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With regard to wind farms connected to the main system via dedicated overhead transmission lines, the available wind power absorbed by the system relies on not only the power generation capacity but also the power transmission threshold. Thus, this study centers on the close relationship between environmental conditions and power transfer limits that involve the thermal limit and steady-state stability limit. Simultaneous equations representing both overhead conductors’ heat balance and power transmission operation are established. In addition, formulations of the maximum transmission power for the steady-state stability limit are derived and then expressed as functions of environmental factors and the line length. The presented approach allows one to analyze the threshold considering not only the thermal limit but also the steady-state stability limit, which could be remarkably different under certain environmental and transmission distance conditions. Then, a scheme to identify the primary limitation and obtain the corresponding threshold value is proposed. Moreover, a simple treatment of wind speed correlation is deployed because of the close distance between a wind farm and its tie-line. Case studies demonstrate that, for a certain wind speed level, the process of transmission rather than generation could become the key factor determining the threshold value. [ABSTRACT FROM AUTHOR]

The papers in this special section examine the enabling of very high penetration renewable energy integration into future power systems. Renewable energy is regarded as one of the main solutions to achieve power system sustainability. In recent years, renewable energy has been experiencing fast development. In 2016, 24.5% of the total power demand in the world was supplied by renewable energy, where 5.5% was produced by wind power and PV [item 1) in the Appendix]. It is estimated that by the end of 2017 the global wind power and PV capacity had reached about 565 GW and 335 GW respectively. Some power systems have already entered the era of high penetration of intermittent renewable energy integration. [ABSTRACT FROM PUBLISHER]

With the largest installed capacity in the world, wind power in China is experiencing a \sim 20\% curtailment during operation. The large portion of the generation capacity from inflexible combined heat and power (CHP) is the major barrier for integrating this variable power source. This paper explores opportunities for increasing the flexibility of CHP units using electrical boilers and heat storage tanks for better integration of wind power. A linear model is proposed for the centralized dispatch for integrated energy systems considering both heat and power, with detailed modeling of the charging processes of the heat storage tanks. The model balances heat and power demands in multiple areas and time periods with various energy sources, including CHP, wind power, electrical boilers, and heat storage. The impact of introducing electrical boilers and heat storage systems is examined using a simple test system with characteristics similar to those of the power systems in Northern China. Our results show that both electrical boilers and heat storage tanks can improve the flexibility of CHP units: introducing electrical boilers is more effective at reducing wind curtailment, whereas heat storage tanks save more energy in the energy system as a whole, which reflect a different heating efficiency of the two solutions. [ABSTRACT FROM PUBLISHER]

The integration of wind power requires the power system to be sufficiently flexible to accommodate its forecast errors. In the market clearing process, the scheduling of flexibility relies on the manner in which the wind power uncertainty is addressed in the unit commitment (UC) model. This paper presents a novel risk-based day-ahead unit commitment (RUC) model that considers the risks of the loss of load, wind curtailment and branch overflow caused by wind power uncertainty. These risks are formulated in detail using the probabilistic distributions of wind power probabilistic forecast and are considered in both the objective functions and the constraints. The RUC model is shown to be convex and is transformed into a mixed integer linear programming (MILP) problem using relaxation and piecewise linearization. The proposed RUC model is tested using a three-bus system and an IEEE RTS79 system with wind power integration. The results show that the model can dynamically schedule the spinning reserves and hold the transmission capacity margins according to the uncertainty of the wind power. A comparison between the results of the RUC, a deterministic UC and two scenario-based UC models shows that the risk modeling facilitates a strategic market clearing procedure with a reasonable computational expense. [ABSTRACT FROM PUBLISHER]

As a critical data input of security constraint unit commitment, bus load forecasting is currently conducted on a bus-by-bus fashion to improve the forecasting accuracy in most provinces in China. On such substation level forecasting, data quality is much worse than the aggregated power demand for the whole system, and identifying and restoring the inaccurate measurement and abnormal disturbance to retrieve the historical trend of load is urged to improve the forecasting accuracy. In this paper, a two-stage identification and restoration method is presented. The typical patterns of inaccurate measurement and abnormal disturbance are detected in the first stage based on statistical criteria independent with normal distribution. Historical trend is further retrieved in the second stage using frequency domain decomposition, and a typical daily curve is generated to compare with the data measurements. The deviations of the data measurements from the typical daily curve obey normal distribution and are used as criteria in the second stage. The effectiveness of the proposed methodology has been confirmed by examples in real bus load forecasting systems in this paper. [ABSTRACT FROM PUBLISHER]

