Three-phase four-wire cascaded STATCOM voltage support control method considering power constraints

Abstract

The present invention discloses an optimized voltage support control method for a four-wire cascaded STATCOM considering active power constraints. Step 1: Calculate the positive, negative, and zero-sequence voltage amplitudes, initial phase angles, and voltage unbalance degree of the PCC point fault in the three-phase four-wire cascaded multilevel energy storage system. Separate the positive, negative, and zero-sequence components of the three-phase current output by the system to obtain the voltage amplitude expressions of the positive, negative, and zero-sequences. Step 2: Based on the derivation of voltage support under active power constraints and current limiting, obtain the amplitude and phase of the optimal reactive component current injected into the power grid. Step 3: Obtain the active component of the reference current to be injected through closed-loop control of the DC capacitor voltage. Generate the switching tube signals of the inverter through the current control loop and the PS-SPWM modulation technique to implement the voltage support control method. After applying the voltage support method proposed by the present invention, the reduction effect of the unbalance degree at the PCC point is significant, and at the same time, the power balance of the cascaded STATCOM is achieved.

Description

Technical Field

[0001] The present invention relates to a voltage support control method, in particular to a calculation method for the optimal voltage support point of a three-phase four-wire cascaded STATCOM considering power constraints, belonging to the technical field of energy storage inverter control. Background Art

[0002] Grid voltage sag is one of the most common faults in power systems, usually caused by short circuits due to accidental contacts at the far end, lightning strikes, and equipment failures. To ensure the reliable power supply operation ability of an independent microgrid during short-term recoverable faults, it is of great significance to study the fault ride-through control of the independent microgrid. The low voltage ride-through ability is an important indicator to measure the stability of modern power systems. Modern circuit systems require equipment to have a certain ability to cope with grid voltage dips in practical applications, and higher requirements for voltage support in low voltage ride-through will be put forward in the next generation of grid connection criteria. Also, due to the existence of the zero-sequence current channel in the three-phase four-wire system, the zero-sequence current at the PCC point is also controllable, enabling the use of zero-sequence components in the voltage support control strategy based on the three-phase four-wire system to optimize the voltage support effect.

[0003] At present, the inter-phase balance control of cascaded multi-level systems is mainly divided into the zero-sequence voltage method and the negative-sequence current method. The literature "Investigation of Negative-Sequence InjectionCapability of Cascaded H-Bridge Converters in Star and Delta Configuration" with a publication date of April 14, 2016 analyzed the relationship between zero-sequence voltage and active power in the abc coordinate system, and achieved inter-phase average active power control, DC voltage control, and reference current tracking control under unbalanced power grids by injecting appropriate phase voltages. The literature "Clustered Voltage Balancing Mechanism and Its ControlStrategy for Star-Connected Cascaded H-Bridge STATCOM" with a publication date of April 14, 2017 controls the negative-sequence modulation index based on unbalanced power information without using any controllers, which results in a steady-state error in the in-phase DC voltage. In addition, estimating the negative-sequence current component according to the positive-sequence transformation and directly adding the feed-forward voltage of each phase to the obtained modulation index will result in a poor dynamic response. When the voltage unbalance degree is small, the zero-sequence voltage injection method can effectively achieve inter-phase power balance and ensure the safe operation of the equipment. However, when the voltage unbalance degree is large, the zero-sequence voltage injection method fails. At this time, negative-sequence current injection needs to be adopted as a voltage ride-through strategy. However, whether it is negative-sequence current or zero-sequence voltage, when dealing with the power balance of a three-phase four-wire cascaded multi-level system under an unbalanced power grid, it will have an adverse impact on the power grid unbalance degree of the system. Therefore, the power balance problem of three-phase four-wire cascaded multi-level systems needs further research.

[0004] Regarding the research on low-voltage ride-through, the literature "Flexible Positive and Negative Sequence Current Control Method and Equivalent Sequence Network Model of Inverter-Type Distributed Generation" with a publication date of July 16, 2018, proposed a positive and negative sequence independent control strategy, injecting positive and negative sequence reactive currents into the power grid during asymmetric faults in the power grid. However, the problem of excessive current during the fault ride-through process was not considered in terms of current limiting. The control strategy mentioned in the literature "Control Strategy for Distribution Generation Inverters to Maximize the Voltage Support in the Lowest Phase During Voltage Sags" with a publication date of August, 2017 aimed to maximize the voltage of the lowest phase. However, only positive sequence current was injected in this strategy, the injection of negative sequence current was ignored, no measures were taken for negative sequence voltage, and no goal of reducing the unbalance degree at the PCC point was proposed. The literature "An Advanced Voltage Support Scheme Considering the Impact of Zero-Sequence Voltage under Microgrid Faults Using Model Predictive Control" with a publication date of February 13, 2020, proposed two control strategies for three-phase four-wire grid-connected inverters: one was to use positive and negative sequence grid currents to compensate for zero-sequence voltage, and the other was to use zero-sequence current to compensate for zero-sequence voltage. By introducing parameters "k" and "k1" to determine whether zero-sequence current is required for the voltage at the PCC point (point-to-point connection point) to remain within the limit value.

