. ref This is a reference value for light intensity; T ref Here is the temperature reference value; a, b, and c are constants, where: a = 0.002, b = 0.5, and c = 0.002; S i Ambient light intensity; T i Ambient temperature;

[0029] Photovoltaic power output is affected by environmental factors. Therefore, a photovoltaic output coefficient is introduced, which is expressed as:

[0030]

[0031] Where: δ i Photovoltaic power output coefficient;

[0032] Photovoltaic power output coefficient δ i With light intensity S i Proportional to temperature T i Inversely proportional, without considering changes in temperature and light intensity, when δ1>δ2, P appears. 1mppt >P o1 =P o2 >P 2mppt Therefore, unreasonable power distribution causes the photovoltaic power source to be in a saturated state, which leads to a drop in DC bus voltage. Therefore, the power distribution of the system needs to be combined with the photovoltaic output coefficient to set a segmented droop characteristic curve.

[0033] Furthermore, the specific method of the adaptive piecewise droop control strategy is as follows:

[0034] According to P oi and The magnitude relationship is used to determine the light and heavy load status of the DC microgrid system. When the output coefficients of each photovoltaic power source are different, the droop coefficient and the output power reference value are combined with the photovoltaic output coefficient to adjust and solve the saturation phenomenon of photovoltaic power sources during power distribution, so that each photovoltaic power source can correctly determine the light and heavy load status.

[0035] Based on the influence of temperature and light intensity on photovoltaic power output, a reference value for output power is set to vary with the photovoltaic output coefficient, and its expression is as follows:

[0036]

[0037] The three photovoltaic power sources have equal rated capacity and reference output power under standard conditions. To achieve reasonable power distribution, the reference output power of each photovoltaic converter and its droop coefficient should satisfy the following relationship:

[0038] K1P o1ref =K2P o2ref =K3P o3ref

[0039] The maximum and reference output power of the photovoltaic converter will change with the photovoltaic output factor, and the droop factor will also change while keeping the voltage control range constant. The expression for the droop factor that adaptively changes with the photovoltaic output factor is:

[0040]

[0041] Furthermore, the specific method for improving the adaptive piecewise droop characteristic curve using a nonlinear function is as follows:

[0042] The adaptive segmented droop control strategy is improved, and the improved droop characteristic curve must meet the following requirements: the voltage and power control range of the droop characteristic curve remains unchanged; when one or more photovoltaic-side converters in the system are operating near their rated operating points, the voltage offset to power offset ratio fluctuation and system circulating current increase should not be caused by sudden changes in the droop coefficient; the entire droop characteristic curve should still show the control effect of reducing the DC bus voltage offset rate under light load and improving the system power distribution accuracy under heavy load.

[0043] An improvement is made by using a nonlinear function: a quadratic function under light load and a linear function under heavy load. The slopes of the droop characteristic curves are equal at the transition points between light and heavy load conditions, meaning that the droop coefficient no longer undergoes abrupt changes at the rated operating point, thus enabling the system to achieve a smooth transition at the rated operating point. The improved adaptive piecewise droop control expression is as follows:

[0044]

[0045] in:

[0046]

[0047] Among them, K ia K is a parameter in the formula. i2 This is the sag coefficient under heavy load conditions.

[0048] Furthermore, the specific method of the improved adaptive piecewise droop control system is as follows:

[0049] The photovoltaic-side DC-DC converter employs dual closed-loop control of output voltage and current to regulate the bus voltage. In the improved adaptive segmented droop control system, firstly, given the voltage reference value, the power reference value under standard conditions, and the maximum power value, the real-time power reference value and maximum power value are calculated using a power calculator by combining the external light intensity and ambient temperature with the photovoltaic output coefficient. Secondly, the droop coefficient is determined using a droop coefficient tuner, enabling the photovoltaic-side converter to match the corresponding droop characteristic curve. Finally, a voltage compensation amount is output through the improved adaptive segmented droop control method. This voltage compensation amount acts on the outer voltage loop, ultimately outputting a reasonable voltage value to control the bus voltage.

[0050] Furthermore, the specific method for modeling the output impedance of the improved adaptive piecewise droop control system is as follows:

[0051] Selecting the inductor current I L and output voltage U oAs the state variables of the control system, neglecting converter losses, the state-space expression of the photovoltaic-side converter is:

[0052]

[0053] Where: X = [I L (t)U o (t)] T ;Y = [I L (t)];U=[V n (t)];V n t represents the power supply voltage of the control system; t represents time; T represents the transpose of the matrix; parameters A, B, and C are as follows:

[0054]

[0055]

[0056] C = [1 0]

[0057] Where: L s The filter inductor of the LLC resonant bidirectional full-bridge converter; f is the frequency; D is the duty cycle; C o For grid-connected capacitors; R o The equivalent load of a DC microgrid; R c R is the resistance of the photovoltaic converter, neglecting converter losses. c =0; sgn(t) is a sign function, and its expression is:

[0058]

[0059] Where: T is the switching period;

[0060] For state variable I L (s) undergoes a Laplace transform, and its expression is:

[0061] I L (s)=C(sI-A) -1 BU(s)

[0062] Where: s is the complex frequency, and s is a variable in the complex frequency domain form; I is the identity matrix;

