CN116706927B - Computing method for optimal voltage support reference current of four-bridge arm inverter - Google Patents

Computing method for optimal voltage support reference current of four-bridge arm inverter Download PDF

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CN116706927B
CN116706927B CN202310990602.5A CN202310990602A CN116706927B CN 116706927 B CN116706927 B CN 116706927B CN 202310990602 A CN202310990602 A CN 202310990602A CN 116706927 B CN116706927 B CN 116706927B
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刘心桐
刘钊
杨浩
吴雪怡
王凯杰
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Nanjing University of Science and Technology
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Abstract

A four-bridge arm inverter optimal voltage support reference current calculation method belongs to the technical field of energy storage inverter control, and solves the problem that the prior art cannot take the minimum PCC point unbalance degree as a control target; calculating positive sequence, negative sequence, zero sequence voltage amplitude and initial phase angle of PCC point faults and voltage unbalance degree; by defining the relation between active and reactive currents, the zero sequence current amplitude is preferentially calculated and converted to obtain an objective function and a limiting condition; converting the optimal solution problem into a solution problem of a type I point and a type II point, respectively calculating to obtain the values of extreme points of the type I point and the type II point, and obtaining an optimal solution through comparison; after the reference current calculation method provided by the invention is applied, the imbalance degree of the PCC point is obviously reduced, and the imbalance degree is reduced to be close to 0.

Description

Computing method for optimal voltage support reference current of four-bridge arm inverter
Technical Field
The invention belongs to the technical field of energy storage inverter control, and relates to a method for calculating an optimal voltage support reference current of a four-bridge arm inverter.
Background
The development of clean energy sources such as photovoltaic wind power and the like can greatly reduce the dependence on traditional fossil energy sources; as more and more distributed low power generation systems are connected to the grid, grid faults become more frequent, at which time meeting the requirements of the grid access guidelines to ensure the stability and reliability of the grid, maintaining the safety of the power infrastructure becomes extremely important.
Voltage slump is a major power quality problem, with a double phase ground fault (DLG fault) that may produce a zero sequence voltage being a common cause of voltage slump. Low Voltage Ride Through (LVRT) capability is the most important requirement to reduce the risk of disconnection of electrical equipment under a faulty electrical network. To improve the ability to handle voltage dips, today the networking guidelines have evolved from ride-through strategies to voltage support strategies.
In recent years, several strategies have been proposed by related researchers to solve the control problem of grid-connected inverters supporting a faulty grid. A three-wire inverter voltage support control strategy is proposed in document Reactive Power Control for Distributed Generation Power Plants to Comply With Voltage Limits During Grid Faults (a. Camacho, IEEE Transactions on Power Electronics, vol. 29, no. 11, pp. 6224-6234) on publication date 1, month 20 of 2014, which sets the voltage support target to increase the point of common coupling voltage to the range allowed by the network entry criteria ([ 0.85-1.10] p.u.). The control strategy mentioned in document Control Strategy for Distribution Generation Inverters to Maximize the Voltage Support in the Lowest Phase During Voltage Sags (m. Castella, IEEE Transactions on Industrial Electronics, vol. 65, no. 3, pp. 2346-2355) published on 8 of 2017 aims at maximizing the voltage of the lowest phase, whereas in this strategy only the positive sequence current is injected, ignoring the injection of the negative sequence current, taking no action on the negative sequence voltage and not proposing a goal of reducing the unbalance of the PCC points. The literature "OptimalVoltage-SupportControlforDistributedGeneration Inverters in RL Grid-fault Networks" on publication No. 10, 30, 2019 (m. Gamnica, IEEE Transactions on Industrial Electronics, vol 67, no. 10, pp., 8405-8415) provides a voltage support control method for a three-wire inverter that avoids APO and maximizes the support of the grid with full use of positive and negative sequence current injection capabilities, however, zero sequence current is omitted from the literature due to the absence of zero sequence current channels. Limited by the lack of zero sequence channels, three-wire inverters have little literature consideration of zero sequence voltage. The four-bridge arm inverter has a fourth bridge arm to accurately control zero-sequence current, so that the four-bridge arm inverter gradually becomes a research hot spot. The method proposed in document Asymmetrical Voltage Support Control of Three-Phase Fourier-Wire Inverters with Zero Active Power Oscillation during Grid Faults (J. Ge, IEEE Energy Conversion Congress and Exposition (ECCE)), pp. 906-911 doi: 10.1109/ECCE47101.2021.9595752, published 10 on 10 months 2021, exploits the flexibility of a Four-branch inverter to maximize positive sequence voltage, minimize zero sequence voltage and eliminate active power oscillations, however, does not target minimum imbalance as voltage support.
