WO2024082730A1 - 一种llcl型电池储能变换器的有限集模型预测控制方法 - Google Patents

一种llcl型电池储能变换器的有限集模型预测控制方法 Download PDF

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WO2024082730A1
WO2024082730A1 PCT/CN2023/107933 CN2023107933W WO2024082730A1 WO 2024082730 A1 WO2024082730 A1 WO 2024082730A1 CN 2023107933 W CN2023107933 W CN 2023107933W WO 2024082730 A1 WO2024082730 A1 WO 2024082730A1
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llcl
value
side current
converter
energy storage
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French (fr)
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高宁
杨铖
陈昊
李波
吴卫民
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上海海事大学
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/01—Arrangements for reducing harmonics or ripples
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/28—Arrangements for balancing of the load in a network by storage of energy
    • H02J3/32—Arrangements for balancing of the load in a network by storage of energy using batteries with converting means
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/12—Arrangements for reducing harmonics from ac input or output
    • H02M1/126—Arrangements for reducing harmonics from ac input or output using passive filters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40—Arrangements for reducing harmonics

Definitions

  • the present invention relates to the field of renewable energy power generation and electric energy storage, and in particular to a finite set model predictive control method for an LLCL type battery energy storage converter.
  • the battery energy storage converter is a key device in the battery energy storage system. It can convert the battery DC power into standard AC power and connect it to the grid, realizing bidirectional energy flow.
  • the finite set model predictive control (FCS-MPC) algorithm is a typical nonlinear control algorithm that has been widely used in the industry. This control method is different from the traditional PI control. This method predicts the grid-connected current of the next cycle based on the model, and then selects the optimal control quantity based on the prediction results. It has clear physical meaning and excellent performance.
  • LLCL filters Compared with traditional filters, LLCL filters insert an inductor in its capacitor branch loop to form a series resonant circuit at the switching frequency, which has good filtering effect and good dynamic performance. In addition, LLCL filters can effectively attenuate the current ripple component at the switching frequency, thereby reducing the overall inductance and the size of passive components, which helps to reduce the cost of the battery energy storage converter.
  • finite set model predictive control algorithms are mostly applied to LCL energy storage converters.
  • Chinese patent application CN201910853161.8 discloses a finite control set model predictive control method for an LCL energy storage converter, which combines state variable estimation with delay compensation, estimates the converter side current, capacitor voltage and grid current by sampling the grid current, and passes the error between the sampled grid current and the estimated grid current through a correction matrix to reduce the impact of model mismatch and parameter drift, and then passes the estimated state variables through a finite control set model predictive control algorithm with a delay compensation link to improve system performance and ultimately achieve control of the LCL energy storage converter.
  • the present invention can reduce the number of sensors, reduce costs, and improve system reliability; combined with the delay compensation algorithm, it eliminates the impact of calculation delays on system performance and improves the quality of grid current.
  • the use of traditional LCL grid-connected filters is relatively expensive and has The problem of unsatisfactory filtering effect leads to low quality of grid current and poor control performance and reliability of the system.
  • the purpose of the present invention is to provide a finite set model predictive control method for an LLCL type battery energy storage converter in order to overcome the defects of the above-mentioned prior art.
  • the present invention applies an LLCL type filter to the energy storage converter and combines it with the FCS-MPC control algorithm to give full play to the advantages of the LLCL type filter, improve the quality of grid-connected power, and achieve optimal control of the energy storage converter.
  • a finite set model predictive control method for LLCL type battery energy storage converter comprises the following steps:
  • the electrical physical quantities include the grid-side current, the converter-side current, the grid voltage and the capacitor voltage at the current moment.
  • the reference values of the converter-side current and the capacitor voltage in the k-th sampling period are derived;
  • a cost function is defined to quantitatively evaluate the control performance of each voltage vector in the finite set
  • the optimal output voltage vector is sent to control the appropriate circuit switch state to work.
  • the construction of the state space mathematical model of the LLCL filter comprises the following steps:
  • i 1 ⁇ is the instantaneous value of the converter side current
  • i 2 ⁇ is the grid side current value
  • i 3 ⁇ is the current value flowing through the capacitor
  • u i ⁇ is the converter output voltage value
  • um ⁇ is the voltage value of the LC branch coupling point
  • u g ⁇ is the grid side voltage value
  • u c ⁇ is the capacitor voltage value
  • C is the capacitor value
  • L 1 is the first inductance value
  • L 2 is the second inductance value
  • equation (6) By substituting equations (3) and (4) into (1) and (2), after variable substitution, the equation group of the ⁇ component is derived as shown in equation (6):
  • L 3 is the third inductance value
  • x ⁇ [i 1 ⁇ i 2 ⁇ u c ⁇ ] T is the state space vector on the ⁇ axis
  • expressions of matrix A, matrix B and matrix B g are respectively:
  • B g [-L 3 /L ⁇ -(L 1 +L 3 )/L ⁇ 0] T ;
  • i 1 ⁇ is the instantaneous value of the converter side current
  • i 2 ⁇ is the grid side current value
  • u i ⁇ is the converter output voltage value
  • ug ⁇ is the grid side voltage value
  • uc ⁇ is the capacitor voltage value