[0063] The closed-loop transfer function of the current inner loop of the control system is:

[0064] G B (s)=G PII (s)G1(s) / [1+G PII (s)G1(s)]

[0065] Among them: G B(s) is the closed-loop transfer function of the inner current loop of the control system; G PII G1(s) is the inner current transfer function of the control system; G1(s) is the I... L The transfer function from (s) to D is expressed as:

[0066]

[0067] According to Thevenin's equivalence theorem, the improved adaptive piecewise droop control system can be equivalently represented as:

[0068]

[0069] Among them: G PIV (s) is the voltage outer loop transfer function of the control system; Z v (s) is U oi with I oi Transfer function between; G v (s) is U oi with U oit Transfer function between; C s I is the transfer function between the inner current loop and the outer voltage loop; oi U is the input current of the control system. oit The voltage modulation parameters after introducing the equivalent impedance are expressed as follows:

[0070] U oit =U oiref -Z eqi I oi

[0071] Where: Z eqi The equivalent impedance of the control system;

[0072] Small-signal processing is performed on the droop control expression:

[0073]

[0074] U oi =U oiref -K i (U oi -U oiref )I oi

[0075] The equivalent impedance for piecewise droop control and adaptive piecewise droop control is:

[0076]

[0077] Small-signal processing is performed on the quadratic function characteristic curve in the improved adaptive piecewise droop control expression:

[0078]

[0079] Therefore, the improved adaptive piecewise droop control equivalent impedance under light load conditions is:

[0080]

[0081] In summary, the equivalent output impedance of the photovoltaic converter is:

[0082] Z oi (s)=G v (s)Z eqi +Z v (s)

[0083] Where: Z oi This is the equivalent output impedance of the photovoltaic-side converter.

[0084] Compared with the prior art, the present invention has the following advantages:

[0085] This paper proposes an improved adaptive piecewise droop control method using nonlinear functions, enabling the droop characteristic curve to smoothly transition at the rated operating point. Secondly, an output impedance model of the photovoltaic converter is established using small-signal analysis, demonstrating that the improved control method effectively suppresses system circulating current. Finally, simulation analysis in MATLAB / Simulink verifies that the improved adaptive piecewise droop control method presented in this paper has better control performance. It not only improves the bus voltage deviation rate under light load conditions and enhances the power distribution accuracy under heavy load conditions, but also makes the system transition process smoother when photovoltaic output changes continuously. Attached Figure Description

[0086] Figure 1 This is a schematic diagram of a DC microgrid topology;

[0087] Figure 2 This is a schematic diagram of the topology of an LLC resonant bidirectional full-bridge converter.

[0088] Figure 3 This is a graph showing the segmented droop control characteristics.

[0089] Figure 4 A simplified circuit model diagram of a DC microgrid;

[0090] Figure 5 For δ i The characteristic curve of the varying adaptive piecewise droop control;

[0091] Figure 6 A schematic diagram of the characteristic curve of the improved adaptive piecewise droop control;

[0092] Figure 7A block diagram for the improved adaptive piecewise droop control;

[0093] Figure 8 This is a schematic diagram showing how light intensity changes over time.

[0094] Figure 9 (a) is a schematic diagram comparing the DC bus voltage of the three control methods; (b) is a schematic diagram comparing the bus voltage of adaptive segmented droop control and improved adaptive segmented droop control.

[0095] Figure 10 Schematic diagrams of the output power waveforms of three photovoltaic-side converters using different control methods;

[0096] Figure 11 This is a schematic diagram of the output power waveform of the photovoltaic-side DC-DC2 converter. Detailed Implementation

[0097] Example 1

[0098] An Improved Adaptive Piecewise Sag Control Method for Photovoltaic DC Microgrids

[0099] First, a DC microgrid containing multiple photovoltaic power sources is established. Second, based on the segmented droop control strategy, a photovoltaic output coefficient determined by ambient temperature and light intensity is introduced. Then, a nonlinear function is used to improve the segmented droop characteristic curve, mitigating the problem of abrupt changes in the droop coefficient at the rated operating point. An improved adaptive segmented droop control system is designed, and then a small-signal analysis method is used to establish an output impedance model for the photovoltaic-side converter to analyze the impact of the improved control method on the system circulating current. Finally, a simulation model is built to verify the effectiveness of the improved control strategy.

[0100] Establish a DC microgrid containing multiple photovoltaic power sources:

[0101] DC microgrid topology such as Figure 1 As shown, the DC microgrid consists of photovoltaic (PV) power sources, DC-DC converters, energy storage devices, DC loads, grid-side inverters, and an AC grid. Each PV power source comprises several PV arrays with equal parameters, and all PV power sources have the same rated capacity. The PV-side DC-DC converter uses an LLC resonant bidirectional full-bridge converter, such as... Figure 2 The topology diagram of the LLC resonant bidirectional full-bridge converter is shown. In addition to providing current isolation, the LLC resonant bidirectional full-bridge converter also has the advantages of a wide input voltage range, high power conversion efficiency, and the ability to achieve zero-voltage turn-on of the full load. The energy storage side DC-DC converter adopts a Buck-Boost structure. In the DC microgrid, the DC-DC converter integrates the power generated by the photovoltaic power source into the DC bus, and the DC bus supplies power to the DC load or transmits the power to the AC grid through the grid-side inverter.