Disclosure of Invention
The invention aims to design an optimal voltage support reference current calculation method of a four-leg inverter so as to solve the problem that the voltage support control reference current calculation method of the four-leg inverter in the prior art cannot take the minimum PCC point unbalance degree as a control target.
The invention solves the technical problems through the following technical scheme:
a four-bridge arm inverter optimal voltage support reference current calculation method comprises the following steps:
step 1, calculating positive sequence, negative sequence, zero sequence voltage amplitude and initial phase angle and voltage unbalance of PCC point faults;
step 2, by defining the relation between active current and reactive current, preferentially calculating the zero sequence current amplitude and converting to obtain an objective function and a limiting condition;
and step 3, converting the optimal solution problem into a solution problem of the type I point and the type II point, respectively calculating to obtain the values of extreme points of the type I point and the type II point, and obtaining the optimal solution through comparison.
Further, the method for calculating the positive sequence, the negative sequence, the zero sequence voltage amplitude and the initial phase angle of the PCC point fault in the step 1 is as follows:
the PCC point voltage in the αβ0 coordinate system is expressed as:
(1)
wherein ,、/>、/>the voltage components of the alpha axis, the beta axis and the 0 axis of the PCC point are respectively; />、/>、/>The voltage components are respectively the alpha axis, the beta axis and the 0 axis of the power grid; />、/>、/>The current components of the alpha axis, the beta axis and the 0 axis are output;
under the unbalanced condition, the PCC point voltage is decomposed into positive sequence, negative sequence and zero sequence components; for a four-bridge arm grid-connected inverter, the grid-side currenti g The method comprises the following steps of:
(2)
in the formula ,、/>respectively representing positive sequence active current amplitude and positive sequence reactive current amplitude, < >>、/>Respectively represent the negative sequence active current amplitude and the negative sequence reactive current amplitude, < >>、/>Representing the zero sequence active and reactive current amplitude, +.>In order to be able to achieve an angular velocity,、/>、/>the primary phases of positive, negative and zero sequence voltages of PCC points are respectively;
decomposing the voltages and currents of the alpha-axis and beta-axis expressions in the formula (1) into positive sequence and negative sequence components to obtain positive sequence PCC point voltage expressions:
(3)
wherein ,respectively PCC point positive sequence voltage alpha and beta axis componentsThe positive sequence voltage alpha and beta axis components of the power grid and the alpha and beta axis components of the output current;
substituting the positive sequence component in the formula (2) into the formula (3), and finishing to obtain:
(4)
in the formula ,representing the initial phase of the positive sequence voltage component of the power grid, +.>Representing the primary phase of the PCC point positive sequence voltage component;
the PCC point positive sequence voltage magnitude is:
(5)
the PCC point negative sequence voltage amplitude is expressed as:
(6)
wherein, for the PCC point zero sequence voltage, the orthogonal form of the zero sequence expression in the structural formula (1) is as follows:
(7)
in the formula ,,/>,/>the power grid voltage zero-sequence voltage components are PCC point zero-sequence voltage components respectively, and current zero-sequence components are output; />,/>,/>Respectively->,/>,/>Is a component of the orthogonal component of (a);
the PCC point zero sequence voltage amplitude is as follows:
(8)
wherein the zero sequence equivalent grid impedance is 4 times of the positive and negative sequence equivalent grid impedance.
Further, the calculation of the voltage unbalance degree in step 1 is as follows:
negative sequence and zero sequence imbalance are defined as:
(9)
(10)
the PCC point voltage imbalance is:
(11)
as can be obtained from equation (11), the voltage imbalance comprises PCC positive sequence, negative sequence, and zero sequence voltages, which are used as an objective function to optimize the integrity.