[0005] In summary, although there have been many studies on voltage support, most of the existing technologies are discussed for traditional three-phase two-level inverters. In the control objectives they achieve, the problem of active power balance is not considered, so they cannot be directly applied to cascaded systems. At the same time, in a three-phase four-wire cascaded STATCOM, due to the existence of the zero-sequence channel, the injection of zero-sequence voltage and negative-sequence current will both exacerbate the grid unbalance degree, which is not conducive to the low-voltage ride-through of the system. At the same time, most of the existing technologies are discussed for traditional three-phase three-wire systems, so they cannot be directly applied to three-phase four-wire cascaded STATCOM. Summary of the Invention

[0006] In order to solve the deficiencies of the above technologies, the present invention provides a voltage support control method for a three-phase four-wire cascaded STATCOM considering power constraints.

[0007] To solve the above technical problems, the technical solution adopted by the present invention is: a three-phase four-wire cascaded STATCOM voltage support control method considering power constraints, comprising the following steps:

[0008] Step 1, calculate the following parameters in the three-phase four-wire cascaded multilevel energy storage system: the positive-sequence, negative-sequence, and zero-sequence voltage amplitudes, the initial phase angle, and the voltage unbalance degree of the PCC point fault;

[0009] Separate the three-phase current output by the multilevel system into positive-sequence, negative-sequence, and zero-sequence components to obtain the positive-sequence, negative-sequence, and zero-sequence current expressions;

[0010] Step 2, based on the derivation of voltage support under active power constraint and current limit, obtain the amplitude and phase of the optimal reactive component current injected into the power grid;

[0011] Step 3, obtain the active component of the required injected reference current through the closed-loop control of the DC capacitor voltage; finally, generate the switching tube signals of the inverter through the current control loop and the PS-SPWM modulation technology to implement the proposed voltage support control method.

[0012] Preferably, in Step 1, decompose the three-phase PCC voltage. After the Clarke transformation, the components v α , v β of the three-phase PCC voltage on the αβ0 axis are expressed as:

[0013]

[0014] Among them, v + α , v + β , v - α , v - ? β are the positive-sequence and negative-sequence components of v α , v β respectively; V + is the positive-sequence voltage amplitude, V - is the negative-sequence voltage amplitude, and V 0 is the zero-sequence voltage amplitude; is the initial phase of the positive-sequence voltage, is the initial phase of the negative-sequence voltage, is the initial phase of the zero-sequence voltage; ω is the fundamental angular frequency of the power grid; ωt represents the electrical angle at which the current changes with time t;

[0015] According to the expression in the stationary coordinate system, derive the expressions for the positive-sequence and negative-sequence voltage amplitudes and the positive-sequence and negative-sequence voltage phase differences as:

[0016]

[0017] Among them, atan2 is the arctangent function, is the initial phase of the voltage at the PCC.

[0018] Preferably, in step one, under the condition of grid voltage sag, the three-phase current expression output by the multilevel system is separated into positive sequence, negative sequence, and zero sequence through Clarke transformation:

[0019]

[0020] where, i α , i β , i0 are the components of the three-phase current on the α, β, and 0 axes respectively; i α + , i α - , i β + , i β - are respectively the positive sequence component and negative sequence component of i α , i β ; I + , I - , I 0 are respectively the current amplitude values of positive sequence, negative sequence, and zero sequence; φ + , φ - , φ 0 are respectively the initial phases of the grid current of positive sequence, negative sequence, and zero sequence, then there are:

[0021]

[0022] where, I p + , I p - , I p 0 are respectively the amplitudes of the active components of the positive sequence, negative sequence, and zero sequence currents; I q + , I q - , I q 0 are respectively the amplitudes of the reactive components of the positive sequence, negative sequence, and zero sequence currents; δ + , δ - , δ 0 are respectively the impedance angles of the positive sequence, negative sequence, and zero sequence currents.

