CN114844027B - Photovoltaic system direct-current bus voltage control method based on finite control set model prediction - Google Patents
Photovoltaic system direct-current bus voltage control method based on finite control set model prediction Download PDFInfo
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- H—ELECTRICITY
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- H—ELECTRICITY
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Abstract
The invention provides a photovoltaic system direct current bus voltage control method based on limited control set model prediction, which comprises the steps of firstly determining an optimal working area of a photovoltaic constant voltage mode, establishing a photovoltaic system discrete model, predicting photovoltaic output current, capacitance current, output current at a high voltage side of a Boost converter and reference values thereof, load current and load current reference values thereof, then establishing a Thevenin equivalent circuit according to linearization processing of a photovoltaic i-u characteristic curve, thereby predicting a photovoltaic output voltage value, and finally performing model prediction control of the photovoltaic Boost converter based on a cost function of the sum of power errors and current errors, so as to realize constant direct current bus voltage. The invention not only ensures the power balance of the direct current micro-grid, but also can inhibit various system disturbance, improve the dynamic performance of the system and strengthen the robustness of the system, thereby ensuring the normal power supply of the direct current load, being easy to realize and execute and having high engineering value of practicability.
Description
Technical Field
The invention belongs to the technical field of electrical engineering, and relates to a photovoltaic system direct current bus voltage control method based on limited control set model prediction.
Background
In a direct current micro grid system, the voltage of a direct current bus is the only standard for evaluating the stability of the direct current micro grid, and the intermittence, uncertainty and load variability of photovoltaic power generation lead to unbalanced system power, cause the voltage fluctuation of the direct current bus and reduce the reliability of power supply of the system, so the voltage control of the direct current bus is a key problem to be solved for ensuring the stable operation of the direct current micro grid system. The control of the voltage of the direct current bus in the photovoltaic direct current micro-grid mainly comprises the control of an energy storage unit and the constant voltage control of a photovoltaic system.
When the energy storage unit is in normal operation, the photovoltaic system adopts maximum power tracking (MPPT) control, and constant control of direct current bus voltage is realized by means of bidirectional DC-DC control of the energy storage unit; when the direct-current bus voltage cannot be stabilized due to overcharge or faults of the energy storage unit, the photovoltaic Boost converter is controlled, so that constant control of the direct-current bus voltage is realized. Aiming at the latter situation, the invention provides a novel constant voltage control method of a photovoltaic system.
The constant voltage control method of the photovoltaic system at present mainly comprises the following steps: it is not difficult to see that the existing control strategies are basically PI-based, but these methods have the following problems respectively:
(1) The PI-based voltage single loop control approach may prevent the system from functioning properly. The cause analysis is as follows: when the system power is balanced, the load power curve and the photovoltaic P-u characteristic curve intersect to form two working points. If the illumination intensity is weakened, the working point of the system changes, the system can possibly migrate to a current source region of a photovoltaic i-u characteristic curve, at the moment, the photovoltaic output power is smaller than the load power, the voltage of a direct current bus is reduced, so that the duty ratio of the Boost converter is increased, the photovoltaic output voltage is reduced, the photovoltaic output power is further reduced, the power imbalance degree of the system is increased, and the operation of the direct current micro-grid system is stopped until the photovoltaic output voltage is zero.
(2) When the system power is deficient in a short time, although the constant voltage control strategy based on PI can restore the voltage of the direct current bus to the voltage value before the direct current bus is interfered by the short time load, the restoring time is longer; when the system power is deficient for a long time, the unbalanced degree of the system power is aggravated until the photovoltaic output voltage is zero and the direct current micro-grid system stops running.
(3) In some constant voltage control researches of photovoltaic systems, the working point of a current source area is used as a system power balance point, so that the stability of the working point of the system is poor, and the photovoltaic internal consumption is increased.
(4) The PI-based double-closed-loop controller needs to set four parameters, the parameter adjusting process is time-consuming, and the system has weak anti-interference capability and poor robustness.