The integration of wind power requires additional operating reserves to cope with the uncertainty in power system operation. Previous research shows that the uncertainty of the wind power forecast varies with the level of its output. Therefore, allocating reserves dynamically according to the specific distribution of the wind power forecast would benefit system scheduling. This paper presents a statistical model to formulate the conditional distribution of forecast error for multiple wind farms using copula theory. The proposed model is tested using a set of synchronous data of wind power and its day-ahead forecast. It is then utilized in a stochastic unit commitment model to simulate the day-ahead and real-time scheduling of the modified IEEE RTS-79 system integrating wind power. The results show that scheduling reserves dynamically according to the modeled conditional forecast error reduces the probability of reserve deficiency while maintaining the same level of operating costs. [ABSTRACT FROM PUBLISHER]

In a carbon-constrained world, CO2 emissions will become a new concern in power system dispatch. Meanwhile, carbon capture power plants (CCPPs), which are a critical low-carbon power generation option, will have a significant impact on power system operation and dispatch. This paper presents research on low-carbon power system dispatch (LCPSD) incorporating CCPPs. The operating mechanism of CCPPs is investigated first. Then, the operating characteristics of CCPPs in power system dispatch are analyzed, including feasible power output limits, ramping rates and relationships between the power outputs and the carbon emissions. A comprehensive LCPSD model is formulated, in which the carbon emissions of power plants are treated as a new set of decision variables, and low-carbon-related cost terms are considered. The dispatch features of CCPPs are elaborately formulated and incorporated into the LCPSD model. The effectiveness and the validity of the proposed LCPSD mode and model are demonstrated using numerical examples based on an IEEE 118-bus tested system. [ABSTRACT FROM PUBLISHER]

Battery-based Energy Storage Transportation (BEST) is the transportation of modular battery storage systems via train cars or trucks representing an innovative solution for a) enhancing Variable Renewable Energy (VRE) utilization and load shifting, and b) providing a potential alternative for managing transmission congestions. This paper focuses on point b) and proposes a long-term transmission-planning model coordinated with both stationary and mobile storage units. The planning-problem objective function minimizes the total system cost, i.e., the sum of i) the investment cost of candidate transmission lines, stationary and mobile storage systems, and ii) the operation cost, including conventional generating units fuel consumption, load shedding penalty and BEST transportation costs. An alternative approach for BEST vehicle scheduling problem is implemented. The contribution lies in the accomplishment of the spatial-temporal scheduling of the mobile storage units by including the Number-of-nonzero mathematical function in the optimization model set of constraints instead of using additional binary variables as generally accomplished. The identification of either storage systems optimal location, or both optimal location and size of storage systems is also allowed. BEST usefulness is analyzed and discussed for a test-system emulating a reals system in China-Northwestern-grid with high VRE penetration divided in five regional areas, of which the most promising one for BEST implementation is identified. [ABSTRACT FROM AUTHOR]

Discrete convolution (DC) is a generally accepted approach for the probabilistic analysis such as reliability assessment and probabilistic load flow. However, it has a strong precondition that the stochastic variables being convolved must be independent, which may not be fully satisfied in all cases. Using copula functions, this letter derives the formulation of DC for dependent variables. The performance of the proposed dependent discrete convolution (DDC) is illustrated using reliability assessment involving wind power. The result shows that the DDC inherits the efficient and reliable performance of DC, indicating a promising potential for practical applications. [ABSTRACT FROM PUBLISHER]

A foreword to the March 15, 2015 issue of "IEEE Transactions on Power Systems" is presented.

