CN115811097A - Voltage quality optimization method based on virtual oscillator control - Google Patents
Voltage quality optimization method based on virtual oscillator control Download PDFInfo
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Abstract
The invention discloses a voltage quality optimization method based on virtual oscillator control, which comprises the steps of firstly establishing a mathematical model of a four-bridge arm inverter; meanwhile, a circuit model of the virtual oscillator is built, and then internal parameters of the virtual oscillator are adjusted to output three-phase balanced power frequency sinusoidal voltage; extracting a positive sequence component and estimating the voltage of a common coupling point; then designing a sliding mode controller, wherein the sliding mode controller forces the voltage of the common coupling point to follow the voltage waveform of the approximate sine wave output by the virtual oscillator; the priority exists in the control of the virtual oscillator, and the priority of the virtual oscillator is lower in the voltage distortion control layer; therefore, sliding mode controllers were introduced to support the application of virtual oscillators in harmonic and unbalanced voltage compensation. The three-phase four-bridge arm and the virtual oscillator are combined for use, the amplitude and the frequency of the output voltage of the inverter are controlled according to the weak nonlinear behavior of the virtual oscillator, and the voltage quality of the system meets the national standard condition under the condition of ensuring the stability of an inertial system.
Description
Technical Field
The invention belongs to the field of power systems, and particularly relates to a voltage quality optimization method based on virtual oscillator control.
Background
In recent years, due to the large-scale integration grid connection of renewable energy sources and the rapid development of power electronic technology, the voltage quality problems caused by the high permeability of the distributed power supply, including voltage harmonics, voltage sag, severe fluctuation, three-phase voltage unbalance and the like, are more and more serious, although the power quality problems can be effectively improved by using power quality compensation devices such as an APF, a UPQC, a STATCOM and the like in a power distribution network, the increase of power electronic equipment can cause the further weakening of the inertia of a microgrid, when large disturbance and load mutation exist, the weak inertia can cause serious voltage or frequency deviation of the power distribution network, and meanwhile, the later-stage equipment maintenance cost of the compensation devices is also higher. Therefore, the inverter behavior control method has high research value by using an efficient control algorithm to control the inverter behavior aiming at the problems that the inertia is weak and the voltage quality is poor in a microgrid and cannot be solved at the same time.
One of the functions of the grid-connected inverter is that the grid-connected inverter is used as a bridge between a distributed power supply and a microgrid bus, if the problem of electric energy quality is solved by using redundant power outside power transmission of the grid-connected inverter, compared with special control equipment such as APF, UPQC, STATCOM and the like, the grid-connected inverter reduces maintenance cost, does not need to consider the problem of weak inertia of the microgrid, and has good application and research values.
The voltage quality problem is compensated on the basis of not influencing the inertia of the power distribution network, the practical significance is profound, the inertia of the power distribution network is not further weakened on the basis of not wasting the capacity of an inverter, and the voltage quality problem is effectively solved.
Documents l.a. budiwicaksana, t.ardriani, j.furqani, a.rizqawan and p.a.dahono, "Improving Inverter Output Current controllers by Using Virtual Impedance," in IEEE Access, vol.9, pp.162359-162369,2021 propose a Virtual Impedance concept for series connection to the Inverter Output, the Inverter behavior changes to a connected real Impedance condition without actually increasing the Impedance, and only an Unbalanced component affects during operation. When the nonlinearity of the inverter is not negligible (such as dead time), the control method based on the virtual impedance is difficult to ensure that the bus voltage power quality is kept within a required range. In the literature, "land, li yu, zhang hu, yan stamen, happy, and unbalanced island load power supply requirements," MMC converter control strategy [ J ]. Southern power grid technology, 201812 (02): 20-26 ", aiming at that negative sequence components are generated when an unbalanced load is accessed by an MMC converter in an island operation mode, a positive-negative sequence independent control strategy is provided, and the electric energy quality of a point of common coupling is ensured to meet the system requirements. The problem of three-phase imbalance can be restrained to a certain extent by decomposing the unbalanced current into positive and negative sequence components for respective control, but because the method has a sequence conversion module, more signals need to be controlled and slow transient response, the actual control is more complex.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a voltage quality optimization method based on virtual oscillator control.
