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The current efforts to address the expansion planning of power and heat production facilities can lead to suboptimal results from a market perspective because these efforts often implicitly assume that power and heat systems are planned by a single entity. The present study addresses this issue by establishing a Nash–Cournot equilibrium model, where the producers determine the quantity of power and heat that they produce independently and simultaneously, and thereby collectively affect the price. The model considers three types of producers, including power-only, combined power and heat, and heat-only producers, where each producer determines its own expansion investment strategies independently with the aim of maximizing its own profit. An investment equilibrium is obtained by reformulating the equilibrium model as a mixed complementarity problem. Numerical results carried out on two test systems illustrate the impact of transmission congestion and supply-side market power on the investment equilibria. [ABSTRACT FROM AUTHOR]

The increasing penetration of electric vehicles (EVs) results in growing interdependency between power and transportation networks. This paper proposes a hybrid economic-emission dispatch model to coordinate the operation of both networks toward social optima. Specifically, carbon emission from gasoline vehicles (GVs) is quantified by the macroscopic emission model, while the emission from EVs is indirectly characterized by that emitted from fossil power plants. To enhance regulation efficiency and improve social welfare, a differentiated pricing scheme is proposed to independently regulate GV traffic flow, EV traffic flow, and EV charging flow. Logarithmic transformation, combined with an accuracy-aware adaptive piecewise linearization (AAPWL) approximation method, is developed to reformulate the original nonlinear model into a tractable mixed-integer quadratic constrained programming. Numerical results from two test systems demonstrate the relationship between economic dispatch and emission dispatch. Meanwhile, the effectiveness and superiority of the proposed pricing scheme and the AAPWL method are validated. [ABSTRACT FROM AUTHOR]

The stochastic cloud cover on photovoltaic (PV) panels affects the solar power outputs, producing high instability in the integrated power systems. It is an effective approach to track the cloud motion during short-term PV power forecasting based on data sources of satellite images. However, since temporal variations of these images are noisy and non-stationary, pixel-sensitive prediction methods are critically needed in order to seek a balance between the forecast precision and the huge computation burden due to a large image size. Hence, a graphical learning framework is proposed in this study for intra-hour PV power prediction. By simulating the cloud motion using bi-directional extrapolation, a directed graph is generated representing the pixel values from multiple frames of historical images. The nodes and edges in the graph denote the shapes and motion directions of the regions of interest (ROIs) in satellite images. A spatial-temporal graph neural network (GNN) is then proposed to deal with the graph. Comparing with conventional deep-learning-based models, GNN is more flexible for varying sizes of input, in order to be able to handle dynamic ROIs. Referring to the comparative studies, the proposed method greatly reduces the redundancy of image inputs without sacrificing the visual scope, and slightly improves the prediction accuracy. [ABSTRACT FROM AUTHOR]

The power and natural-gas industries have narrowed the time differences between daily power market clearing and natural-gas market clearing. This facilitates the gas-power coordination in day-ahead scheduling. However, using natural-gas-fired power units to balance the variability of renewable energy production may cause fluctuations in natural-gas demand, which result in risks to the natural-gas system in actual operation. As such, gas-power coordination at all time is highly desirable. We analyze the coordinated operation of power and natural-gas systems at the scheduling stage and in actual operation. We assume that the two systems are operated independently, but with information interchange. We use a Lagrangian decomposition approach to identify an operational equilibrium involving the two systems. Numerical results on two test systems verify the value of gas-power coordination in actual operation. [ABSTRACT FROM AUTHOR]

Developing solar power generation technology is an efficient approach to relieving the global environmental crisis. However, solar energy is an energy source with strong uncertainty, which restricts large-scale photovoltaic (PV) applications until accurate solar energy predictions can be achieved. PV power forecasting methods have been widely researched based on existing predictions of satellite-derived solar irradiance, whereas modeling cloud motion directly from satellite images is still a tough task. In this study, an end-to-end short-term forecasting model is proposed to take satellite images as inputs, and it can learn the cloud motion characteristics from stacked optical flow maps. In order to reduce the huge size of measurements, static regions of interest (ROIs) are scoped based on historical cloud velocities. With its well-designed deep learning architecture, the proposed model can output multi-step-ahead prediction results sequentially by shifting receptive attention to dynamic ROIs. According to comparisons with related studies, the proposed model outperforms persistence and derived methods, and enhances its learning capability relative to conventional learning models via the novel architecture. The model can be applied to PV plants or arrays in different areas, suitable for forecast horizons within three hours. [ABSTRACT FROM AUTHOR]

