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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 first prove the strong monotonicity of the game. Then, the GNG is converted into an equivalent optimization problem. An algorithm based on Nesterov’s methods is thereby devised to solve the equivalent 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 1888 prosumers.

In chance-constrained OPF models, joint chance constraints (JCCs) offer a stronger guarantee on security compared to single chance constraints (SCCs). Using Boole's inequality or its improved versions to decompose JCCs into SCCs is popular, yet the conservativeness introduced is still significant. In this letter, a non-parametric iterative framework is proposed to achieve the decomposition of JCCs with negligible conservativeness. An adaptive risk allocation strategy is also proposed and embedded in the framework. Results on an IEEE test case show that the conservativeness using the framework is nearly eliminated, thereby reducing the generation cost considerably.

The extensive penetration of wind farms (WFs) presents challenges to the operation of distribution networks (DNs). Building a probability distribution of the aggregated wind power forecast error is of great value for decision making. However, as a result of recent government incentives, many WFs are being newly built with little historical data for training distribution models. Moreover, WFs with different stakeholders may refuse to submit the raw data to a data center for model training. To address these problems, a Gaussian mixture model (GMM) is applied to build the distribution of the aggregated wind power forecast error; then, the maximum a posteriori (MAP) estimation method is adopted to overcome the limited training data problem in GMM parameter estimation. Next, a distributed MAP estimation method is developed based on the average consensus filter algorithm to address the data privacy issue. The distribution control center is introduced into the distributed estimation process to acquire more precise estimation results and better adapt to the DN control architecture. The effectiveness of the proposed algorithm is empirically verified using historical data.

Fault diagnosis of PV arrays is important to improve reliability, efficiency, and safety of PV 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 paper. GMM is applied to represent the probabilistic distribution functions (PDF) of different PV module output, and based on Sandia PV Array Performance Model (SPAM), an orientation independent vector C is then developed to eliminate the probability distribution differences of power outputs caused by varying azimuth angles and tilt angles. Three methods (a pseudo method, a method of fitting and a method of group testing) are proposed to obtain PDF of the orientation independent variable. Jensen-Shannon (JS) divergence, which captures the differences between probability density of C of each PV module, are generated and used as a fault indicator. Simulation data acquired from SPAM are used to assess the performance of the proposed approaches, which are later compared in terms of ability to detect, the response time and the generalization capability. Results show that the proposed approaches can successfully detects faults in PV systems, but the method of fitting and method of group testing can detect faults more accurately. 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 installation of irradiance or temperature sensors.

Probabilistic load flow (PLF) allows to evaluate uncertainties introduced by renewable energy sources on system operation. Ideally, the PLF calculation is implemented for an entire grid requiring all the parameters of the transmission lines and node load/generation to be available. However, in a multi-regional interconnected grid, the independent system operators (ISOs) across regions may not share the parameters of their respective areas with other ISOs. Consequently, the challenge is how to identify the functional relationship between the flows in the regional grid and the uncertain power injections of renewable generation sources across regions without full information about the entire grid. To overcome this challenge, we first propose a privacy-preserving distributed accelerated projection-based consensus algorithm for each ISO to calculate the corresponding coefficient matrix of the desired functional relationship. Then, we leverage a privacy-preserving accelerated average consensus algorithm to allow each ISO to obtain the corresponding constant vector of the same relationship. Using the two algorithms, we finally derive a privacy-preserving distributed PLF method for each ISO to analytically obtain its regional joint PLF in a fully distributed manner without revealing its parameters to other ISOs. The correctness, effectiveness, and efficiency of the proposed method are verified through a case study on the IEEE 118-bus system.

Electrical load profiling supports retailers in identifying consumer categories for customizing tariff design. However, each retailer only has access to the data of the customers it serves. Centralized joint clustering on retailers’ union load dataset either enables the identification of more types of users that allows to design more customized retail plans, or informs whether each retailer already has a sufficiently broad customer base. However, the centralized clustering requires access to the confidential data of retailers. This may cause privacy issues among retailers, because retailers can not or do not want to share their confidential information with others. To tackle this issue, we propose a privacy-preserving distributed clustering framework by developing a privacy-preserving accelerated average consensus (PP-AAC) algorithm. Using the proposed framework, we modify several commonly used clustering methods, including k-means, fuzzy C-means, and Gaussian mixture model, to provide privacy-preserving distributed clustering methods. In this way, the clustering on retailers’ union dataset can be achieved only by local calculations and information sharing between neighboring retailers without sacrificing privacy. The correctness, privacy-preserving property, time-saving feature, and robustness to random communication failures of the proposed methods are verified using a real-world Irish residential dataset.

