Improved Predictive Control Method of MMC-UPQC under Unbalanced Grid Voltage

Abstract

This invention relates to an improved predictive control method for MMC-UPQC under unbalanced grid voltage, comprising the following steps: constructing an equivalent mathematical model of MMC-UPQC based on the topology of a modular multilevel converter and a unified power quality controller; discretizing the model to obtain a discretized mathematical model of MMC-UPQC; establishing cost functions for the series-side voltage and parallel-side current of MMC-UPQC; obtaining multi-step predictive control cost functions for the series-side voltage and parallel-side current of MMC-UPQC; obtaining the arm voltage and the number of conducting submodules, and establishing a predictive control finite set; reducing the predictive control finite set; suppressing the internal circulating current of MMC-UPQC and stabilizing the capacitor voltage of the conducting submodules; finding the optimal switching combination, and finally outputting the compensation voltage and compensation current. Compared with the prior art, this invention has advantages such as improving power quality under unbalanced grid conditions.

Description

Technical Field

[0001] This invention relates to the field of MMC-UPQC control technology, and in particular to an improved predictive control method for MMC-UPQC under unbalanced grid voltage. Background Technology

[0002] Electrical energy is a vital resource, and with the increasing complexity of power grid systems, many scholars have paid close attention to power quality. Power quality includes voltage quality and current quality, both of which affect the normal operation of the power grid and equipment. The Modular Multilevel Converter-Unified Power Quality Conditioner (MMC-UPQC) can restore power quality to meet reliable power supply requirements and is suitable for medium- and high-voltage power grids. However, current control strategies for MMC-UPQC are mainly designed for linear control under balanced grid voltage conditions, resulting in slow response times, poor compensation effects, limited applicability, and difficulty in determining control parameters when the system is disturbed. Due to the presence of nonlinear loads and numerous power electronic devices, the dynamic equations constructed based on the MMC-UPQC topology are nonlinear, making nonlinear control strategies such as passive control, sliding mode control, and Lyapunov control more suitable. However, passive control is highly dependent on system parameters, sliding mode control suffers from jitter, and the Lyapunov function is difficult to select. Therefore, when the power grid is unbalanced, especially when it is medium or high voltage and has a large number of modules, the compensation and management of voltage and current become very unsatisfactory and often fail to achieve satisfactory results. Since power grid imbalance is a very common power grid condition, it is necessary to study the nonlinear control strategy of MMC-UPQC under power grid imbalance.

[0003] Model Predictive Control (MPC) offers several advantages over other control methods. These include simpler system design, the ability to control multiple objectives, and excellent dynamic performance. MPC eliminates the need to adjust control parameters and can remove the nonlinear effects introduced by the system itself. Currently, MPC is applied to control Modular Multilevel Converters (MMCs). By utilizing a cost function, MPC can easily achieve control of MMCs. Furthermore, researchers have focused on improving the accuracy of MPC, proposing multi-step MPC as a means to achieve better control precision. Multi-step MPC is developed based on the single-step MPC method; it utilizes all possible switching states in single-step MPC to predict the value in the next discrete time step to achieve long-term optimal control. However, theoretically, while multi-step MPC can effectively improve control performance, it involves a large number of switches and requires numerous computational steps. Since MMCs contain many Submodules (SMs), multi-step MPC incurs a significant computational burden. This heavy computational burden leads to slow response times and reduced control performance. Due to the complexity of the MMC-UPQC system, multi-step MPC strategies still require additional computational steps. Furthermore, although MPC has been widely used in the control systems of various power electronic devices, the complexity and diversity of power quality issues make it difficult to directly apply MPC to MMC-UPQC. Especially when facing diverse power quality problems, single-step MPC methods struggle to select the optimal switching state, resulting in ineffective power quality recovery. Currently, existing literature on MMC-UPQC control strategies mainly focuses on the recovery of parallel-side current, with less attention paid to the series-side voltage. However, voltage quality is also crucial, affecting the stable operation of sensitive equipment. Particularly under unbalanced power grids, voltage sags, harmonics, and frequency shifts can occur, thus requiring more comprehensive research on the series side of MMC-UPQC. Summary of the Invention

[0004] The purpose of this invention is to provide an improved predictive control method for MMC-UPQC under unbalanced grid voltage to improve power quality in unbalanced grids.

[0005] The objective of this invention can be achieved through the following technical solutions:

[0006] An improved predictive control method for MMC-UPQC under unbalanced grid voltage includes the following steps:

[0007] Based on the topology of the modular multilevel converter and the unified power quality controller, an equivalent mathematical model of MMC-UPQC is constructed.

[0008] The MMC-UPQC equivalent mathematical model is discretized to obtain the MMC-UPQC discretized mathematical model;

[0009] Based on the discretized mathematical model of MMC-UPQC, a single-step predictive control method is used to establish the cost functions of the series side voltage and parallel side current of MMC-UPQC.

[0010] Based on the cost functions of the series-side voltage and parallel-side current of the MMC-UPQC, a multi-step predictive control method is adopted to obtain the multi-step predictive control cost functions of the series-side voltage and parallel-side current of the MMC-UPQC.

[0011] Based on the MMC-UPQC discretized mathematical model, the bridge arm voltage and the number of conducting sub-modules are obtained, and a predictive control finite set is established;

[0012] Based on the bridge arm voltage and the number of conducting submodules, the finite set of the predictive control is reduced;

[0013] Based on the bridge arm voltage and the number of conducting submodules, circulating current suppression method and voltage equalization control method are used to suppress the internal circulating current of MMC-UPQC and stabilize the capacitor voltage of the conducting submodules;

[0014] Based on suppressing the internal circulating current of MMC-UPQC and stabilizing the capacitor voltage of the conducting submodule, the optimal switching combination is found in the reduced predictive control finite set based on the multi-step predictive control cost function, and finally the compensation voltage and compensation current are output.

[0015] Furthermore, the equivalent mathematical model of MMC-UPQC is:

[0016]

[0017] In the formula: s = r and g represent the series and parallel sides, respectively; u ss For the series or parallel side MMC output voltage; e sz Output voltage on the series or parallel side; L seq The equivalent inductance for the series or parallel side; i sz For the series or parallel line current; R s This refers to the resistance of the series or parallel line.