The increasing complexity of power systems, particularly the high renewable energy penetration, raises the necessity of incorporating detailed power system operation models into long-term planning studies. The classic short-term operation model, i.e., network-constrained unit commitment (NCUC), involves many binary variables and introduces computational challenges when applied to long-term planning optimizations. A high-efficiency and simplified NCUC model is required to incorporate operational flexibility in power system planning studies. This paper proposes a linearized NCUC formulation that has a high calculation performance and minor approximation errors compared to the full NCUC model. The proposed model combines the dispatch-only (DO) operation model and clustered unit commitment (CUC) model by introducing linking constraints between them such that the overall model guarantees both the transmission security constraints that are formulated in the DO model and the start-up/shut-down constraints of generating units that are formulated in the CUC model. A case study of a modified IEEE RTS-79 system is provided to demonstrate the validation and efficiency of the proposed simplified NCUC model as well as its effectiveness for power system planning studies. [ABSTRACT FROM AUTHOR]

Multi-energy systems can provide a constant level of service to end-use energy demands, while deriving delivered energy from a variety of primary/secondary energy sources. This fuel-switching capability can be used to reduce operating expenses, reduce environmental impacts, improve flexibility to accommodate renewable energy, and improve reliability. This paper presents four frameworks for incentivizing energy hub equipment investments for low-carbon operation targets. These frameworks vary in the measures taken to achieve low-carbon operation (explicit constraint versus carbon pricing) and in the relationship between the hub builder and operator (cooperative versus uncoordinated). The underlying energy hub model upon which these frameworks are built is an enhanced greenfield model, introducing “energy buses” to reduce dimensionality. A case study is conducted for a campus being designed in Beijing, and results from each framework are compared to illustrate their relative costs. When the operator cannot be trusted to cooperate in controlling emissions, the system must be “overbuilt” with more expensive equipment to ensure emissions target are met. A taxation-based approach increases overall costs at moderate emissions targets, but this effect decreases at aggressive targets. This paper also compares the cost of less efficient institutional frameworks with the most efficient approach, i.e., cooperation between builder and operator with constraints on emissions. [ABSTRACT FROM AUTHOR]

Composite power system reliability evaluation is computationally time-consuming because the optimal power flow (OPF) with the least load curtailment is calculated for a large number of samples. Most current studies of probabilistic simulation methods focus on sampling techniques to improve the sampling efficiency and decrease the calculations of the OPF. This paper proposes a fast reliability evaluation method that accelerates the calculation of the OPF using multi-parametric linear programming (MPLP). In this paper, the sampled transmission line statuses are considered by the transmission line status dictionary (TLSD). We match the line status of each sample with the scenarios in the TLSD. For matching samples, the generation status and the sampled load are treated as MPLP parameters of the DC-OPF evaluation model. A dynamic learning algorithm is applied to solve the MPLP problem. Case studies are conducted on both IEEE Reliability Test Systems and a provincial power system in China. The results show that the proposed method improves the evaluation efficiency by 23–30 times compared with the normal DC-OPF-based model. [ABSTRACT FROM AUTHOR]

In the power system stochastic unit commitment (SUC) model, the uncertainty and variability of the renewable energy generation, such as wind power, are usually expressed by multiple scenarios. The performance of SUC is driven by how well the selected scenarios represent the stochastic nature, since too few scenarios may lose or distort the uncertainty or variability characteristics, while too many scenarios usually cause computational difficulty. This paper proposes a novel scenario representation method referred to as scenario mapping technology (SMT), which is able to compact large amount of scenarios while preserving the uncertainty and variability features of wind power as much as possible. Specifically, SMT proposes to combine similar wind power generation into a state at each period and contains the possible multiple transitions linking the states in adjacent periods. A novel two-stage SUC model is proposed based on SMT. The numerical results demonstrate a solid improvement of the performance for the SMT-based SUC model on both cost-efficiency and calculation efficiency, compared with traditional two-stage SUC model based on the scenario reduction technique. [ABSTRACT FROM AUTHOR]

The integration of high penetration of renewable energy brings greater uncertainties for the operation of future power systems due to its intermittency and lack of predictability. The uncertainties brought by wide scale renewables might have dependencies with each other because their outputs are mainly influenced by weather. However, an analysis of such uncertainties with complex dependencies faces the “curse of dimensionality”. This challenges the power system uncertainty analysis in probabilistic forecasting, power system operation optimization, and power system planning. This paper proposes an efficient approach that is able to handle high-dimensional dependencies. The approach uses the high-dimensional Copula theory and discrete convolution method to conduct a high-dimensional dependent discrete convolution (DDC) calculation. A recursive algorithm is proposed to decompose the computation of DDC into multiple convolutions between each pair of stochastic variables so that the “curse of dimensionality” is solved. The computational complexity of the proposed method is linear with respect to the number of dimensions and guarantees computational efficiency. Finally, illustrative examples of power system reserve requirement evaluation and wind power capacity credit assessment analysis are used to verify the effectiveness and superiority of the proposed approach. [ABSTRACT FROM PUBLISHER]

