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This is the second part of a two-part tutorial on data-driven power flow linearization (DPFL). The motivations, challenges, and training algorithms for DPFL were reviewed and discussed in Part I. In this part, the supportive methods for DPFL training and the experiments used to verify DPFL models are surveyed. The lack of a linearity metric in existing experiments is also discussed. Accordingly, this paper proposes a data-driven indicator to measure the linearity of any given system. The proposed indicator is intuitive, unbiased, and easy to calculate. Based on this indicator, various linearity evaluations are conducted. Results show that system linearity is not consistently related to either system scale or load level. In addition, voltages always exhibit high linearity regardless of the system scale and the load level. Yet, angles and line flows do not. Additionally, some specific systems demonstrate high and stable linearity even when the load conditions change, whereas others consistently show very low linearity. Finally, we conclude this paper by discussing various potential directions for future research in DPFL.

The accuracy limitation of physics-driven power flow linearization approaches and the widespread deployment of advanced metering infrastructure render data-driven power flow linearization (DPFL) methods a valuable alternative. While DPFL is still an emerging research topic, substantial studies have already been carried out in this area. However, a comprehensive overview and comparison of the available DPFL approaches are missing in the existing literature. This paper intends to close this gap and, therefore, provides a narrative overview of the current DPFL research. Both the challenges (including data-related and power-system-related issues) and methodologies (namely regression-based and tailored approaches) in DPFL studies are surveyed in this paper; numerous future research directions of DPFL analysis are discussed and summarized as well.

The widespread deployment of advanced metering infrastructure has led to an increased interest in data-driven power flow linearization (DPFL) methods. To date, substantial studies have already been carried out in the field of DPFL, which have shown that DPFL models are often more accurate than physics-based power flow linearization models. In this paper, a tutorial on this topic is provided. This tutorial reviews the motivations, challenges, training algorithms, supportive techniques, and numerical experiments with respect to DPFL. The derivations of the algorithms/techniques and their (closed-form) solutions are both mathematically revisited and discussed. Numerous future research directions for DPFL are identified and summarized. Additionally, an intuitive, unbiased, easily calculateable indicator for measuring the linearity level of any given system is proposed and employed on various power systems. This tutorial is divided into two parts, and this paper, as the first part, covers the surveys on the motivations, challenges, and training algorithms for DPFL.

Hydrogen, an essential resource in the decarbonized economy, is commonly produced as a by-product of chemical plants. To promote the use of by-product hydrogen, this paper proposes a supply chain model among chemical plants, hydrogen-storage salt caverns, and end users, considering time-of-use (TOU) hydrogen price, coalition strategies of suppliers, and road transportation of liquefied and compressed hydrogen. The transport route planning problem among multiple chemical plants is modeled through a cooperative game, while the hydrogen market among the salt cavern and chemical plants is modeled through a Stackelberg game. The equilibrium of the supply chain model gives the transportation and trading strategies of individual stakeholders. Simulation results demonstrate that the proposed method can provide useful insights on by-product hydrogen market design and analysis.

Probabilistic load flow (PLF) calculation, as a fundamental tool to analyze transmission system behavior, has been studied for decades. Despite a variety of available methods, existing PLF approaches rarely take system control into account. However, system control, as an automatic buffer between the fluctuations in random variables and the variations in system states, has a significant impact on the final PLF result. To consider control actions' influence, this paper proposes the first analytical PLF method for the transmission grid that takes into account primary and secondary frequency controls. This method is based on a high-precision linear power flow model, whose precision is even further improved in this paper by an original correction approach. This paper also proves that if the joint probability distribution (JPD) of random variables is expressed by a Gaussian mixture model (GMM), then the JPD of system states (e.g., nodal voltages) is an infinite GMM. By leveraging this proposition, the proposed method can generate the joint PLF of the whole system, is applicable to random variables obeying any distributions, and is capable of capturing their correlation. The high accuracy and satisfactory efficiency of this method are verified on test cases scaling from 14 to 1354 buses.

Probabilistic load flow (PLF) calculation, as a fundamental tool to analyze transmission system behavior, has been studied for decades. Despite a variety of available methods, existing PLF approaches rarely take system control into account. However, system control, as an automatic buffer between the fluctuations in random variables and the variations in system states, has a significant impact on the final PLF result. To consider control actions' influence, this paper proposes the first analytical PLF method for the transmission grid that takes into account primary and secondary frequency controls. This method is based on a high-precision linear power flow model, whose precision is even further improved in this paper by an original correction approach. This paper also proves that if the joint probability distribution (JPD) of random variables is expressed by a Gaussian mixture model (GMM), then the JPD of system states (e.g., nodal voltages) is an infinite GMM. By leveraging this proposition, the proposed method can generate the joint PLF of the whole system, is applicable to random variables obeying any distributions, and is capable of capturing their correlation. The high accuracy and satisfactory efficiency of this method are verified on test cases scaling from 14 to 1354 buses.

