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                    基于稀疏學習的微電網負載建模

                    平作為 何維 李俊林 楊濤

                    平作為, 何維, 李俊林, 楊濤. 基于稀疏學習的微電網負載建模. 自動化學報, 2020, 46(9): 1798?1808 doi: 10.16383/j.aas.c200154
                    引用本文: 平作為, 何維, 李俊林, 楊濤. 基于稀疏學習的微電網負載建模. 自動化學報, 2020, 46(9): 1798?1808 doi: 10.16383/j.aas.c200154
                    Ping Zuo-Wei, He Wei, Li Jun-Lin, Yang Tao. Sparse learning for load modeling in microgrids. Acta Automatica Sinica, 2020, 46(9): 1798?1808 doi: 10.16383/j.aas.c200154
                    Citation: Ping Zuo-Wei, He Wei, Li Jun-Lin, Yang Tao. Sparse learning for load modeling in microgrids. Acta Automatica Sinica, 2020, 46(9): 1798?1808 doi: 10.16383/j.aas.c200154

                    基于稀疏學習的微電網負載建模

                    doi: 10.16383/j.aas.c200154
                    基金項目: 國家自然科學基金委重大項目 (61991403, 61991400)資助
                    詳細信息
                      作者簡介:

                      平作為:華中科技大學人工智能與自動化學院博士研究生. 主要研究方向為智能電網, 系統辨識與非線性控制.E-mail: pingzuowei@hust.edu.cn

                      何維:華中科技大學電氣與電子工程學院博士后. 主要研究方向為電力電子裝備建模, 穩定分析與控制.E-mail: hewei5590@hust.edu.cn

                      李俊林:華中科技大學人工智能與自動化學院博士研究生. 主要研究方向為系統辨識, 稀疏信號恢復, 非凸優化與高維統計.E-mail: jlli@hust.edu.cn

                      楊濤:東北大學流程工業綜合自動化國家重點實驗室教授. 主要研究方向為工業人工智能, 信息物理系統, 分布式協同控制和優化. 本文通信作者.E-mail: yangtao@mail.neu.edu.cn

                    Sparse Learning for Load Modeling in Microgrids

                    Funds: Supported by Major Program of National Natural Science Foundation of China (61991403, 61991400)
                    • 摘要: 微電網由負載、儲能系統和分布式電源互聯集成到能源系統中, 微電網系統可以作為一個整體系統與電網并行運行或以孤島模式運行. 負載建模是微電網運行和管理中的一個基本問題. 本文著重解決以下兩個關鍵問題: 1)協調負載模型結構的合理性和簡潔性; 2)負載模型參數的校準. 與常規負載建模方法不同, 本文提出了一類數據驅動建模方法以同時實現負載模型結構選擇和參數校準. 具體地, 該方法從量測數據中稀疏學習靜態負載模型和動態負載模型, 其關鍵方法分別來自于稀疏貝葉斯學習方法和交替方向方法, 即從一組備選非線性字典函數中稀疏學習最主要的非線性項以平衡數據擬合度并實現模型學習. 所提出的方法將機器學習與稀疏表示相結合, 旨在對負載模型從物理角度提供機理解釋并向配電網系統操作員提供有關負載的動態信息. 在孤島微電網測試系統中驗證并評估了所提出的算法. 研究測例表明所提出算法從量測數據中實現負載稀疏學習的合理性和對于噪聲的魯棒性.
                    • 圖  1  微電網通過公共連接點連接主網

                      Fig.  1  A generic MG is connected to the main grid at the point of common coupling

                      圖  2  廣義Hammerstein模型表示負載功率關系

                      Fig.  2  A general Hammerstein model represenstation for load power

                      圖  3  孤島微電網測試系統

                      Fig.  3  Islanded microgrid test system

                      圖  4  電壓輸出和恒定阻抗(Z)負載有功功率辨識結果

                      Fig.  4  Voltage output and identified real power of constant impedance load

                      圖  5  電壓輸出和恒定電流(I)負載有功功率辨識結果

                      Fig.  5  Voltage output and identified real power of constant current load

                      圖  6  電壓輸出和恒定功率(P)負載有功功率辨識結果

                      Fig.  6  Voltage output and identified real power of constant power load

                      圖  7  孤島微電網對于ZIP負載的電壓輸出

                      Fig.  7  Voltage output of the islanded microgrid for ZIP load

                      圖  8  ZIP負載有功功率和無功功率辨識結果

                      Fig.  8  Identified real and reactive power output of ZIP load

                      圖  9  指數負載有功功率和無功功率辨識結果

                      Fig.  9  Identified real and reactive power output of exponential load

                      圖  10  電壓輸出和動態負載有功功率辨識結果

                      Fig.  10  Voltage output and identified real power of dynamic load

                      圖  11  有功功率真實值與擬合殘差

                      Fig.  11  Fitting error of real power

                      表  1  不同負載元件指數值$ n_p $$ n_q $[34]

                      Table  1  Values of the exponents $ n_p $ and $ n_q $ for different load components[34]