The technical scheme for solving the technical problem is to provide a voltage quality optimization method based on virtual oscillator control, which is characterized by comprising the following steps of:
the circuit model for building the virtual oscillator is specifically as follows:
virtual oscillator control is achieved by filtering the inductor current i at the output of the inverter L As an input quantity, a virtual oscillator dynamic equation obtained according to a system structure of the virtual oscillator is as follows:
in formulae (6) to (8), L osc Is an inductance in the virtual oscillator circuit; i.e. i Losc To flow through L osc The current value of (a); v c Is the output voltage, V, of the oscillator before the scale factor is fused oc Superimposing the output voltage of the virtual oscillator with the output quantity, K, of the voltage scale factor gain v Is a voltage scaling factor, C, that couples the virtual oscillator input and output quantities to the physical and electrical feedback signals osc For the capacitance in the virtual oscillator circuit, sigma = -1/R is the conductance negative value, R is the filter resistance, alpha is the oscillator design parameter, K i Is a current scaling factor, i, that couples the virtual oscillator input and output quantities to the physical and electrical feedback signals L ＝[i Lα i Lβ i Lλ ] T The filter inductance current is the filter inductance current, i is the total current of the output end of the inverter, and the dynamic equation of the oscillator is obtained by the digital controller by utilizing the feedback of the output current of the inverter;
the virtual oscillator is used as the reference voltage input quantity of the sliding mode controller, and when the unbalanced load is required to be connected to a certain phase or any phase is unbalanced, the reference voltages provided by the virtual oscillator are required to be the same; extraction of inductor current i by using bi-quad generalized integrator method Lα The positive sequence component is filtered, the negative sequence component is filtered and used as the input of the virtual oscillator, and the virtual oscillator can output the same reference voltage when the unbalanced load is connected to any phase;
in order to compensate for voltage unbalance and harmonic distortion of the point of common coupling, the voltage of the point of common coupling is calculated and used as the feedback input of a sliding mode controller; by designing the line impedance coefficient lambda m Voltage V at point of common coupling pcc After the impedance coefficient is added, the estimation formula of the voltage of the common coupling point is as follows:
in the formula (12), V o Outputting voltage for the four-bridge arm inverter; l is f Is the inductance of the inverter output; l is a radical of an alcohol line Is the line inductance from the inverter output to the point of common coupling; r is a filter resistance; r is line Is the line impedance from the inverter output to the point of common coupling;
step 3, designing a sliding mode controller on the basis of finishing the estimation work of the virtual oscillator and the voltage of the point of common coupling, wherein the sliding mode controller forces the voltage of the point of common coupling to follow the voltage waveform of the approximate sine wave output by the virtual oscillator; the priority level exists in the control of the virtual oscillator, and the priority level of the virtual oscillator is lower in the voltage distortion control layer; therefore, a sliding mode controller is introduced to support the application of a virtual oscillator in harmonic and unbalanced voltage compensation;
aiming at a plurality of uncertainties in an island micro-grid, two unknown interference terms mu are added on the basis of the formula (6) and the formula (8) i And mu v ：
In formulae (13) and (14), V c-ref Is a reference value of the filter capacitor voltage; i.e. i L-ref Is a reference value of the inverter output terminal current;
the control variables were constructed as:
slip form surfaceS V Constructed as the sum of the products of the state variables and the controller parameters, from the state variable x 1 、x 2 Linear representation:
S V ＝Γ 1 x 1 +Γ 2 x 2 (16)
in formula (16), r 1 And r 2 Is a controller control parameter and is a positive real number;
in order to obtain a function state variable control law, an expected control target of the sliding mode controller is constructed as follows:
in formula (17), V eq 、V s Respectively an approaching law component and a discontinuous switching law component of the sliding mode controller; v eq Showing the control relationship between the slip form surface and the output quantity, V S The method has good processing effect on bounded interference in a dynamic system;
and (3) applying the sliding mode surface design in the formula (16) to a controller to derive a control law, and deriving the formula (16):
suppose V eq To stabilize the equilibrium point, V eq For the system to remain on the slip-form surface, the system state variable starts along any initial condition of the slip-form surface, and on this basis the slip-form surface derivative must be equal to zero, and corresponding to equation (18), the system state variable will slide along the slip-form surface towards the equilibrium point, V eq I.e. differential equation dS v Solution of/dt = 0; di in formula (13) L Dt and dV in formula (14) oc The substitution of/dt into (18) yields:
in the formula (19), N and Q are combined parameters in the sliding mode controller;
μ＝Γ 1 μ i +Γ 2 μ v synthesizing unknown interference item synthesis parameters for the system;
solve to obtain V eq Comprises the following steps:
in order to eliminate the buffeting effect of a sliding mode controller model based on a four-bridge arm inverter, a continuous and smooth hyperbolic tangent function is adopted as a sliding prevailing constraint condition to inhibit the buffeting problem existing in the traditional sliding mode control design;
sliding mode control based on the hyperbolic tangent function redefines the sliding prevalence conditions: the square value of the positive definite function distance reaching the sliding mode surface is gradually reduced along the system running track, and the running track is converged to the sliding mode surface within a limited time;
in formula (21), tanh (S) = (e) S -e -S )/(e S +e -S ) Is a hyperbolic tangent function, and eta is a strict positive parameter; equation (21) represents a positive constant function tanh to the slip form surface 2 The value of (S) is reduced along all system tracks, the tracks are constrained to point to the direction of the sliding mode surface, and the tracking error e tends to 0;
selecting a switching law component according to the sliding mode constraint condition in the formula (21) as follows:
V s ＝ηtanh(ξS v ) (22)
in the formula (22), ξ is a positive real parameter large enough to satisfy the formula (21);
selecting a random estimation self-adaptive control law as a sliding mode surface integral function:
in the formula (23), the compound represented by the formula,
is an uncertainty mu modeling estimation value in the system; gamma-shaped 3 Is a controller control parameter and is a positive real number;
according to the formulas (20) to (23), the complete control law of the sliding mode controller after the switching law is integrated as follows:
analyzing the stability of the sliding mode controller by using a Lyapunov stability criterion; under the condition of not considering the load, the four-bridge arm inverter is restricted by an equation (13) and an equation (14); the Lyapunov function is constructed as follows:
obtained by the formula (21):
the derivation conclusion can be drawn that the derivation of the Lyapunov function is negative and half fixed, and the proposed sliding mode control is proved to be asymptotically stable.