With the largest installed capacity in the world, wind power in China is experiencing a ∼20% curtailment. The inflexible combined heat and power (CHP) has been recognized as the major barrier for integrating the wind source. The approach to reconcile the conflict between inflexible CHP units and variable wind power in Chinese energy system is yet unclear. This paper explores the technical and economic feasibility of deploying the heat storage tanks and electric boilers under typical power grids and practical operational regulations. A mixed integer linear optimization model is proposed to simulate an integrated power and heating energy systems, including a CHP model capable of accounting for the commitment decisions and nonconvex energy generation constraints. The model is applied to simulate a regional energy system (Jing–Jin–Tang) covering 100-million population, with hourly resolution over a year, incorporating actual data, and operational regulations. The results project an accelerating increase in wind curtailment rate at elevated wind penetration. Investment for wind breaks even at 14% wind penetration. At such penetration, the electric boiler (with heat storage) is effective in reducing wind curtailment. The investment in electric boilers is justified on a social economic basis, but the revenues for different stakeholders are not distributed evenly. [ABSTRACT FROM AUTHOR]

A new challenge has arisen in power generation scheduling recently, as the rapid increase in the number of gas-fired units has made power systems more vulnerable to failures in natural gas networks. The large-scale integration of wind power further exacerbates the problem because gas-fired units are usually scheduled to catch up wind power uncertainty and thus lead to great variations in the state of gas network. To meet this challenge, it is necessary to commit and dispatch the gas-fired units considering both wind uncertainty and natural gas network security. However, the dynamic characteristics of gas flow are remarkably slower than those of power flow, which should be appropriately modeled to explore its benefits for power system operation. Because directly applying partial differential equations overly complicates the already complicated generation scheduling problem, we address this problem by proposing an approximated transient matrix-form gas flow model. A two-stage robust generation scheduling model is then proposed considering the dynamic security constraints of gas networks and the wind power uncertainty. Moreover, we successfully avoid the nonlinearity of gas flow constraints by developing a new solution methodology. Finally, an illustrative case is presented to demonstrate the effect of gas network dynamics in generation scheduling. [ABSTRACT FROM AUTHOR]

In the future power system with high penetration of renewables, renewable energy is expected to undertake part of the responsibility for frequency regulation, just as the conventional generators. Wind power and battery storage are complementary in accuracy and durability when providing frequency regulation. Therefore, it would be profitable to combine wind power and battery storage as a physically connected entity or a virtual power plant to provide both energy and frequency regulation in the markets. This paper proposes a real-time cooperation scheme to exploit their complementary characteristics and an optimal bidding strategy for them in joint energy and regulation markets, considering battery cycle life. The proposed cooperation scheme is adopted in a real-time battery operating simulation and then incorporated into the optimal bidding model. The scheme could improve the wind regulation performance score and allow for more regulation bids without affecting the battery life, thus significantly increasing the overall revenue. The validity of the proposed scheme and strategy are proved by the case study. [ABSTRACT FROM PUBLISHER]

Linearized power flow models are of great interest in power system studies such as contingency analyses and reliability assessments, especially for large-scale systems. One of the most popular models—the classical DC power flow model—is widely used and praised for its state independence, robustness, and computational efficiency. Despite its advantages, however, the DC power flow model fails to consider reactive power or bus voltage magnitude. This paper closes this gap by proposing a decoupled linearized power flow (DLPF) model with respect to voltage magnitude and phase angle. The model is state independent but is distinguished by its high accuracy in voltage magnitude. Moreover, this paper presents an in-depth analysis of the DLPF model with the purpose of accelerating its computation speed, leading to the fast DLPF (FDLPF) model. The approximation that is applied to obtain the FDLPF model from the DLPF model is justified by a theoretical derivation and numerical tests. The proposed methods are provably accurate and robust for several cases, including radial distribution systems, meshed large-scale transmission systems and ill-conditioned systems. Finally, expressions for sensitivity with regard to MW flow and bus voltage are provided as a potential application. [ABSTRACT FROM PUBLISHER]