[0023] Preferably, in step one, the injected current vector is decomposed into the sum of four vectors, that is, the active components and reactive components of positive sequence and negative sequence, to obtain I p + , I p- , I p 0 , I q + , I q - , I q 0 :

[0024]

[0025] Among them, R g and L g is the grid side impedance, write the instantaneous current i of each phase a ,i b ,i c , current amplitude I a ,

[0026] I b , I c and the positive and negative zero sequence current amplitude I + , I - , I 0 The relationship is:

[0027]

[0028] Preferably, in step 2, the three-phase currents in the three-phase four-wire cascade multi-level energy storage system are listed:

[0029]

[0030] in, is the initial phase of the A-phase grid voltage, is the initial phase of the B-phase grid voltage, is the initial phase of the C-phase grid voltage; θ A ,θ B ,θ C is the phase difference between the grid voltage and grid current of each phase; i n , v n are the neutral current and neutral voltage respectively; the grid side impedance Z, the impedance angle θ L Respectively expressed as:

[0031]

[0032] Use R to replace the grid side resistor R g , use l to replace the grid-side inductor L g , that is,

[0033]

[0034] The zero-sequence current under unbalanced power grid can be expressed as:

[0035]

[0036] Preferably, in step two, in order to suppress the power flow between phases, offset the unbalanced power flow caused by grid faults while ensuring that the active power output of each phase is zero, the active power of the three phases is analyzed, and we have:

[0037]

[0038] Meanwhile, let θ A = θ B = θ C = θ, we can get:

[0039]

[0040] where V ga 、V gb 、V gc are the amplitudes of the three-phase grid voltages respectively;

[0041] After simplification, the amplitudes of the three-phase currents I a ,I b ,I c can be expressed as:

[0042]

[0043] Preferably, in step two, when the amplitudes of the three-phase currents of the three-phase four-wire cascaded STATCOM satisfy the expression in (16), the active power constraint condition is achieved;

[0044] At this time, the three-phase currents I a ,I b ,I c are all only related to the single variable θ, and each component is represented by θ. In order to mathematically model this system, the voltage support problem of the model is equivalent to:

[0045]

[0046] s.t. can be expressed as the conditions that need to be satisfied to make this inequality hold under this condition, where I max is the magnitude of the maximum current amplitude allowed to pass through after the three-phase current is limited.

[0047] Preferably, in step two, based on (19), since:

[0048]

[0049] After simplification, we get:

[0050]

[0051] Among them, V ga , V gb , V gc are respectively the amplitudes of the three-phase grid voltages. Similarly, the expressions for the positive, negative, and zero-sequence current amplitudes can be obtained:

[0052]

[0053] It can be deduced that the positive, negative, and zero-sequence voltage amplitudes can be respectively expressed as:

[0054]

[0055] T A0 , T A1 , T A2 , T B0 , T B1 , T B2 , T c0 , T c1 , T c2 are respectively process quantities, having no actual physical meaning, only facilitating calculations.

[0056] Preferably, in step two, for f(θ) in equation (19), it is a function with a period of 2π, and the change of the function value is analyzed in the interval [0, 2π] to determine that the minimum value of the function is always obtained at π / 2 + θ L and 3π / 2 + θ L ;

[0057] If the current limiting condition is satisfied when θ = 3π / 2 + θ L , the optimal value is taken as 3π / 2 + θ L ;

[0058] When θ = 3π / 2 + θ L does not satisfy the current limiting condition, since the amplitude of each phase current increases monotonically with θ in the interval [3π / 2, 3π / 2 + θ L , there must be θ = θ L in [3π / 2, 3π / 2 + θ x such that the maximum amplitude of each phase current is I max , and at this time the grid unbalance degree is the smallest at this point, that is:

[0059] max{I a , I b , I c} = I max (26)

[0060] Simplify equation (18), let:

[0061]

[0062] Then at this time:

[0063]

[0064] After determining the value of θ when determining the optimal support, the injection currents \(i_{a}\), \(i_{b}\), \(i_{c}\) of each phase can be determined from (27); a , \(i_{b}\) b , \(i_{c}\) c At the same time, due to the condition of active power constraint, the \(i_{a}\), \(i_{b}\), \(i_{c}\) obtained at this time will only generate reactive power with the voltage \(v_{PCC}\) at the PCC point. Therefore, the \(i_{a}\), \(i_{b}\), \(i_{c}\) obtained at this time are the reactive currents \(i_{qa}\), \(i_{qb}\), \(i_{qc}\) required to inject for voltage support at the PCC point. a , \(i_{b}\) b , \(i_{c}\) c At the PCC point, and will not pcc generate active power. Therefore, the \(i_{a}\), \(i_{b}\), \(i_{c}\) obtained at this time are the reactive currents \(i_{qa}\), \(i_{qb}\), \(i_{qc}\) required to inject for voltage support at the PCC point. a , \(i_{b}\) b , \(i_{c}\) c That is, the reactive current \(i_{qa}\), \(i_{qb}\), \(i_{qc}\) required to inject for voltage support at the PCC point. a q , \(i_{b}\) b q , \(i_{c}\) c q .

[0065] Preferably, in step three, in order to balance the switching loss and the capacitor voltage drop caused by restoring the unbalanced power grid, an active current \(i_{pa}\), \(i_{pb}\), \(i_{pc}\) perpendicular to the phase of \(i_{a}\), \(i_{b}\), \(i_{c}\) needs to be injected into each phase, which is implemented by adding a DC capacitor voltage loop. a q , \(i_{b}\) b q , \(i_{c}\) c q )]]That is, the active current \(i_{pa}\), \(i_{pb}\), \(i_{pc}\). a p , \(i_{b}\) b p , \(i_{c}\) c p .