Compared with the prior art, the invention has the beneficial effects that:
(1) The three-phase four-bridge arm and the virtual oscillator are combined for use, the amplitude and the frequency of the output voltage of the inverter are controlled according to the weak nonlinear behavior of the virtual oscillator, and the system voltage quality meets the national standard condition under the condition of ensuring the stability of an inertial system.
(2) A power distribution network simulation model is built on a Matlab/Simulink simulation platform and is compared with various control strategies, and the effectiveness and the excellence of the control strategy are verified.
(3) Compared with the traditional PID control, the adopted sliding mode control strategy designs the switching rate of disturbance resistance, and the stability analysis is carried out by using the Lyapunov stability criterion, so that the process from implementation control to target realization is more stable, the disturbance is smaller, and the precision is higher.
Drawings
FIG. 1 is a topology diagram of a three-phase four leg inverter for use with the present invention;
FIG. 2 is a system block diagram of a virtual oscillator designed in accordance with the present invention;
FIG. 3 is a graph of instantaneous frequency output variation for different values of ε · σ in accordance with the present invention;
FIG. 4 is a diagram of the virtual oscillator oscillation limit cycle of the present invention under different values of ε · σ;
FIG. 5 is a structural diagram of a forward sequence component extraction model based on a biquad generalized integrator according to the present invention;
FIG. 6 is a diagram of the trace condition of the add constraint command signal according to the present invention;
FIG. 7 is a diagram illustrating signal tracking after adding a constraint instruction according to the present invention;
FIG. 8 is a block diagram of an experimental simulation model established in accordance with the present invention;
FIG. 9 is a waveform diagram illustrating the three-phase unbalanced load simulation under conventional droop control according to the present invention;
FIG. 10 is a diagram of a simulated waveform under the control of virtual impedance when three-phase unbalanced load is connected;
FIG. 11 is a simulation waveform diagram of the present invention under the condition that the virtual oscillator is controlled to be connected to the unbalanced three-phase load;
FIG. 12 is a waveform diagram illustrating the simulation of the current of the single-phase load under the control of the virtual oscillator according to the present invention;
FIG. 13 is a simulation waveform diagram of the single-phase load voltage accessed under the control of the virtual oscillator according to the present invention;
FIG. 14 is a waveform diagram illustrating the accessing of a nonlinear load simulation under conventional droop control in accordance with the present invention;
FIG. 15 is a simulation waveform diagram under the control of virtual impedance for accessing nonlinear load according to the present invention;
FIG. 16 is a waveform diagram of simulation under the condition that the virtual oscillator is controlled to be connected to the nonlinear load according to the present invention.
Detailed Description
Specific examples of the present invention are given below. The specific examples are only for illustrating the present invention in further detail and do not limit the scope of the claims of the present invention.
The invention provides a voltage quality optimization method (short for method) based on virtual oscillator control, which is characterized by comprising the following steps:
preferably, in step 1, the mathematical model of the four-leg inverter is specifically established as follows:
output voltage V of four-bridge arm inverter o And the inductor current i L The relationship between them is:
in the formula (1), V AG 、V BG 、V CG For the output voltage V of the inverter O The three-phase voltage of (1); l is a radical of an alcohol f Is the inductance of the inverter output; i.e. i La 、i Lb 、i Lc The inductance current value of three phases at the output end of the inverter; r is the resistance of the output end of the inverter; van, vbn, vcn are the voltages from the three phases of the inverter output to the neutral; l is n Is the inductance on the neutral line; i.e. i n Is the current flowing through the neutral line;
will i n ＝i La +i Lb +i Lc Substitution of formula (1) gives:
so far, the modeling of the four-bridge arm inverter under the abc coordinate system is completed; applying kirchhoff current law to nodes a, b and c; under kirchhoff's current law, the load capacitance voltages are equal, resulting in equation (3):
in the formula (3), C a 、C b 、C c Three-phase capacitance values of the output end of the inverter are respectively; i.e. i a 、i b 、i c Respectively flowing through the output end capacitor C of the inverter a 、C b 、C c The current of (a);
equations (2) and (3) are four-leg inverter models with a fourth leg established in the abc coordinate system; for the off-diagonal elements of the inductance matrix in equation (2), it can be seen that at the inductor current i L Inductance L between the neutral line and the neutral line n A direct proportional strong coupling relationship; since the inductor current also occurs in equation (3), the above coupling also exists in the load voltage; therefore, in the four-leg inverter model with the fourth leg established in the abc coordinate system, there is coupling among the four-leg inverters a, b and c, which makes the control design difficult and complicated; thus according to four leg controlThe structure is manufactured, and the elimination of the coupling is more favorable than the elimination of the fourth branch inductor; generally, the inductance and the capacitance of the LC filter are uniformly selected so as to avoid unbalanced working conditions except for asymmetrical faults on the load side;