Achieving the low-carbon transition of power systems requires the coordination of renewable energy generation and other emerging electricity technologies. Their technical indicators are changing rapidly since these technologies are in the initial stages of development. Determining the technical and policy targets for achieving the low-carbon transition is critical for regulators and power system planners. This paper defines this problem as a backcasting problem, whose concept is derived from environmental science research. We introduce it into the power system planning field and innovatively model it as a bi-level optimization problem. According to the characteristics of the backcasting problem, an improved barrier method is proposed to solve it efficiently. The effectiveness of the proposed model and algorithm are verified through case studies on a modified Garver’s 6-bus system and a realistic Northwest China power system, and they are compared with state-of-the-art solution techniques. The results of the backcasting problem provide a new perspective on the economic impacts of the low-carbon transition and are helpful in energy policy formulation for power systems. [ABSTRACT FROM AUTHOR]

With the rapidly increasing penetration of wind power, wind producers are becoming increasingly responsible for the deviation of the wind power output from the forecast. Such uncertainty results in revenue losses to the wind power producers (WPPs) due to penalties in ex-post imbalance settlements. This paper explores the opportunities available for WPPs if they can purchase or schedule some reserves to offset part of their deviation rather than being fully penalized in the real-time market. The revenue for WPPs under such mechanism is modeled. The optimal strategy for managing the uncertainty of wind power by purchasing reserves to maximize the WPP's revenue is analytically derived with rigorous optimality conditions. The amount of energy and reserves that should be bid in the market is explicitly quantified by the probabilistic forecast and the prices of the energy and reserves. A case study using the price data from ERCOT and wind power data from NREL is performed to verify the effectiveness of the derived optimal bidding strategy and the benefits of reserve purchasing. Additionally, the proposed bidding strategy can also reduce the risk of variations on WPP's revenue. [ABSTRACT FROM AUTHOR]

Smart meters play vital roles in the aspects of the management and operation of smart grids such as demand response, energy efficiency improvement, and electricity pricing. Massive amounts of data are being collected owing to the popularity of smart meters. Two main issues should be addressed in this context. One is the communication and storage of big data from smart meters at reduced cost. The other is the effective extraction of useful information from this massive dataset. In this paper, the K-SVD sparse representation technique, which includes two phases (dictionary learning and sparse coding), is used to decompose load profiles into linear combinations of several partial usage patterns (PUPs), which allows the smart meter data to be compressed and hidden electricity consumption patterns to be extracted. Then, a linear support vector machine (SVM) based method is used to classify the load profiles into two groups, residential customers and small and medium-sized enterprises (SMEs), based on the extracted patterns. Comprehensive comparisons with the results of k-means clustering, the discrete wavelet transform (DWT), principal component analysis (PCA), and piecewise aggregate approximation (PAA) are conducted on real datasets in Ireland. The results show that our proposed technique outperforms these methods in both compression ratio and classification accuracy. [ABSTRACT FROM AUTHOR]

The rapid development of wind power has led to an increased demand for spinning reserve in power systems today. However, one of the most severe challenges to China's power systems is the mismatch between wind power installation capacity and the capability for supplying spinning reserve within each independently operated provincial power system. Coordinating the spinning reserve across multiple areas would providentially improve the accommodation of wind power. This paper proposes a game-theoretical model for spinning reserve trading between provincial systems that treat spinning reserve as a commodity. Based on the incomplete information, the trading price is calculated by satisfying the Bayesian Nash equilibrium, and then the trading quantity is determined. This ensures that both the buyer and the seller are able to maximize their expected profit. Case studies are performed using a 2-bus interconnected system and a 3-area IEEE RTS system. The results show that the proposed model is valid and effective. [ABSTRACT FROM AUTHOR]