In order to avoid the defects and problems of PI control, ensure the stable and reliable operation of the photovoltaic system, and have better dynamic performance and stronger robustness, the invention provides a photovoltaic system direct current bus voltage control method based on limited control set model prediction.
Disclosure of Invention
The invention aims to solve the problems in the prior art, provides a photovoltaic system direct current bus voltage control method based on limited control set model prediction, and solves the problem that an energy storage unit in an optical storage direct current micro-grid system cannot stabilize the direct current bus voltage due to overcharge or faults and the like.
For this purpose, the invention adopts the following technical scheme:
a photovoltaic system direct current bus voltage control method based on limited control set model prediction comprises the following steps:
a. based on a photovoltaic characteristic curve, selecting a voltage source area as an optimal working area in a photovoltaic constant voltage mode, and establishing a photovoltaic system discrete mathematical model according to kirchhoff voltage law and a Euler forward difference method;
b. c, predicting the capacitance current, the output current of the high-voltage side of the Boost converter, the reference value of the capacitance current and the output current, the load current and the reference value of the load current based on the discrete mathematical model of the photovoltaic system in the step a;
c. establishing a Thevenin equivalent circuit with the characteristic linearization of the photovoltaic i-u, and predicting the photovoltaic voltage by combining with the step b;
d. based on the power fluctuation and the load current fluctuation of the direct-current micro-grid, and in order to compensate the inherent one-step time delay of the digital controller, a cost function of two-step prediction is adopted;
e. and d, comparing the values of different switching states of each working period in the cost function, selecting the S1 switching state corresponding to the minimum cost function as an optimal control signal of the Boost converter so as to achieve the purpose of stabilizing the voltage of the direct current bus, and establishing a photovoltaic model prediction constant voltage control mathematical model based on a limited control set.
Further, the discrete mathematical model of the photovoltaic system in the step a is as follows:
wherein T is s Represents the sampling time, L represents the Boost converter inductance, U PV (k)、I PV (k)、U dc (k) Respectively represent kT s Output voltage, current and DC bus voltage of photovoltaic at moment, I PV (k+1) represents (k+1) T s The output current is predicted by the photovoltaic at the moment.
Further, in the step b, the predicted value of the capacitance current is:
wherein C is dc Represents bus capacitance, N represents correction coefficient, U dcref Indicating the reference value of the voltage of the direct current bus, I C (k+1) represents (k+1) T s And predicting the current value of the direct current bus capacitor at the moment.
The predicted value of the output current of the Boost converter at the high voltage side is as follows:
wherein I is 1 (k+1) represents (k+1) T s The high side of the Boost converter outputs a predicted value of current at the moment.
The load current predicted value is as follows:
I load (k+1)＝I 1 (k+1)-I C (k+1)
wherein I is load (k+1) represents (k+1) T s Load current predicted value at time.
The reference value of the load current predicted value is as follows:
wherein I is load (k) Representation of kT s Load current at moment, I loadref Represents (k+1) T s The moment load references the current prediction value.
The reference value of the predicted value of the output current of the high-voltage side of the Boost converter is as follows:
I 1ref ＝I loadref +I C (k+1)
wherein I is loadref 、I C (k+1) represents (k+1) T s A moment load current reference value and a bus capacitor current predicted value.
Further, the predicted photovoltaic voltage value in the step c is:
in U eq (k)、R eq (k) Respectively represents the voltage and the equivalent resistance of the equivalent ideal voltage source of the photovoltaic cell Thevenin, U PV (k+1) represents (k+1) T s The moment photovoltaic predicts the output voltage.
Further, the cost function in the step d is:
wherein lambda is 1 The weight coefficient is represented by a number of weight coefficients,P ref respectively represent (k+2) T s Time photovoltaic output power predicted value and photovoltaic reference power predicted value, +.>I loadref Respectively represent (k+2) T s Time load current predicted value and load reference value current predicted value.