Due to the uncertainty of distributed wind generations (DWGs), a better understanding of the probability distributions (PDs) of their wind power forecast errors (WPFEs) can help market participants (MPs) who own DWGs perform better during trading. Under the premise of an accurate PD model, considering the correlation among DWGs and absorbing the new information carried by the latest data are two ways to maintain an accurate PD. These two ways both require the historical and latest wind power and forecast data of all DWGs. Each MP, however, only has access to the data of its own DWGs and may refuse to share these data with MPs belonging to other stakeholders. Besides, because of the endless generation of new data, the PD updating burden increases sharply. Therefore, a distributed strategy is used to avoid raw data collection. In addition, the incremental learning strategy is further applied to reduce the updating burden. Finally, a distributed incremental update scheme is proposed to make each MP continually acquire the latest conditional PD of its DWGs’ WPFE. Specifically, the Gaussian-mixture-model-based (GMM-based) joint PD is first used to characterize the correlation among DWGs. Then, a distributed modified incremental GMM algorithm is proposed to enable MPs to update the parameters of the joint PD in a distributed and incremental manner. After that, a distributed derivation algorithm is further proposed to make MPs derive their conditional PD of WPFE from the joint one in a distributed way. Combining the two original algorithms, the complete distributed incremental update scheme is finally achieved, by which each MP can continually obtain its latest conditional PD of its DWGs’ WPFE via neighborhood communication and local calculation with its own data. The effectiveness, correctness, and efficiency of the proposed scheme are verified using the dataset from the NREL., International Journal of Electrical Power and Energy Systems, 121

Building the conditional probability distribution of wind power forecast errors benefits both wind farms (WFs) and independent system operators (ISOs). Establishing the joint probability distribution of wind power and the corresponding forecast data of spatially correlated WFs is the foundation for deriving the conditional probability distribution. Traditional parameter estimation methods for probability distributions require the collection of historical data of all WFs. However, in the context of multi-regional interconnected grids, neither regional ISOs nor WFs can collect the raw data of WFs in other regions due to privacy or competition considerations. Therefore, based on the Gaussian mixture model, this paper first proposes a privacy-preserving distributed expectation-maximization algorithm to estimate the parameters of the joint probability distribution. This algorithm consists of two original methods: (1) a privacy-preserving distributed summation algorithm and (2) a privacy-preserving distributed inner product algorithm. Then, we derive each WF’s conditional probability distribution of forecast error from the joint one. By the proposed algorithms, WFs only need local calculations and privacy-preserving neighboring communications to achieve the whole parameter estimation. These algorithms are verified using the wind integration data set published by the NREL., Renewable Energy, 163, ISSN:0960-1481, ISSN:1879-0682

The integrated energy system (IES) combined with electricity and heat networks is a research hotspot in energy field in recent years. As the foundation of security and economy analysis of IES, the steady-state multi-carrier energy flow (MEF) analysis is important but difficult to converge. An integrated method for solving MEF has been presented and adopted in some published literatures. In this paper, we investigate the integrated method and point out its two problems: one is the failure of the integrated method when energy reverses during iteration in some exceptional cases; the other is the high sensitivity of the method to the initial value. Thereafter, the fundamental causes for the two problems are revealed. Moreover, we modify the integrated method based on the fundamental causes to deal with the two problems. The cost and benefit of the modified integrated method are analyzed as well. Finally, the integrated method and the modified integrated method are discussed on the basis of theoretical and simulation results. The results show that with fewer iteration times and less calculation time, the modified integrated method has better applicability to exceptional cases and less sensitivity to the initial value., 2018 IEEE Power & Energy Society General Meeting (PESGM), ISBN:978-1-5386-7703-2, ISBN:978-1-5386-7702-5, ISBN:978-1-5386-7704-9

Ab stract—At present, the broadcast of PM2.5 can’t be accurate to all the spot of the city. This paper discusses a new method to draw the distribution of PM2.5 of a city by using mass data provided by the monitoring stations, which can be accurate to all the spot. In order to solve the problem efficiently, we present modified Gauss plume model. In the proposed model, firstly, for the accuracy of the model, we put forward a new method to calculate the wind direction. In addition, through the geometric inversion of the wind direction, the pollution source can be found. Moreover, in order to simulate the real situation, we replace the normal distribution by chi square distribution in Gauss plume model. Finally, the whole distribution of PM2.5 of the city can be draw. The PM2.5 distribution of Beijing in 2014 March indicates the proposed model is effective and feasible.