[0018] Furthermore, the Eulerian approximation method is used to discretize the MMC-UPQC equivalent mathematical model.

[0019] Furthermore, the MMC-UPQC discretization mathematical model is as follows:

[0020]

[0021]

[0022] In the formula: i gz (k), u rz (k) represent the parallel-side current and series-side voltage at discrete time k, respectively; gz (k+1),e rz (k+1) represent the output voltages of the parallel and series MMCs at discrete time k+1, respectively; R g For the parallel side line resistance; L geq The equivalent inductance on the parallel side; T1 is; i gz i rz These represent the parallel or series line currents at discrete time k; u gz (k+1), u rz (k+1) represent the parallel-side current and series-side voltage at discrete time k+1, respectively; C2 is the series-side capacitance; L r For the series-side line inductance; i rz1 (k+1) represents the current flowing through C2 at the discrete time k+1.

[0023] Furthermore, the cost function for the series-side voltage and parallel-side current of the MMC-UPQC is:

[0024]

[0025] In the formula: J r1 and J g1 These are the cost functions for the series-side voltage and parallel-side current of the MMC-UPQC, respectively. and These represent the desired voltage on the series side and the desired current on the parallel side at discrete time k+1, respectively; i gz (k+1) represents the parallel-side line current at discrete time k+1; u rz (k+1) is the series side voltage at discrete time k+1.

[0026] Furthermore, the specific steps for obtaining the multi-step predictive control cost function of the MMC-UPQC series-side voltage and parallel-side current include:

[0027] Based on the cost functions of the series-side voltage and parallel-side current of the MMC-UPQC, a multi-step predictive control discretization model for the series-side voltage and parallel-side current is constructed using a multi-step predictive control method, as follows:

[0028]

[0029]

[0030] In the formula: i gz(k+2) and u rz (k+2) represents the parallel-side current and series-side voltage at discrete time k+2; e gz (k+2) and e rz (k+2) represents the output voltages of the parallel and series MMCs at discrete time k+2; R g For the parallel side line resistance; L geq The equivalent inductance on the parallel side; u gz (k+2) is; i gz (k) represents the parallel-side line current at discrete time k; i rz (k+2) represents the series-side line current at discrete time k+2; N is the number of submodules; T1 is the sampling period; C2 is the series-side capacitor; L r For the series-side line inductance; i rz1 (k+2) represents the current flowing through C2 at the discrete time k+2;

[0031] Based on the aforementioned multi-step predictive control discretization model, the multi-step predictive control cost functions for the series-side voltage and parallel-side current of the MMC-UPQC are obtained, as follows:

[0032]

[0033] In the formula: J r2 and J g2 These are the multi-step predictive control cost functions for the series-side voltage and parallel-side current of the MMC-UPQC, respectively. and These represent the desired series-side voltage and the desired parallel-side current at discrete time k+2, respectively; i gz (k+2) and u rz (k+2) represents the parallel current and series voltage at discrete time k+2, respectively.

[0034] Furthermore, the specific steps for establishing the predictive control finite set include:

[0035] The discretized model of the output voltage, obtained based on the MMC-UPQC discretized mathematical model, is as follows:

[0036]

[0037] In the formula: e sz (k+1) represents the output voltage on the series or parallel side at discrete time k+1; R s For the series or parallel line resistance; L req The equivalent inductance on the series side is specifically the sum of the series-side line inductance and half of the bridge arm inductance; i sz For the series or parallel line current; u sz(k+1) represents the MMC output voltage on the series or parallel side at discrete time k+1; T1 is the sampling period; s = r and g represent the series and parallel sides, respectively;

[0038] Based on the discretized model of the output voltage, the discretized model of the bridge arm voltage is derived as follows:

[0039]

[0040] In the formula: e psz (k+1) and e fsz (k+1) represent the output voltages of the upper and lower bridge arms at discrete time k+1, respectively; V dc This is the DC side voltage value; e sz (k+1) represents the output voltage on the series or parallel side at discrete time k+1;

[0041] Based on the discretized model of the bridge arm voltage, the number of conducting sub-modules in the upper and lower bridge arms can be deduced as follows:

[0042]

[0043] In the formula: e psz (k+1) and e fsz (k+1) represents the output voltages of the upper and lower bridge arms at discrete time k+1, respectively.

[0044] V dc This is the DC side voltage value; e sz (k+1) represents the output voltage on the series or parallel side at discrete time k+1; s = r and g represent the series and parallel sides, respectively.

[0045] The number of the upper and lower bridge arm conducting sub-modules is rounded down, and the number of the sub-modules adjacent to them is selected as the predictive control finite set.

[0046] Furthermore, the specific steps for reducing the predictive control finite set include:

[0047] Calculate the rate of change of the bridge arm's output voltage based on the bridge arm's output voltage.

[0048] The predictive control finite set is reduced based on the rate of change of the bridge arm output voltage and the number of conducting submodules.

[0049] Furthermore, the specific steps for reducing the predictive control finite set based on the rate of change of the bridge arm output voltage and the number of conducting submodules include:

[0050] Determine whether the rate of change of the output voltage of the bridge arm is greater than 0. If it is, increase the number of conducting submodules to reduce the predictive control finite set. If not, decrease the number of conducting submodules to reduce the predictive control finite set.

[0051] Furthermore, the internal circulating current of the MMC-UPQC is suppressed by changing the magnitude of the circulating current through the insertion of a compensation voltage.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] (1) Single-step MPC easily overlooks important information about some switching states. This invention uses multi-step MPC to further optimize and select more suitable switching states. Furthermore, by adopting improved multi-step MPC, MMC-UPQC can reduce oscillations and maintain optimal control over a long period. In addition, to maintain the internal stability of MMC-UPQC, this invention also designs an MPC strategy for circulating current and capacitor voltage to suppress circulating current and balance voltage. Based on internal stability operation, it seeks the optimal switching state to output current and voltage, thereby improving power quality.