Further, the method for preferentially calculating the zero sequence current amplitude and converting the zero sequence current amplitude to obtain the objective function and the limiting condition by defining the relation between the active current and the reactive current in the step 2 is specifically as follows:
the objective function and the constraint are expressed as:
(12)
wherein Respectively a phase, a b phase and a c phase, and the central line current amplitude value;
in order to simplify the injection current relationship, the positive sequence, negative sequence and zero sequence active and reactive currents are specified as follows:
,/>,/>(13)
when the formula (13) is satisfied, the positive sequence, negative sequence and zero sequence active and reactive current ratios are fixed, and the change in the objective function and the isocenter constraint is changed into the positive sequence, negative sequence and zero sequence current amplitude values、/>、/>The six-element optimization problem is simplified to a three-element optimization problem; and when formula (13) is satisfied, the PCC point positive sequence, negative sequence and zero sequence voltages will remain unchanged;
substituting formula (13) into formula (5), formula (6) and formula (8), the positive sequence, negative sequence and zero sequence voltage amplitude of the PCC point are expressed as:
(14)
(15)
(16)
the method is characterized in that the method comprises the steps of (1) obtaining from formulas (14) - (16), and when the power grid impedance and the ratio of positive sequence, negative sequence and zero sequence active current to reactive current are fixed, the positive sequence, the negative sequence and the zero sequence voltage of PCC points are only influenced by the positive sequence, the negative sequence and the zero sequence current amplitude;
because the zero sequence current impedance is four times of the positive sequence negative sequence current, the zero sequence current injection is preferably considered to reduce the zero sequence voltage, and the zero sequence current amplitude reference value is obtained as follows:
(17)
wherein ,as a safety threshold, the neutral line current will be controlled at the safety threshold after the zero sequence current amplitude is confirmed>Inside;
whereas the objective function in equation (12) will sum only the positive sequence, negative sequence current magnitude,/>In relation, the equality constraint is also only relevant for the three-phase current amplitude and the safety threshold +.>At this time, the optimization problem is reduced to:
(18)。
further, the method for converting the optimal solution problem into the solution problem of the type I point and the type II point in the step 3, respectively calculating the values of the extreme points of the type I point and the type II point, and obtaining the optimal solution by comparing is as follows:
1) Type I Point
Defining type I points as objective functions on three-phase current amplitude curvesThe maximum point, type I point +.>Solving the mode;
since the three-phase current magnitude curve is plotted in the first quadrant as a non-standard elliptic equation, it is assumed that on the non-standard elliptic equation curve, the objective function is madeMaximum point->(x=a, b, c) is located in the first quadrant, and then the type I point on the three-phase current amplitude curve is the type I point; for->Can be obtained by Lagrange multiplier method; is finished with->The expression of (2) is:
(19)
in the formula ,，
；
when solved according to formula (19),/>When non-negative values cannot be satisfied at the same time, type I Point +.>(x=a, b, c) solving for three-phase current amplitude +.>The intersection point of the curve and the coordinate axis is obtained:
(20)
(21)
2) Type II Point
Definition type II Point(y=ab, bc, ca) is the intersection of the three-phase current magnitude curves in the first quadrant, solved by the simultaneous three-phase current magnitude expression:
(22)
due to the provision of the physical meaning of the terms,,/>are all non-negativeReal numbers, so only points in the first quadrant in the real number domain can be preserved; after the elimination treatment of the element (22), solving a unitary fourth-order equation by adopting a Ferrari method, and finally removing the solution of non-positive real numbers to obtain a type II point, wherein the point with the maximum objective function is the optimal solution only by comparing the objective function value of the type I point and the objective function value of the type II point which fall on an equi-number constraint curve;
when it is obtainedThen, positive sequence, negative sequence and zero sequence active and reactive current reference values are deduced according to a formula (13):
(23)。
the invention has the advantages that:
the method aims at reducing the unbalance degree of the PCC points, and restores the voltage of the PCC points to a state before the unbalance fault occurs as much as possible under the condition that the amplitude of the three-phase current and the neutral line current does not exceed the allowable maximum output current amplitude of the three-phase four-bridge arm grid-connected inverter; the method obtains positive sequence, negative sequence and zero sequence active and reactive current reference values through solving the nonlinear inequality constraint optimization problem, and obtains the most numerical solution solving algorithm through mathematical proof and proper simplification; the optimality and the effectiveness of the calculation method are verified by carrying out experimental comparison on a hardware-in-loop experimental platform; after the reference current calculation method provided by the invention is applied, the imbalance degree of the PCC point is obviously reduced, and the imbalance degree is reduced to be close to 0.