[0066] The present invention discloses a three-phase four-wire cascaded STATCOM voltage support control method considering power constraints. According to the characteristic that the STATCOM cannot provide active power, by introducing the zero-sequence component in the three-phase four-wire system as a new controllable degree of freedom of the system, the active power constraint and voltage support are effectively balanced. And under the conditions of current limiting and active power constraint, a reasonable three-phase four-wire cascaded STATCOM voltage support control method is designed to improve the low-voltage ride-through ability of the system. After applying the voltage support method proposed by the present invention, the unbalance degree at the PCC point is significantly reduced, and at the same time, the power balance of the cascaded STATCOM is achieved. Brief Description of the Drawings

[0067] Figure 1 is the function of the grid unbalance degree in the interval [0, 2π] of the present invention;

[0068] Figure 2 is the function of the grid unbalance degree in the interval [3π / 2, 5π / 2] in the implementation of the present invention;

[0069] Figure 3 is the typical topological structure diagram of the three-phase four-wire cascaded STATCOM in the implementation of the present invention;

[0070] Figure 4 is the block diagram of the closed-loop control of the DC capacitor voltage in the implementation of the present invention;

[0071] Figure 5 is the block diagram of the voltage support control of the three-phase four-wire cascaded STATCOM in the embodiment of the present invention;

[0072] Figure 6 is the experimental diagram of the grid current in the embodiment of the present invention;

[0073] Figure 7 is the experimental diagram of the neutral line current in the embodiment of the present invention.

[0074] Figure 8 is the experimental diagram of the PCC voltage in the embodiment of the present invention.

[0075] Figure 9 is the experimental diagram of the capacitor voltage in the embodiment of the present invention.

[0076] Figure 10 is the experimental diagram of the active power at the PCC point in the embodiment of the present invention. Specific implementation manner

[0077] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0078] Aiming at the problem that the active power constraint and voltage support are contradictory in some cases in the three-phase four-wire cascaded STATCOM, the present invention proposes a voltage support control method for the three-phase four-wire cascaded STATCOM considering power constraints, specifically an optimized voltage support control method. According to the characteristic that the STATCOM cannot provide active power, by introducing the zero-sequence component in the three-phase four-wire system as a new controllable degree of freedom of the system, the active power constraint and voltage support are effectively balanced. And under the conditions of current limiting and active power constraint, a reasonable design of the voltage support control method for the three-phase four-wire cascaded STATCOM is carried out to improve the low-voltage ride-through ability of the system. It has important significance for the research on the voltage support strategy considering power balance in the three-phase four-wire cascaded multi-level energy storage system.

[0079] The calculation method of the optimal voltage support reference current of the three-phase four-wire cascaded STATCOM in the embodiment of the present invention includes the following content:

[0080] Step 1: Calculate the following parameters in the three-phase four-wire cascaded multilevel energy storage system: the positive-sequence, negative-sequence, and zero-sequence voltage amplitudes, the initial phase angles, and the voltage unbalance degree at the PCC point. Separate the three-phase current output by the system into positive-sequence, negative-sequence, and zero-sequence components to obtain the positive-sequence, negative-sequence, and zero-sequence current expressions;

[0081] The topological structure of the three-phase four-wire cascaded STATCOM is as Figure 3 shown. This system adopts a star connection method. Each of the three phases is composed of H-bridge inverters in the box connected in series. C is the DC-side capacitor. Through the LC filter (L, C f ), filter out the harmonics, and use the method of active damping to effectively increase the system damping and improve the stability of the system operation. R g and L g are the grid-side impedances. i gx (x = a, b, c) is the grid-side current; i x (x = a, b, c) is the cascaded H-bridge side current; i n is the current flowing through the neutral line; V gx (x = a, b, c) is the grid voltage.

[0082] Decompose the three-phase PCC voltage. After the Clarke transformation, the components of the PCC phase voltage on the αβ0 axis, v α , v β , v0 are expressed as:

[0083]

[0084] where v + α , v + β , v - α , v - β are the positive-sequence component and negative-sequence component of v α , v β respectively; V + is the positive-sequence voltage amplitude, V - is the negative-sequence voltage amplitude, V 0 is the zero-sequence voltage amplitude; is the initial phase of the positive-sequence voltage, is the initial phase of the negative-sequence voltage, is the initial phase of the zero-sequence voltage; ω is the grid fundamental angular frequency; ωt represents the electrical angle at which the current changes with time t.