Due to the stochastic and non-stationary characteristics of wind speed, the wind power generation is highly uncertain and fluctuating, which significantly challenges the operation of the power system and the associated electricity market. In this article, a new spatial-temporal method is proposed for short-term wind power prediction based on image inputs and augmented convolutional network. First, the geographical locations of various wind farms and the relevant wind vectors are processed into a series of multiframe spatial-temporal wind images, which can be handled by the convolutional networks. Then, wind power conversion and prediction models are developed based on those networks, where recurrent paths and attention mechanism are introduced to enhance the model architecture. The testing results have validated the high performance of the proposed method within a forecast horizon of up to seven hours. In particular, even when the terrain information is not available, the implicit wind flow field within the original inputs can still be approximately learned by the proposed convolutional networks. [ABSTRACT FROM AUTHOR]

We study the equilibria reached in electricity, natural-gas, and carbon-emission markets, where power producers simultaneously participate in these three markets. We use a conjectural-variations equilibrium model to represent both electricity and natural-gas markets, in which power/natural gas-producers play a quantity game and adjust their production decisions in reaction to the production levels of their rivals. We use a cap-and-trade mechanism to model the carbon-emission market. We develop a direct approach to identify equilibria involving the three markets, in which the optimality conditions of all players and market clearing conditions are gathered and solved jointly. Numerical results from two test systems illustrate the impact of carbon-emission trading and transmission constraints on the equilibria reached. Additionally, we compare equilibrium results under different types of competition. [ABSTRACT FROM AUTHOR]

Extreme weather events pose a serious threat to energy distribution systems. We propose a distributionally robust optimization model for the resilient operation of the integrated electricity and heat energy distribution systems in extreme weather events. We develop a strengthened ambiguity set that incorporates both moment and Wasserstein metric information of uncertain contingencies, which provides a more accurate characterization of the true probability distribution. We first recast the proposed model into an equivalent framework which is similar to a conventional two-stage robust model and then utilize a modified column-and-constraint generation algorithm to solve the recast model. Numerical results from three test systems validate the enhanced resilience of the distributionally robust approach, the reduced conservatism of the strengthened ambiguity set, and the computational efficiency of the proposed solution algorithm. [ABSTRACT FROM AUTHOR]

Solar energy is a strongly intermittent renewable energy source, which is affected by varied meteorological conditions, and thus produces arbitrary power outputs in photovoltaic (PV) power generation. Complex weather variations make it challenging to develop an efficient PV power forecasting method. In this study, a graph modeling method is proposed for short-term PV power prediction. Unlike many conventional machine-learning models, the proposed model is capable of evaluating interconnections among various meteorological input factors. This study details the design and operation of graph modeling, including graph construction, node feature construction, message transfer, and readout. An entire model is established consisting of spectral graph convolution, multiple graphical edges and a hierarchical output manner. The testing results suggest that the proposed multi-graph model outperforms other benchmark models in terms of accuracy under day-ahead forecasting cases. Besides, the single-graph model achieves a reduced cost of training time comparing to deep-learning benchmark models. [ABSTRACT FROM AUTHOR]

A prior knowledge of residential load demand is critical for power system operations at the distribution level, such as economic dispatch, demand response and energy storage schedule. However, as residential customers perform more casual and active consumption behaviors, prediction of such highly volatile loads can be much harder. Owing to the development of sensor technology, micrometeorological data can be sampled with a high geographic resolution. Those data that represent the weather condition on the land surface show a strong relationship to the residential load evidently, whereas it remains unsolved on how to fully utilize those great number of datasets. This paper proposes a day-ahead probabilistic residential load forecasting method based on a novel deep learning model, named convolutional neural network with squeeze-and-excitation modules (CNN-SE), and micrometeorological data. The model can employ multi-channel input data with dissimilar weights, suitable for analyzing massive relevant input factors. A feature extraction method is adopted for customer consumption pattern based on sparse auto-encoder (SAE), which can help correct probabilistic forecasting results. A case study that covers 8 residential communities and 18 micrometeorological sites is conducted to validate the feasibility and accuracy of the proposed hybrid method. [ABSTRACT FROM AUTHOR]