[0102] When the AC grid has no power dispatch requirements for the DC microgrid, the grid-side inverter stops operating, and the DC microgrid is in islanded mode. When the AC grid has power dispatch requirements for the DC microgrid, the grid-side inverter adopts PQ control. At this time, the AC grid is equivalent to a constant power load of the DC microgrid, and the system is equivalent to an islanded mode. This islanded mode has an additional constant power load compared to the islanded mode when the AC grid has no power dispatch requirements for the DC microgrid.

[0103] Based on the different requirements of the system for the photovoltaic unit, the photovoltaic unit is divided into three operating modes according to the bus voltage signal, as shown in Table 1: Mode 1: When the bus voltage U dc ≥1.05U oiref In mode one, the photovoltaic power supply is controlled by segmented drooping, and the energy storage device operates in constant power charging mode; in mode two, when the bus voltage is 0.95U... oiref dc <1.05U oiref At this time, the photovoltaic power supply is controlled by MPPT, and the energy storage device is under droop control; Mode 3: when the bus voltage U dc ≤0.95U oiref At that time, the photovoltaic power supply is controlled by MPPT, and the energy storage device is in constant power discharge mode;

[0104] Table 1 System Operation Mode

[0105]

[0106] Among them, U dc U represents the DC bus voltage. oiref This indicates the reference value for the DC bus voltage.

[0107] When the system is operating in mode one, the output power of the photovoltaic unit is greater than the power required by the system, and the photovoltaic power supply operates under reduced load to maintain the stability of the bus voltage. When the system is operating in other modes, in order to make full use of photovoltaic energy, the photovoltaic power supply does not undertake the function of bus voltage regulation.

[0108] Segmented droop control strategy:

[0109] The droop control of the photovoltaic-side converter in a DC microgrid is expressed as follows:

[0110]

[0111] The droop coefficient for droop control is expressed as:

[0112]

[0113] Among them: U oi For the input DC bus voltage; U oiref K is the reference value for the DC bus voltage.​i P is the droop factor of the photovoltaic converter. oi This refers to the output power of the photovoltaic-side converter. This is a reference value for the output power of the photovoltaic-side converter under standard conditions; U represents the maximum output power of the photovoltaic power source under standard conditions. oimax U oimin P represents the maximum and minimum values ​​of the input DC bus voltage. oimax P oimin P represents the maximum and minimum output power of the photovoltaic converter. oimax It equals the maximum output power of the photovoltaic power source under standard conditions.

[0114] The reference value for the output power of the droop-controlled photovoltaic power supply is:

[0115]

[0116] Where: α is the proportional constant for reduced load operation, α<1, and its value is usually in the range of 0.6 to 0.8, and is taken as 0.6;

[0117] Under the same system load, when the output power allocated by the photovoltaic power source does not exceed the rated operating point, the system load is light; when the output power allocated by the photovoltaic power source exceeds the rated operating point, the system load is heavy. After the photovoltaic power source reduces its load, the system's regulation performance differs under light and heavy load conditions. Segmented droop control is adopted to meet the requirements of the DC microgrid under different conditions.

[0118] The sagging coefficient for segmented sagging control is expressed as:

[0119]

[0120] The segmented droop control characteristic curve is as follows: Figure 3 As shown, where K i1 K is the sag factor under light load conditions. i2 A is the droop factor under heavy load conditions. i This is the rated operating point. ΔU is U oi with U oiref The difference; ΔP is P oi and The difference between |ΔP| and |ΔU| decreases as the droop coefficient increases when ΔU remains constant, and vice versa. Therefore, a smaller droop coefficient is more beneficial for stable voltage control, while a larger droop coefficient is more beneficial for precise power distribution. Figure 3 It can be seen that setting different droop coefficients for light load and heavy load conditions is beneficial to meeting the requirements of the system under different states.

[0121] A simplified circuit model of a DC microgrid with photovoltaic converters in parallel is as follows: Figure 4 As shown, where U z R is the load voltage; i This is the output impedance of the converter.

[0122] according to Figure 4 The output power ratio of the photovoltaic-side converter can be obtained as follows:

[0123]

[0124] Among them, R line1 R line2 The impedances on the lines connecting photovoltaic converters 1 and 2 respectively;

[0125] The relationship between the converter and the load voltage satisfies U o1 ≈U o2 ≈U o3 When the line impedance is the same, the droop factor plays a decisive role in the output power distributed by the converter. When the environmental factors and the rated capacity of the photovoltaic power source are the same, the power output of the converter will also be the same if the same droop factor is set.