  • sampling period is the battery energy storage switching period, and the sampling period is set to T s .
  • the state space mathematical model expression (7) of the LLCL filter is discretized by using the zero-order holder method, and the discrete model expression of the LLCL filter is obtained as follows:
  • ⁇ res is the equivalent resonant angular frequency of the LLCL filter, and its expression is:
  • the given value of the grid-side current in the kth sampling period is used and Derive the reference value of the capacitor voltage at the current moment, that is, in the kth sampling period and And the reference value of the converter side current and They are respectively expressed as:
  • ⁇ is the grid angular frequency
  • the reference values of the grid-side current, capacitor voltage and converter-side current in the k+1th sampling period are obtained, and their expressions are:
  • i 1 ⁇ * (k+1) and i 1 ⁇ * (k+1) represent the reference values of the converter side current at time k+1
  • i 2 ⁇ * (k+1) and i 2 ⁇ * (k+1) represent the reference values of the grid side current at time k+1
  • uc ⁇ * (k+1) and uc ⁇ * (k+1) represent the reference values of the capacitor voltage at time k+1.
  • cost function is defined as:
  • ⁇ i2 and ⁇ uc represent the priority of the modulation weight factor control
  • ⁇ i1 represents the error between the converter side current reference value and the predicted value at the next moment
  • ⁇ i2 represents the error between the grid side current reference value and the predicted value at the next moment
  • ⁇ uc represents the error between the capacitor voltage reference value and the predicted value at the next moment.
  • i 1 ⁇ * (k+1) and i 1 ⁇ * (k+1) represent the reference values of the converter side current at time k+1
  • i 2 ⁇ * (k+1) and i 2 ⁇ * (k+1) represent the reference values of the grid side current at time k+1
  • uc ⁇ * (k+1) and uc ⁇ * (k+1) represent the reference values of the capacitor voltage at time k+1
  • i 1 ⁇ (k+1) and i 1 ⁇ (k+1) represent the predicted values of the converter side current at time k+1
  • i 2 ⁇ (k+1) and i 2 ⁇ (k+1) represent the predicted values of the grid side current at time k+1
  • uc ⁇ (k+1) and uc ⁇ (k+1) represent the predicted values of the capacitor voltage at time k+1.
  • the voltage vectors u ⁇ (k) and u ⁇ (k) in the finite set of battery energy storage converters are numbered 0-7 respectively, and the voltage vectors are substituted into the discrete model of the LLCL filter as claimed in claim 4 to obtain the predicted value at time k+1.
  • the predicted value at time k+1 is substituted into the cost function to obtain the cost function calculation result corresponding to each voltage vector; the voltage vectors numbered 0-7 in the finite set are defined to correspond to The corresponding cost function expression is J 0 -J 7 ;
  • J 1 >J 4 then further calculate J 0 , J 3 and J 5 , and compare the sizes of J 0 , J 3 , J 5 and J 4 , and select the voltage vector that minimizes the cost function result, which is recorded as the optimal vector.
  • the optimal vector is selected between voltage vector 0 and voltage vector 7 according to the principle of minimum number of switch switching.
  • the present invention has the following beneficial effects:
  • the present invention adopts LLCL filter as a power converter system connected to the power grid, adopts finite control set model predictive control method to control the energy storage converter based on LLCL filter, derives the mathematical model of LLCL filter, and further obtains the specific expression of discrete model, obtains the reference value conversion relationship and recursive expression, applies LLCL filter and introduces the algorithm of the present invention, can improve the performance of battery energy storage converter, makes the battery energy storage converter can effectively suppress harmonics, reduce total inductance, improve the quality of grid-connected electric energy, thereby improves the quality of grid-connected electric energy, and enhances the control performance and reliability of the system.
  • FIG1 is a block diagram of the overall control system corresponding to the present invention.
  • FIG2 is a schematic diagram of the definition of various variables of an LLCL energy storage converter provided by an embodiment of the present invention.
  • FIG3 is a simplified LLCL filter circuit diagram provided by an embodiment of the present invention.
  • FIG4 is a complete control set of a battery energy storage converter provided by an embodiment of the present invention.
  • FIG. 5 is a diagram showing simulation results of grid-connected current and grid-connected voltage provided by an embodiment of the present invention.
  • the present invention is mainly aimed at the application of battery energy storage converters in the field related to power automation equipment, and specifically relates to a finite set model predictive control method for LLCL type battery energy storage converters, wherein the finite set model predictive control method (Finite control set model predictive control) is abbreviated as FCS-MPC.
  • FCS-MPC Finite control set model predictive control
  • the present embodiment provides a finite set model predictive control method for an LLCL type battery energy storage converter.
  • the method uses a finite control set model predictive control method to control an energy storage converter based on an LLCL filter.
  • a state space mathematical model of the LLCL type battery energy storage converter is established and discretized to obtain a discrete model.
  • a grid-side current reference value is converted into a converter-side current and capacitor voltage reference value.
  • a cost function is defined, and the output result of the prediction model is compared with the reference value.
  • the optimal voltage vector is selected and the most appropriate switch state is selected for operation.
  • the energy storage converter used in this embodiment is a typical two-level voltage source battery energy storage converter.
  • FIG1 it is a system overall control block diagram corresponding to the present invention; on this system, executing a finite set model predictive control method of LLCL type battery energy storage converter includes the following steps:
  • Step 1 Use sensors to collect electrical physical quantities to obtain the grid-side current, converter-side current, grid voltage and capacitor voltage at the current moment, and construct a state space mathematical model of the LLCL filter based on the collected electrical physical quantities; in this embodiment, the capacitor voltage refers to the filter capacitor voltage.
  • a two-phase stationary coordinate system ⁇ - ⁇ coordinate system is established, and the state space mathematical model of LLCL filter is derived in the ⁇ - ⁇ coordinate system;
  • i1 ⁇ is the instantaneous value of the converter side current
  • i2 ⁇ is the grid side current value
  • i3 ⁇ is the current value flowing through the capacitor
  • u1 ⁇ is the converter output voltage value
  • um ⁇ is the voltage value of the LC branch coupling point
  • ug ⁇ is the grid side voltage value
  • uc ⁇ is the capacitor voltage value
  • C is the capacitance value
  • L1 is the first inductance value
  • L2 is the second inductance value.
  • equation (6) By substituting equations (3) and (4) into (1) and (2), after variable substitution, the equation group of the ⁇ component is derived as shown in equation (6):
  • L 3 is the third inductance value
  • the state space mathematical model of the LLCL filter on the ⁇ -axis can be obtained by replacing ⁇ with ⁇ .
  • the state space variables of i 1 , i 2 and u c can be obtained jointly, that is, the state space mathematical model of the LLCL filter on the ⁇ - ⁇ coordinate system is:
  • x ⁇ [i 1 ⁇ i 2 ⁇ u c ⁇ ] T is the state space vector on the ⁇ axis
  • x ⁇ [i 1 ⁇ i 2 ⁇ u c ⁇ ] T is the state space vector on the ⁇ axis
  • the expressions of matrix A, matrix B and matrix B g are respectively:
  • B g [-L 3 /L ⁇ -(L 1 +L 3 )/L ⁇ 0] T ;
  • Step 2 Set the sampling period, that is, the battery energy storage switching period is T s , and use the zero-order holder method to discretize the state space mathematical model (7) of the LLCL filter to obtain the discrete model expression of the LLCL filter:
  • ⁇ res is the equivalent resonant angular frequency of the LLCL filter, and its expression is:
  • Step 3 Based on the phasor method, use the given value of the grid-side current in the kth sampling period and The reference values of the capacitor voltage and the converter current at the current moment, i.e., in the kth sampling period, are derived.
  • the simplified process includes the following steps:
  • filter capacitor voltage U c is as follows:
  • the reference value of the capacitor voltage is and
  • the reference value of the converter side current is and
  • the present invention adopts the Lagrange n-order extrapolation method to predict the reference value of the reference variable at the k+1th moment based on the reference values of the converter side current and capacitor voltage in the kth sampling period;
  • i 1 ⁇ * (k+1) and i 1 ⁇ * (k+1) represent the reference values of the converter side current at time k+1
  • i 2 ⁇ * (k+1) and i 2 ⁇ * (k+1) represent the reference values of the grid side current at time k+1
  • uc ⁇ * (k+1) and uc ⁇ * (k+1) represent the reference values of the capacitor voltage at time k+1.
  • Step 4 Define a cost function to quantitatively evaluate the control of each voltage vector in the finite set performance
  • the cost function J is defined as:
  • ⁇ i2 , ⁇ uc represent the priority of the modulation weight factor control
  • ⁇ i1 represents the error between the converter side current reference value and the predicted value at the next moment
  • ⁇ i2 represents the error between the grid side current reference value and the predicted value at the next moment
  • ⁇ uc represents the error between the capacitor voltage reference value and the predicted value at the next moment.
  • i 1 ⁇ * (k+1) and i 1 ⁇ * (k+1) represent the reference values of the converter side current at time k+1
  • i 2 ⁇ * (k+1) and i 2 ⁇ * (k+1) represent the reference values of the grid side current at time k+1
  • uc ⁇ * (k+1) and uc ⁇ * (k+1) represent the reference values of the capacitor voltage at time k+1
  • i 1 ⁇ (k+1) and i 1 ⁇ (k+1) represent the predicted values of the converter side current at time k+1
  • i 2 ⁇ (k+1) and i 2 ⁇ (k+1) represent the predicted values of the grid side current at time k+1
  • uc ⁇ (k+1) and uc ⁇ (k+1) represent the predicted values of the capacitor voltage at time k+1.
  • control set of the battery energy storage converter includes eight voltage vectors, numbered 0-7, and each voltage vector has a corresponding circuit switch state.
  • the corresponding relationship between each vector number, switch state and voltage vector is shown in Table 1.
  • the cost function J is defined, the cost function corresponding to each voltage vector is calculated based on the reference value at time k+1, and the optimal output voltage vector that minimizes the cost function result is selected; the elements in the control set shown in Figure 4 are respectively substituted into the prediction model.
  • the details are as follows:
  • J 1 and J 4 are calculated. If J 1 ⁇ J 4 , J 0 , J 2 and J 6 are further calculated. The sizes of J 0 , J 2 , J 6 and J 1 are compared. The voltage vector that minimizes the cost function result is selected and recorded as the optimal vector. At this time, vectors 3, 4 and 5 in the control set are excluded.
  • J 1 >J 4 then J 0 , J 3 and J 5 are further calculated, and the sizes of J 0 , J 3 , J 5 and J 4 are compared. At this time, vectors 1, 2 and 6 in the control set are excluded, and the voltage vector that minimizes the cost function result is selected and recorded as the optimal vector.
  • the optimal vector is selected between vectors 0 and 7 according to the principle of minimum number of switch changes.
  • vector 1 (100) means that the upper tube of phase A is turned on, the lower tube of phase B is turned on, and the lower tube of phase C is turned on. And so on.
  • FCS-MPC aims to select the most appropriate switch state from the complete control set as shown in FIG4 to operate.
  • the LLCL grid-connected converter can be stably operated under the support of the finite set model predictive control algorithm.
  • this embodiment uses a simulation model for verification, and the waveforms of the grid-connected current and grid-connected voltage are obtained as shown in FIG5 . It can be seen that the grid-connected converter controlled by the present invention works normally and can meet the grid-connected requirements.