In response to the computational challenges produced by the integrated dispatch of generation and load (IDGL), this paper proposes a novel and efficient decomposition method. The IDGL is formulated using the mixed-integer quadratic constrained programming (MIQCP) method. To efficiently solve this complex optimization problem, the nodal equivalent load shifting bidding curve (NELSBC) is proposed to represent the aggregated response characteristics of customers at a node. The IDGL is subsequently decomposed into a two-level optimization problem. At the upper level, grid operators optimize load shifting schedules based on the NELSBC of each node. Transmission losses are explicitly incorporated into the model to coordinate them with generating costs and load shifting costs. At the bottom level, customer load adjustments are optimized at individual nodes given the nodal load shifting requirement imposed by the grid operators. The key advantage of the proposed method is that the load shifting among different nodes can be coordinated via NELSBCs without iterations. The proposed decomposition method significantly improves the efficiency of the IDGL. Parallel computing techniques are utilized to accelerate the computations. Using numerical studies of IEEE 30-bus, 118-bus, and practically sized 300-bus systems, this study demonstrates that accurate and efficient IDGL scheduling results, which consider the nonlinear impact of transmission losses, can be achieved. [ABSTRACT FROM PUBLISHER]

Coordinated preheating can potentially enhance the flexibility of the electricity system, thereby driving significant economic savings. In this context, this paper proposes a novel game-theory based preheating coordination scheme aimed at guaranteeing the effectiveness of collective preheating performed by a large population of households. By adopting an innovative two-phase iterative algorithm, individual households autonomously schedule their heating power allocation to seek for savings in energy bills while smartly maintaining thermal comfort. Meanwhile, the total electricity generation cost decreases at each iteration and converges to an equilibrium solution asymptotically. Compared to the centralised optimization-based energy management control methods, the proposed algorithm effectively reduces the information exchange while significantly reduces computational complexity. The simulation results indicate that the proposed coordination strategy can drive 12.30% cost saving when all households participate in the preheating scheme whereas 11.35% cost increase will be incurred if coordination is absent. Overall, the proposed preheating control algorithm simultaneously benefits both individual households and the whole system by intelligently linking local behaviour with global interests. [ABSTRACT FROM AUTHOR]

In the last decade, a number of severe urban power outages have been caused by extreme natural disasters, e.g., hurricanes, snowstorms and earthquakes, which highlights the need for rethinking current planning principles of urban energy systems and expanding the classical reliability-oriented view. In addition to being reliable to low-impact and high-probability outages, power system should also have high level of resilience to withstand high-impact and low-probability (HILP) events. Compared with power system, multi-energy systems (MESs) have advantages in improving resilience through energy shifting across multiple energy sectors, a variety of generalized energy storage resources and thermal inertia of heat/cooling loads. This paper proposes a resilience-oriented planning method to determine optimal configuration of distribution level MES, e.g., urban energy supply systems, considering comprehensive impacts from supply, network and demand sides in MES. Impacts of energy shifting at supply side, pipe storage at network side and thermal inertia at demand side are described in the same linear modeling framework using energy hub (EH) model. Generalized energy storage resources including centralized and distributed energy storage devices, pipe network storage and building heat capacity are all modeled into centralized energy storage to facilitate an efficient configuration planning of MES. [ABSTRACT FROM AUTHOR]

There is an opportunity in modern power systems to explore the demand flexibility by incentivizing consumers with dynamic prices. In this paper, we quantify demand flexibility using an efficient tool called time-varying elasticity, whose value may change depending on the prices and decision dynamics. This tool is particularly useful for evaluating the demand response potential and system reliability. Recent empirical evidences have highlighted some abnormal features when studying demand flexibility, such as delayed responses and vanishing elasticities after price spikes. Existing methods fail to capture these complicated features because they heavily rely on some predefined (often over-simplified) regression expressions. Instead, this paper proposes a model-free methodology to automatically and accurately derive the optimal estimation pattern. We further develop a two-stage estimation process with Siamese long short-term memory (LSTM) networks. Here, a LSTM network encodes the price response, while the other network estimates the time-varying elasticities. In the case study, the proposed framework and models are validated to achieve higher overall estimation accuracy and better description for various abnormal features when compared with the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Cellular Base Stations (BSs) are equipped with backup batteries. These batteries have some spare capacity over time while maintaining the power supply reliability, so they are potential flexible resources for power systems. This letter exhibits the insight to explore the BS dispatch potential towards power system frequency regulation. For each BS, the feasible dispatch boundaries of participating in frequency regulation are estimated. Then a framework is proposed to coordinate BSs to provide frequency support. By incorporating massive distributed BSs, the power system frequency performances can be improved. [ABSTRACT FROM AUTHOR]