Further, the photovoltaic model prediction constant voltage control mathematical model based on the finite control set in the step e is as follows:
wherein S1 opt Representing the Boost converter optimal control signal.
The invention has the beneficial effects that:
1. the invention considers the power error and the load current error simultaneously by adopting the cost function, so that the photovoltaic output power can be matched with the load power as soon as possible, and the load current can track the reference current value as soon as possible;
2. the photovoltaic system can still stably run when the photovoltaic system is in power shortage for a long time, and when partial load is cut off to enable the photovoltaic output power to be matched with the load power, the system direct current bus voltage can be quickly recovered to an ideal reference value;
3. when the photovoltaic system lacks short-time power, the voltage fluctuation of the direct-current bus of the system is obviously reduced, and the system can be quickly restored to an ideal reference value;
4. the method omits a PWM modulation process, has few parameters to be set, has simple control algorithm, easy execution and low cost, provides an effective new method for constant control of the busbar voltage of the direct current micro-grid of the photovoltaic system, and has high engineering value.
Drawings
FIG. 1 is a schematic diagram of a DC micro-grid power flow in the present invention;
FIG. 2 is a schematic diagram of the P-u characteristic of the photovoltaic system of the present invention;
FIG. 3 is a schematic diagram of the i-u characteristic of the photovoltaic system of the present invention;
FIG. 4 is a simplified photovoltaic system topology diagram of the present invention with the photovoltaic internal resistance ignored;
FIG. 5 is a schematic diagram of the topology of the photovoltaic system of the present invention with Boost converter S1 in the on state;
FIG. 6 is a topology diagram of the photovoltaic system of the present invention with Boost converter S1 off;
FIG. 7 is a schematic diagram of the change in the voltage source region operating point of the photovoltaic i-u characteristic curve according to the present invention;
FIG. 8 is a block diagram of a photovoltaic model predictive DC bus voltage control system based on a finite control set in accordance with the present invention;
FIG. 9 is a schematic diagram of a comparison of the conventional PI constant voltage control method and the photovoltaic output voltage according to the present invention;
FIG. 10 is a diagram showing the comparison between the conventional PI constant voltage control method and the DC bus voltage according to the present invention.
Detailed Description
The technical scheme of the invention is described in the following with reference to the accompanying drawings and the implementation method.
As shown in FIG. 1, C in the figure dc Equivalent electricity for DC busCapacitor, P C Charging and discharging power U of equivalent capacitance of direct current bus dc Is the voltage of a direct current bus, P PV Photovoltaic output power, P Load Is the load power. Fig. 1 shows the charge/discharge power P of the dc bus equivalent capacitor C The method comprises the following steps:
P C ＝P PV -P load
DC bus voltage U dc And photovoltaic output power P PV Load power P Load The relation between the two is:
as can be seen from the above, when the system power is balanced, the dc bus voltage is constant; when the system power is excessive or insufficient, the DC bus voltage will rise or fall. Therefore, in order to achieve power balance of the dc micro-grid system, the dc bus voltage must be maintained at a constant reference value.
Fig. 2 and 3 are a P-u characteristic diagram and an i-u characteristic diagram of the photovoltaic system, respectively. As can be seen from fig. 2 and 3, when the photovoltaic system operates in the constant voltage mode, for the same load power, there are two power balance points (hereinafter referred to as operating points) respectively located in the voltage source region and the current source region of the system, and the conditions of the two operating points are analyzed below to select an optimal operating region of the operating points.
In the photovoltaic constant voltage mode, the photovoltaic power is matched with the load power P load In this case, the photovoltaic P-u characteristic curve has two operating points a and B, which are located in the current source region and the voltage source region, respectively. Regarding the working performance of these two working points, the analysis can be made from the following two aspects.