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Abstract

本发明涉及一种LLCL型电池储能变换器的有限集模型预测控制方法，该方法采用有限控制集模型预测控制方法对基于LLCL滤波器的储能变换器加以控制，通过建立LLCL型电池储能变换器的状态空间数学模型，将其离散化得到一个离散模型，同时基于相量法，将电网侧电流参考值转化为变换器侧电流和电容电压参考值，定义代价函数，将预测模型输出结果和参考值进行对比，选取最优电压矢量并选择最合适的开关状态进行工作，与现有技术相比，本发明能有效降低入网谐波，提升电能质量，同时充分利用了LLCL滤波器更佳的滤波性能，最终优化LLCL型储能变换器的输出电能质量。

Description

一种LLCL型电池储能变换器的有限集模型预测控制方法
本申请要求于2022年10月17日提交中国专利局、申请号为202211264741.1、发明名称为“一种LLCL型电池储能变换器的有限集模型预测控制方法”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本发明涉及新能源发电与电能存储领域，尤其是涉及一种LLCL型电池储能变换器的有限集模型预测控制方法。
背景技术
电池储能变换器是电池储能系统中的关键设备，能够将电池直流电能转化为标准交流电能并入电网，可实现能量双向流动。有限集模型预测控制(FCS-MPC)算法是一种典型的非线性控制算法，在工业界已被大量应用。该控制方法与传统PI控制不同，该方法基于模型预测下一周期的并网电流，然后根据预测结果选取最优控制量，物理含义明确，性能优越。
LLCL滤波器与传统的滤波器相比，它在其电容分支环路中插入一个电感，在开关频率处构成串联谐振电路，滤波效果佳，有着良好的动态性能。除此之外，LLCL型滤波器可以有效衰减开关频率处的电流纹波分量，从而降低总体电感量，减小无源器件体积，有助于削减电池储能变换器整机成本。
现有技术中，多为在LCL型储能变换器上应用有限集模型预测控制算法，如中国申请专利CN201910853161.8公开了一种LCL型储能变换器的有限控制集模型预测控制方法，将状态变量估算与延时补偿相结合，通过采样电网电流估算出变换器侧电流、电容电压以及电网电流，并且将采样的电网电流和估算的电网电流之间的误差通过一个校正矩阵，以此减小由模型失配和参数漂移带来的影响，再将估算出来的状态变量通过带延时补偿环节的有限控制集模型预测控制算法，以此提高系统性能，最终实现LCL型储能变换器的控制。本发明虽然可以减少传感器数量，降低成本，提高系统可靠性；结合延时补偿算法，消除计算延时对系统性能的影响，提高入网电流质量。但使用传统LCL型并网滤波器成本较高，且存 在滤波效果不理想的问题，从而导致入网电流质量低，系统的控制性能与可靠性也较差。
发明内容
本发明的目的就是为了克服上述现有技术存在的缺陷而提供一种LLCL型电池储能变换器的有限集模型预测控制方法，本发明将LLCL型滤波器应用于储能变换器中，与FCS-MPC控制算法相结合，可发挥出LLCL型滤波器的优势，提升入网电能质量，实现储能变换器的最优控制。
本发明的目的可以通过以下技术方案来实现：
一种LLCL型电池储能变换器的有限集模型预测控制方法，包括以下步骤：
利用传感器采集电气物理量，所述电气物理量包括当前时刻的电网侧电流、变换器侧电流、电网电压及电容电压；
基于所述电气物理量，构建LLCL滤波器的状态空间数学模型；
设定采样周期，对所述LLCL滤波器的状态空间数学模型进行离散化，得到离散模型；
利用第k个采样周期中电网侧电流的给定值，推导出第k个采样周期中变换器侧电流和电容电压的参考值；
基于第k个采样周期中变换器侧电流和电容电压的参考值，根据所述离散模型，预测k+1时刻的参考值；
定义代价函数，用于定量评估有限集中每个电压矢量的控制性能；
基于所述k+1时刻的参考值，计算每个电压矢量对应的代价函数，选出使代价函数结果最小的最优输出电压矢量；
根据各个电压矢量与电路开关的对应关系，通过发送最优输出电压矢量以控制合适的电路开关状态进行工作。
进一步地，所述构建LLCL滤波器的状态空间数学模型包括以下步骤：
建立两相静止坐标系α-β坐标系；
以流经电感L1的电流i1、和流经电感L2的电流i2及电容C的电压uc为状态空间变量，基于电池储能变换器的整体拓扑结构，建立α坐标轴下各回路的基本方程组：

i3α＝i1α-i2α；(3)