This article proposes a forecasting-aided medium-voltage (MV) distribution system state estimation (SE) method using a robust ensemble Kalman filter (REnKF). In the proposed solution, low-voltage (LV) measurements at the LV side of secondary substations are used together with the mathematical model of the MV/LV substations to derive new equivalent MV measurements. This yields the improvement of measurement redundancy and robustness of the REnKF to bad data and unknown system process noise. Specifically, we rely on the temporal correlations of the constructed innovation vector as well as the projection statistics (PS) to detect and modify the measurement error covariance matrix. Furthermore, the system process noise covariance matrix is updated adaptively to mitigate the impacts of uncertainties ON-state forecasting and measurement filtering. Extensive comparisons have been carried out with both the traditional EnKF and other SE formulations under balanced and unbalanced distribution system conditions. The results reveal that our proposed REnKF is able to obtain accurate SE results under various operation conditions, including the presence of intermittent renewable energy sources, bad data, and system unbalance. [ABSTRACT FROM AUTHOR]

We study investment equilibria in electricity and gas markets wherein electricity producers and natural gas suppliers behave strategically. We consider also hybrid producers that own both generating units and gas sources. Each strategic producer determines its investment decisions in gas-fired units, and its offering and bidding strategies to maximize its own profit, anticipating electricity and gas market-clearing outcomes. Producers owning gas-fired units submit bids to the gas market to procure fuel and offers to the electricity market to sell electricity. The resulting model is recast as an equilibrium problem with equilibrium constraints that we solve using a direct approach. Numerical results from two test systems illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

The increasing penetration of electric vehicles (EVs) and emerging dynamic wireless charging techniques have strengthened the coupling between traffic networks and power distribution networks. This increased coupling necessitates greater coordination between the two networks. This paper proposes a multi-period optimal traffic and power flow model that considers time-varying electricity and traffic demands. The distribution of traffic flow is represented by a semi-dynamic traffic assignment (SDTA) model, which considers flow propagation between adjacent periods. Combined second-order cone, convex hull, and McCormick envelope relaxations are employed to convexify the power and traffic flow model. Optimization-based bound tightening (OBBT) method combined with a heuristic sequential bound tightening (SBT) method is employed to improve the tightness of the relaxation. The modeling of multi-period scheduling provided by the SDTA model is thoroughly compared with that provided by the conventional static traffic assignment model. In addition, the proposed traffic and power flow model is employed to conduct congestion analysis of the coupled networks. Numerical results on two test systems demonstrate both the spatial and temporal impacts of congestion on each of the coupled networks. Moreover, numerical results verify that the proposed OBBT-SBT-based convex relaxation is sufficiently tight. [ABSTRACT FROM AUTHOR]

The combined operations of power distribution and district heating networks catalyze ongoing progressions to smart cities. This paper proposes a distributionally robust energy and reserve co-optimization approach for combined power distribution and district heating networks. In particular, smart buildings are modeled as equivalent storage devices representing cost-effective resources to enhance operational flexibility and provide additional reserves in power systems. Uncertainties pertaining to renewable energy resource power and ambient temperature are captured within an ambiguity set that comprises a variety of statistical characterizations (e.g., the expected value, the variance, and the covariance) to generate more trustworthy and less conservative solutions. Linear decision rules and the second-order cone duality are employed to enhance the computational tractability of the proposed approach by transforming the original problem into a second-order cone program. Finally, numerical results provided based on the real-world Barry Island system demonstrate the risk-reduction and economic benefits of the proposed approach. [ABSTRACT FROM AUTHOR]