[0126] Photovoltaic power output power and temperature T i and light intensity S i The relationship between them is:

[0127]

[0128] ΔS i =S i / S ref -1

[0129] ΔT i =T i -T ref

[0130] Where: P imppt The maximum output power of the photovoltaic power source under any conditions; S represents the maximum output power of the photovoltaic power source under standard conditions. ref This is a reference value for light intensity; T ref Here is the temperature reference value; a, b, and c are constants, where: a = 0.002, b = 0.5, and c = 0.002; S i Ambient light intensity; T i Ambient temperature;

[0131] Photovoltaic power output is affected by environmental factors. Therefore, a photovoltaic output coefficient is introduced, which is expressed as:

[0132]

[0133] Where: δ i Photovoltaic power output coefficient;

[0134] Photovoltaic power output coefficient δ i With light intensity S i Proportional to temperature T i Inversely proportional, without considering changes in temperature and light intensity, when δ1>δ2, P appears. 1mppt >P o1 =P o2 >P 2mppt Therefore, unreasonable power distribution causes the photovoltaic power source to be in a saturated state, which leads to a drop in DC bus voltage. Therefore, the power distribution of the system needs to be combined with the photovoltaic output coefficient to set a segmented droop characteristic curve.

[0135] Adaptive segmented droop control strategy:

[0136] According to P oi and The magnitude relationship is used to determine the light and heavy load status of the DC microgrid system. When the output coefficients of each photovoltaic power source are different, the droop coefficient and the output power reference value are combined with the photovoltaic output coefficient to adjust and solve the saturation phenomenon of photovoltaic power sources during power distribution, so that each photovoltaic power source can correctly determine the light and heavy load status.

[0137] Based on the influence of temperature and light intensity on photovoltaic power output, a reference value for output power is set to vary with the photovoltaic output coefficient, and its expression is as follows:

[0138]

[0139] The three photovoltaic power sources have equal rated capacity and reference output power under standard conditions. To achieve reasonable power distribution, the reference output power of each photovoltaic converter and its droop coefficient should satisfy the following relationship:

[0140] K1P o1ref =K2P o2ref =K3P o3ref

[0141] The maximum and reference output power of the photovoltaic converter will change with the photovoltaic output factor, and the droop factor will also change while keeping the voltage control range constant. The expression for the droop factor that adaptively changes with the photovoltaic output factor is:

[0142]

[0143] The output factor measures the power output capability of a photovoltaic (PV) power source; the power output increases with the increase of the PV output factor. With a DC bus voltage reference value of 800V, δ is plotted based on the expression for the droop factor, which adaptively varies with the PV output factor. iThe adaptive piecewise droop control characteristic curve from 0.4 to 1.5 is shown below. Figure 5 As shown.

[0144] The photovoltaic (PV) output factor affects the power allocated by the PV power source in the system. A higher PV output factor will allocate more power, while a lower PV output factor will allocate less power. The droop factor determines the relationship between ΔU and ΔP. The system's light and heavy load states will switch back and forth with changes in PV output. Sudden changes in the droop factor will cause fluctuations in the ratio of voltage offset to power offset, reducing system stability.

[0145] The adaptive piecewise droop characteristic curve is improved by using a nonlinear function:

[0146] The adaptive segmented droop control strategy is improved, and the improved droop characteristic curve must meet the following requirements: the voltage and power control range of the droop characteristic curve remains unchanged; when one or more photovoltaic-side converters in the system are operating near their rated operating points, the voltage offset to power offset ratio fluctuation and system circulating current increase should not be caused by sudden changes in the droop coefficient; the entire droop characteristic curve should still show the control effect of reducing the DC bus voltage offset rate under light load and improving the system power distribution accuracy under heavy load.

[0147] An improvement is made by using a nonlinear function: a quadratic function under light load and a linear function under heavy load. The slopes of the droop characteristic curves are equal at the transition points between light and heavy load conditions, meaning that the droop coefficient no longer undergoes abrupt changes at the rated operating point, thus enabling the system to achieve a smooth transition at the rated operating point. The improved adaptive piecewise droop control expression is as follows:

[0148]

[0149] in:

[0150]

[0151] Among them, K ia K is a parameter in the formula. i2 This represents the sag coefficient under heavy load conditions.

[0152] Based on the above formula, the improved adaptive piecewise droop control characteristic curve is plotted as follows: Figure 6 As shown, where A i The slope at a point is equal to the slope of the second straight line. (From...) Figure 6 It can be seen that the improved adaptive segmented droop control solves the problem of abrupt changes in the droop coefficient at the rated operating point without changing the voltage and power control range. Furthermore, under light load conditions, the minimum slope of the improved adaptive segmented droop control is less than that of the adaptive segmented droop control, thus further improving the bus voltage deviation rate.

[0153] Design an improved adaptive segmented droop control system:

[0154] The photovoltaic-side DC-DC converter employs dual closed-loop control of output voltage and current to regulate the bus voltage. The control block diagram of the photovoltaic-side converter using improved adaptive segmented droop control is shown below. Figure 7 As shown, in the improved adaptive segmented droop control system, firstly, given the voltage reference value, the power reference value under standard conditions, and the maximum power value, the real-time power reference value and the maximum power value are calculated by a power calculator using the external light intensity and ambient temperature in conjunction with the photovoltaic output coefficient; secondly, the droop coefficient is determined using a droop coefficient tuner, so that the photovoltaic-side converter matches the corresponding droop characteristic curve; finally, a voltage compensation quantity is output through the improved adaptive segmented droop control method, which acts on the voltage outer loop, and finally outputs a reasonable voltage value to achieve control of the bus voltage.