[0054] (2) This invention further reduces the finite set of MPC, thus greatly reducing the computational burden on the controller in each loop. In addition, even if the number of modules in MMC-UPQC increases, the finite set of the improved multi-step MPC of this invention will not increase, thus not increasing the computational load.

[0055] (3) The improved MPC of this invention can realize control on both the series and parallel sides, thereby restoring voltage and current quality under various power quality problems. In addition, by reducing the finite set, the MPC of this invention has lower requirements for hardware computing power and exhibits a faster response speed. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0057] Figure 2 This is the main circuit topology of the MMC-UPQC of this invention;

[0058] Figure 3 This invention relates to the principle of multi-step predictive control.

[0059] Figure 4 This is a diagram showing the relationship between the output and conduction submodules of this invention;

[0060] Figure 5 For the present invention when η ps A finite set of different predictive controls when >0;

[0061] Figure 6 This is a schematic diagram illustrating the process of implementing multi-step MPC in an embodiment of the present invention;

[0062] Figure 7The following are voltage waveforms under grid voltage sag conditions according to an embodiment of the present invention: (a) is the grid voltage waveform, (b) is the voltage waveform under improved predictive control on the series side, (c) is the compensation voltage waveform under improved predictive control on the series side, (d) is the voltage waveform under conventional predictive control on the series side, (e) is the compensation voltage waveform under conventional predictive control on the series side, (f) is the voltage harmonic distortion rate under improved predictive control on the series side, and (g) is the voltage harmonic distortion rate under conventional predictive control on the series side under grid voltage sag conditions according to an embodiment of the present invention.

[0063] Figure 8 The following are voltage waveforms under the condition of grid voltage injection harmonics in an embodiment of the present invention, wherein (a) is the grid voltage waveform, (b) is the voltage waveform under improved predictive control on the series side, (c) is the compensation voltage waveform under improved predictive control on the series side, (d) is the voltage waveform under conventional predictive control on the series side, (e) is the compensation voltage waveform under conventional predictive control on the series side, (f) is the voltage harmonic distortion rate under improved predictive control on the series side, and (g) is the voltage harmonic distortion rate under conventional predictive control on the series side.

[0064] Figure 9 The following are voltage waveforms under the condition of grid voltage frequency deviation in an embodiment of the present invention: (a) is the grid voltage waveform, (b) is the voltage waveform under improved predictive control on the series side, (c) is the compensation voltage waveform under improved predictive control on the series side, (d) is the voltage waveform under conventional predictive control on the series side, (e) is the compensation voltage waveform under conventional predictive control on the series side, (f) is the voltage harmonic distortion rate under improved predictive control on the series side, and (g) is the voltage harmonic distortion rate under conventional predictive control on the series side.

[0065] Figure 10 The following are current waveforms under grid voltage sag conditions according to an embodiment of the present invention: (a) is the grid current waveform, (b) is the current waveform under improved predictive control on the parallel side, (c) is the compensation current waveform under improved predictive control on the parallel side, (d) is the current waveform under conventional predictive control on the parallel side, (e) is the compensation current waveform under conventional predictive control on the parallel side, (f) is the current harmonic distortion rate under improved predictive control on the parallel side, and (g) is the current harmonic distortion rate under conventional predictive control on the parallel side under grid voltage sag conditions according to an embodiment of the present invention.

[0066] Figure 11The following are current waveforms under load switching conditions in an embodiment of the present invention: (a) is the grid current waveform, (b) is the current waveform under improved predictive control on the parallel side, (c) is the compensation current waveform under improved predictive control on the parallel side, (d) is the current waveform under conventional predictive control on the parallel side, (e) is the compensation current waveform under conventional predictive control on the parallel side, (f) is the current harmonic distortion rate under improved predictive control on the parallel side, and (g) is the current harmonic distortion rate under conventional predictive control on the parallel side under load switching conditions in an embodiment of the present invention.

[0067] Figure 12 The following are current waveforms under grid voltage harmonic injection conditions according to an embodiment of the present invention: (a) is the grid current waveform, (b) is the current waveform under improved predictive control on the parallel side, (c) is the compensation current waveform under improved predictive control on the parallel side, (d) is the current waveform under conventional predictive control on the parallel side, (e) is the compensation current waveform under conventional predictive control on the parallel side, (f) is the current harmonic distortion rate under improved predictive control on the parallel side, and (g) is the current harmonic distortion rate under conventional predictive control on the parallel side.

[0068] Figure 13 This is the RTLAB hardware-in-the-loop simulation platform according to an embodiment of the present invention;

[0069] Figure 14 The following are experimental voltage waveforms under the condition of grid voltage spurt in an embodiment of the present invention: (a) is the grid voltage experimental waveform, (b) is the voltage experimental waveform under improved predictive control on the series side, and (c) is the voltage experimental waveform under conventional predictive control on the series side.

[0070] Figure 15 The following are experimental voltage waveforms under the condition of grid voltage injection harmonics in an embodiment of the present invention, wherein (a) is the grid voltage experimental waveform, (b) is the voltage experimental waveform under improved predictive control on the series side, and (c) is the voltage experimental waveform under conventional predictive control on the series side.

[0071] Figure 16 The following are experimental current waveforms under the condition of grid voltage sag in an embodiment of the present invention, wherein (a) is the grid current experimental waveform, (b) is the current experimental waveform under the improved predictive control on the parallel side, and (c) is the current experimental waveform under the conventional predictive control on the parallel side.

[0072] Figure 17 The following are experimental current waveforms under the condition of grid voltage injection harmonics in an embodiment of the present invention, wherein (a) is the grid current experimental waveform, (b) is the current experimental waveform under the improved predictive control on the parallel side, and (c) is the current experimental waveform under the conventional predictive control on the parallel side. Detailed Implementation

[0073] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0074] This embodiment provides an improved predictive control method for MMC-UPQC under unbalanced grid voltage, such as... Figure 1 As shown, the method includes the following steps:

[0075] Step 1: Based on the topology of MMC and UPQC, construct an equivalent mathematical model of MMC-UPQC.