其中，对于α坐标轴，i1α为变换器侧电流的瞬时值，i2α为电网侧电流值，i3α为流经电容的电流值，uiα为变换器输出电压值，umα为LC支路耦合点的电压值，ugα为电网侧电压值，ucα为电容电压值，C为电容值，L1为第一电感值，L2为第二电感值；
通过将式(3)和(4)代入(1)和(2)，经过变量代换，推导出α分量的方程组如式(6)所示：
其中，L3为第三电感值；
得到LLCL滤波器在α轴上的状态空间数学模型表达式为：
其中，xα＝[i1α i2α ucα]T为α轴上的状态空间向量，矩阵A、矩阵B和矩阵Bg的表达式分别为：
B＝[(L2+L3)/LΣ L3/LΣ 0]T；
Bg＝[-L3/LΣ -(L1+L3)/LΣ 0]T；
其中LΣ＝L1L2+L1L3+L2L3。
进一步地，所述α-β坐标系的α轴和β完全对称，将α替换为β可得到LLCL滤波器在β轴上的状态空间数学模型表达式为：
其中，xβ＝[i1β i2β ucβ]T为β轴上的状态空间向量，对于β坐标轴，i1β为变换器侧电流的瞬时值，i2β为电网侧电流值，uiβ为变换器输出电压值，ugβ为电网侧电压值，ucβ为电容电压值；
则得到LLCL滤波器在α-β坐标系上的状态空间数学模型为：
进一步地，所述采样周期即电池储能开关周期，设定采样周期为Ts，采用零阶保持器法，对LLCL滤波器的状态空间数学模型表达式(7)进行离散化，得到LLCL滤波器的离散模型表达式为：
其中，k表示周期时刻，系统矩阵Ad、输入矩阵Bd和Bgd的详细表达式如下：


其中ωres为LLCL滤波器的等效谐振角频率，其表达式为：
进一步地，基于相量法，利用第k个采样周期中电网侧电流的给定值和推导出当前时刻，即第k个采样周期中，电容电压的参考值和以及变换器侧电流的参考值和其分别表示为：

其中，ω为电网角频率。
进一步地，基于拉格朗日n阶外推法，获得第k+1个采样周期中，电网侧电流、电容电压及变换器侧电流的参考值，其表达式为：
其中，i1α *(k+1)及i1β *(k+1)表示k+1时刻变换器侧电流的参考值，i2α *(k+1)及i2β *(k+1)表示k+1时刻电网侧电流的参考值，ucα *(k+1)及ucβ *(k+1)表示k+1时刻电容电压的参考值。
进一步地，定义代价函数为：
其中λi2及λuc表示调制权重因子控制的优先级，εi1表示下一时刻变换器侧电流参考值和预测值之间的误差，εi2表示下一时刻电网侧电流参考值和预测值之间的误差，εuc表示下一时刻电容电压参考值和预测值之间的误差，其表达式为：
其中，i1α *(k+1)及i1β *(k+1)表示k+1时刻变换器侧电流的参考值，i2α *(k+1)及i2β *(k+1)表示k+1时刻电网侧电流的参考值，ucα *(k+1)及ucβ *(k+1)表示k+1时刻电容电压的参考值；i1α(k+1)及i1β(k+1)表示k+1时刻变换器侧电流的预测值，i2α(k+1)及i2β(k+1)表示k+1时刻电网侧电流的预测值，ucα(k+1)及ucβ(k+1)表示k+1时刻电容电压的预测值。
进一步地，对电池储能变换器有限集中的电压矢量uα(k)及uβ(k)分别编号为0-7，将所述电压矢量代入如权利要求4所述的LLCL滤波器的离散模型中，得到k+1时刻的预测值。
进一步地，将所述k+1时刻的预测值代入代价函数，得到各个电压矢量对应的代价函数计算结果；定义有限集中编号0-7的电压矢量分别对 应的代价函数表达式为J0-J7；
首先计算J1及J4，若J1<J4，则进一步计算J0、J2和J6，并比较J0、J2、J6及J1的大小，选出使代价函数结果最小的电压矢量，记为最优矢量；
若J1>J4，则进一步计算J0、J3和J5，并比较J0、J3、J5和J4的大小，选出使代价函数结果最小的电压矢量，记为最优矢量。
进一步地，若J0为最小代价函数，则按开关切换数最少原则，在电压矢量0和电压矢量7之间选取最优矢量。
与现有技术相比，本发明具有以下有益效果：
本发明采用LLCL滤波器作为功率变换器系统并入电网，采用有限控制集模型预测控制方法对基于LLCL滤波器的储能变换器加以控制，通过推导出LLCL滤波器数学模型，并进一步得到离散模型的具体表达式，得出参考值换算关系与递推表达式，应用LLCL滤波器并引入本发明所述算法后，可提高电池储能变换器的性能，使得电池储能变换器能够有效抑制谐波，降低总电感量，提高入网电流质量，从而改善并网的电能质量，提升系统控制性能与可靠性。
说明书附图
为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动性的前提下，还可以根据这些附图获得其他的附图。
图1为本发明对应的系统整体控制框图；
图2为本发明实施实例提供的LLCL储能变换器各变量定义示意图；
图3为本发明实施实例提供的简化的LLCL滤波电路图；
图4为本发明实施实例提供的电池储能变换器完整控制集；
图5为本发明实施实例提供的并网电流与并网电压仿真结果图。
具体实施方式
以下由特定的具体实施例说明本发明的实施方式，熟悉此技术的人士可由本说明书所揭露的内容轻易地了解本发明的其他优点及功效。为了更 好地了解本发明的目的、结构及功能，下面结合附图，对本发明一种风力发电机组的嵌入式风轮结构做进一步详细的描述。
本发明主要面向电力自动化设备相关领域中的电池储能变换器应用，具体涉及一种针对LLCL型电池储能变换器的有限集模型预测控制方法，其中有限集模型预测控制方法(Finite control set model predictive control)简称为FCS-MPC。
本实施例提供了一种LLCL型电池储能变换器的有限集模型预测控制方法，该方法采用有限控制集模型预测控制方法对基于LLCL滤波器的储能变换器加以控制，通过建立LLCL型电池储能变换器的状态空间数学模型，将其离散化得到一个离散模型，同时基于相量法，将电网侧电流参考值转化为变换器侧电流和电容电压参考值，定义代价函数，将预测模型输出结果和参考值进行对比，选取最优电压矢量并选择最合适的开关状态进行工作。
本实施例中使用的储能变换器为典型的两电平电压源型电池储能变换器。
如图1所示，为本发明对应的系统整体控制框图；在此系统上，执行一种LLCL型电池储能变换器的有限集模型预测控制方法包括以下步骤：
步骤1、利用传感器采集电气物理量，获取当前时刻的电网侧电流、变换器侧电流、电网电压及电容电压，基于采集的电气物理量，构建LLCL滤波器的状态空间数学模型；本实施例中，所述电容电压指滤波电容电压。
具体步骤为：
建立两相静止坐标系α-β坐标系，在α-β坐标系进行LLCL滤波器的状态空间数学模型推导；
如图2所示，为LLCL储能变换器各变量定义示意图；
以流经电感L1的电流i1、和流经电感L2的电流i2及电容C的电压uc为状态空间变量，根据电池储能变换器的整体拓扑结构，建立α坐标轴下各回路的基本方程组：