Drawings
Fig. 1 is a typical topology of a four-leg inverter according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of two types of numerical points defined by embodiments of the present invention;
FIG. 3 is a flow chart of type I point computation defined by an embodiment of the present invention;
FIG. 4 is a flow chart of type II point computation defined by an embodiment of the present invention;
fig. 5 is a flowchart of a method for calculating an optimal voltage support reference current of a four-leg inverter according to an embodiment of the present invention;
FIG. 6 (a) is a diagram showing the voltage supporting effect according to the embodiment of the present invention;
FIG. 6 (b) is a graph of an abc phase output current experiment according to an embodiment of the present invention;
FIG. 6 (c) is a plot of the centerline output current of an embodiment of the present invention;
fig. 6 (d) is an experimental diagram of the effect of reducing unbalance of the embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions in the embodiments of the present invention will be clearly and completely described in the following in conjunction with the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The technical scheme of the invention is further described below with reference to the attached drawings and specific embodiments:
example 1
The method for calculating the optimal voltage support reference current of the four-bridge arm inverter comprises the following steps of:
1. calculating positive sequence, negative sequence and zero sequence voltage amplitude and initial phase angle and voltage unbalance of PCC point fault
In order to analyze the voltage supporting basic principle of the three-phase four-bridge arm grid-connected inverter, the power grid is considered to be not a pure voltage source model, and meanwhile, the power grid impedance is contained, at the moment, a circuit equivalent model is shown in fig. 1, wherein Vdc is direct-current link voltage and is a constant value. The inverter is obtained using a damped LCL filterA grid side current with low harmonic content and connected to the grid at PCC (Point of Common Coupling, common point); when a grid fault occurs, the voltage support control intervenes in compensating the PCC point voltage. The electric network impedance of each phase is assumed to be the same, and the resistor is adoptedR g And (3) withL g Inductance simulation equivalent power grid impedance and power grid voltagev ga 、 v gb 、v gc Simulating an unbalanced voltage dip. The equivalent power grid impedance can be measured by an impedance measuring and calculating device, and the specific reference can be seen in the literature: a method for identification of the equivalent inductance and resistance in the plant model of current-controlled grid-charged controllers (A. Vidal et al, IEEE Trans. Power Electron., vol. 30, no. 12, pp. 7245-7261, dec.).
The PCC point voltage in the αβ0 coordinate system can be expressed as:
(1)
wherein ,、/>、/>the voltage components of the alpha axis, the beta axis and the 0 axis of the PCC point are respectively; />、/>、/>The voltage components are respectively the alpha axis, the beta axis and the 0 axis of the power grid; />、/>、/>The output is the alpha-axis, beta-axis and 0-axis current components.
As can be derived from equation (1), the PCC voltage is related to the injected grid current and the equivalent grid impedance, both of which are critical to voltage support control.
In the unbalanced condition, the PCC point voltage can be decomposed into positive sequence, negative sequence and zero sequence components; for the four-bridge arm grid-connected inverter, flexible controllability and grid-side current are fully utilizedi g Can be decomposed into:
(2)
in the formula ,、/>respectively representing positive sequence active current amplitude and positive sequence reactive current amplitude, < >>、/>Respectively representing the negative sequence active current amplitude and the negative sequence reactive current amplitude. But it is notable that->、/>The amplitude of the zero sequence active and reactive currents is not represented in a physical sense, and the amplitude of the zero sequence active and reactive currents only represents two parts of the zero sequence current,/->In the same direction as zero sequence voltage->Hysteresis zero sequence voltage 90 DEG, but in unified form, also called zero sequence active and reactive current,/->Is the angular velocity.
、/>、/>The primary phase of the positive, negative and zero sequence voltages of the PCC point.
According to a symmetrical component method, the alpha-axis and beta-axis expression voltages and currents in the formula (1) are decomposed into positive sequence and negative sequence components, and positive sequence PCC point voltage expressions are obtained:
(3)
wherein ,the positive sequence voltage alpha and beta axis components of the PCC point, the positive sequence voltage alpha and beta axis components of the power grid and the output current alpha and beta axis components are respectively.