[0155] Improved output impedance modeling for adaptive piecewise droop control systems:

[0156] Selecting the inductor current I L and output voltage U o As the state variables of the control system, neglecting converter losses, the state-space expression of the photovoltaic-side converter is:

[0157]

[0158] Where: X = [I L (t)U o (t)] T ;Y = [I L (t)];U=[V n (t)];V n t represents the power supply voltage of the control system; t represents time; parameters A, B, and C are as follows:

[0159]

[0160]

[0161] C = [1 0]

[0162] Where: L s The filter inductor of the LLC resonant bidirectional full-bridge converter; f is the frequency; D is the duty cycle; C o For grid-connected capacitors; R o The equivalent load of a DC microgrid; R c R is the resistance of the photovoltaic converter, neglecting converter losses. c =0; sgn(t) is a sign function, and its expression is:

[0163]

[0164] Where: T is the switching period;

[0165] For state variable I L (s) undergoes a Laplace transform, and its expression is:

[0166] I L (s)=C(sI-A) -1 BU(s)

[0167] Where: s is the complex frequency; I is the identity matrix;

[0168] The closed-loop transfer function of the current inner loop of the control system is:

[0169] G B (s)=G PII (s)G1(s) / [1+G PII (s)G1(s)]

[0170] Among them: G B (s) is the closed-loop transfer function of the inner current loop of the control system; G PII G1(s) is the inner current transfer function of the control system; G1(s) is the I... L The transfer function from (s) to D is expressed as:

[0171]

[0172] According to Thevenin's equivalence theorem, the improved adaptive piecewise droop control system can be equivalently represented as:

[0173]

[0174] Among them: G PIV (s) is the voltage outer loop transfer function of the control system; Z v (s) is U oi with I oi Transfer function between; G v (s) is U oi with U oit Transfer function between; C s I is the transfer function between the inner current loop and the outer voltage loop; oi U is the input current of the control system. oit The voltage modulation parameters after introducing the equivalent impedance are expressed as follows:

[0175] U oit =U oiref -Z eqi I oi

[0176] Where: Z eqi The equivalent impedance of the control system;

[0177] Small-signal processing is performed on the droop control expression:

[0178]

[0179] U oi =U oiref -K i (U oi -U oiref )I oi

[0180] The equivalent impedance for piecewise droop control and adaptive piecewise droop control is:

[0181]

[0182] Small-signal processing is performed on the quadratic function characteristic curve in the improved adaptive piecewise droop control expression:

[0183]

[0184] Therefore, the improved adaptive piecewise droop control equivalent impedance under light load conditions is:

[0185]

[0186] In summary, the equivalent output impedance of the photovoltaic converter is:

[0187] Z oi (s)=G v (s)Z eqi +Z v (s)

[0188] Where: Z oi This is the equivalent output impedance of the photovoltaic-side converter.

[0189] Example 2: The effect of improved adaptive piecewise droop control on system circulation

[0190] Based on the simplified circuit model of a DC microgrid, assuming the photovoltaic output coefficients of photovoltaic power sources PV1 and PV2 are δ1 and δ2 respectively, the expression for the circulating power between the two photovoltaic converters is:

[0191]

[0192] When the output voltages of the systems are equal and the impedance relationship satisfies equation (20), the circulating power P h When the value equals 0, circulating current can be completely eliminated between photovoltaic-side converters.

[0193]

[0194] The main parameters of the DC microgrid system are shown in Table 2. The equivalent droop coefficient K is set. eqi The ratio of the equivalent impedance to the voltage deviation term can be obtained from equations (18) and (19):

[0195]

[0196] Table 2 Main System Parameters

[0197]

[0198] The following analysis uses two photovoltaic power sources as an example. The temperature of PV1 is set to 25℃, and the irradiance is 1400W / m². 2 The temperature of PV2 is 25℃, and the light intensity is 1000W / m². 2 The equivalent droop coefficient K of various control methods eq The values ​​are shown in Table 3.

[0199] Table 3 Equivalent droop coefficients for various control methods

[0200]

[0201] As shown in Table 3, the ratio of the output impedances of PV1 and PV2 under segmented droop control is:

[0202]

[0203] The improved adaptive piecewise droop control and the ratio of the output impedances of PV1 to PV2 under adaptive piecewise droop control are:

[0204]

[0205] Therefore, when the output of each photovoltaic power source is different, segmented droop control will lead to a large circulating current between the photovoltaic-side converters. Ignoring (Z... v (s)+R linei In the case of item ), the improved adaptive segmented droop control and adaptive segmented droop control can completely eliminate circulating current between each photovoltaic-side converter. Therefore, the improved adaptive segmented droop control method proposed in this invention can effectively suppress circulating current between photovoltaic units.

[0206] Example 3 Simulation Analysis

[0207] Simulation model of segmented droop control system

[0208] A simulation model of a DC microgrid was built in MATLAB / Simulink. The main parameters of the system are shown in Table 4. The temperature of the photovoltaic power source was set to 23℃. The change of light intensity over time is shown in Table 4. Figure 8 As shown, the output coefficient of each photovoltaic power source will change with the changes in the external environment.