i3α＝i1α-i2α(3)

其中，对于α坐标轴，i1α为变换器侧电流的瞬时值，i2α为电网侧电流值，i3α为流经电容的电流值，uiα为变换器输出电压值，umα为LC支路耦合点的电压值，ugα为电网侧电压值，ucα为电容电压值，C为电容值，L1为第一电感值，L2为第二电感值。
通过将式(3)和(4)代入(1)和(2)，经过变量代换，推导出α分量的方程组如式(6)所示：
其中，L3为第三电感值；
进一步地，由于α-β坐标系的α轴和β完全对称，将α替换为β即可得到LLCL滤波器在β轴上的状态空间数学模型，联立可得到i1、i2及uc的状态空间变量，即得到LLCL滤波器在α-β坐标系上的状态空间数学模型为：
其中，xα＝[i1α i2α ucα]T为α轴上的状态空间向量，xβ＝[i1β i2β ucβ]T为β轴上的状态空间向量，矩阵A、矩阵B和矩阵Bg的表达式分别为：
B＝[(L2+L3)/LΣ L3/LΣ 0]T；
Bg＝[-L3/LΣ -(L1+L3)/LΣ 0]T；
其中LΣ＝L1L2+L1L3+L2L3。
步骤2、设定采样周期，即电池储能开关周期为Ts，采用零阶保持器法，对LLCL滤波器的状态空间数学模型(7)进行离散化，得到LLCL滤波器的离散模型表达式为：
其中，k表示周期时刻，系统矩阵Ad、输入矩阵Bd和Bgd的详细表达式如下：


其中ωres为LLCL滤波器的等效谐振角频率，其表达式为：
步骤3、基于相量法，利用第k个采样周期中电网侧电流的给定值和推导出当前时刻，即第k个采样周期中，电容电压和变换器测电流的参考值。其简化过程包括以下步骤：
首先，LLCL滤波器的简化电路如图3所示，其中Ui表示输入电压，Ug表示输出电压，ω为电网角频率，I1为流经电感L1的电流值，I2为流经电感L2的电流值，I3为流经电容C的电流值，将其定义为：
其次，根据基尔霍夫电压定律(KVL)与基尔霍夫电流定律(KCL)，公共耦合点处电压值Um与流经电感L1的电流值I1的表达式如式(14)及式(15)所示：

滤波电容电压Uc的表达式如下所示：
其中：
最后，将式(17)代入式(15)，并根据稳态下各相量与α-β坐标系下 的基本数量关系，即可推导出第k时刻，变换器侧电流和滤波电容电压的参考值可表示为：