therefore, the model is converted from the abc coordinate system to the α β γ coordinate system, and the model of the four-leg inverter in the α β γ coordinate system is represented by equations (4) and (5):
in the formulae (4) and (5), V αG 、V βG 、V γG V expressed for inverter under alpha beta gamma coordinate system O Three-phase voltage values; v αn 、V βn 、V γn The voltage from three phases of the output end of the inverter to a neutral line under an alpha beta gamma coordinate system; i.e. i L ＝[i Lα i Lβ i Lλ ] T Is a filter inductor current; i.e. i Lα 、i Lβ 、i Lγ The inductance current value of the three phases at the output end of the inverter under an alpha beta gamma coordinate system; i.e. i α 、i β 、i γ The three phases of the inverter respectively flow through the current of a neutral point under an alpha beta gamma coordinate system;
according to the formula (4) and the formula (5), different component state equations can be completely decoupled from each other; each component is evaluated independently so as to design the controller quickly and easily; in addition, each component is influenced by external action and cannot interfere with other components; by using the dynamic models of the formula (4) and the formula (5), the four-bridge arm inverter with the fourth bridge arm inductance can be regarded as three independent single-phase inverters, and the advantages of the four-bridge arm inductance are kept;
preferably, in step 1, a circuit model of the virtual oscillator is built as follows:
virtual oscillator control is achieved by filtering the inductor current i at the output of the inverter L As input quantity, based onThe virtual oscillator dynamic equation obtained by the system structure of the pseudo oscillator (as shown in fig. 2) is:
in formulae (6) to (8), L osc Is an inductance in the virtual oscillator circuit; i all right angle Losc To flow through L osc The current value of (a); v c The oscillator is the output voltage before the fusion scale factor, V oc The output quantity, K, of the virtual oscillator output voltage after the voltage scale factor gain is superposed v Is a voltage scaling factor, C, that couples the virtual oscillator input and output quantities to the physical and electrical feedback signals osc For the capacitance in the virtual oscillator circuit, σ = -1/R is the conductance negative value, α is the oscillator design parameter, K i Is a current scale factor, i, that couples the virtual oscillator input and output quantities to the physical and electrical feedback signals L ＝[i Lα i Lβ i Lλ ] T For filtering the inductor current, i is the total current at the output end of the inverter, and the dynamic equation of the oscillator is obtained by the digital controller by utilizing the feedback of the output current of the inverter.
Preferably, in step 1, adjusting internal parameters of the virtual oscillator to output a three-phase balanced power frequency sinusoidal voltage specifically includes:
selection of parameters for each portion of the virtual oscillator is based on specific system performance criteria, such as voltage and frequency regulation, dynamic response, and harmonic suppression; therefore, the primary control target is to adjust the internal parameters of the oscillator to output three-phase balanced power frequency sinusoidal voltage at the virtual oscillator control layer;
the formula (6) is substituted into the formula (8), and a second-order dynamic differential equation of the virtual oscillator is obtained, which is shown in the formula (9):
in the formula (9), the reaction mixture is,
as a combined parameter of the virtual oscillator, g s Is the control unit equivalent conductance;
the oscillator output instantaneous frequency is defined as:
in the formula (10), the compound represented by the formula (10),
Θ * is the phase shift compared to ω t, which is the reference value for the oscillation frequency;
vibration frequency f according to virtual oscillator kinetic equation i Derivation is carried out:
in the formula (11), f * The power frequency is 50HZ, the instantaneous frequency output characteristic of the virtual oscillator is shown in figure 3, the selection of parameters epsilon and sigma of the virtual oscillator has obvious influence on the output frequency, and the frequency is not kept relatively stable near the power frequency any more along with the increase of the epsilon value; conversely, by gradually decreasing ε and σ, the frequency will gradually converge to a constant value, similar to an ideal sine wave; the time-varying frequency characteristic is an inherent component in the output of the virtual oscillator, and the inverter outputs three-phase balanced power frequency sinusoidal voltage by reasonably selecting epsilon and sigma values in the parameter design of the virtual oscillator.
It can be seen from fig. 4 that the closer to perfect circle, the less the harmonic content of the output voltage of the oscillator, the closer to perfect sine wave the output waveform; however, if the values of epsilon and sigma are adjusted to be too small, the load carrying capacity of the circuit is reduced, and the transition time is prolonged, so that the values of epsilon and sigma are not as small as possible, the debugging process needs to be determined according to the actual network operation condition and the control target, and the product of epsilon and sigma is 0.1 in the embodiment.