[0209] Table 4. Main System Parameters

[0210]

[0211] Simulation results of piecewise droop control, adaptive piecewise droop control, and improved adaptive piecewise droop control methods are compared and analyzed. The DC bus voltage waveforms of different control methods are shown in the figure. Figure 9 As shown.

[0212] Comparative Analysis of Simulation Results

[0213] To verify that the improved adaptive segmented droop control method proposed in this invention has better effects on DC bus voltage stability control and precise photovoltaic power allocation, simulation results of segmented droop control, adaptive segmented droop control, and the improved adaptive segmented droop control method are compared and analyzed. The DC bus voltage waveforms of different control methods are shown below. Figure 9 As shown.

[0214] Depend on Figure 9 (a) It can be seen that for the bus voltage variation range, the segmented droop control is 825–725V; the adaptive segmented droop control is 818–790V; and the improved adaptive segmented droop control is 814–790V. When the output of each photovoltaic power source changes, the segmented droop control cannot maintain the stability of the bus voltage. In the 1.5–2.5s range, the system is misjudged as lightly loaded due to the low photovoltaic output, resulting in a very large bus voltage deviation. The improved adaptive segmented droop control and the adaptive segmented droop control can effectively control the bus voltage when the photovoltaic output changes, with voltage variations all within the range of 760–840V.

[0215] Depend on Figure 9 (b) It can be seen that, since the minimum droop coefficient of the improved adaptive segmented droop control under light load conditions is less than that of the adaptive segmented droop control, the smaller droop coefficient is beneficial to the stable control of the bus voltage. The bus voltage deviation rate under light load conditions is reduced from 2.25% of the adaptive segmented droop control to 1.75%. Therefore, the improved adaptive segmented droop control has a better control effect on improving the bus voltage deviation rate.

[0216] The output power waveforms of the three photovoltaic-side converters with different control methods are as follows: Figure 10 As shown.

[0217] Depend on Figure 10 (a) It can be seen that segmented droop control cannot meet the requirements of reasonable power distribution. Since the droop coefficient of segmented droop control does not change with the photovoltaic output, the power is not distributed according to the photovoltaic output ratio. Therefore, when the photovoltaic output coefficient changes, the photovoltaic power source with the smaller output coefficient outputs less power, and the photovoltaic power source with the larger output coefficient outputs more power. As a result, the output power of each photovoltaic converter varies greatly from 1.5 to 4 seconds, leading to unreasonable power distribution in the system.

[0218] Depend on Figure 10 As shown in (b) and (c), the improved adaptive segmented droop control and adaptive segmented droop control can improve the power distribution accuracy of the system. Since these two control methods can distribute the power required by each photovoltaic power source according to the photovoltaic output ratio, in the 0–1s range, when the overall output of the photovoltaic power sources is large and the system is under light load, the power source with a larger photovoltaic output coefficient will reduce its output power according to the photovoltaic output ratio; in the 1.5–2.5s range, when the system is under heavy load, the power source with a smaller photovoltaic output coefficient will increase its output power according to the photovoltaic output ratio; in the 3–4s range, PV1 and PV2 have larger photovoltaic output coefficients, while PV3 has a smaller photovoltaic output coefficient, and the photovoltaic power sources will increase or decrease their output power according to the corresponding ratio.

[0219] Adaptive segmented droop control and improved adaptive segmented droop control photovoltaic-side DC-DC2 converter output power waveform as shown in the figure. Figure 11 As shown.

[0220] exist Figure 11 In (a), due to the abrupt change in the droop coefficient at the rated operating point in the adaptive piecewise droop control, the photovoltaic output coefficient continuously changes between 1–1.5s and 2.5–3s, causing power fluctuations. Figure 11 In (b), the problem of sudden changes in the droop coefficient is improved by introducing a nonlinear function. In the range of 1 to 1.5 s and 2.5 to 3 s, as the photovoltaic output coefficient changes continuously, the improved adaptive piecewise droop control can effectively improve the power fluctuation phenomenon and make the system transition process smoother. Therefore, the improved adaptive piecewise droop control has a better control effect on the precise allocation of power.

[0221] Contents not described in detail in this specification are prior art known to those skilled in the art. Although illustrative specific embodiments of the invention have been described above to facilitate understanding by those skilled in the art, it should be understood that the invention is not limited to the scope of the specific embodiments. Various modifications are readily apparent to those skilled in the art as long as they fall within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of this invention are protected.