Substituting the positive sequence component in the formula (2) into the formula (3), and finishing to obtain the product:
(4)
in the formula ,representing the initial phase of the positive sequence voltage component of the power grid, +.>Representing the primary phase of the PCC point positive sequence voltage component; generally, consider +.>Approximately equal to->The negative sequence zero sequence is similar to the positive sequence.
The PCC point positive sequence voltage magnitude is:
(5)
the PCC point negative sequence voltage amplitude is expressed as:
(6)
in the formula, for the zero sequence voltage of the PCC point, the orthogonal form of the zero sequence expression in the formula (1) can be constructed by means of the concept of virtual orthogonal quantity:
(7)
in the formula ,,/>,/>the zero-sequence voltage components of the PCC points, the zero-sequence voltage components of the grid voltage and the zero-sequence components of the output current are respectively obtained. />,/>,/>Respectively->,/>,/>Is included in the first and second components.
Similar to the derivation of the PCC point positive sequence voltage amplitude, the PCC point zero sequence voltage amplitude can be obtained as follows:
(8)
the PCC point zero sequence voltage amplitude expression is similar to the positive sequence and negative sequence amplitude expression, but it is noted that the equivalent grid impedance in the zero sequence circuit is 4 times of the equivalent grid impedance in the positive and negative sequences.
By calculating the voltage amplitude, the negative sequence and zero sequence imbalance are defined as:
(9)
(10)
the PCC point voltage imbalance is:
(11)
it can be seen that the voltage unbalance degree comprises the positive sequence, the negative sequence and the zero sequence voltage of the PCC points, and the voltage unbalance degree is used as an objective function to optimize the integrity.
2. By defining the relation between active and reactive currents, the zero sequence current amplitude is preferentially calculated and converted to obtain an objective function and a limiting condition;
the invention has the maximum innovation point that positive and negative zero sequence active and reactive currents are distributed through calculationAt an output current not exceeding a safety threshold +.>Reducing the PCC point voltage imbalance n to a minimum.
The objective function and constraints can be expressed as:
(12)
wherein The phase a, the phase b and the phase c are respectively adopted, and the neutral current amplitude is realized. When only the positive sequence voltage is considered, the positive sequence current amplitude is equal to the maximum outputtable current amplitude +.>And the positive sequence active and reactive current satisfies +.>The PCC point positive sequence voltage is the largest. It has been demonstrated in the literature of Optimal Voltage-Support Control for Distributed Generation Inverters in RL Grid-Faulty Networks (M. Garnica, IEEE Transactions on Industrial Electronics, vol. 67, no. 10, pp. 8405-8415). In other words, when the maximum outputtable current amplitude is changed, the positive sequence voltage of the PCC point with the maximum improvement can be realized only by maintaining the ratio of the active current to the reactive current. The same can be analyzed for negative sequence as well as zero sequence. Therefore, to simplify the injection current relationship, the positive sequence, negative sequence and zero sequence active and reactive currents are specified as follows:
,/>,/>(13)
when the formula (13) is satisfied, the positive sequence, the negative sequence and the zero sequence active and reactive current ratio are fixed,at this time, the change in the objective function and the isocenter constraint becomes positive sequence, negative sequence and zero sequence current amplitude,/>,/>That is, the six-member optimization problem is reduced to the three-member optimization problem. And when equation (13) is satisfied, the PCC point positive sequence, negative sequence and zero sequence voltages will remain unchanged.
Substituting formula (13) into formula (5), formula (6) and formula (8), the positive sequence, negative sequence and zero sequence voltage amplitude of the PCC point are expressed as:
(14)
(15)
(16)
the PCC point positive sequence, negative sequence and zero sequence voltages are only affected by the positive sequence, negative sequence and zero sequence current amplitudes when the power grid impedance and the ratio of positive sequence, negative sequence and zero sequence active current to reactive current are fixed.