其中，电容电压的参考值为和变换器侧电流的参考值为和
根据以上推导结果，可以解决变换器在当前时刻电流参考值和滤波电容电压参考值无法直接给定的问题。
在获取LLCL滤波器第k时刻参考值后，需要获得k+1时刻的参考值以选出使代价函数结果最小的最优输出电压矢量，本发明采用拉格朗日n阶外推法，基于第k个采样周期中变换器侧电流和电容电压的参考值，预测参考变量k+1时刻的参考值；
拉格朗日n阶外推法预测参考变量未来值的公式如式(20)所示：
对于电池储能变换器所涉及的正弦参考值，选取n＝2，可获得k+1时刻的参考值表达式如式(21)所示：
其中，i1α *(k+1)及i1β *(k+1)表示k+1时刻变换器侧电流的参考值，i2α *(k+1)及i2β *(k+1)表示k+1时刻电网侧电流的参考值，ucα *(k+1)及ucβ *(k+1)表示k+1时刻电容电压的参考值。
步骤4、定义代价函数，用于定量评估有限集中每个电压矢量的控制 性能；
为实现模型预测控制的目标，在获取参考变量预测值后，应定义代价函数，以便定量评估有限控制集中每个向量的控制性能。因此，代价函数的构建是FCS-MPC中的重要问题。在本实施例中，代价函数J定义为：
其中λi2,λuc表示调制权重因子控制的优先级，εi1表示下一时刻变换器侧电流参考值和预测值之间的误差，εi2表示下一时刻电网侧电流参考值和预测值之间的误差，εuc表示下一时刻电容电压参考值和预测值之间的误差，其表达式如式(23)所示：
其中，i1α *(k+1)及i1β *(k+1)表示k+1时刻变换器侧电流的参考值，i2α *(k+1)及i2β *(k+1)表示k+1时刻电网侧电流的参考值，ucα *(k+1)及ucβ *(k+1)表示k+1时刻电容电压的参考值；i1α(k+1)及i1β(k+1)表示k+1时刻变换器侧电流的预测值，i2α(k+1)及i2β(k+1)表示k+1时刻电网侧电流的预测值，ucα(k+1)及ucβ(k+1)表示k+1时刻电容电压的预测值。
如图4所示，电池储能变换器的控制集中包括八个电压矢量，分别编号为0-7，各个电压矢量具有对应的电路开关状态。各个矢量编号、开关状态及电压矢量的对应关系如表1所示。
表1

代价函数J定义完毕后，基于k+1时刻的参考值，计算每个电压矢量对应的代价函数，选出使代价函数结果最小的最优输出电压矢量；将图4所示控制集中的元素分别代入预测模型。具体如下：
定义有限集中编号0-7的电压矢量分别对应的代价函数表达式为J0-J7。首先计算J1及J4，令[uα(k) uβ(k)]T＝Udc×[2/3 0]T，代入式(8)，可得到k+1时刻参考值的预测值，将预测结果代入式(22)，即可得到代价函数计算结果J1，其中Udc代表直流侧电池电压(可认为是一常量)。
然后令[uα(k) uβ(k)]T＝Udc×[-2/3 0]T，步骤同上，代入式(8)得到预测值后代入式(22)，可得到结果J4。
首先计算J1及J4，若J1<J4，则进一步计算J0、J2和J6，并比较J0、J2、J6及J1的大小，选出使代价函数结果最小的电压矢量，记为最优矢量；此时控制集中的矢量3、4、5被排除；
若J1>J4，则进一步计算J0、J3和J5，并比较J0、J3、J5和J4的大小，此时控制集中的矢量1、2、6被排除，选出使代价函数结果最小的电压矢量，记为最优矢量。
如果经计算最小J对应的下角标为0，则按开关切换数最少原则，在矢量0和7之间选取最优矢量。
最后，根据电压矢量与电路开关管的对应关系，通过发送最优输出电压矢量以控制合适的电路开关状态进行工作。例如：矢量1(100)代表A相上管开通，B相下管开通，C相下管开通。以此类推。
通常，FCS-MPC旨在从如图4所示的完整控制集中选择最合适的开关状态进行工作，根据本实施例所述的实施步骤，就可以实现LLCL并网变换器在有限集模型预测控制算法支持下稳定工作。
为验证这一控制算法，本实施例利用仿真模型进行验证，得到并网电流及并网电压的波形如图5所示，可见基于本发明控制的并网变换器工作正常，可满足并网要求。
虽然，上文中已经用一般性说明及具体实施例对本发明作了详尽的描述，但在本发明基础上，可以对之作一些修改或改进，这对本领域技术人员而言是显而易见的。因此，在不偏离本发明精神的基础上所做的这些修改或改进，均属于本发明要求保护的范围。

Claims (10)

  1. 一种LLCL型电池储能变换器的有限集模型预测控制方法，其特征在于，包括以下步骤：
    利用传感器采集电气物理量，所述电气物理量包括当前时刻的电网侧电流、变换器侧电流、电网电压及电容电压；
    基于所述电气物理量，构建LLCL滤波器的状态空间数学模型；
    设定采样周期，对所述LLCL滤波器的状态空间数学模型进行离散化，得到离散模型；
    利用第k个采样周期中电网侧电流的给定值，推导出第k个采样周期中变换器侧电流和电容电压的参考值；
    基于第k个采样周期中变换器侧电流和电容电压的参考值，根据所述离散模型，预测k+1时刻的参考值；
    定义代价函数，用于定量评估有限集中每个电压矢量的控制性能；
    基于所述k+1时刻的参考值，计算每个电压矢量对应的代价函数，选出使代价函数结果最小的最优输出电压矢量；
    根据各个电压矢量与电路开关的对应关系，通过发送最优输出电压矢量以控制合适的电路开关状态进行工作。
  2. 根据权利要求1所述的一种LLCL型电池储能变换器的有限集模型预测控制方法，其特征在于，所述构建LLCL滤波器的状态空间数学模型包括以下步骤：
    建立两相静止坐标系α-β坐标系；
    以流经电感L1的电流i1、和流经电感L2的电流i2及电容C的电压uc为状态空间变量，基于电池储能变换器的整体拓扑结构，建立α坐标轴下各回路的基本方程组：


    i3α＝i1α-i2α        (3)