                      負載元件/指數值 $ {n_p} $ $ {n_q} $
                      空調 $ 0.50 $ $ 2.50 $
                      電阻加熱器 $ 2.00 $ $ 0.00 $
                      $ 1.00 $ $ 3.00 $
                      泵機 $ 0.08 $ $ 1.60 $
                      大型工業電機 $ 0.05 $ $ 0.50 $
                      小型工業電機 $ 0.10 $ $ 0.60 $
                      下載: 導出CSV

                      表  2  輸電線路參數

                      Table  2  Parameters of transmission lines

                      輸電線路 線路1 線路2 線路3
                      $ \Omega^{-1} $ 10 10.67 9.82
                      下載: 導出CSV

                      表  3  微電網系統參數

                      Table  3  Parameters of the islanded microgrid

                      參數 $ \mu G_1 $ $ \mu G_2 $ $ \mu G_3 $ $ \mu G_4 $
                      DG $ \tau_{P}(s) $ 0.16 0.16 0.16 0.16
                      $ K_{P}(s) $ $ 4\times 10^{-5} $ $ 2\times 10^{-5} $ $ 3\times 10^{-5} $ $ 4\times 10^{-5} $
                      $ \tau_{Q}(s) $ 0.16 0.16 0.16 0.16
                      $ K_{Q}(s) $ $ 4.2\times 10^{-4} $ $ 4.2\times 10^{-4} $ $ 4.2\times 10^{-4} $ $ 4.2\times 10^{-4} $
                      Load $ P_{Z} $ 0.01 0.02 0.03 0.04
                      $ P_{I} $ 1 2 3 4
                      $ P_{P} $ $ 1\times 10^{4} $ $ 1.1\times 10^{4} $ $ 1.2\times 10^{4} $ $ 1.3\times 10^{4} $
                      $ Q_{Z} $ 0.01 0.02 0.03 0.04
                      $ Q_{I} $ 1 2 3 4
                      $ Q_{P} $ $ 1\times 10^{4} $ $ 1.1\times 10^{4} $ $ 1.2\times 10^{4} $ $ 1.3\times 10^{4} $
                      下載: 導出CSV

                      表  4  負載Z, I, P稀疏辨識結果

                      Table  4  Sparse identification results for Z, I, P load

                      字典函數 Z I P
                      1 0 0 $1\times 10^{-4} $
                      $ V_1 $ 0 1.001 0
                      $ V_1^2 $ 0.098 0 0
                      $ V_1^3 $ 0 0 0
                      $ V_1^4 $ 0 0 0
                      1 0 0 $1.1\times 10^{-4} $
                      $ V_2 $ 0 1.998 0
                      $ V_2^2 $ 0.019 0 0
                      $ V_2^3 $ 0 0 0
                      $ V_2^4 $ 0 0 0
                      1 0 0 $1.2\times 10^{-4} $
                      $ V_3 $ 0 2.999 0
                      $ V_3^2 $ 0.031 0 0
                      $ V_3^3 $ 0 0 0
                      $ V_3^4 $ 0 0 0
                      1 0 0 $1.4\times 10^{-4} $
                      $ V_4 $ 0 3.999 0
                      $ V_4^2 $ 0.039 0 0
                      $ V_4^3 $ 0 0 0
                      $ V_4^4 $ 0 0 0
                      下載: 導出CSV

                      表  5  ZIP負載稀疏辨識結果

                      Table  5  Sparse identification results for ZIP load

                      字典函數 $ 1 $ $ V $ $ V^2 $ $ V^3 $ $ V^{3.5} $ $ V^4 $ $ V^6 $
                      負載1 $1\times 10^{4}$ 1.001 0.011 0 0 0 0
                      負載2 $1.1\times 10^{4}$ 2.005 0.019 0 0 0 0
                      負載3 $1.2\times 10^{4}$ 2.993 0.029 0 0 0 0
                      負載4 $1.3\times 10^{4}$ 4.009 0.041 0 0 0 0
                      下載: 導出CSV

                      表  6  指數負載稀疏辨識結果

                      Table  6  Sparse identification results for exponential load

                      字典函數 $ 1 $ $ V^{0.05} $ $ V^{0.08} $ $ V^{0.1} $ $ V^{0.5} $ $ V $ $ V^{2.5} $
                      空調 0 0 0 0 1 0 0
                      泵機 0 0 1 0 0 0 0
                      大型工業電機 0 1 0 0 0 0 0
                      小型工業電機 0 0 0 1 0 0 0
                      下載: 導出CSV

                      表  7  動態負載稀疏辨識結果

                      Table  7  Sparse identification results for dynamic load

                      字典函數 有功功率 無功功率
                      $ y(t) $ 1.0001 1.0001
                      $ q^{-1}y(t) $ ?1.6003 ?0.8997
                      $ q^{-2}y(t) $ 0.7998 0.5003
                      $ q^{-3}y(t) $ 0 0
                      $ q^{-4}y(t) $ 0 0
                      $ 1 $ 0.9002 0.8905
                      $ V(t) $ 0.4003 0.0984
                      $ V^2(t) $ 0.1727 0.4447
                      $ V^3(t) $ 0 0
                      $ V^4(t) $ 0 0
                      下載: 導出CSV
                      360彩票
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                    • 收稿日期:  2020-03-23
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