Because the zero-sequence current impedance is four times of the positive-sequence negative-sequence current, the zero-sequence current injection is preferably considered to reduce the zero-sequence voltage, and the zero-sequence current amplitude reference value can be obtained：
(17)
wherein ,as a safety threshold, the neutral line current will be controlled at the safety threshold after the zero sequence current amplitude is confirmed>Inside. Whereas the objective function in equation (12) will be equal to the positive sequence current magnitude +.>,/>In relation, the equality constraint is also only relevant for the three-phase current amplitude and the safety threshold +.>. At this time, the optimization problem is reduced to:
(18)
3. converting the optimal solution problem into two defined point solving problems, respectively calculating to obtain values of two types of extreme points, and obtaining an optimal solution through comparison;
when the zero sequence current amplitude is fixed, the current amplitude of each phase is related to the positive sequence current amplitude and the negative sequence current amplitude,/>Is an expression of a non-standard elliptic equation in the first quadrant. Thus, the medium constraint of equation (18) can be represented by FIG. 2; FIG. 2 is a schematic diagram of a specific grid, wherein three curves respectively represent three-phase current magnitude curves, and the broken line of the partial components of each phase current magnitude curve represents the equality constraint in equation (18), that is, the maximum objective function of equation (18) needs to be found from the broken line curves ∈ ->Optimal solution of->。
The invention classifies possible optimal value points into type I points (type I points) and type II points (type II points). The final optimum point is found in type I and type II points.
1) Type I Point
Defining type I points as objective functions on three-phase current amplitude curvesThe maximum point, type I point +.>And solving the mode.
Since the three-phase current magnitude curve is plotted in the first quadrant as a non-standard elliptic equation, it is assumed that on the non-standard elliptic equation curve, the objective function is madeMaximum point->(x=a, b, c) is located in the first quadrant, and the type I point on the three-phase current amplitude curve is the type I point. For->Can be obtained by Lagrange multiplier method. Comprehensive arrangement of available->The expression of (2) is:
(19)
in the formula ,，
。
when solved according to formula (19),/>When non-negative values cannot be satisfied at the same time, type I Point +.>(x=a, b, c) the three-phase current amplitude +.>The intersection point of the curve and the coordinate axis is obtained:
(20)
(21)/>
in summary, a flow chart of type I point calculation on the three-phase current amplitude curve is shown in fig. 3.
2) Type II Point
Definition type II Point(y=ab, bc, ca) is the intersection of the three-phase current magnitude curves in the first quadrant. Can be solved by the simultaneous three-phase current amplitude expression.
(22)
Due to the provision of the physical meaning of the terms,,/>are non-negative real numbers and therefore only remain at points in the real domain that are located in the first quadrant. After the elimination of the element in the step (22), the solution of the unitary four-time equation is carried out by adopting the Ferrari method, and finally the solution of the non-positive real number is eliminated, so that a type II point is obtained, and the calculation flow can be seen in fig. 4. As long as the objective function values of the type I point and the type II point falling on the isocenter constraint curve are compared, the point where the objective function is maximized is not only the optimal solution; among them, the solution of the first-order four-way equation by the Ferrari Method is the prior art, and reference is specifically made to the document Current Minimizing Torque Control of the IPMSM Using Ferrari's Method (in IEEE Transactions on Power Electronics, vol. 28, no. 12, pp. 5603-5617, dec. 2013).
When it is obtainedThen, positive sequence, negative sequence and zero sequence active and reactive current reference values can be deduced according to the formula (13):
(23)
in summary of the above analysis, the improved optimal voltage support control algorithm flow is shown in fig. 5.
4. Simulation test verification
Hardware-in-the-loop simulation experiment verification is carried out on the method by using a Typhoon HIL404 and TI TMS320F28335DSP controller, and specific simulation experiment parameters are shown in the following table 1.