[0076] Figure 1 The topology of the MMC-UPQC is shown, namely a back-to-back connection. Simultaneously, by utilizing the DC bus capacitor on the DC link as a medium for energy exchange, a stable DC termination for MMC-UPQC compensation can be established. The series-side MMC can restore the grid voltage to a sinusoidal waveform in the event of voltage sags, dips, and injected harmonics. Due to the use of nonlinear loads, a large number of harmonics are generated, and these harmonics flowing into the grid affect current quality. The parallel-side MMC can generate compensating current to counteract the harmonics flowing into the grid. Figure 2 In the MMC-UPQC, there are 6 bridge arms and N SMs. Ideally, the MMC with N modules can generate 2N+1 levels, thereby reducing harmonic distortion as the level increases.

[0077] Based on Kirchhoff's laws and the equivalent circuit of MMC-UPQC, the mathematical model for the series side is derived as follows:

[0078]

[0079]

[0080] In the formula: z = any one of the three phases a, b, and c; e rz It is the output voltage on the series side; u rk1 This refers to the primary voltage of the transformer; u rz This refers to the output voltage of the MMC on the series side; L req The equivalent inductance on the series side is specifically the sum of the series-side line inductance and half of the bridge arm inductance; R r For the series side line resistance; i rz This represents the current in the series-connected circuit.

[0081] Similarly, the parallel side relationship can be obtained as follows:

[0082]

[0083] In the formula: u gzThis refers to the output voltage of the parallel-side MMC; L geq R is the equivalent inductance on the parallel side; g For the parallel side line resistance; i gz This represents the current in the parallel-connected line.

[0084] By combining equations (1) and (3), the equivalent mathematical model of MMC-UPQC is obtained as follows:

[0085]

[0086]

[0087] In the formula: s = r, g represents the series side and the parallel side; e fsz and e psz It is the output voltage of the upper and lower bridge arms.

[0088] Step 2: Discretize the equivalent mathematical model of MMC-UPQC to obtain the discretized model of MMC-UPQC.

[0089] Specifically:

[0090] By using Euler's method, the discrete-time model of MMC-UPQC can be obtained, as follows:

[0091]

[0092]

[0093] In the formula: i gz (k), u rz (k) represent the parallel-side current and series-side voltage at discrete time k, respectively; gz (k+1),e rz (k+1) represent the output voltages of the parallel and series MMCs at discrete time k+1, respectively; R g For the parallel side line resistance; L geq The equivalent inductance on the parallel side; T1 is the sampling period; i gz i rz These represent the parallel or series line currents at discrete time k; u gz (k+1), u rz (k+1) represent the parallel-side current and series-side voltage at discrete time k+1, respectively; C2 is the series-side capacitance; L r For the series-side line inductance; i rz1 (k+1) represents the current flowing through C2 at the discrete time k+1.

[0094] According to equation (4), the reference value for the output voltage is:

[0095]

[0096] The bridge arm voltage can be derived as follows:

[0097]

[0098] In the formula: e psz (k+1) and e fsz (k+1) represents the output voltages of the upper and lower bridge arms at discrete time k+1; V dc This is the DC side voltage value.

[0099] Step 3: Based on the discretized mathematical model of MMC-UPQC, a single-step predictive control method is used to establish the cost functions of the series side voltage and parallel side current of MMC-UPQC.

[0100] Based on the principle of single-step predictive control, the cost functions of voltage and current in MMC-UPQC can be obtained. The voltage reference is represented as... The current reference is represented as The cost function of line current and output voltage can be defined as:

[0101]

[0102] In the formula: J r1 and J g1 These are the cost functions for the series-side voltage and parallel-side current of the MMC-UPQC, respectively. and These represent the desired voltage on the series side and the desired current on the parallel side at discrete time k+1, respectively; i gz (k+1) represents the parallel-side line current at discrete time k+1; u rz (k+1) represents the series voltage at discrete time k+1.

[0103] Step 4: Based on the cost functions of the series-side voltage and parallel-side current of the MMC-UPQC, a multi-step predictive control method is adopted to obtain the multi-step predictive control cost functions of the series-side voltage and parallel-side current of the MMC-UPQC.

[0104] Specifically, the MPC method is based on rolling optimization, using a finite number of switch combinations to select the optimal switch. However, single-step MPC cannot guarantee that the objective variable is optimal in the next time interval because it ignores the optimal information that other switch states may contain. Ignoring important switching states negatively impacts the effectiveness of MPC. To overcome the potential negative impact of single-step MPC, multi-step MPC is introduced into MMC-UPQC. Multi-step MPC determines the more accurate number of inserted SMs by calculating all values ​​in the finite set of single-step MPC values ​​in the next discrete time interval and further comparing these values. Figure 2 The process of finding the optimal value in a multi-step MPC is shown, where x opt (k) represents the optimal control effect, marked with a dashed line. t k+1 The line represents the predicted value of the target variable, which is calculated using all possible switching states in a finite set of single-step MPC.

[0105] The line current and output voltage at discrete time k+2 can be obtained as follows:

[0106]

[0107]

[0108] In the formula: i gz (k+2) and u rz (k+2) represents the parallel-side current and series-side voltage at discrete time k+2; e gz (k+2) and e rz (k+2) represents the output voltages of the parallel and series MMCs at discrete time k+2; R g For the parallel side line resistance; L geq The equivalent inductance on the parallel side; u gz (k+2) is; i gz (k) represents the parallel-side line current at discrete time k; i rz (k+2) represents the series-side line current at discrete time k+2; N is the number of submodules; T1 is the sampling period; C2 is the series-side capacitor; L r For the series-side line inductance; i rz1 (k+2) represents the current flowing through C2 at the discrete time k+2.

[0109] According to equation (8), the output voltage reference value is derived as follows:

[0110]

[0111] In multi-step MPC, the voltage and current references are expressed as and The cost function at discrete time k+2 can be defined as:

[0112]

[0113] In the formula: J r2 and J g2 These are the multi-step predictive control cost functions for the series-side voltage and parallel-side current of the MMC-UPQC, respectively. and These represent the desired series-side voltage and the desired parallel-side current at discrete time k+2, respectively; i gz(k+2) and u rz (k+2) represents the parallel current and series voltage at discrete time k+2, respectively.