[0085] According to the expressions in the stationary coordinate system, derive the expressions for the positive-sequence and negative-sequence voltage amplitudes and the positive-sequence and negative-sequence voltage phase differences as:

[0086]

[0087] where atan2 is the arctangent function, is the initial phase of the voltage at the PCC.

[0088] During a power grid dip, the three-phase current expression output by the system is separated into positive, negative, and zero sequences through Clarke transformation:

[0089]

[0090] where i α , i β , and i0 are the components of the three-phase current on the α, β, and 0 axes respectively; i α + , i α - , i β + , i β - are the positive-sequence and negative-sequence components of i α , i β respectively; I + , I - , I 0 are the current amplitude values of the positive sequence, negative sequence, and zero sequence respectively; φ + , φ - , φ 0 are the initial phases of the grid currents of the positive sequence, negative sequence, and zero sequence respectively, then there are:

[0091]

[0092] where I p + , I p - , I p 0 are the amplitudes of the active components of the currents of the positive sequence, negative sequence, and zero sequence respectively, I q + , I q - , I q 0 are the amplitudes of the reactive components of the currents of the positive sequence, negative sequence, and zero sequence respectively; δ + , δ - , δ 0 are the impedance angles of the positive sequence, negative sequence, and zero sequence currents respectively.

[0093] Decompose the injected current vector i into the sum of four vectors, namely the active and reactive powers of the positive and negative sequences, to obtain I p + , I p - , I p0 , I q + , I q - , I q 0 :

[0094]

[0095] Among them, R g and L g are the grid-side impedances. Write down the instantaneous currents of each phase, i a , i b , i c , the current amplitude I a ,

[0096] I b , I c The relationship between the positive, negative, and zero-sequence current amplitudes I + , I-, I 0 is as follows:

[0097]

[0098] Step 2:

[0099] Based on the derivation of voltage support under active power constraint and current limit, obtain the amplitude and phase of the optimal reactive component current injected into the power grid;

[0100] First, write down the three-phase currents of the three-phase four-wire cascaded STATCOM system:

[0101]

[0102] Among them, is the initial phase of the grid voltage of phase A, is the initial phase of the grid voltage of phase B, is the initial phase of the grid voltage of phase C; θ A , θ B , θ C is the phase difference between the grid voltage and the grid current of each phase; i n , v n are the neutral line current and the neutral line voltage respectively;

[0103] The grid-side impedance Z and the impedance angle θ L are respectively expressed as:

[0104]

[0105] For the convenience of writing formulas below, hereinafter, R is uniformly used to replace the grid-side resistance R g , and l is used to replace the grid-side inductance L g , that is, let:

[0106]

[0107] The zero-sequence current under an unbalanced power grid can be expressed as:

[0108]

[0109] To suppress the power flow between phases, offset the unbalanced power flow caused by grid faults, and ensure that the active power output of each phase is zero, the active power of the three phases is analyzed as follows:

[0110]

[0111] At the same time, let θ A = θ B = θ C = θ, and we can get:

[0112]

[0113] Among them, V ga , V gb , V gc are the amplitudes of the three-phase grid voltages respectively. After simplification, the amplitudes of the three-phase currents I a , I b , I c can be expressed as:

[0114]

[0115] It can be seen that when the amplitudes of the three-phase currents of the three-phase four-wire cascaded STATCOM satisfy the expression in (16), the active power constraint condition is achieved at this time. At this time, the amplitudes of the three-phase currents I a , I b , I c are all only related to the single variable θ. Therefore, each component of this model can also be represented by θ, so a mathematical model is established for this system. Therefore, the voltage support problem of this model can be equivalent to:

[0116]

[0117] s.t. can be expressed as the conditions that need to be satisfied to make this inequality hold under this condition, where I max is the magnitude of the maximum current amplitude allowed to pass through after the three-phase current is limited.

[0118] And since:

[0119]

[0120] After simplification, we can get:

[0121]

[0122] Among them, V ga , V gb , V gc are respectively the amplitudes of the three-phase grid voltages. Similarly, the expressions for the amplitudes of the positive, negative, and zero-sequence currents can be obtained:

[0123]

[0124] It can be deduced that the amplitudes of the positive, negative, and zero-sequence voltages can be respectively expressed as:

[0125]

[0126] T A0 , T A1 , T A2 , T B0 , T B1 , T B2 , T c0 , T c1 , T c2 are respectively process quantities, having no actual physical meaning, only facilitating calculations. Analyze f(θ) in Equation (19). Since this equation is a function with a period of 2π, analyze the change of its function values in [0, 2π], as Figure 1 shown.

[0127] The change of the function values in [0, 2π] is as Figure 1 shown, and its minimum value is always taken at π / 2 + θ L and 3π / 2 + θ L . To make the calculation results of the amplitudes of each phase current in the above equation positive, for the convenience of calculation, take the interval [3π / 2, 5π / 2] for discussion, as Figure 2 shown.