in conventional virtual oscillator control, the output voltage V c By extracting the filter inductor current i Lα Due to the presence of an unbalanced load, i Lα The components not only including the positive-sequence component i Lα + Also contains a negative sequence component i Lα - (ii) a If the inverter is directly output with the current i Lα Fed back to the virtual oscillator to output voltage V under different unbalanced conditions c Different, therefore, the method of directly extracting components is not suitable for unbalanced working conditions;
the virtual oscillator is used as a reference voltage input quantity of a Sliding Mode Controller (SMC), and when an unbalanced load is required to be connected to a certain phase or any phase is unbalanced, the reference voltages provided by the virtual oscillator are required to be the same; the inductor current i is extracted by using a biquad generalized integrator method (as shown in fig. 5) Lα The positive sequence component and the negative sequence component are filtered and used as the input of the virtual oscillator, so that the virtual oscillator can output the same reference voltage when the unbalanced load is connected to any phase;
in order to compensate for Point of Common Coupling (PCC) voltage imbalance and harmonic distortion, the point of common coupling voltage is calculated and used as the feedback input of a sliding mode controller; however, due to ineffectiveness factors such as geographical position and weather conditions, the line impedance L from the pcc to the inverter output point line The size cannot be accurately calculated, and the theoretical calculation is far from the actual impedance; therefore, by designing the line impedance coefficient λ m Voltage V at point of common coupling pcc After the impedance coefficient is added, the estimation formula of the voltage of the common coupling point is as follows:
in the formula (12), V o Outputting voltage for the four-bridge arm inverter; l is f Is the inductance of the inverter output; l is a radical of an alcohol line Is the line inductance from the inverter output to the point of common coupling; r is a filter resistance; r is line Is the line impedance from the inverter output to the point of common coupling;
step 3, designing a sliding mode controller on the basis of finishing the estimation work of the virtual oscillator and the voltage of the point of common coupling, wherein the sliding mode controller forces the voltage of the point of common coupling to follow the voltage waveform of the approximate sine wave output by the virtual oscillator; the priority exists in the control of the virtual oscillator, and the priority of the virtual oscillator is lower in the voltage distortion control layer; therefore, a sliding mode controller is introduced to support the application of the virtual oscillator in harmonic and unbalanced voltage compensation;
aiming at a plurality of uncertainties in an island micro-grid, two unknown interference terms mu are added on the basis of the formula (6) and the formula (8) i And mu v ：
In formulae (13) and (14), V c-ref Is a reference value of the filter capacitor voltage; i.e. i L-ref Is a reference value for the current at the output of the inverter;
the control variables were constructed as:
slip form surface S V Constructed as the sum of the products of the state variables and the controller parameters, from the state variable x 1 、x 2 Linear representation:
S V ＝Γ 1 x 1 +Γ 2 x 2 (16)
in formula (16), r 1 And r 2 Is a controller control parameter;
in order to obtain a function state variable control law, the expected control target of the sliding mode controller is constructed as follows:
in the formula (17), V eq 、V s Respectively an approaching law component and a discontinuous switching law component of the sliding mode controller; v eq Showing the control relationship between the slip form surface and the output quantity, V S The method has good processing effect on bounded interference in a dynamic system;
the sliding mode surface design in the formula (16) is applied to a controller to derive a control law, and the derivation is carried out on the formula (16):
suppose V eq To stabilize the equilibrium point, V eq For the system to remain on the slip-form surface, the system state variable is started along any initial condition of the slip-form surface, and on this basis the slip-form surface derivative must be equal to zero, and in correspondence with the above differential equation the system state variable will slide along the slip-form surface towards the equilibrium point, V eq I.e. differential equation dS v A solution of/dt = 0; di in formula (13) L Dt and dV in formula (14) oc The substitution of/dt into (18) yields:
in equation (19), N and Q are combined parameters in the sliding mode controller;
μ＝Γ 1 μ i +Γ 2 μ v synthesizing unknown interference item synthesis parameters for the system;
solve to obtain V eq Comprises the following steps:
the method comprises the steps that a discontinuous sign function is contained in a traditional sliding mode control switching law component, when a system reaches a sliding mode surface, the output of a controller generates obvious buffeting, and in order to eliminate the buffeting effect of a sliding mode controller model based on a four-bridge arm inverter, a continuous and smooth hyperbolic tangent function is used as a sliding prevailing constraint condition to inhibit the buffeting problem existing in the traditional sliding mode control design;
sliding mode control based on the hyperbolic tangent function redefines the sliding prevalence conditions: the square value of the positive definite function distance reaching the sliding mode surface is gradually reduced along the system running track, and the running track is converged to the sliding mode surface within a limited time;
in the formula (21), tanh (S) = (e) S -e -S )/(e S +e -S ) Is a hyperbolic tangent function, and eta is a strict real parameter; equation (21) represents a positive constant function tanh to the slip form surface 2 The value of (S) is reduced along all system tracks, the tracks are constrained to point to the direction of the sliding mode surface, and the tracking error e tends to 0;
selecting a switching law component according to the sliding mode constraint condition in the formula (21) as follows:
V s ＝ηtanh(ξS v ) (22)
in the formula (22), ξ is a positive real parameter large enough to satisfy the formula (21);
because of a plurality of uncertainties in the system, accurate modeling is difficult to perform, and the modeling is often given in a generalized form; the invention selects a random estimation self-adaptive control law as a sliding mode surface integral function:
in the formula (23), the compound represented by the formula,
is an uncertainty mu modeling estimation value in the system;
according to the formulas (20) to (23), the complete control law of the sliding mode controller after the switching law is integrated as follows:
selecting the switching law according to the formula (21), wherein the simulation result of the tracking signal of the sliding mode controller after adding the constraint instruction is shown in fig. 7, and the output buffeting suppression effect is obvious;
analyzing the stability of the sliding mode controller by using a Lyapunov stability criterion; under the condition of not considering the load, the four-leg inverter is restricted by an equation (13) and an equation (14); the lyapunov function is constructed as follows:
obtained by the formula (21):
the derivation conclusion can lead the derivation of the Lyapunov function to be negative and half definite, which proves that the proposed sliding mode control is asymptotically stable.