[0114] Step 5: Based on the MMC-UPQC discretized mathematical model, obtain the bridge arm voltage and the number of conducting sub-modules, and establish a predictive control finite set.

[0115] Specifically:

[0116] This invention proposes an improved MPC method that reduces the number of finite sets. The number of inserted SMs is inversely calculated to form a finite set. Then, this invention investigates the relationship between the output voltage of the bridge arm and the number of inserted SMs. This relationship can be used to reduce the number of finite sets. The specific improvement steps of MPC are as follows.

[0117] The number of inserted submodules is as follows:

[0118]

[0119] In the formula: e psz (k+1) and e fsz (k+1) represent the output voltages of the upper and lower bridge arms at discrete time k+1, respectively; V dc This is the DC side voltage value; e sz (k+1) represents the output voltage on the series or parallel side at discrete time k+1; s = r and g represent the series and parallel sides, respectively.

[0120] The number of conducting submodules calculated by equation (15) is usually not an integer. To ensure the accuracy of the finite set, n psz and n fsz The set is rounded to an integer, and the number of adjacent submodules is selected as the finite set. Therefore, the finite set can be adjusted to {n}. psz -1,n psz ,n psz +1} and {n fsz -1,n fsz ,n fsz +1}. Using this reverse reasoning method, multi-step MPC has only nine state combinations in the finite set. Compared to traditional MPC, the number of switch states that need to be searched in the finite set is reduced, thus reducing the computational burden of MPC. However, since MMC contains a large number of SMs, multi-step MPC still results in a significant computational burden.

[0121] Step 6: Based on the bridge arm voltage and the number of conducting submodules, reduce the predictive control finite set.

[0122] Specifically, to further improve operating efficiency and reduce computational burden, the relationship between the rate of change of output voltage and the number of inserted SMs was analyzed. Since the output voltage of the bridge arm is symmetrical, this invention takes the output voltage of the upper bridge arm as an example to analyze the variation of a finite set. The rate of change η of the bridge arm output voltage... ps Can be described as

[0123]

[0124] exist Figure 3 In the middle, with n psz The increase in value, η ps When n is greater than 0, the number of inserted SMs increases. psz During the descent, η ps If the value is less than 0, the number of inserted SMs decreases.

[0125] Different η ps The finite set of values ​​is shown in Table 1. The rate of change η of the upper arm output voltage during the entire compensation process... ps The following situations are possible:

[0126] Case 1: When η ps When n > 0, n psz It shows an upward trend, with an increase in the number of inserted SMs. When η ps When n is greater than 0, psz -1 is excluded, and the finite set can be adjusted to {n}. psz ,n psz +1}.

[0127] Case 2: When η ps When n < 0, psz The trend is downward, and the number of inserted SMs is decreasing. If η ps If the value is less than 0, n can be excluded. psz +1, adjust the finite set to {n psz -1,n psz}

[0128] Based on this correlation, the finite set of the proposed MPC can be reduced from N to 2, thereby further reducing the control options to 4.

[0129] Table 1. Comparison of Finite Sets for Different Predictive Control Strategies

[0130]

[0131] Figure 4 It shows when η ps Finite sets of different MPCs when >0. The finite sets of traditional MPCs are highlighted with a white box. For example... Figure 4As shown, the switching states of the traditional MPC range from 0 to N. The finite set of the MPC improved by the inversion method is marked with vertical lines, where the MPC using the inversion method has 3 switching states. The finite set of the MPC proposed in this invention is marked with diagonal lines. The proposed MPC occupies only the minimum area and has only 2 switching states. Therefore, the proposed MPC has the potential to reduce the finite set.

[0132] Table 2 shows the computational cost of MPC when the number of SMs N = 10, 20, and 30. Traditional MPC requires a large amount of computation. The proposed multi-step MPC only requires 4 computations. Through comparison and analysis of the two MPC methods, the computational burden of the proposed multi-step MPC is significantly reduced.

[0133] Table 2 Comparison of computational complexity for different predictive control strategies

[0134]

[0135] Table 3 Comparison of computation time for different predictive control strategies

[0136]

[0137] Table 3 shows the computation time for different MPC methods. The computation time using traditional MPC is 102 microseconds, and it increases rapidly with the number of SMs. The improved MPC requires less computation time. As shown in Table 3, the improved MPC can effectively reduce the computation time.

[0138] Step 7: Based on the bridge arm voltage and the number of conducting submodules, use circulating current suppression method and voltage equalization control method to suppress the internal circulating current of MMC-UPQC and stabilize the capacitor voltage of the conducting submodules.

[0139] Specifically: When the power grid is unbalanced, the severity of circulating current in the MMC increases, and the circulating current includes both DC and second-harmonic AC components. Circulating current affects the operation of the MMC-UPQC and increases system losses. Therefore, this invention employs MPC to suppress circulating current. From equations (4) and (5), the internal current i of the MMC... diffz It has no effect on the output characteristics. The dynamic characteristics of the internal current of each bridge arm can be described as follows:

[0140]

[0141] As shown in equation (17), the circulating current is only related to the arm voltage and the DC side voltage. The voltage difference determines the external output characteristics of the MMC-UPQC. As long as the arm voltage difference remains constant, it will not affect the phase current control. Therefore, the circulating current can be controlled by adjusting the sum of the upper and lower arm voltages. Specifically, after obtaining the arm voltage reference through equation (15), if the voltage reference is not zero, an identical compensation level U is inserted into the arm. diff The range of compensation levels is... The method for calculating internal current is...

[0142]

[0143] The cost function of the circulating current can be defined as follows:

[0144]

[0145] In the formula: i * dc This is the expected value of the DC-side current.

[0146] The output waveform of the MMC-UPQC is affected by the stability of the capacitor voltage of each SM. Controlling the capacitor voltage is crucial to preventing fluctuations in the output waveform. Therefore, MPC is also used to stabilize the capacitor voltage. For an uninserted SM, its capacitor voltage remains constant. When an SM is inserted, its capacitor voltage at the next discrete time can also be described as...