[0128] Then if θ = 3π / 2 + θ L satisfies the current limiting condition, the optimal value is taken as 3π / 2 + θ L .

[0129] And when θ = 3π / 2 + θ L does not satisfy the current limiting condition, since it is not difficult to see from Equation (16) that the amplitudes of each phase current increase monotonically with θ in the interval [3π / 2, 3π / 2 + θ L , so there must be θ = θ L in [3π / 2, 3π / 2 + θ x such that the maximum amplitude of each phase current is I max , and at this time the grid unbalance degree is the smallest at this point, that is:

[0130] max{I a , I b, I c} = I max (26)

[0131] Simplify Equation (18) and let:

[0132]

[0133] Then at this time:

[0134]

[0135] After determining the value of θ when determining the optimal support, the injection currents i a , i b , i c of each phase can be determined from (27). At the same time, due to the condition of active power constraint, the i a , i b , i c obtained at this time will only generate reactive power with the voltage v pcc at the PCC. Therefore, the i a , i b , i c obtained at this time is the reactive current i a q , i b q , i c q .

[0136] Step 3:

[0137] Obtain the active component of the reference current to be injected through the DC capacitor voltage closed-loop control. Finally, generate the switching tube signals of the inverter through the current control loop and the PS-SPWM modulation technology to realize the proposed optimal voltage support control method of the three-phase four-wire cascaded STATCOM considering the active power constraint.

[0138] To balance the switching losses and the voltage drop of the capacitor caused by restoring the unbalanced grid, an active current i a q , i b q , i c q perpendicular to the phase of i a p , i b p , i c pTherefore, a DC capacitor voltage loop needs to be added to achieve capacitor voltage stabilization. Since this current is small and only used to restore the capacitor voltage and compensate for the switching losses of the circuit, it will hardly affect the result. However, when the zero-sequence current is small, it may still have a slight impact on the waveform, but it will not affect the voltage support effect of the system and the current limiting condition. Thus, an optimized voltage support control process for a three-phase four-wire cascaded STATCOM considering active power constraints can be established. At this time, the active power constraint is strictly guaranteed, and the current limiting condition is also satisfied. On this basis, the optimal support for the three-phase four-wire cascaded STATCOM can be achieved through this control method. The DC capacitor voltage closed-loop control block diagram is as Figure 4 shown.

[0139] Through the analysis above, the control block diagram of the optimized voltage support control method for a three-phase four-wire cascaded multi-level energy storage system considering power balance is as Figure 5 shown.

[0140] Experimental verification,

[0141] Furthermore, the voltage support method for the three-phase four-wire cascaded STATCOM considering power constraints in this embodiment is verified through experiments. The specific experimental parameters are shown in Table 1 below.

[0142] Table 1 Experimental parameters of the three-phase four-wire cascaded multi-level energy storage system

[0143]

[0144] In the two-phase voltage dip experiment, it is assumed that the voltages of phases b and c drop and are set to 0.6 p.u., while the voltage of phase a remains unchanged.

[0145] In the simulation, different control strategies are adopted at different time periods. Specifically, when the power grid is balanced from 0 to t1, balanced current control is used; a voltage dip occurs at t1, but no voltage support control strategy is implemented from t1 to t2, and the current control used when the power grid is balanced is still maintained; from t2, the complete optimized voltage support control method for the three-phase four-wire cascaded STATCOM considering active power constraints mentioned above is adopted.

[0146] From 0 to t1, at this time, the three-phase power grid is balanced, the system outputs three-phase balanced currents, the capacitor voltages are balanced, the three-phase PCC reactive power is 0, and the current flowing through the neutral line is 0.

[0147] From t1 to t2, at this time, the power grid becomes three-phase unbalanced. Since no balancing control is applied, the system still outputs three-phase balanced currents, the capacitor voltages start to drop, and a small amount of current flows through the neutral line. The three-phase PCC points start to generate active power. At this time, the power grid unbalance degree at the PCC is 0.37.

[0148] Starting from t2, the proposed three-phase four-wire cascaded STATCOM optimal voltage support control method considering active power constraints is applied. As Figure 6 and Figure 7 shown, the three-phase grid currents and neutral line currents before and after voltage support are controlled within the safe current threshold I max , meeting the constraint conditions for current limiting, which is the same as the simulation results. As Figure 8 shown, the voltage support effect at the PCC is obvious at this time. The unbalance degree of the grid after control drops from 0.45 to 0.36, and the unbalance degree of the grid is significantly improved. Due to the limitation of the oscilloscope, Figure 8 is the result of subtracting the initial voltage of 600V from the capacitor voltage. Figure 9 and Figure 10 show that the capacitor realizes voltage stabilization, meeting the conditions of active power constraints, which is consistent with the simulation results. At the same time, the active power at the PCC is 0 after control, meeting the requirements for the active power constraints of the cascaded STATCOM. The experimental results prove the effectiveness of the four-wire cascaded STATCOM optimal voltage support control method considering active power constraints. It shows that the four-wire cascaded STATCOM optimal voltage support control method considering active power constraints can effectively support the PCC voltage under an unbalanced grid, while meeting the power constraints and current limiting conditions, ensuring the normal operation of the system.