Example 1
In the invention, a sliding mode controller with robust characteristics to parameter disturbance is utilized to track the reference voltage of the virtual oscillator, and the voltage estimation value of the point of common coupling is integrated, so that harmonic distortion and imbalance of the point of common coupling caused by imbalance and nonlinear load access are optimized. In order to test the control effect, the invention selects three control algorithms and two load connection working conditions under actual operation to test.
The simulation model is established as shown in fig. 8, two DG systems connected by an inverter are arranged on an ac bus, and a three-phase balanced load, a three-phase unbalanced load, a single-phase load and a nonlinear load are connected to the ac bus, and the main simulation parameters are shown in table 1.
TABLE 1
In two working conditions designed by the invention, a system operates under the traditional droop control with voltage and power as control targets before 0.16s, and the system is accessed to a corresponding voltage quality control strategy after 0.16 s.
The working condition I is as follows: three-phase unbalanced loads having different power factors are connected to each phase. Fig. 9 shows the voltage waveform of the pcc under the conventional droop control strategy operation mode, the phenomena of spikes and jumps of the three-phase voltage output waveform are not obviously observed, but the three-phase amplitude and the phase have significant deviations, and the negative sequence voltage VUF% and the zero sequence voltage VUF% are respectively 7.85% and 3.25%.
According to the simulation result of fig. 10, after 0.16s is enabled based on the control of the virtual impedance, the negative sequence voltage VUF% and the zero sequence voltage VUF% are respectively 1.45% and 1.22%, and the amplitude and the phase deviation of the voltage waveform of the point of common coupling are obviously reduced compared with the traditional droop control.
Fig. 11 shows that after 0.16s, the pcc voltage waveform is significantly improved based on the virtual oscillator control grid connection. The pcc voltage zero and the negative sequence component VUF% were 0.92% and 0.65%, respectively, after incorporation of the proposed control strategy. Compared with a virtual impedance control simulation result, the three-phase voltage waveform symmetry is better, and the voltage waveform of a point of common coupling is improved. In the unbalanced condition of the load side, the condition that a single-phase load is accessed under the operation of the system is a serious unbalanced load condition.
As shown in fig. 12, in the present experiment, a single-phase load was connected to the C-phase, the C-phase current and the neutral point current were equal in value, and the a-phase and B-phase currents were approximately 0.
In fig. 13, when the operation is performed under the conventional droop control before 0.16s, the percentage of the negative sequence VUF% and the percentage of the zero sequence VUF% of the pcc voltage are 10.96% and 5.63%, respectively. After 0.16s, the control strategy designed by the invention is incorporated into a system, the voltage of the point of common coupling is close to a sine wave, and the voltage of the point of common coupling, namely the negative-sequence component VUF% and the zero-sequence component VUF% are reduced from 4.87% and 2.62% to 1.35% through calculation, so that the control strategy designed by the invention can still effectively improve the output voltage waveform under the unbalanced limit working condition.
Working conditions are as follows: nonlinear loads generally act as harmonic current sources in a microgrid, and the quality of output power can be seriously degraded if not controlled. Fig. 14 simulation results show that after a nonlinear load is connected under the traditional droop control, the voltage waveform of the point of common coupling is distorted, and the total harmonic distortion degrees of the three-phase voltage of the point of common coupling are respectively 16.59%, 13.37% and 12.65%.
As shown in fig. 15, after applying the virtual impedance-based design enable grid-connection for 0.16s, the distortion waveform is improved compared to the conventional droop control operation. The pcc voltages THD% are 4.53%, 3.98%, 3.85%, respectively.
According to the simulation result of fig. 16, after 0.16s, the designed virtual oscillator control is applied to enable grid connection, and the THD% of the phases a, B and C of the common coupling point is calculated to be reduced from 16.59%, 13.37% and 12.65% to 3.82%, 2.79% and 2.25%. Even under severe unbalanced load and harmonic current pollution, the proposed control strategy can still adjust the voltage of the pcc to follow the balanced sinusoidal voltage output from the virtual oscillator, but compared with the control effect based on the virtual impedance design, the control effect is more symmetrical and smoother, and the quality of the voltage output waveform is significantly improved.
The invention is applicable to the prior art where nothing is said.