Table 1 simulation test parameters
In the experiment, the fault power grid is set to be positive sequence, negative sequence and zero sequence, the power grid voltage amplitude is 226.27V, 61.09V and 30.49V, and the initial phase angle is 0, pi/6 and-pi/3. The method has the advantages that the effects of PCC point voltage supporting effect, abc three-phase output current, neutral line output current and unbalance degree reduction are shown in fig. 6 (a), 6 (b), 6 (c) and 6 (d) under defined fault grid conditions; in the first stage (0.1-0.14 s), the three-phase four-bridge arm grid-connected inverter does not inject current into the power grid, and the PCC point voltage is the power grid voltage at the moment; in the second stage (0.14-0.22 s), the four-leg inverter adopts a traditional voltage support control strategy in the literature An Advanced Voltage Support Scheme Considering the Impact of Zero-Sequence Voltage Under Microgrid Faults Using Model Predictive Control (in IEEE Transactions on Industrial Electronics, vol. 67, no. 10, pp. 8957-8968, oct. 2020), and the voltage support control strategy of the literature does not take the minimum unbalance degree as a control target; in the third stage (0.22-0.3 s), the control strategy of the optimal voltage support reference current calculation method is adopted. FIG. 6 (a) shows that the PCC point voltage is significantly more balanced after the reference current calculation method proposed by the present invention is applied; FIG. 6 (b) shows that the three-phase current peak value does not exceed the maximum value, and meets the maximum current constraint in the calculation method of the present invention; FIG. 6 (c) shows that the peak line current does not exceed the maximum value, meeting the maximum current constraint in the calculation method of the present invention; fig. 6 (d) shows that the effect of decreasing the unbalance degree of the PCC point is remarkable, and the unbalance degree is decreased to be close to 0 after the reference current calculation method provided by the present invention is applied.
The method aims at reducing the unbalance degree of the PCC points, and restores the voltage of the PCC points to a state before the unbalance fault occurs as much as possible under the condition that the amplitude of the three-phase current and the neutral line current does not exceed the allowable maximum output current amplitude of the three-phase four-bridge arm grid-connected inverter. The method obtains the positive sequence, negative sequence and zero sequence active and reactive current reference values through solving the nonlinear inequality constraint optimal problem, and obtains the most numerical solution solving algorithm through mathematical proof and proper simplification. The optimality and effectiveness of the calculation method are verified by experimental comparison of hardware in a loop experimental platform.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (1)

1. The method for calculating the optimal voltage support reference current of the four-bridge arm inverter is characterized by comprising the following steps of:
step 1, calculating positive sequence, negative sequence, zero sequence voltage amplitude and initial phase angle and voltage unbalance of PCC point faults;
the method for calculating the positive sequence, the negative sequence, the zero sequence voltage amplitude and the initial phase angle of the PCC point fault comprises the following steps:
the PCC point voltage in the αβ0 coordinate system is expressed as:
(1)
wherein ,、/>、/>the voltage components of the alpha axis, the beta axis and the 0 axis of the PCC point are respectively; />、/>、/>The voltage components are respectively the alpha axis, the beta axis and the 0 axis of the power grid; />、/>、/>The current components of the alpha axis, the beta axis and the 0 axis are output;
under the unbalanced condition, the PCC point voltage is decomposed into positive sequence, negative sequence and zero sequence components; for a four-bridge arm grid-connected inverter, the grid-side currenti g The method comprises the following steps of:
(2)
in the formula ,、/>respectively representing positive sequence active current amplitude and positive sequence reactive current amplitude, < >>、/>Respectively represent the negative sequence active current amplitude and the negative sequence reactive current amplitude, < >>、/>Representing zero sequence active and reactive currentsAmplitude of->For angular velocity +.>、/>、/>The primary phases of positive, negative and zero sequence voltages of PCC points are respectively;
decomposing the voltages and currents of the alpha-axis and beta-axis expressions in the formula (1) into positive sequence and negative sequence components to obtain positive sequence PCC point voltage expressions:
(3)
wherein ,the positive sequence voltage alpha and beta axis components of the PCC point, the positive sequence voltage alpha and beta axis components of the power grid and the output current alpha and beta axis components are respectively;
substituting the positive sequence component in the formula (2) into the formula (3), and finishing to obtain:
(4)
in the formula ,representing the initial phase of the positive sequence voltage component of the power grid, +.>Representing the primary phase of the PCC point positive sequence voltage component;
the PCC point positive sequence voltage magnitude is:
(5)
the PCC point negative sequence voltage amplitude is expressed as:
(6)
wherein, for the PCC point zero sequence voltage, the orthogonal form of the zero sequence expression in the structural formula (1) is as follows:
(7)