[0149] In summary, the three-phase four-wire cascaded STATCOM voltage support control method considering power constraints proposed in the present invention analyzes the voltage support problem of the three-phase four-wire cascaded STATCOM based on the characteristics of the output active power of the STATCOM being zero. A mathematical model of the three-phase four-wire cascaded STATCOM voltage support under an unbalanced grid is constructed through the conditions of current limiting and active power constraints, and the optimal values of the reactive current injected into each phase required for the optimal voltage support under these conditions are obtained from the active power constraints and current limiting. At the same time, capacitor voltage stabilization is achieved through closed-loop control of the DC capacitor voltage. Under this strategy, a small amount of active power will be absorbed in the system, but the overall absorbed active power is almost 0. This control method significantly improves the unbalance degree of the grid while stabilizing the DC-side capacitor voltage. Then, the overall control method of the four-wire cascaded STATCOM optimal voltage support control method considering active power constraints is designed. Finally, the proposed voltage support control strategy is verified through a hardware-in-the-loop experiment, verifying the effectiveness and feasibility of this method.

[0150] The above embodiments are not limitations on the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions, or substitutions made by those skilled in the art within the scope of the technical solutions of the present invention also fall within the protection scope of the present invention.

Claims

1. A three-phase four-wire cascaded STATCOM voltage support control method considering power constraints, characterized in that: It includes the following steps: Step 1: Calculate the following parameters in the three-phase four-wire cascaded multilevel energy storage system: the positive-sequence, negative-sequence, and zero-sequence voltage amplitudes, the initial phase angle, and the voltage unbalance degree of the PCC point fault; Separate the positive-sequence, negative-sequence, and zero-sequence components of the three-phase current output by the multilevel system to obtain the positive-sequence, negative-sequence, and zero-sequence current expressions; Step 2: Derive the amplitude and phase of the optimal reactive component current injected into the power grid based on the voltage support under the active power constraint and current limit; Step 3: Obtain the active component of the required injected reference current through the closed-loop control of the DC capacitor voltage; finally, generate the switching tube signals of the inverter through the current control loop and the PS-SPWM modulation technology to implement the proposed voltage support control method; In the said Step 2, list the three-phase currents in the three-phase four-wire cascaded multilevel energy storage system: Among them, is the initial phase of the grid voltage of phase A, is the initial phase of the grid voltage of phase B, is the initial phase of the grid voltage of phase C; θ A , θ B , θ C are the phase differences between the grid voltages of each phase and the grid current; i n , v n are the neutral line current and the neutral line voltage respectively; the grid-side impedance Z and the impedance angle θ L are respectively expressed as: Uniformly use R to replace the grid-side resistance R g , use l to replace the grid-side inductance L g , that is, let: The zero-sequence current under the unbalanced power grid is expressed as: To suppress the power flow between phases, cancel the unbalanced power flow caused by the power grid fault, and ensure that the active power output of each phase is zero, analyze the active power of the three phases, and we have: At the same time, let θ A = θ B = θ C = θ, we can get: Among them, V ga , V gb , V gc are respectively the amplitudes of the three-phase grid voltages; After simplification, the amplitudes of the three-phase currents \(I\) a , \(I\) b , \(I\) c can be expressed as: When the three-phase current amplitudes of the three-phase four-wire cascaded STATCOM satisfy the expression in (16), the active power constraint condition is achieved; At this time, the three-phase currents I a , I b , I c are all only related to the single variable θ, and each component is represented by θ. To perform mathematical modeling on this system, the voltage support problem of the model is equivalent to: s.t. can be expressed as the conditions that need to be satisfied for the inequality to hold under this condition, where I max is the magnitude of the maximum current amplitude allowed to pass through after the three-phase current is limited.

2. The three-phase four-wire cascaded STATCOM voltage support control method considering power constraints according to claim 1, characterized in that: In the first step, the three-phase PCC voltage is decomposed. After Clarke transformation, the components of the three-phase PCC voltage on the αβ0 axis, v α , v β , and v0 are expressed as: Among them, v + α , v + β , v - α , v - β are respectively the positive-sequence component and the negative-sequence component of v α ; V β is the positive-sequence voltage amplitude, V + is the negative-sequence voltage amplitude, V - is the zero-sequence voltage amplitude; 0 is the initial phase of the positive-sequence voltage, is the initial phase of the negative-sequence voltage, is the initial phase of the zero-sequence voltage; ω is the fundamental angular frequency of the power grid; ωt represents the electrical angle by which the current varies with time t;​ According to the expression in the stationary coordinate system, derive the expressions for the positive-sequence and negative-sequence voltage amplitudes and the positive-sequence and negative-sequence voltage phase differences as: where atan2 is the arc tangent function, is the initial phase of the voltage at the PCC.

