Leveraging Sparsity in Distribution Grids: System Identification and Harmonic State Estimation

Extended Abstract; Omid Ardakanian

摘要

Power distribution grids are sparse networks. The admittance matrix of a (radial or non-radial) power distribution grid is sparse, safety-critical events are relatively sparse at any given time compared with the number of nodes, and loads that produce significant harmonics at a specific order are also sparse. In this highlight talk, we define different types of sparsity in unbalanced three-phase power distribution systems, and explain how sparsity can be leveraged to address three increasingly important problems: 1 How to identify the topology of a distribution network and estimate parameters of distribution network components (e.g., lines and transformers)? 2 How to identify, classify, and locate faults and certain categories of events in quasi real-time? 3 How to monitor harmonic generation and propagation across the distribution network? Power distribution grids had a simple design for several decades. With radial topology, one-way power flow, and predictable demand curves, distribution systems operators (DSOs) were only required to evaluate the envelope of design conditions to ensure reliability and power quality. The rapid growth in the deployment of power electronic interfaces and distributed energy resources (DERs), such as solar and wind systems, energy storage systems, and plug-in electric vehicles, has complicated distribution system planning and operation in recent years. The DERs can create complex dynamics spanning multiple timescales, introduce distortion in the fundamental waveform of voltages and currents, and pose new challenges in maintaining safe and reliable grid operation. The techniques we present in this talk would enable DSOs to effectively address these challenges. Available measurements: measurements in distribution networks are mainly from smart meters installed at customer premises monitoring average power consumption and service voltage, and a small number of distribution-level pha-sor measurement units (DPMUs) sampling voltage and current magnitudes and phase angles at high frequency in several locations across the network [1]. Nevertheless, DPMU coverage is currently limited at the distribution level [5] and there are data quality issues that must be addressed before this data can be used for the following applications. Model parameter estimation is the problem of jointly estimating model parameters of distribution system components, and the real-time operational structure of the distribution network. The distribution system model is often unavailable or outdated due to the continuous integration of DERs and frequent reconfiguration of feeders [8]. Drawing on sparsity-based regularization techniques [4, 7, 3], we adopt adaptive lasso [10] to uniquely identify the full admittance matrix of the distribution system, when possible. To tackle the low rank structure of a distribution network, we develop a novel algorithm based on matrix decomposition which is capable of identifying a large part of the admittance matrix. Event detection and localization is the problem of detecting the occurrence of safety-critical events in a power system, such as outages, switching operations, or cyber attacks, and pinpointing these events to a small geographical area. Accurate and timely detection and localization is crucial for determining possible remedial control actions to prevent cascading outages, restore service, and reduce the wear and tear of critical equipment. We present an online algorithm for event detection and localization, which involves convex relaxation and matrix partitioning techniques to tackle the low rank structure of the DPMU data [2]. The proposed algorithm does not require a priori knowledge of the underlying network topology and relies only on the available DPMU data. We show that any event that induces a change in the admittance matrix can be detected immediately after it occurs and its type and approximate location can be determined in a sub-second time frame. Harmonic state estimation is the problem of locating harmonic sources and estimating the distribution of harmonic voltages in unbalanced three-phase power distribution systems. We utilize supervised learning techniques to (a) predict the demand of each customer in the secondary distribution network from historical smart meter data, and (b) learn the relationship between power flow in the primary distribution network and demands of downstream customers measured by smart meters. We then predict the aggregate power consumption at each node in the primary network and update the measurement matrix based on these pseudo measurements. The state estimation is then performed using the fine-grained DPMU measurements. Drawing on the idea of sparse Bayesian learning [6, 9], we propose a har- monic state estimator, which is capable of locating harmonic sources with sufficiently high accuracy even when there are only a small number of DPMTJs. This work is done in collaboration with Wei Zhou and Ye Yuan both from the School of Automation at Huazhong University of Science and Technology, Wuhan, China.

机译：配电网是稀疏网络。（径向或非径向）配电网的导纳矩阵稀疏，在任何给定时间，与节点数量相比，安全关键事件相对稀疏，并且按特定顺序产生重要谐波的负载也稀疏。在此重点演讲中，我们定义了不平衡三相配电系统中不同类型的稀疏性，并解释了如何利用稀疏性来解决三个日益重要的问题：1如何识别配电网络的拓扑结构并估算配电网络的参数组件（例如线路和变压器）？ 2如何准实时地识别，分类和定位故障和某些类别的事件？ 3如何监视配电网络中谐波的产生和传播？配电网的设计简单了几十年。借助径向拓扑，单向潮流和可预测的需求曲线，配电系统运营商（DSO）仅需要评估设计条件的范围，以确保可靠性和电能质量。近年来，电力电子接口和分布式能源（例如太阳能和风能系统，储能系统和插电式电动汽车）的部署迅速增长，使配电系统的规划和运营变得复杂。 DER可以创建跨越多个时间尺度的复杂动态，在电压和电流的基本波形中引入失真，并在维持安全可靠的电网运行方面提出新的挑战。我们在本次演讲中介绍的技术将使DSO能够有效应对这些挑战。可用的测量：配电网络中的测量主要来自安装在客户场所的智能电表，用于监视平均功耗和服务电压，以及少数配电级相量测量单元（DPMU）在高电压下采样电压，电流幅值和相角网络中多个位置的频率[1]。尽管如此，DPMU的覆盖范围目前仅限于分发级别[5]，在将这些数据用于以下应用程序之前，必须解决数据质量问题。模型参数估计是联合估计配电系统组件的模型参数和配电网络的实时运行结构的问题。由于DER的持续集成和馈线的频繁重新配置，分配系统模型通常不可用或过时[8]。利用基于稀疏性的正则化技术[4，7，3]，我们采用自适应套索[10]来尽可能唯一地识别分配系统的整个导纳矩阵。为了解决配电网的低秩结构，我们开发了一种基于矩阵分解的新算法，该算法能够识别大部分导纳矩阵。事件检测和定位是检测电源系统中安全关键事件（例如中断，切换操作或网络攻击）的发生并将这些事件定位到较小地理区域的问题。准确，及时的检测和定位对于确定可能的补救控制措施，防止级联中断，恢复服务并减少关键设备的磨损至关重要。我们提出了一种用于事件检测和定位的在线算法，其中涉及凸松弛和矩阵划分技术，以解决DPMU数据的低秩结构[2]。所提出的算法不需要基础网络拓扑的先验知识，而仅依赖于可用的DPMU数据。我们表明，任何导致导纳矩阵发生变化的事件都可以在发生后立即检测到，并且可以在不到一秒的时间内确定其类型和大致位置。谐波状态估计是在不平衡的三相配电系统中定位谐波源和估计谐波电压分布的问题。我们利用监督学习技术来（a）根据历史智能电表数据预测二次配电网中每个客户的需求，以及（b）了解一次配电网的潮流与智能电表测得的下游客户需求之间的关系。然后，我们预测主网络中每个节点的总功耗，并基于这些伪测量值更新测量矩阵。然后使用细粒度DPMU测量执行状态估计。利用稀疏贝叶斯学习的思想[6，9]，我们提出了一个调和状态估计器，即使DPMTJ数量很少，也能够以足够高的精度定位谐波源。这项工作是与武汉华中科技大学自动化学院的周伟和叶媛共同完成的。

Leveraging Sparsity in Distribution Grids: System Identification and Harmonic State Estimation

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