Claims

1. An improved adaptive piecewise droop control method for photovoltaic DC microgrids, characterized in that: First, a DC microgrid with multiple photovoltaic power sources is established. Second, based on the segmented droop control strategy, a photovoltaic output coefficient determined by ambient temperature and light intensity is introduced. Then, a nonlinear function is used to improve the segmented droop characteristic curve, mitigating the problem of abrupt changes in the droop coefficient at the rated operating point. An improved adaptive segmented droop control system is designed, and then a small-signal analysis method is used to establish an output impedance model for the photovoltaic-side converter to analyze the impact of the improved control method on the system circulating current. Finally, a simulation model is built to verify the effectiveness of the improved control strategy. The specific method for establishing a DC microgrid containing multiple photovoltaic power sources is as follows: A DC microgrid consists of photovoltaic (PV) power sources, DC-DC converters, energy storage devices, DC loads, grid-side inverters, and an AC grid. Each PV power source comprises several PV arrays with equal parameters and equal rated capacity. The PV-side DC-DC converter uses an LLC resonant bidirectional full-bridge converter. In addition to providing current isolation, the LLC resonant bidirectional full-bridge converter has the advantages of a wide input voltage range, high power conversion efficiency, and the ability to achieve zero-voltage start-up under full load. The energy storage-side DC-DC converter adopts a Buck-Boost structure. In the DC microgrid, the DC-DC converter integrates the electrical energy generated by the PV power sources into the DC bus. The DC bus supplies power to the DC loads or transmits the electrical energy to the AC grid via the grid-side inverter. When the AC grid has no power dispatch requirements for the DC microgrid, the grid-side inverter stops operating, and the DC microgrid is in islanded mode. When the AC grid has power dispatch requirements for the DC microgrid, the grid-side inverter adopts PQ control. At this time, the AC grid is equivalent to a constant power load of the DC microgrid, and the system is equivalent to an islanded mode. This islanded mode has an additional constant power load compared to the islanded mode when the AC grid has no power dispatch requirements for the DC microgrid. Based on the different requirements of the system for the photovoltaic unit, the photovoltaic unit is divided into three operating modes according to the bus voltage signal: Mode 1: When the bus voltage U dc ≥ 1.05U oiref In mode one, the photovoltaic power supply is controlled by segmented drooping, and the energy storage device operates in constant power charging mode; in mode two, when the bus voltage is 0.95U... oiref < U dc < 1.05U oiref In mode 3, the photovoltaic power supply is controlled by MPPT, and the energy storage device is under droop control; when the bus voltage U dc ≤ 0.95U oiref At that time, the photovoltaic power supply is controlled by MPPT, and the energy storage device operates in constant power discharge mode; where U dc U represents the DC bus voltage. oiref This indicates the reference value for the DC bus voltage. When the system is operating in mode one, the output power of the photovoltaic unit is greater than the power required by the system, and the photovoltaic power supply operates under reduced load to maintain the stability of the bus voltage. When the system is operating in other modes, in order to make full use of photovoltaic energy, the photovoltaic power supply does not undertake the function of bus voltage regulation.

2. The improved adaptive segmented droop control method for a photovoltaic DC microgrid according to claim 1, characterized in that: The segmented droop control strategy is specifically as follows: The droop control of the photovoltaic-side converter in a DC microgrid is expressed as follows: ； The droop coefficient for droop control is expressed as: ； Among them: U oi For the input DC bus voltage; U oiref K is the reference value for the DC bus voltage. i P is the droop factor of the photovoltaic converter. oi U represents the output power of the photovoltaic converter; P* oiref is the reference value of the output power of the photovoltaic converter under standard conditions; P* imppt is the maximum output power of the photovoltaic power source under standard conditions. oimax U oimin P represents the maximum and minimum values ​​of the input DC bus voltage. oimax P oimin P represents the maximum and minimum output power of the photovoltaic converter. oimax It equals the maximum output power of the photovoltaic power source under standard conditions; The reference value for the output power of the droop-controlled photovoltaic power supply is: ； Where: α is the proportional constant for reduced load operation, α < 1, and its value ranges from 0.6 to 0.8, with 0.6 being the value; Under the same system load, when the output power allocated by the photovoltaic power source does not exceed the rated operating point, the system load is light; when the output power allocated by the photovoltaic power source exceeds the rated operating point, the system load is heavy. After the photovoltaic power source is unloaded, the system's regulation performance is different under light and heavy load conditions. Segmented droop control is used to meet the requirements of the DC microgrid under different states. The sagging coefficient for segmented sagging control is expressed as: ； Photovoltaic power output power and temperature T i and light intensity S i The relationship between them is: ； ； ； Where: P imppt P*imppt represents the maximum output power of the photovoltaic power source under any conditions; P*imppt represents the maximum output power of the photovoltaic power source under standard conditions; Sp ref This is a reference value for light intensity; T ref Here is a temperature reference value; a, b, and c are constants, where: a = 0.002, b = 0.5, and c = 0.002; S i Ambient light intensity; T i Ambient temperature; Photovoltaic power output is affected by environmental factors. Therefore, a photovoltaic output coefficient is introduced, which is expressed as: ； Where: δ i Photovoltaic power output coefficient; Photovoltaic power output coefficient δ i With light intensity S i Proportional to temperature T i Inversely proportional, without considering changes in temperature and light intensity, when δ1 > δ2, P appears. 1mppt > P o1 = P o2 > P 2mppt Therefore, unreasonable power distribution causes the photovoltaic power source to be in a saturated state, which leads to a drop in DC bus voltage. Therefore, the power distribution of the system needs to be combined with the photovoltaic output coefficient to set a segmented droop characteristic curve.