Claims (3)
1. A voltage quality optimization method based on virtual oscillator control is characterized by comprising the following steps:
step 1, establishing a mathematical model of a four-bridge arm inverter; meanwhile, a circuit model of the virtual oscillator is built, and then internal parameters of the virtual oscillator are adjusted to output three-phase balanced power frequency sinusoidal voltage;
the circuit model for building the virtual oscillator is specifically as follows:
virtual oscillator control is by filtering the inductor current i at the output of the inverter L As an input quantity, a virtual oscillator dynamic equation obtained according to a system structure of the virtual oscillator is as follows:
in formulae (6) to (8), L osc Is an inductance in the virtual oscillator circuit; i.e. i Losc To flow through L osc The current value of (a); v c The oscillator is the output voltage before the fusion scale factor, V oc Outputting voltage for virtual oscillatorOutput, K, after superimposing a gain of a voltage scaling factor v Is a voltage scaling factor, C, that couples the virtual oscillator input and output quantities to the physical and electrical feedback signals osc For the capacitance in the virtual oscillator circuit, sigma = -1/R is the conductance negative value, R is the filter resistance, alpha is the oscillator design parameter, K i Is a current scale factor, i, that couples the virtual oscillator input and output quantities to the physical and electrical feedback signals L ＝[i Lα i Lβ i Lλ ] T The filter inductance current is the filter inductance current, i is the total current of the output end of the inverter, and the dynamic equation of the oscillator is obtained by the digital controller by utilizing the feedback of the output current of the inverter;
step 2, extracting a positive sequence component and estimating a voltage of a common coupling point;
the virtual oscillator is used as the reference voltage input quantity of the sliding mode controller, and when the unbalanced load is required to be connected to a certain phase or any phase is unbalanced, the reference voltages provided by the virtual oscillator are required to be the same; extraction of inductor current i by using bi-quad generalized integrator method Lα The positive sequence component and the negative sequence component are filtered and used as the input of the virtual oscillator, so that the virtual oscillator can output the same reference voltage when the unbalanced load is connected to any phase;
in order to compensate for voltage unbalance and harmonic distortion of the point of common coupling, the voltage of the point of common coupling is calculated and used as the feedback input of a sliding mode controller; by designing the line impedance coefficient lambda m Voltage V of common coupling point is carried out pcc The estimation formula of the voltage of the point of common coupling after the impedance coefficient is added is as follows:
in the formula (12), V o Outputting voltage for the four-bridge arm inverter; l is f Is the inductance of the inverter output; l is line Is the line inductance from the inverter output to the point of common coupling; r is a filter resistance; r line Is the line impedance from the inverter output to the point of common coupling;
step 3, designing a sliding mode controller on the basis of finishing the estimation work of the virtual oscillator and the voltage of the point of common coupling, wherein the sliding mode controller forces the voltage of the point of common coupling to follow the voltage waveform of the approximate sine wave output by the virtual oscillator; the priority level exists in the control of the virtual oscillator, and the priority level of the virtual oscillator is lower in the voltage distortion control layer; therefore, a sliding mode controller is introduced to support the application of the virtual oscillator in harmonic and unbalanced voltage compensation;
aiming at a plurality of uncertainties in an island micro-grid, two unknown interference terms mu are added on the basis of the formula (6) and the formula (8) i And mu v ：
In formulae (13) and (14), V c-ref Is a reference value of the filter capacitor voltage; i all right angle L-ref Is a reference value for the current at the output of the inverter;
the control variables were constructed as:
slip form surface S V Constructed as the sum of the products of the state variables and the controller parameters, from the state variable x 1 、x 2 Linear representation:
S V ＝Γ 1 x 1 +Γ 2 x 2 (16)
in formula (16), r 1 And r 2 Is a controller control parameter and is a positive real number;
in order to obtain a function state variable control law, an expected control target of the sliding mode controller is constructed as follows:
in the formula (17), V eq 、V s Respectively an approaching law component and a discontinuous switching law component of the sliding mode controller; v eq Representing the control relationship between the slip form surface and the output quantity, V S The method has good processing effect on bounded interference in a dynamic system;
the sliding mode surface design in the formula (16) is applied to a controller to derive a control law, and the derivation is carried out on the formula (16):
suppose V eq To stabilize the equilibrium point, V eq For the system to remain on the slip-form surface, the system state variable starts along any initial condition of the slip-form surface, and on this basis the slip-form surface derivative must be equal to zero, and corresponding to equation (18), the system state variable will slide along the slip-form surface towards the equilibrium point, V eq I.e. differential equation dS v Solution of/dt = 0; di in formula (13) L Dt and dV in formula (14) oc The substitution of/dt into (18) yields:
in equation (19), N and Q are combined parameters in the sliding mode controller;
μ＝Γ 1 μ i +Γ 2 μ v synthesizing unknown interference item synthesis parameters for the system;
solve to obtain V eq Comprises the following steps:
the method comprises the steps that a discontinuous sign function is contained in a traditional sliding mode control switching law component, when a system reaches a sliding mode surface, the output of a controller generates obvious buffeting, and in order to eliminate the buffeting effect of a sliding mode controller model based on a four-bridge arm inverter, a continuous and smooth hyperbolic tangent function is used as a sliding prevailing constraint condition to inhibit the buffeting problem existing in the traditional sliding mode control design;
the sliding mode control based on the hyperbolic tangent function redefines the sliding prevalence conditions: the square value of the distance of the positive definite function reaching the sliding mode surface is gradually reduced along the running track of the system, and the running track is converged to the sliding mode surface within limited time;
in formula (21), tanh (S) = (e) S -e -S )/(e S +e -S ) Is a hyperbolic tangent function, and eta is a strict positive parameter; equation (21) represents a positive constant function tanh to the slip form surface 2 The value of (S) is reduced along all system tracks, the tracks are constrained to point to the direction of the sliding mode surface, and the tracking error e tends to 0;
selecting a switching law component according to the sliding mode constraint condition in the formula (21) as follows:
V s ＝ηtanh(ξS v ) (22)
in the formula (22), ξ is a positive real parameter large enough to satisfy the formula (21);
selecting a random estimation self-adaptive control law as a sliding mode surface integral function:
in the formula (23), the compound represented by the formula,
is an uncertainty mu modeling estimation value in the system; gamma-shaped 3 Is a controller control parameter and is a positive real number;
and (3) integrating the switching law according to the formulas (20) to (23) to obtain the complete control law of the sliding mode controller:
analyzing the stability of the sliding mode controller by using a Lyapunov stability criterion; under the condition of not considering the load, the four-bridge arm inverter is restricted by an equation (13) and an equation (14); the lyapunov function is constructed as follows:
derived from formula (21):
the derivation conclusion can be drawn that the derivation of the Lyapunov function is negative and half fixed, and the proposed sliding mode control is proved to be asymptotically stable.