    其中，对于α坐标轴，i1α为变换器侧电流的瞬时值，i2α为电网侧电流值，i3α为流经电容的电流值，uiα为变换器输出电压值，umα为LC支路耦合点的电压值，ugα为电网侧电压值，ucα为电容电压值，C为电容值，L1为第一电感值，L2为第二电感值；
    通过将式(3)和(4)代入(1)和(2)，经过变量代换，推导出α分量的方程组如式(6)所示：
    其中，L3为第三电感值；
    得到LLCL滤波器在α轴上的状态空间数学模型表达式为：
    其中，xα＝[i1α i2α ucα]T为α轴上的状态空间向量，矩阵A、矩阵B和矩阵Bg的表达式分别为：

    B＝[(L2+L3)/LΣ L3/LΣ 0]T
    Bg＝[-L3/LΣ -(L1+L3)/LΣ 0]T
    其中LΣ＝L1L2+L1L3+L2L3。
  3. 根据权利要求2所述的一种LLCL型电池储能变换器的有限集模型预测控制方法，其特征在于，所述α-β坐标系的α轴和β完全对称，将α 替换为β可得到LLCL滤波器在β轴上的状态空间数学模型表达式为：
    其中，xβ＝[i1β i2β ucβ]T为β轴上的状态空间向量，对于β坐标轴，i1β为变换器侧电流的瞬时值，i2β为电网侧电流值，uiβ为变换器输出电压值，ugβ为电网侧电压值，ucβ为电容电压值；
    则得到LLCL滤波器在α-β坐标系上的状态空间数学模型为：
  4. 根据权利要求3所述的一种LLCL型电池储能变换器的有限集模型预测控制方法，其特征在于，所述采样周期即电池储能开关周期，设定采样周期为Ts，采用零阶保持器法，对LLCL滤波器的状态空间数学模型表达式(7)进行离散化，得到LLCL滤波器的离散模型表达式为：
    其中，k表示周期时刻，系统矩阵Ad、输入矩阵Bd和Bgd的详细表达式如下：


    其中ωres为LLCL滤波器的等效谐振角频率，其表达式为：
  5. 根据权利要求2所述的一种LLCL型电池储能变换器的有限集模型预测控制方法，其特征在于，基于相量法，利用第k个采样周期中电网侧电流的给定值和推导出当前时刻，即第k个采样周期中，电容电压的参考值和以及变换器侧电流的参考值和其分别表示为：

    其中，ω为电网角频率。
  6. 根据权利要求5所述的一种LLCL型电池储能变换器的有限集模型预测控制方法，其特征在于，基于拉格朗日n阶外推法，获得第k+1个采样周期中，电网侧电流、电容电压及变换器侧电流的参考值，其表达式为：
    其中，i1α *(k+1)及i1β *(k+1)表示k+1时刻变换器侧电流的参考值，i2α *(k+1)及i2β *(k+1)表示k+1时刻电网侧电流的参考值，ucα *(k+1)及ucβ *(k+1)表示k+1时刻电容电压的参考值。
  7. 根据权利要求4所述的一种LLCL型电池储能变换器的有限集模型预测控制方法，其特征在于，定义代价函数为：
    其中λi2及λuc表示调制权重因子控制的优先级，εi1表示下一时刻变换器侧电流参考值和预测值之间的误差，εi2表示下一时刻电网侧电流参考值和预测值之间的误差，εuc表示下一时刻电容电压参考值和预测值之间的误差，其表达式为：
    其中，i1α *(k+1)及i1β *(k+1)表示k+1时刻变换器侧电流的参考值，i2α *(k+1)及i2β *(k+1)表示k+1时刻电网侧电流的参考值，ucα *(k+1)及ucβ *(k+1)表示k+1时刻电容电压的参考值；i1α(k+1)及i1β(k+1)表示k+1时刻变换器侧电流的预测值，i2α(k+1)及i2β(k+1)表示k+1时刻电网侧电流的预测值，ucα(k+1)及ucβ(k+1)表示k+1时刻电容电压的预测值。
  8. 根据权利要求7所述的一种LLCL型电池储能变换器的有限集模型预测控制方法，其特征在于，对电池储能变换器有限集中的电压矢量uα(k)及uβ(k)分别编号为0-7，将所述电压矢量代入所述的LLCL滤波器的离散模型中，得到k+1时刻的预测值。
  9. 根据权利要求8所述的一种LLCL型电池储能变换器的有限集模型预测控制方法，其特征在于，将所述k+1时刻的预测值代入代价函数，得到各个电压矢量对应的代价函数计算结果；定义有限集中编号0-7的电压矢量分别对应的代价函数表达式为J0-J7；
    首先计算J1及J4，若J1<J4，则进一步计算J0、J2和J6，并比较J0、J2、J6及J1的大小，选出使代价函数结果最小的电压矢量，记为最优矢量；
    若J1>J4，则进一步计算J0、J3和J5，并比较J0、J3、J5和J4的大小，选出使代价函数结果最小的电压矢量，记为最优矢量。
  10. 根据权利要求9所述的一种LLCL型电池储能变换器的有限集模型预测控制方法，其特征在于，若J0为最小代价函数，则按开关切换数最少原则，在电压矢量0和电压矢量7之间选取最优矢量。
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