[0147]

[0148] In the formula: u zm (k+1) is the capacitor voltage of the m-th submodule, and C3 is the capacitor of the submodule.

[0149] According to equation (20), the cost function of capacitor voltage is defined as

[0150]

[0151] In the uninvested SM, the cost function J is selected. c Smaller SMs are inserted. For each inserted SM, the upper switch is turned on and the lower switch is turned off. For the remaining SMs, the upper switch is turned off and the lower switch is turned on. The insertion process is repeated until the required number of inserted SMs is reached.

[0152] Step 8: Based on suppressing the internal circulating current of MMC-UPQC and stabilizing the capacitor voltage of the conducting submodule, the optimal switching combination is found in the reduced predictive control finite set based on the multi-step predictive control cost function, and finally the compensation voltage and compensation current are output.

[0153] Based on the stable operation within the MMC-UPQC, the optimal switching combination is sought according to the derived multi-step predictive control cost function. Since the finite set has been reduced, the optimization process is simplified. The improved predictive controller of this invention can reduce the computational burden and quickly and accurately restore voltage and current quality.

[0154] To verify the effectiveness of the above method, this embodiment uses MMC-UPQC under a certain power grid imbalance for verification. The following steps demonstrate the implementation of the proposed multi-step MPC, and the flowchart is as follows: Figure 6 As shown.

[0155] (1) Set the minimum value J of the cost function min The initial value is infinite.

[0156] (2) Substitute the output voltage and current values ​​of discrete time k+1 into equation (15) to determine the number of insertions in the bridge arm.

[0157] (3) To ensure fault tolerance, n psz and n fsz The number of adjacent submodules is selected as the finite set and rounded to the nearest integer.

[0158] (4) Set the upper and lower limits of the finite set to n. max and n min This makes it convenient to override the upper and lower limit values ​​in a loop.

[0159] (5) Then, by determining the rate of change η of the upper bridge arm output voltage. ps This eliminates unnecessary switching states in the finite set, thereby reducing the number of finite sets.

[0160] (6) If the rate of change is greater than 0, then let n max =n psz +1 and n min =n psz If the rate of change is less than 0, then let n max =n psz and n min =n psz -1.

[0161] (7) Set the optimal number of sub-modules to n opt。

[0162] (8) Calculate the cost functions for the series side and the parallel side.

[0163] (9) J at discrete time k+2 r2 and J g2 With J min In comparison. If compared to J min If the value is small, then the current cost function value is selected as J. min .

[0164] (10) Then judge n opt Is it equal to n? max。 If they are equal, then choose n. opt The number of submodules to be added; if they are not equal, then n is set to n. opt Add 1 and then return to step 8.

[0165] (11) Calculate the cost functions of circulation and equalization.

[0166] (12) Based on the MPC method of circulating current and capacitor voltage, find the cost function J. diff and J c The minimum value determines which submodules need to be enabled or disabled.

[0167] This embodiment verifies and explains the technical effects of the method used in this study. Different methods were selected and compared with this method in the comparative tests. The experimental results were compared using scientific verification methods, and simulation and a hardware-in-the-loop platform were used to verify the real-world effectiveness of the method. The effectiveness of the proposed MMC-UPQC multi-step MPC was verified in the MATLAB / Simulink environment. The main simulation parameters of the system are shown in Table 4. By comparing with traditional MPC, it is demonstrated that the improved multi-step MPC of this invention not only achieves good control performance but also has a lower computational burden.

[0168] Table 4 System parameters for simulation and experiment

[0169]

[0170] (1) Voltage compensation simulation of MMC on the series side

[0171] Figure 7 This demonstrates the compensation effects of two MPC methods under grid voltage sags. For example... Figure 7 As shown in (a), the voltage of phase a experiences a brief rise in 0.08 seconds. Figure 7 Figures (b) and (c) show that the improved multi-step MPC can rapidly recover the voltage within 0.03 seconds. However, due to... Figure 7 As shown in (d) and (e), the traditional MPC exhibits overshoot at 0.1 seconds and then stabilizes at 0.02 seconds. In summary, from... Figure 7 The voltage total harmonic distortion (THD) of the improved MPC in (f) and (g) is 1.74%, while the THD of the conventional MPC is 4.18%. In summary, the multi-step MPC of this invention exhibits superior dynamic and static characteristics under grid voltage expansion.

[0172] like Figure 8In the simulation shown in (a), a third harmonic of 2000V was injected at 0.05 seconds, resulting in high total harmonic distortion (THD = 28%). This was done to evaluate the effectiveness of the MPC of the present invention in handling grid voltage harmonics. Regarding the compensation amount, such as... Figure 8 As shown in (c) and (e)-(g), the improved MPC exhibits smaller fluctuations, with a THD of only 1.35%. Figure 8 As can be seen in (b) and (d) of the present invention, compared with the conventional MPC, the MPC of the present invention exhibits superior compensation effect and faster response speed.

[0173] like Figure 9 (a) shows the voltage compensation of MMC-UPQC with a frequency offset of 0.5Hz. In this case, from Figure 9 As can be seen from (b) and (c) in the present invention, the MPC of the present invention initiates load voltage recovery from the start of frequency offset. Figure 9 Figures (d) and (e) show that voltage compensation becomes ineffective from 0.06 seconds onwards because the conventional MPC cannot select an ideal switching state. Furthermore, Figure 9 (f) and (g) in the figure show the harmonic content of the two control methods. The improved multi-step MPC of the present invention can maintain stability and good compensation in the case of grid frequency deviation.

[0174] (2) Simulation of current compensation for parallel-side MMC

[0175] Both simulations and experiments used nonlinear loads to verify the improved MPC strategy of MMC-UPQC in this invention. Figure 1 In this circuit, the nonlinear load consists of a resistor and an insulated gate bipolar transistor (IGBT), connected by an RL buffer circuit.