On the one hand, there are documents that give stability analysis from both the frequency and time domains. From the frequency domain analysis, the logarithmic frequency characteristic analysis of the original gain function of the photovoltaic system shows that: to load power P load In other words, the phase angle margin of the point B of the voltage source area is larger than that of the point A of the current source area, so that the point B has better stability than the point A; from time domain analysis, photovoltaicThe actual output voltage waveform indicates: for the same load power, the initial value of the photovoltaic voltage is in the current source region, the stability of the output voltage is poor, the smaller the initial value is, the worse the actual output waveform is, and the stability of the actual output voltage of the photovoltaic initial value is relatively good in the voltage source region.
On the other hand, as can be seen from the photovoltaic i-u characteristics, the load power P load In other words, the current at the current source region A is larger than the current at the voltage source region B, and the phenomenon is more remarkable when the load power is smaller, for example, the load power P load1 The current at point D of the current source is much greater than the current at point E of the voltage source. Therefore, when the photovoltaic constant voltage mode works, if the load power is smaller, the current source area working point current is larger, and the photovoltaic equivalent resistance is larger, so that the photovoltaic internal consumption is increased. The operating point of the voltage source region is just opposite to that of the current source region, namely if the load power is smaller, the current of the operating point of the voltage source region is smaller, and the photovoltaic equivalent resistance is smaller, so that the photovoltaic internal consumption is smaller.
In summary, comparison analysis of the stability of the working points of the photovoltaic i-u characteristic current source region and the voltage source region and the photovoltaic internal consumption shows that the performance of the working point of the voltage source region is better than that of the working point of the current source region for the same load power, so that the voltage source region is selected as the optimal working region under the photovoltaic constant voltage mode.
Through the analysis, the invention provides a photovoltaic model prediction constant voltage control method based on limited control set model prediction, which is used for ensuring constant voltage of a direct current bus and comprises the following steps:
fig. 4 is a simplified photovoltaic system topology structure diagram neglecting internal resistance of photovoltaic, and fig. 5 and 6 are topology structure diagrams of a Boost converter S1 in the photovoltaic system in on and off states.
a. According to kirchhoff's voltage law, euler forward difference method and fig. 4-6, a discrete mathematical model of the photovoltaic system is established:
wherein T is s Represents the sampling time, L represents the Boost converter inductance, U PV (k)、I PV (k)、U dc (k) Respectively represent kT s Output voltage, current and DC bus voltage of photovoltaic at moment, I PV (k+1) represents (k+1) T s The output current is predicted by the photovoltaic at the moment.
b. Based on the discrete mathematical model of the photovoltaic system in the step a, the capacitance current, the output current of the high-voltage side of the Boost converter and the reference value thereof, the load current and the load current reference value are predicted, and the (k+1) T is obtained by the graphs of fig. 5, 6 and the equation (1) s The predicted value of the output current of the high-voltage side of the Boost converter at the moment is:
as can be seen from FIG. 4, the capacitance current is I C ＝C dc ·dU dc Dt, from which the discretization equation can be derived (k+1) T s Time I C The predicted values are:
in U dc (k+1) represents (k+1) T s And predicting the voltage of the direct current bus at the moment.
Because of the DC bus voltage U dc Desirably controlled to its reference value U dcref Therefore, formula (3) U dc (k+1) with its expected value U dcref Instead, at the same time, an adjustment coefficient N (N>1) To avoid excessive capacitive currents. After considering these factors, I C The predicted value is corrected as follows:
according to the DC bus voltage U dc (k) And load current I load (k) Can obtain (k+1) T s The moment load current reference predicted value is:
from kirchhoff's law of current, (k+1) T s The reference prediction of the high-side output current of the Boost converter at the moment is:
I 1ref ＝I loadref +I C (k+1) (6)
from the formula (2) and the formula (4), a value of (k+1) T is obtained s The predicted value of the load current at the moment is
I load (k+1)＝I 1 (k+1)-I C (k+1) (7)
c. Establishing a Thevenin equivalent circuit with linearized photovoltaic i-u characteristics, and predicting photovoltaic voltage by combining the equivalent circuit with the step b, wherein the linearized photovoltaic i-u characteristics can be obtained by performing linearization treatment on the photovoltaic i-u characteristics, and the equivalent Thevenin model is as follows:
wherein R is eq (k)、U eq (k) Is the equivalent resistance and the equivalent ideal voltage source voltage of the equivalent circuit in the south of the light Fu Daiwei.
