Sparse Learning for Load Modeling in Microgrids
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摘要: 微电网由负载、储能系统和分布式电源互联集成到能源系统中, 微电网系统可以作为一个整体系统与电网并行运行或以孤岛模式运行. 负载建模是微电网运行和管理中的一个基本问题. 本文着重解决以下两个关键问题: 1)协调负载模型结构的合理性和简洁性; 2)负载模型参数的校准. 与常规负载建模方法不同, 本文提出了一类数据驱动建模方法以同时实现负载模型结构选择和参数校准. 具体地, 该方法从量测数据中稀疏学习静态负载模型和动态负载模型, 其关键方法分别来自于稀疏贝叶斯学习方法和交替方向方法, 即从一组备选非线性字典函数中稀疏学习最主要的非线性项以平衡数据拟合度并实现模型学习. 所提出的方法将机器学习与稀疏表示相结合, 旨在对负载模型从物理角度提供机理解释并向配电网系统操作员提供有关负载的动态信息. 在孤岛微电网测试系统中验证并评估了所提出的算法. 研究测例表明所提出算法从量测数据中实现负载稀疏学习的合理性和对于噪声的鲁棒性.Abstract: The microgrid is integrated into the energy system by interconnected loads, energy storage systems and distributed energy sources, which can be operated in parallel with the grid as a whole system or run in island mode. Load modeling is a fundamental issue in the operation and control of the microgrid. This paper focuses on solving following two key problems, one is the coordination of the reasonability and conciseness of load model structure, the other is the parameters calibration of the load model. Different from conventional load modeling methods, this article proposes data-driven modeling methods to achieve structural selection and parameter calibration of load models simultaneously. Specifically, the key methodologies of sparse learning static load models and dynamic load models from measurement data draw from sparse Bayesian learning method and alternating direction method, and select the most dominant nonlinear terms from a pool of dictionary functions, which balance the data fitness and achieve model learning. The proposed methods combine the machine learning technique with sparse representation, aiming to provide physical interpretation for load model and offer insight to the distribution system operators about dynamics of load. We validate and evaluate the proposed algorithms on the islanded microgrid test system. Case studies demonstrate the effectiveness of proposed algorithms in achieving load modeling from measurement data in terms of reasonability and robustness against measurement noises.
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Key words:
- Static load /
- dynamic load /
- load modeling /
- microgrids /
- machine learning /
- sparse learning
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图 1 微电网通过公共连接点连接主网
Fig. 1 A generic MG is connected to the main grid at the point of common coupling
图 2 广义Hammerstein模型表示负载功率关系
Fig. 2 A general Hammerstein model represenstation for load power
图 4 电压输出和恒定阻抗(Z)负载有功功率辨识结果
Fig. 4 Voltage output and identified real power of constant impedance load
图 5 电压输出和恒定电流(I)负载有功功率辨识结果
Fig. 5 Voltage output and identified real power of constant current load
图 6 电压输出和恒定功率(P)负载有功功率辨识结果
Fig. 6 Voltage output and identified real power of constant power load
图 9 指数负载有功功率和无功功率辨识结果
Fig. 9 Identified real and reactive power output of exponential load
图 10 电压输出和动态负载有功功率辨识结果
Fig. 10 Voltage output and identified real power of dynamic load
表 1 不同负载元件指数值
$ n_p $ 和$ n_q $ [34]Table 1 Values of the exponents
$ n_p $ and$ n_q $ for different load components[34]负载元件/指数值 $ {n_p} $ $ {n_q} $ 空调 $ 0.50 $ $ 2.50 $ 电阻加热器 $ 2.00 $ $ 0.00 $ 灯 $ 1.00 $ $ 3.00 $ 泵机 $ 0.08 $ $ 1.60 $ 大型工业电机 $ 0.05 $ $ 0.50 $ 小型工业电机 $ 0.10 $ $ 0.60 $ 
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表 2 输电线路参数
Table 2 Parameters of transmission lines
输电线路 线路1 线路2 线路3 $ \Omega^{-1} $ 10 10.67 9.82
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表 3 微电网系统参数
Table 3 Parameters of the islanded microgrid
参数 $ \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} $
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表 4 负载Z, I, P稀疏辨识结果
Table 4 Sparse identification results for Z, I, P load
字典函数 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
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表 5 ZIP负载稀疏辨识结果
Table 5 Sparse identification results for ZIP load
字典函数 $ 1 $ $ V $ $ V^2 $ $ V^3 $ $ V^{3.5} $ $ V^4 $ $ V^6 $ 负载1 $1\times 10^{4}$ 1.001 0.011 0 0 0 0 负载2 $1.1\times 10^{4}$ 2.005 0.019 0 0 0 0 负载3 $1.2\times 10^{4}$ 2.993 0.029 0 0 0 0 负载4 $1.3\times 10^{4}$ 4.009 0.041 0 0 0 0
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表 6 指数负载稀疏辨识结果
Table 6 Sparse identification results for exponential load
字典函数 $ 1 $ $ V^{0.05} $ $ V^{0.08} $ $ V^{0.1} $ $ V^{0.5} $ $ V $ $ V^{2.5} $ 空调 0 0 0 0 1 0 0 泵机 0 0 1 0 0 0 0 大型工业电机 0 1 0 0 0 0 0 小型工业电机 0 0 0 1 0 0 0
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表 7 动态负载稀疏辨识结果
Table 7 Sparse identification results for dynamic load
字典函数 有功功率 无功功率 $ 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
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