3. The improved adaptive segmented droop control method for a photovoltaic DC microgrid according to claim 1, characterized in that: The specific method of the adaptive piecewise droop control strategy is as follows: According to P oi The relationship between P* and oiref is used to determine the light and heavy load conditions of the DC microgrid system. When the output coefficients of each photovoltaic power source are different, the droop coefficient and the output power reference value are combined with the photovoltaic output coefficient to adjust the photovoltaic power source to solve the saturation phenomenon of the photovoltaic power source during the power distribution process, so that each photovoltaic power source can correctly determine the light and heavy load conditions. Based on the influence of temperature and light intensity on photovoltaic power output, a reference value for output power is set to vary with the photovoltaic output coefficient, and its expression is as follows: ； The three photovoltaic power sources have equal rated capacity and reference output power under standard conditions. To achieve reasonable power distribution, the reference output power of each photovoltaic converter and its droop coefficient should satisfy the following relationship: ； The maximum and reference output power of the photovoltaic converter will change with the photovoltaic output factor. Under the condition that the voltage control range remains unchanged, the droop factor will also change. The expression for the droop factor that adaptively changes with the photovoltaic output factor is: 。 4. The improved adaptive segmented droop control method for a photovoltaic DC microgrid according to claim 1, characterized in that: The specific method for improving the adaptive piecewise droop characteristic curve using a nonlinear function is as follows: An improvement to the adaptive piecewise droop control strategy is required, and the improved droop characteristic curve must meet the following requirements: the voltage and power control ranges of the droop characteristic curve remain unchanged. When one or more photovoltaic-side converters in the system are operating near their rated operating points, the voltage offset to power offset ratio fluctuations and system circulating current increases should not be caused by sudden changes in the droop coefficient. The entire droop characteristic curve should still show the control effect of reducing the DC bus voltage offset rate under light load and improving the system power distribution accuracy under heavy load. An improvement is made by using a nonlinear function: a quadratic function under light load and a linear function under heavy load. The slopes of the droop characteristic curves are equal at the transition points between light and heavy load conditions, meaning that the droop coefficient no longer undergoes abrupt changes at the rated operating point, thus enabling the system to achieve a smooth transition at the rated operating point. The improved adaptive piecewise droop control expression is as follows: ； in: ； Among them, K ia K is a parameter in the formula. i2 This is the sag coefficient under heavy load conditions.

5. An improved adaptive segmented droop control method for a photovoltaic DC microgrid according to claim 1, characterized in that: The specific method of the improved adaptive piecewise droop control system is as follows: The photovoltaic-side DC-DC converter employs dual closed-loop control of output voltage and current to regulate the bus voltage. In the improved adaptive segmented droop control system, firstly, given the voltage reference value, the power reference value under standard conditions, and the maximum power value, the real-time power reference value and maximum power value are calculated using a power calculator by combining the external light intensity and ambient temperature with the photovoltaic output coefficient. Secondly, the droop coefficient is determined using a droop coefficient tuner, enabling the photovoltaic-side converter to match the corresponding droop characteristic curve. Finally, a voltage compensation amount is output through the improved adaptive segmented droop control method. This voltage compensation amount acts on the outer voltage loop, ultimately outputting a reasonable voltage value to control the bus voltage.

6. An improved adaptive segmented droop control method for a photovoltaic DC microgrid according to claim 1, characterized in that: The specific method for modeling the output impedance of the improved adaptive piecewise droop control system is as follows: Selecting the inductor current I L and output voltage U o As the state variables of the control system, neglecting converter losses, the state-space expression of the photovoltaic-side converter is: ； Where: X = [I L (t)U o (t)] T ;Y = [I L (t)];U = [V n (t)];V n t represents the power supply voltage of the control system; t represents time; T represents the transpose of the matrix; parameters A, B, and C are as follows: ； ； ； Where: L s The filter inductor of the LLC resonant bidirectional full-bridge converter; f is the frequency; D is the duty cycle; C o For grid-connected capacitors; R o The equivalent load of a DC microgrid; R c R is the resistance of the photovoltaic converter, neglecting converter losses. c = 0; sgn(t) is a symbolic function, and its expression is: ； Where: T is the switching period; For state variable I L (s) undergoes a Laplace transform, and its expression is: ； Where: s is the complex frequency; I is the identity matrix; The closed-loop transfer function of the current inner loop of the control system is: ； Among them: G B (s) is the closed-loop transfer function of the inner current loop of the control system; G PII G1(s) is the inner current transfer function of the control system; G1(s) is the I... L The transfer function from (s) to D is expressed as: ； in, This indicates finding the partial derivatives of the function; According to Thevenin's equivalence theorem, the improved adaptive piecewise droop control system can be equivalently represented as: ； Among them: G PIV (s) is the voltage outer loop transfer function of the control system; Z v (s) is U oi with I oi Transfer function between; G v (s) is U oi with U oit Transfer function between; C s I is the transfer function between the inner current loop and the outer voltage loop; oi U is the input current of the control system. oit The voltage modulation parameters after introducing the equivalent impedance are expressed as follows: ； Where: Z eqi The equivalent impedance of the control system; Small-signal processing is performed on the droop control expression: ； ； The equivalent impedance for piecewise droop control and adaptive piecewise droop control is: ； Small-signal processing is performed on the quadratic function characteristic curve in the improved adaptive piecewise droop control expression: ； Therefore, the improved adaptive piecewise droop control equivalent impedance under light load conditions is: ； In summary, the equivalent output impedance of the photovoltaic converter is: ； Where: Z oi This is the equivalent output impedance of the photovoltaic-side converter.

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