From the second formula in formula (8) kT is obtainable s The photovoltaic output voltage at the moment is:
U PV (k)＝U eq (k)-R eq (k)I PV (k) (9)
as can be seen from the change in the photovoltaic i-u characteristic curve of FIG. 7 near point B, the equivalent resistance at the adjacent sampling time is considered to be unchanged when the sampling period is sufficiently small, taking point B of FIG. 7 as an example, (k-1) T s 、kT s And (k+1) T s Tangential slopes l and l at three working points corresponding to three moments 1 Can be considered to be substantially unchanged, so that the equivalent resistance at these two tangents satisfies R eq (k)≈R eq (k+1). In view of the above, formula (1) brings formula (9) into (k+1) T s The predicted value of the photovoltaic voltage at the moment is as follows:
in U eq (k)、R eq (k) Respectively representing the voltage of the photovoltaic cell Thevenin equivalent ideal voltage source and the equivalent resistance.
d. Considering DC micro-grid power fluctuation and load current fluctuation, the cost function is defined as
P ref ＝U dcref ·I 1ref (k+1) (13)
Wherein lambda is 1 The weight coefficient is represented by a number of weight coefficients,P ref respectively represent (k+1) T s Photovoltaic output power predicted value at moment and reference power predicted value thereof.
To compensate for the inherent one-step delay of the digital controller, the present invention employs a two-step predictive cost function:
wherein lambda is 1 The weight coefficient is represented by a number of weight coefficients,P ref respectively represent (k+2) T s Time photovoltaic output power prediction value and reference power prediction value, +.>I loadref Respectively represent (k+2) T s Time load electricityA flow prediction value and a load reference current prediction value.
e. By comparing J for each duty cycle in the cost function of step d S1＝0 And J S1＝1 The S1 switch state corresponding to the minimum cost function is selected as a control signal of the Boost converter so as to achieve the purpose of stabilizing the voltage of the direct current bus, wherein a photovoltaic constant voltage control mathematical model based on the prediction of a finite control set model is as follows:
wherein S1 opt Representing the Boost converter optimal control signal.
In order to verify the effectiveness and feasibility of the method, a photovoltaic system simulation model based on MATLAB/Simulink is built for verification. The parameters involved are the maximum power point voltage U of the photovoltaic m =34V, current I m 28.4A, output maximum power 960W, boost converter inductance l=0.35 mH, capacitance C dc =7mf, dc bus voltage rating U dcref The photovoltaic constant voltage control system block diagram based on finite control set model prediction is shown in fig. 8, with a sampling period ts=20μs and 50V.
The test conditions of this embodiment are: t=0.1-0.3 s, the illumination intensity is 1000W/m 2 The load is 700W, and the temperature is 45 ℃; t=0.3-0.5 s, and the illumination intensity is 600W/m 2 The load is 300W, and the temperature is 20 ℃; t=0.5-0.7 s, and the illumination intensity is 900W/m 2 The load was 800W. The temperature was 35 ℃.
Under the condition that the illumination intensity, the load power and the ambient temperature are suddenly changed at the same time, fig. 9-10 show comparison results of constant voltage control of the photovoltaic system based on PI and the invention, it can be seen that the system controlled by the former has large overshoot and long response time no matter the photovoltaic output voltage or the direct current bus voltage, and the system controlled by the latter has almost no overshoot and high response speed, and in addition, the system controlled by the latter has stronger robustness to external interference such as illumination intensity change, ambient temperature change and load power change. In general, the invention is superior to the conventional control method based on PI photovoltaic constant voltage.