One of the key steps for optimal bidding in power markets is to estimate the rivals’ bidding behaviors. However, for most participants, it would be difficult to directly forecast the rivals’ individual bids due to the information privacy and volatile characteristics of individual bidding behaviors. From another point of view, the aggregation of individual bids, denoted as aggregated supply curve (ASC), might be helpful to offset the uncertainties of individual bidding behaviors and can be used as reference for optimal bidding. In fact, the real ASC data contains bidding information from thousands of participants, which would be formulated with high dimensionality and unstructured formats, not applicable for general forecasting methods. Thus, a novel data-driven ASC forecasting framework based on long-short term memory (LSTM) model and corresponding data processing techniques is proposed in this paper. In detail, A paradigmatic data integration method is proposed to fix the unstructured data formats. A feature extraction method is developed to simplify the high dimensionality of ASC. Then, a LSTM model is customized to forecast ASCs. At last, real data from Midcontinent Independent System Operator market in the U.S. are utilized to demonstrate the forecasting performance of the proposed framework. [ABSTRACT FROM AUTHOR]

Due to the deregulation of power systems worldwide, bidding behavior simulation research has gained prominence. One crucial element in these studies is accurately defining and modelling the individual reward function (or objective function). Considering the ubiquitous information barriers between market participants and researchers, the common way is to develop reward functions based on theoretical assumptions, which will inevitably cause deviations from the real world. However, since market data have gradually become transparent in recent years, especially data regarding historical bidding behaviors, it is feasible to introduce data-driven methods to identify the individual reward functions that are hidden in raw bidding data. Thus, this paper proposes a data-driven bidding objective function identification framework with three procedures. First, the bidding decision processes of participants are formulated as a standard Markov decision process. Second, a deep inverse reinforcement learning method that is based on maximum entropy is introduced to identify individual reward functions, whose high-dimensional nonlinearity could be saved in multilayer perceptions (MLPs). Third, a deep Q-network method is customized to simulate the individual bidding behaviors based on the obtained MLP-based objective functions. The effectiveness and feasibility of the proposed framework and methods are tested based on real market data from the Australian electricity market. [ABSTRACT FROM AUTHOR]

Dynamic Security Assessment (DSA) for the future power system is expected to be increasingly complicated with the higher level penetration of renewable energy sources (RES) and the widespread deployment of power electronic devices, which drive new dynamic phenomena. As a result, the increasing complexity and the severe computational bottleneck in real-time operation encourage researchers to exploit machine learning to extract offline security rules for the online assessment. However, traditional machine learning methods lack in providing information on the confidence of their corresponding predictions. A better understanding of confidence of the prediction is of key importance for Transmission System Operators (TSOs) to use and rely on these machine learning methods. Specifically, from the perspective of topological changes, it is often unclear whether the machine learning model can still be used. Hence, being aware of the confidence of the prediction supports the transition to using machine learning in real-time operation. In this paper, we propose a novel Conditional Bayesian Deep Auto-Encoder (CBDAC) based security assessment framework to compute a confidence metric of the prediction. This informs not only the operator to judge whether the prediction can be trusted, but it also allows for judging whether the model needs updating. A case study based on IEEE 68-bus system demonstrates that CBDAC outperforms the state-of-the-art machine learning-based DSA methods and the models that need updating under different topologies can be effectively identified. Furthermore, the case study verifies that effective updating of the models is possible even with very limited data. [ABSTRACT FROM AUTHOR]

Multi-energy systems (MESs) make it possible to satisfy consumer's energy demand using multiple coupled energy infrastructures, thus increasing the reliability of the energy supply compared to separate energy systems (SESs). To accurately and efficiently assess and improve the reliability of MESs, this paper proposes a MES reliability and vulnerability assessment method using energy hub (EH) model. The energy conversion, transmission and storage in MESs are compactly and linearly described by EH model, making reliability and vulnerability assessment of MESs tractable. Indices for MES vulnerability assessment are proposed to find the key components for improving MES reliability. Multi-parametric linear programming (MPLP) with a self-adaptive critical region set is proposed to reduce the computational burden caused by iteratively solving LP problems for a large number of samples during the assessment process. The results of a case study show that the proposed reliability and vulnerability assessment method is able to effectively evaluate the energy supply reliability of different energy sectors in MES as well as find the critical component of an MES from reliability perspective to support its planning. The proposed algorithm, i.e., MPLP with a self-adaptive critical region set, can improve the computational efficiency by an order of magnitude compared to the traditional LP method. [ABSTRACT FROM AUTHOR]