2. The virtual oscillator control-based voltage quality optimization method according to claim 1, wherein in step 1, a mathematical model of the four-leg inverter is established as follows:
output voltage V of four-bridge arm inverter o And the inductor current i L The relationship between them is:
in the formula (1), V AG 、V BG 、V CG For the inverter output voltage V O The three-phase voltage of (1); l is a radical of an alcohol f Is the inductance of the inverter output; i.e. i La 、i Lb 、i Lc The inductance current value of three phases at the output end of the inverter; r is the resistance of the output end of the inverter; van, vbn, vcn are the voltages from the three phases of the inverter output to the neutral; l is n Is the inductance on the neutral line; i.e. i n Is the current flowing through the neutral line;
will i n ＝i La +i Lb +i Lc Substituting formula (1) to obtain:
so far, the modeling of the four-bridge arm inverter under the abc coordinate system is completed; applying kirchhoff current law to nodes a, b and c; under kirchhoff's current law, the load capacitance voltages are equal, resulting in equation (3):
in the formula (3), C a 、C b 、C c Three-phase capacitance values of the output end of the inverter are respectively; i all right angle a 、i b 、i c Respectively flowing through the output end capacitor C of the inverter a 、C b 、C c The current of (a);
equations (2) and (3) are four-leg inverter models with a fourth leg established in the abc coordinate system; in a four-bridge-arm inverter model with a fourth bridge arm established in an abc coordinate system, coupling exists among four-bridge-arm inverters a, b and c;
therefore, the model is converted from the abc coordinate system to the α β γ coordinate system, and the model of the four-leg inverter in the α β γ coordinate system is shown in equations (4) and (5):
in the formulae (4) and (5), V αG 、V βG 、V γG V expressed by an alpha, beta and gamma coordinate system for an inverter O Three-phase voltage values; v αn 、V βn 、V γn The voltage from three phases of the output end of the inverter to a neutral line under an alpha beta gamma coordinate system; i.e. i Lα 、i Lβ 、i Lγ The inductance current value of the three phases at the output end of the inverter under an alpha beta gamma coordinate system; i.e. i α 、i β 、i γ The three phases of the inverter respectively flow through the current of a neutral point under an alpha beta gamma coordinate system;
by using the dynamic models of the formula (4) and the formula (5), the four-bridge arm inverter with the fourth-bridge arm inductor can be regarded as three independent single-phase inverters, and the advantages of the four-bridge arm inductor are kept.
3. The virtual oscillator control-based voltage quality optimization method according to claim 1, wherein in step 1, adjusting internal parameters of the virtual oscillator to output three-phase balanced power frequency sinusoidal voltage specifically comprises:
the formula (6) is substituted into the formula (8), and a second-order dynamic differential equation of the virtual oscillator is obtained as shown in the formula (9):
in the formula (9), the reaction mixture is,
as a combined parameter of the virtual oscillator, g s For equivalent electricity of the control unitLeading;
the oscillator output instantaneous frequency is defined as:
in the formula (10), the compound represented by the formula (10),
Θ * is the phase shift compared to ω t, which is the reference value for the oscillation frequency;
vibration frequency f according to virtual oscillator kinetic equation i Derivation is carried out:
in the formula (11), f * The power frequency is adopted, the selection of parameters epsilon and sigma of the virtual oscillator has obvious influence on the output frequency, and the frequency is not kept relatively stable near the power frequency any more along with the increase of epsilon value; conversely, by gradually decreasing ε and σ, the frequency will gradually converge to a constant value, similar to an ideal sine wave; the time-varying frequency characteristic is an inherent component in the output of the virtual oscillator, and the inverter outputs three-phase balanced power frequency sinusoidal voltage by reasonably selecting epsilon and sigma values in the parameter design of the virtual oscillator.
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