in the formula ,,/>,/>the power grid voltage zero-sequence voltage components are PCC point zero-sequence voltage components respectively, and current zero-sequence components are output; />,/>,/>Respectively->,/>,/>Is a component of the orthogonal component of (a);
the PCC point zero sequence voltage amplitude is as follows:
(8)
the zero sequence equivalent power grid impedance is 4 times of the positive sequence equivalent power grid impedance;
the voltage unbalance is calculated as follows:
negative sequence and zero sequence imbalance are defined as:
(9)
(10)
the PCC point voltage imbalance is:
(11)
as can be obtained from formula (11), the voltage unbalance degree comprises PCC point positive sequence, negative sequence and zero sequence voltages, and the voltage unbalance degree is used as an objective function to optimize the integrity;
step 2, by defining the relation between active current and reactive current, preferentially calculating the zero sequence current amplitude and converting to obtain an objective function and a limiting condition; the method comprises the following steps:
the objective function and the constraint are expressed as:
(12)
wherein ,a phase, a b phase, a c phase and a neutral current amplitude;
in order to simplify the injection current relationship, the positive sequence, negative sequence and zero sequence active and reactive currents are specified as follows:
,/>,/>(13)
when the formula (13) is satisfied, the positive sequence, negative sequence and zero sequence active and reactive current ratios are fixed, and the change in the objective function and the isocenter constraint is changed into the positive sequence, negative sequence and zero sequence current amplitude values、/>、/>The six-element optimization problem is simplified to a three-element optimization problem; and when formula (13) is satisfied, the PCC point positive sequence, negative sequence and zero sequence voltages will remain unchanged;
substituting formula (13) into formula (5), formula (6) and formula (8), the positive sequence, negative sequence and zero sequence voltage amplitude of the PCC point are expressed as:
(14)
(15)
(16)
the method is characterized in that the method comprises the steps of (1) obtaining from formulas (14) - (16), and when the power grid impedance and the ratio of positive sequence, negative sequence and zero sequence active current to reactive current are fixed, the positive sequence, the negative sequence and the zero sequence voltage of PCC points are only influenced by the positive sequence, the negative sequence and the zero sequence current amplitude;
because the zero sequence current impedance is four times of the positive sequence negative sequence current, the zero sequence current injection is preferably considered to reduce the zero sequence voltage, and the zero sequence current amplitude reference value is obtained as follows:
(17)
wherein ,as a safety threshold, the neutral line current will be controlled at the safety threshold after the zero sequence current amplitude is confirmed>Inside;
whereas the objective function in equation (12) will sum only the positive sequence, negative sequence current magnitude,/>In relation, the equality constraint is also only relevant for the three-phase current amplitude and the safety threshold +.>At this time, the optimization problem is reduced to:
(18)
step 3, converting the optimal solution problem into a solution problem of a type I point and a type II point, respectively calculating to obtain the values of extreme points of the type I point and the type II point, and obtaining an optimal solution through comparison; the method comprises the following steps:
1) Type I Point
Defining type I points as objective functions on three-phase current amplitude curvesThe maximum point, type I point, is given belowSolving the mode;
since the three-phase current magnitude curve is plotted in the first quadrant as a non-standard elliptic equation, it is assumed that on the non-standard elliptic equation curve, the objective function is madeMaximum point->(x=a, b, c) is located in the first quadrant, and then the type I point on the three-phase current amplitude curve is the type I point; for->Can be obtained by Lagrange multiplier method; is finished with->The expression of (2) is:
(19)
in the formula ,，
；
when solved according to formula (19),/>Cannot be usedWhen the non-negative value is satisfied, type I point +.>(x=a, b, c) solving for three-phase current amplitude +.>The intersection point of the curve and the coordinate axis is obtained:
(20)
(21)
2) Type II Point
Definition type II Point(y=ab, bc, ca) is the intersection of the three-phase current magnitude curves in the first quadrant, solved by the simultaneous three-phase current magnitude expression:
(22)
due to the provision of the physical meaning of the terms,,/>are non-negative real numbers and therefore only remain at points in the real domain that are located in the first quadrant; after the elimination of element (22), the solution of the unitary four-way equation is carried out by adopting the Ferrari method, and finally the arrangement is carried outUnless a solution of a positive real number is adopted, a type II point is obtained, and only the objective function values of the type I point and the type II point falling on an equi-number constraint curve are compared, wherein the point with the maximum objective function is the optimal solution;
when it is obtainedThen, positive sequence, negative sequence and zero sequence active and reactive current reference values are deduced according to a formula (13):
(23)。
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