[0176] like Figure 10 Figure (a) shows the current recovery on the parallel side of the MMC-UPQC when the grid voltage rises slightly in phase a. Due to the nonlinear load in the MMC-UPQC, the THD of the grid current reaches 26.53%. Figure 10 As can be seen in (b), (c) and (f), the improved multi-step MPC can effectively restore the grid current with a THD of 1.07%. Figure 10 Figures (d), (e), and (g) show that the THD of the conventional MPC is 3.41%, and its compensation effect is not as good as that of the improved MPC. The conventional MPC requires more than 0.3 seconds to achieve three-phase balance. In summary, the MPC of this invention can restore the grid current on the parallel side faster and more accurately.

[0177] like Figure 11 (a) shows the current compensation of the MPC when a load switch occurs within 0.08 seconds. Figure 11As shown in (d), (e), and (g), the traditional MPC has a very slow response speed, resulting in a THD of 4.64%. Figure 11 Figures (b), (c), and (f) show that the improved MPC of the present invention has a lower THD of 0.56% at the end of compensation. In this case, the improved MPC can better recover the grid current.

[0178] To demonstrate the ability of the improved MPC of this invention to handle power grid current harmonics, such as Figure 12 As shown in (a), a 2000V third harmonic is injected at 0.05 seconds. (From...) Figure 12 As shown in (b)-(e), when voltage harmonics are injected, the conventional MPC exhibits a significant fluctuation at 0.08 seconds. Figure 12 Figures (f) and (g) show that the improved MPC has a lower harmonic distortion rate and a more stable grid current, demonstrating its superior compensation effect on grid current.

[0179] HIL experimental platform based on RT-LAB, such as Figure 13 As shown. In the experiment, the MMC-UPQC system was simulated using RT-LAB OP5700. The MPC proposed in this invention was implemented on a Texas Instruments TMS320F28335 digital signal processor (DSP). The output waveform and device operation were observed using a Tektronix MDO34 oscilloscope and the host computer.

[0180] (1) Series side voltage compensation experiment

[0181] Figure 14 and 15 The results of the series-side MMC experiment are shown when the grid experiences voltage sags and injected harmonics.

[0182] Figure 14 (a) shows load voltage recovery using improved MPC in the event of a grid voltage spurt. In this case, from Figure 14 As can be seen in (b) of this invention, the improved MPC can rapidly recover unbalanced voltage within 0.002 seconds. Furthermore, Figure 14 (c) shows that the conventional MPC takes longer to compensate for the load voltage than the improved MPC, and the compensated voltage fluctuates. The improved MPC of this invention can better recover the voltage in the event of a voltage spurt.

[0183] exist Figure 15 In (a), the injection of the third harmonic significantly affects the voltage waveform, and the voltage recovery capability of different MPCs is compared in the figure. Figure 15The key aspects of the control effect of the two MPCs in (b) and (c) are enlarged with boxes for easy observation. The improved MPC strategy of this invention produces a smoother output waveform. The improved MPC can reduce the THD of the load voltage to 1.23%. However, after recovery by conventional MPC, the load voltage still exhibits a THD of 4.62%. Therefore, the improved MPC of this invention can achieve better control performance even with injected harmonics.

[0184] (2) Parallel side current compensation experiment

[0185] The current recovery experiment of the parallel-side MMC was conducted under two conditions: voltage sag and harmonic injection. Figure 16 and 17 As shown.

[0186] Figure 16 Tables (a)-(c) show the grid current compensation under voltage expansion conditions for the two MPC methods. The improved MPC of this invention can recover the grid current within 0.003 seconds. However, conventional MPC methods result in some overshoot and steady-state errors. Figure 16 In this model, the improved MPC offers better control and a shorter response time.

[0187] Figure 17 (a) shows the grid current recovery using two different MPCs when a 2000V third harmonic is injected. Figure 17 As shown in (b) and (c), when using the improved MPC of this invention, the grid current can be restored to a sine wave within 0.0005 seconds, while the conventional MPC requires 0.001 seconds. Furthermore, the improved MPC has a fast response and eliminates the transient fluctuations that occur in the conventional MPC. After restoration using the improved MPC, the THD of the current can reach 1.73%. When using the conventional MPC, some harmonics cannot be eliminated, resulting in a THD of 4.83% for the grid current. Therefore, the MPC proposed in this invention can quickly restore the grid current and accurately solve the current harmonic problem.

[0188] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. An improved predictive control method for MMC-UPQC under unbalanced grid voltage, characterized in that, Includes the following steps: Based on the topology of the modular multilevel converter and the unified power quality controller, an equivalent mathematical model of MMC-UPQC is constructed. The MMC-UPQC equivalent mathematical model is discretized to obtain the MMC-UPQC discretized mathematical model; Based on the discretized mathematical model of MMC-UPQC, a single-step predictive control method is used to establish the cost functions of the series-side voltage and parallel-side current of MMC-UPQC. The discretized mathematical model of MMC-UPQC is as follows: In the formula: i gz ( k ), u rz ( k () represent discrete time intervals. k The parallel-side current and series-side voltage at that time; e gz ( k +1) e rz ( k +1) represent discrete time intervals. k The output voltages of the parallel and series MMCs at +1; R g For the parallel side line resistance; L geq This is the equivalent inductance on the parallel side; T 1 represents the sampling period; i gz , i rz Discrete time points k The parallel or series line current at that time; u gz ( k +1) u rz ( k +1) represent discrete time intervals. k The parallel side voltage and the series side voltage at +1; C 2 is the series capacitor; L r For the series-side line inductance; i rz1 ( k +1) represents the discrete time. k +1 flow C The current of 2; The cost function for the series-side voltage and parallel-side current of the MMC-UPQC is: In the formula: J r1 and J g1 These are the cost functions for the series-side voltage and parallel-side current of the MMC-UPQC, respectively. and Discrete time points k Desired voltage on the series side and desired current on the parallel side at +1; i gz ( k +1) represents the discrete time. k Parallel side line current at +1; u rz ( k +1) represents the discrete time. k Series side voltage at +1; Based on the cost functions of the series-side voltage and parallel-side current of the MMC-UPQC, a multi-step predictive control method is adopted to obtain the multi-step predictive control cost functions of the series-side voltage and parallel-side current of the MMC-UPQC. Based on the MMC-UPQC discretized mathematical model, the bridge arm voltage and the number of conducting sub-modules are obtained, and a predictive control finite set is established. The number of conducting sub-modules of the upper and lower bridge arms is determined according to the MMC-UPQC discretized mathematical model and the mapping relationship between the bridge arm voltage and the conducting sub-modules of the upper and lower bridge arms, thereby constructing the predictive control finite set. Based on the bridge arm voltage and the number of conducting submodules, the finite set of the predictive control is reduced; Based on the bridge arm voltage and the number of conducting submodules, circulating current suppression method and voltage equalization control method are used to suppress the internal circulating current of MMC-UPQC and stabilize the capacitor voltage of the conducting submodules; Based on suppressing the internal circulating current of MMC-UPQC and stabilizing the capacitor voltage of the conducting submodule, the optimal switching combination is found in the reduced predictive control finite set based on the multi-step predictive control cost function, and finally the compensation voltage and compensation current are output.