Claims (4)
1. The photovoltaic system direct current bus voltage control method based on the finite control set model prediction is characterized by comprising the following steps of:
a. based on a photovoltaic characteristic curve, selecting a voltage source area as an optimal working area in a photovoltaic constant voltage mode, and establishing a photovoltaic system discrete mathematical model according to kirchhoff voltage law and a Euler forward difference method;
the photovoltaic system comprises a PV array, a Boost converter and a bus capacitor, wherein the PV array is connected with the low-voltage side of the Boost converter, the high-voltage side of the Boost converter is connected with the bus capacitor in parallel, and a switch of the Boost converter is an S1 switch;
b. c, predicting the capacitance current, the output current of the high-voltage side of the Boost converter, the reference value of the capacitance current and the output current, the load current and the reference value of the load current based on the discrete mathematical model of the photovoltaic system in the step a;
c. establishing a Thevenin equivalent circuit with the characteristic linearization of the photovoltaic i-u, and predicting the photovoltaic voltage by combining with the step b;
d. based on the power fluctuation and the load current fluctuation of the direct-current micro-grid, and in order to compensate the inherent one-step time delay of the digital controller, a cost function of two-step prediction is adopted;
e. d, comparing the values of different switching states of each working period in the cost function, selecting the S1 switching state corresponding to the minimum cost function as an optimal control signal of the Boost converter so as to achieve the purpose of stabilizing the voltage of the direct current bus, and establishing a photovoltaic model prediction constant voltage control mathematical model based on a limited control set;
in the step e, the photovoltaic model prediction constant voltage control mathematical model based on the limited control set is as follows:
wherein S1 opt Represents the optimal control signal of the Boost converter, J S1∈{0,1} Lambda as a function of cost 1 The weight coefficient is represented by a number of weight coefficients,P ref respectively represent (k+2) T s Photovoltaic output power predicted value and photovoltaic reference power predicted value at the moment,I loadref respectively represent (k+2) T s A time load current predicted value and a load reference current predicted value.
2. The photovoltaic system direct current bus voltage control method based on finite control set model prediction according to claim 1, wherein the photovoltaic system discrete mathematical model in the step a is:
wherein T is s Represents the sampling time, L represents the Boost converter inductance, U PV (k)、I PV (k)、U dc (k) Respectively represent kT s Output voltage, current and DC bus voltage of photovoltaic at moment, I PV (k+1) represents (k+1) T s The output current is predicted by the photovoltaic at the moment.
3. The method for controlling the dc bus voltage of the photovoltaic system based on the model prediction of the finite control set according to claim 2, wherein the predicted value of the capacitance current in the step b is:
wherein C is dc Represents bus capacitance, N represents correction coefficient, U dcref Indicating the reference value of the voltage of the direct current bus, I C (k+1) represents (k+1) T s Predicting a value of the direct current bus capacitor current at moment;
the predicted value of the output current of the Boost converter at the high voltage side is as follows:
wherein I is 1 (k+1) represents (k+1) T s Outputting a current predicted value at the high-voltage side of the Boost converter at the moment;
the load current predicted value is as follows:
I load (k+1)＝I 1 (k+1)-I C (k+1)
wherein I is load (k+1) represents (k+1) T s A predicted value of the load current at the moment;
the reference value of the load current predicted value is as follows:
wherein I is load (k) And I loadref Respectively represent kT s A moment load current predicted value and a load reference current predicted value;
the reference value of the predicted value of the output current of the high-voltage side of the Boost converter is as follows:
I 1ref ＝I loadref +I C (k+1)
wherein I is 1ref Represents (k+1) T s The high-voltage side of the Boost converter outputs a reference value of the current predicted value at the moment.
4. The method for controlling the dc bus voltage of the photovoltaic system based on the model prediction of the finite control set according to claim 3, wherein the predicted photovoltaic voltage value in the step c is:
in U eq (k)、R eq (k) Respectively represents the voltage and the equivalent resistance of the equivalent ideal voltage source of the photovoltaic cell Thevenin, U PV (k+1) represents (k+1) T s The moment photovoltaic predicts the output voltage.
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