3. The three-phase four-wire cascaded STATCOM voltage support control method considering power constraints according to claim 2, characterized in that: In the said Step 1, under the power grid voltage dip condition, separate the positive-sequence, negative-sequence, and zero-sequence components of the three-phase current expression output by the multilevel system through the Clarke transformation; where i α , i β , and i0 are the components of the three-phase current on the α, β, and 0 axes respectively; i α + , i α - , and i β + , i β - are the positive-sequence and negative-sequence components of i α , i β respectively; I + , I - , and I 0 are the current amplitudes of the positive-sequence, negative-sequence, and zero-sequence respectively; φ + , φ - , and φ 0 are the initial phases of the grid currents of the positive-sequence, negative-sequence, and zero-sequence respectively, then we have: Among them, I p + , I p - , I p 0 are the magnitudes of the active components of the positive-sequence, negative-sequence, and zero-sequence currents respectively; I q + , I q - , I q 0 are the magnitudes of the reactive components of the positive-sequence, negative-sequence, and zero-sequence currents respectively; δ + , δ - , δ 0 are the impedance angles of the positive-sequence, negative-sequence, and zero-sequence currents respectively.

4. The three-phase four-wire cascaded STATCOM voltage support control method considering power constraints according to claim 3, characterized in that: In the first step, the injected current vector is decomposed into the sum of four vectors, namely the active and reactive components of the positive and negative sequences, to obtain I p + , I p - , I p 0 , I q + , I q - , I q 0 : Among them, R g and L g are the grid-side impedances. Write down the instantaneous currents of each phase \(i\) a , \(i\) b , \(i\) c , the current amplitudes \(I\) a , \(I\) b , \(I\) c and the relationship between the positive, negative and zero-sequence current amplitudes \(I\) + , \(I\) - , \(I\) 0 , that is:

5. The three-phase four-wire cascaded STATCOM voltage support control method considering power constraints according to claim 4, characterized in that: In the said Step 2, based on (19), since: After simplification, we get: where V ga , V gb , V gc are respectively the amplitudes of the three-phase grid voltages; Similarly, the expressions for the amplitudes of the positive, negative, and zero-sequence currents can be obtained: It can be deduced that the positive and negative zero-sequence voltage amplitudes can be respectively expressed as: T A0 、T A1 、T A2 、T B0 、T B1 、T B2 、T c0 、T c1 、T c2 are process variables respectively, having no actual physical meaning and only being convenient for calculation.

6. The three-phase four-wire cascaded STATCOM voltage support control method considering power constraints according to claim 5, characterized in that: In the second step, for \(f(\theta)\) in Equation (19), it is a function with a period of \(2\pi\). Analyze the variation of the function values in the interval \([0, 2\pi]\) to determine that the minimum value of the function is always obtained at \(\frac{\pi}{2}+\theta\) L and \(\frac{3\pi}{2}+\theta\) L ; If θ = 3π / 2 + θ L the current limiting condition is satisfied, and the optimal value is taken as 3π / 2 + θ L ; When θ = 3π / 2 + θ L the current limiting condition is not satisfied. Since the amplitude of each phase current increases monotonically as θ varies in the interval [3π / 2, 3π / 2 + θ L , there must exist a θ = θ L in the interval [3π / 2, 3π / 2 + θ x such that the maximum amplitude of each phase current is I max , and at this time the grid unbalance degree is the smallest at this point, that is: max{I a ,I b ,I c} = I max (26) Simplify Equation (18), let: Then at this time: After determining the value of θ for the optimal support, the injection currents \(i\) of each phase are determined by (27). a , \(i\) b , \(i\) c The magnitudes and phases of are obtained; at the same time, due to the condition of active power constraint, the \(i\) obtained at this time a , \(i\) b , \(i\) c will only generate reactive power with the voltage \(v\) at the PCC. Therefore, the \(i\) obtained at this time pcc is the reactive current \(i\) required for voltage support at the PCC a , \(i\) b , \(i\) c That is, \(i_{q}\), \(i_{q}\), \(i_{q}\). a , \(i_{q}\) b , \(i_{q}\) c ​ 7. The three-phase four-wire cascaded STATCOM voltage support control method considering power constraints according to claim 6, characterized in that: In the third step, in order to balance the switching loss and the capacitor voltage drop caused by restoring the unbalanced grid, an active current i a q, i b q, i c q whose phase is perpendicular to i a p, i b p, i c p needs to be injected into each phase, and this is implemented by adding a DC capacitor voltage loop.

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