Coordinated operations of electricity and district heating networks offer a potential for mitigating inherent variability of renewable energy sources (RES) in the ongoing transition to smart grids. This paper proposes a two-stage distributionally robust optimization (DRO) approach to determine the optimal day-ahead unit commitment in coordinated electricity and district heating networks with variable RES power output. The proposed formulation is to minimize the worst-case expected total cost over an ambiguity set comprising a family of probability distributions with given support and moments of RES power output. As such, the proposed DRO approach can overcome the limitations of stochastic programming in its inherent dependence of exact probability distributions along with a huge computational burden, but also becomes less conservative than classical robust optimization. The pertinent DRO model is eventually reformulated as a tractable mixed-integer second-order cone (SOC) programming after employing linear decision rules and the SOC duality. Simplified affine policies are utilized to further improve computational tractability and performance. Finally, case studies are conducted based on Barry Island electricity and district heating networks. The numerical results demonstrate the decision-making superiority of the proposed method as compared with deterministic, stochastic programming, and robust optimization approaches. They also validate the computational improvement of the proposed approach by employing simplified affine policies. [ABSTRACT FROM AUTHOR]

We study market equilibria that are achieved by strategic firms that participate in electricity and natural gas markets. Strategic firms submit their offers and bids to both markets with the aim of maximizing profit or utility and we consider firms that can include a combination of electricity and natural gas supply and demand. The strategic actions of these firms are represented by upper-level problems that are optimized subject to shared lower-level problems that represent the clearing of electricity and natural gas markets. This market structure and our modeling approach yields a multiple-leader/two-follower complementarity problem. We develop a modeling approach that can find equilibria with different characteristics, e.g., maximized social welfare, producer profits, or consumer welfare. We demonstrate numerically that producers aim typically to increase market prices while consumers seek to decrease them. [ABSTRACT FROM AUTHOR]

Increasing interdependency between electric power and gas systems results in tremendous operational challenges. This paper proposes an $N$ –1 security-constrained optimal power and gas flow (SCOPGF) framework that includes contingencies in both energy systems. A bi-directional gas flow model is employed to provide more flexibility for addressing gas system contingencies. We further propose an iterative algorithm to identify binding contingency subsets, which contributes toward ensuring a tractable SCOPGF model. Numerical results on two test systems verify the computational advantages of the proposed SCOPGF model employing a reduced binding contingency subset. The necessity of adopting a bi-direction gas flow model under post-contingency conditions is also discussed. [ABSTRACT FROM AUTHOR]

Electric power and natural gas systems typically are operated independently. However, their operations are interrelated due to the proliferation of natural gas-fired generating units. We analyze the independent but interrelated day-ahead operation of the two systems. We use a direct approach to identify operational equilibria involving these two systems, in which the Karush-Kuhn-Tucker conditions of both electric power and natural gas operational models are gathered and solved jointly. We characterize the equilibria that are obtained under different levels of temporal and spatial granularity in conveying information between the two system operators. Numerical results from the Belgian system are used to examine the impacts of different levels of information interchange on prices, operational costs, and decisions in the two systems. [ABSTRACT FROM AUTHOR]

The real-time monitoring and control of distribution systems are an essential step toward the future smart grid. This paper presents an interval state estimation model for low-voltage (LV) systems based on smart meter data provided by electrical customers. The formulation is based on a two-level approach, constituted of a nodal processor and a system state estimator. The nodal processor filters the smart meter data and provides a smaller amount of clean processed data to the upper level system state estimator. The system state estimator, based on the extreme value theory, provides the maximum and minimum values of the system states. To obtain narrow interval images, a scaling parameter is used to consider the fact that the errors of downstream smart meters are rarely at the maximum values simultaneously. The presented approach allows removing the assumption on the particular probability distribution of the smart meter measurement errors. Simulations are carried out on a sample LV network to show the characteristics and performance of the proposed approach. [ABSTRACT FROM AUTHOR]

The interdependency of electric power and natural gas systems requires co-ordinated operational planning. We propose a unit commitment model that integrates a second-order-cone relaxation of a non-convex nonlinear natural-gas flow model that considers pipeline line pack. The model is enhanced by using convex envelopes of bilinear terms, which tighten the relaxation. By fixing the binary variables at their optimal values and linearizing the natural gas-flow-balance equations around the solution that is obtained, we obtain electricity and natural gas locational marginal prices as the dual variables of electricity- and natural gas-flow-balance equations, respectively. The interdependence between these sets of prices is discussed. Numerical results from two test systems validate the solution-quality and computational-efficiency benefits of the proposed modeling methodology. [ABSTRACT FROM AUTHOR]