2. The improved predictive control method for MMC-UPQC under unbalanced grid voltage as described in claim 1, characterized in that, The equivalent mathematical model of MMC-UPQC is: In the formula: s =r and g represent the series side and the parallel side, respectively; u ss This refers to the MMC output voltage on the series or parallel side. e sz Output voltage on the series or parallel side; L seq This is the equivalent inductance for the series or parallel side; i sz This refers to the line current on the series or parallel side. R s This refers to the resistance of the series or parallel line.

3. The improved predictive control method for MMC-UPQC under unbalanced grid voltage as described in claim 1, characterized in that, The Eulerian approximation method is used to discretize the equivalent mathematical model of MMC-UPQC.

4. The improved predictive control method for MMC-UPQC under unbalanced grid voltage as described in claim 1, characterized in that, The specific steps for obtaining the multi-step predictive control cost function of the MMC-UPQC series-side voltage and parallel-side current include: Based on the cost functions of the series-side voltage and parallel-side current of the MMC-UPQC, a multi-step predictive control discretization model for the series-side voltage and parallel-side current is constructed using a multi-step predictive control method, as follows: In the formula: i gz ( k+ 2) and u rz ( k+ 2) is the discrete time. k+ Parallel side current and series side voltage at time 2; e gz ( k+ 2) and e rz ( k+ 2) is the discrete time. k+ Output voltages of the parallel and series MMCs at time 2; R g For the parallel side line resistance; L geq This is the equivalent inductance on the parallel side; i gz ( k () represents discrete time. k The parallel-side line current at that time; i rz ( k+ 2) For discrete time intervals k+ The series-side line current at time 2; N The number of submodules; T 1 represents the sampling period; C 2 is the series capacitor; L r For the series-side line inductance; i rz1 ( k +2) represents discrete time. k+ The flow of time 2 C The current of 2; Based on the aforementioned multi-step predictive control discretization model, the multi-step predictive control cost functions for the series-side voltage and parallel-side current of the MMC-UPQC are obtained, as follows: In the formula: J r2 and J g2 These are the multi-step predictive control cost functions for the series-side voltage and parallel-side current of the MMC-UPQC, respectively. and Discrete time points k Desired series voltage and desired parallel current at +2; i gz ( k+ 2) and u rz ( k+ 2) These are discrete time intervals. k+ The parallel side current and series side voltage at time 2.

5. The improved predictive control method for MMC-UPQC under unbalanced grid voltage as described in claim 1, characterized in that, The specific steps for establishing the predictive control finite set include: The discretized model of the output voltage, obtained based on the MMC-UPQC discretized mathematical model, is as follows: In the formula: e sz ( k +1) represents the discrete time. k Output voltage on the series or parallel side at +1; R s For the series or parallel line resistance; The equivalent inductance on the series side is specifically the sum of the series-side line inductance and half of the bridge arm inductance. This refers to the line current on the series or parallel side. ( k +1) represents the discrete time. k The MMC output voltage on the series or parallel side at +1; T 1 represents the sampling period; s =r and g represent the series side and the parallel side, respectively; Based on the discretized model of the output voltage, the discretized model of the bridge arm voltage is derived as follows: In the formula: e psz ( k +1) and e fsz ( k +1) represent discrete time intervals. k+ The output voltages of the upper and lower bridge arms at time 1; V dc This is the DC side voltage value; e sz ( k +1) represent discrete time intervals. k+ Output voltage on the series or parallel side at time 1; Based on the discretized model of the bridge arm voltage, the number of conducting sub-modules in the upper and lower bridge arms can be deduced as follows: In the formula: e psz ( k +1) and e fsz ( k +1) represent discrete time intervals. k+ The output voltages of the upper and lower bridge arms at time 1; V dc This is the DC side voltage value; e sz ( k +1) represent discrete time intervals. k+ Output voltage on the series or parallel side at time 1; s =r and g represent the series side and the parallel side, respectively; The number of the upper and lower bridge arm conducting sub-modules is rounded down, and the number of the sub-modules adjacent to them is selected as the predictive control finite set.

6. The improved predictive control method for MMC-UPQC under unbalanced grid voltage as described in claim 5, characterized in that, The specific steps for reducing the predictive control finite set include: Calculate the rate of change of the bridge arm's output voltage based on the bridge arm's output voltage. The predictive control finite set is reduced based on the rate of change of the bridge arm output voltage and the number of conducting submodules.

7. The improved predictive control method for MMC-UPQC under unbalanced grid voltage as described in claim 6, characterized in that, The specific steps for reducing the predictive control finite set based on the rate of change of the bridge arm output voltage and the number of conducting submodules include: Determine whether the rate of change of the output voltage of the bridge arm is greater than 0. If it is, increase the number of conducting submodules to reduce the predictive control finite set. If not, decrease the number of conducting submodules to reduce the predictive control finite set.

8. The improved predictive control method for MMC-UPQC under unbalanced grid voltage as described in claim 1, characterized in that, The internal circulating current of the MMC-UPQC is suppressed by changing the magnitude of the circulating current through the insertion of a compensation voltage.

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