Given the increased percentage of wind power in power systems, chance-constrained optimal power flow (CC-OPF) calculation, as a means to take wind power uncertainty into account with a guaranteed security level, is being promoted. Compared to the local CC-OPF within a regional grid, the global CC-OPF of a multi-regional interconnected grid is able to coordinate across different regions and therefore improve the economic efficiency when integrating high percentage of wind power generation. In this global problem, however, multiple regional independent system operators (ISOs) participate in the decision-making process, raising the need for distributed but coordinated approaches. Most notably, due to regulation restrictions, commercial interest, and data security, regional ISOs may refuse to share confidential information with others, including generation cost, load data, system topologies, and line parameters. But this information is needed to build and solve the global CC-OPF spanning multiple areas. To tackle these issues, this paper proposes a distributed CC-OPF method with confidentiality preservation, which enables regional ISOs to determine the optimal dispatchable generations within their regions without disclosing confidential data. This method does not require parameter tunings and will not suffer from convergence challenges. Results from IEEE test cases show that this method is highly accurate.

Faults in photovoltaic (PV) systems can seriously affect the efficiency, energy yield as well as the security of the entire PV plant, if not detected and corrected quickly. Therefore, fault diagnosis of PV arrays is indispensable for improving the reliability, efficiency, productivity and safety of PV power stations. Instead of conventional thresholding methods and artificial intelligent (AI) machine learning approaches, an innovative Gaussian Mixture Model (GMM) based fault detection approach is proposed in this work. This approach combines the superiority of GMM in modeling stochastic power outputs of PV modules and the flexibility and simplicity of Sandia PV Array Performance Model (SPAM) to accurately detect under-performing modules. Firstly, GMM is proposed to represent the probabilistic distribution functions (PDF) of different PV modules' power outputs, and the parameter sets of which are obtained by Expectation Maximization algorithm. Secondly, a simplified explicit expression for output power of PV modules, which highlights the influences of tilt and azimuth angles, is deduced based on the SPAM. Then, an orientation independent vector C is developed to eliminate the probability distribution differences of power outputs caused by varying azimuth angles and tilt angles. Jensen-Shannon (JS) divergence, which captures the differences between probability density of C of each PV module, are generated and used as fault indicators. Simulation data acquired from the original SPAM are used to assess the performance of the proposed approach. Results show that the proposed approach successfully detects faults in PV systems. This work is especially suitable for the PV modules that have different installation parameters such as azimuth angles and tilt angles, and it does not require the use of irradiance or temperature sensors.

With the proliferation of distributed generators and energy storage systems, traditional passive consumers in power systems have been gradually evolving into the so-called "prosumers", i.e., proactive consumers, which can both produce and consume power. To encourage energy exchange among prosumers, energy sharing is increasingly adopted, which is usually formulated as a generalized Nash game (GNG). In this paper, a distributed approach is proposed to seek the Generalized Nash equilibrium (GNE) of the energy sharing game. To this end, we convert the GNG into an equivalent optimization problem. A Krasnosel'ski{\v{i}}-Mann iteration type algorithm is thereby devised to solve the problem and consequently find the GNE in a distributed manner. The convergence of the proposed algorithm is proved rigorously based on the nonexpansive operator theory. The performance of the algorithm is validated by experiments with three prosumers, and the scalability is tested by simulations using 123 prosumers.

Adopting Secure scalar product and Secure sum techniques, we propose a privacy-preserving method to build the joint and conditional probability distribution functions of multiple wind farms' output considering the temporal-spatial correlation. The proposed method can protect the raw data of wind farms (WFs) from disclosure, and are mathematically equivalent to the centralized method which needs to gather the raw data of all WFs.

This manuscript provides additional case analysis for the parameters setting of the distributed probabilistic modeling algorithm for the aggregated wind power forecast error.

The 2050 carbon-neutral vision spawns a novel energy structure revolution, and the construction of the future energy structure is based on equipment innovation. Insulating material, as the core of electrical power equipment and electrified transportation asset, faces unprecedented challenges and opportunities. The goal of carbon neutral and the urgent need for innovation in electric power equipment and electrification assets are first discussed. The engineering challenges constrained by the insulation system in future electric power equipment/devices and electrified transportation assets are investigated. Insulating materials, including intelligent insulating material, high thermal conductivity insulating material, high energy storage density insulating material, extreme environment resistant insulating material, and environmental-friendly insulating material, are categorised with their scientific issues, opportunities and challenges under the goal of carbon neutrality being discussed. In the context of carbon neutrality, not only improves the understanding of the insulation problems from a macro level, that is, electrical power equipment and electrified transportation asset, but also offers opportunities, remaining issues and challenges from the insulating material level. It is hoped that this paper envisions the challenges regarding design and reliability of insulations in electrical equipment and electric vehicles in the context of policies towards carbon neutrality rules. The authors also hope that this paper can be helpful in future development and research of novel insulating materials, which promote the realisation of the carbon-neutral vision., High Voltage, 7 (4), ISSN:2397-7264