In response to the challenges brought by uncertain bus load and volatile wind power to power system security, this paper presents a novel unit commitment formulation based on interval number optimization to improve the security as well as economy of power system operation. By using full-scenario analysis, the worst-case impact of volatile node injection on unit commitment is acquired, so that the proposed model can always provide a secure and economical unit commitment result to the operators. Scenarios generation and reduction method based on interval linear programming theory are used to accelerate the solution procedure without loss of optimality. Benders decomposition is also implemented to reduce the complexity of this large-scale interval mixed integer linear programming, and prove the rationality and rigor of our proposed method. The numerical results indicate better secure and economical features of the proposed method comparing with the traditional one. [ABSTRACT FROM PUBLISHER]

Short-term load forecasting (STLF) is the basis of power system planning and operation. With regard to the fast-growing load in China, a novel two-stage hybrid forecasting method is proposed in this paper. In the first stage, daily load is forecasted by time-series methods; in the second stage, the deviation caused by time-series methods is forecasted considering the impact of relative factors, and then is added to the result of the first stage. Different from other conventional methods, this paper does an in-depth analysis on the impact of relative factors on the deviation between actual load and the forecasting result of traditional time-series methods. On the basis of this analysis, an adaptive algorithm is proposed to perform the second stage which can be used to choose the most appropriate algorithm among linear regression, quadratic programming, and support vector machine (SVM) according to the characteristic of historical data. These ideas make the forecasting procedure more accurate, adaptive, and effective, comparing with SVM and other prevalent methods. The effectiveness has been demonstrated by the experiments and practical application in China. [ABSTRACT FROM PUBLISHER]

Previous robust transmission expansion planning (RTEP) studies have rarely considered the important question of how large the uncertainty set should be, and hence, how the uncertainty budget can be determined objectively. This study addresses this issue by proposing a novel adaptive optimization method that optimizes the value of the uncertainty budget to minimize the size of the uncertainty set while considering the underlying risk for wind power generation (WPG) fluctuations residing outside of the proposed uncertainty set. As such, the proposed method ensures a good tradeoff between the robustness and costs of RTEP solutions. In addition, the proposed method optimizes investment strategies under forecasted WPG scenarios, while providing a security guarantee under extreme WPG scenarios. The variable-limit integral terms introduced by the proposed method are addressed in the solution process by applying the piecewise linearization approximation method combined with the quadratic Newton-Gregory interpolating polynomial technique, which allows the solution process to be cast as a mixed integer linear programming problem. The good performance and effectiveness of the proposed adaptive uncertainty set optimization method are verified by numerical results. [ABSTRACT FROM AUTHOR]

The coordinated multi-area economic dispatch enables optimal resource utilization in a larger spatial range. To overcome drawbacks such as heavy communication burden, convergence failure, and weak scalability of iterative coordination methods, this paper proposes a fully non-iterative multi-area coordination framework. The proposed framework is based on a novel system reduction technique termed as the condensed system representation (CSR). The CSR makes external equivalence of the dispatch problem of each area by exploiting power system operating characteristics, i.e., only a small number of generators may become marginal units and only a minority of security constraints may be active. An algorithm based on the optimality condition analysis is developed to identify the CSR by fixing non-marginal units to their output bounds, eliminating redundant security constraints, and making Norton equivalence of the internal network. With CSRs submitted by local areas, the multi-area system can be optimized without iterative information exchange. Case studies based on a 3-area 9-bus system verify the effectiveness of the CSR-based coordination framework. Larger-scale test systems are constructed to validate the computational efficiency, robustness, and scalability of the proposed method. [ABSTRACT FROM AUTHOR]

Increasing the penetration of variable generation has a substantial effect on the operational reliability of power systems. The higher level of uncertainty that stems from this variability makes it more difficult to determine whether a given operating condition will be secure or insecure. Data-driven techniques provide a promising way to identify security rules that can be embedded in economic dispatch model to keep power system operating states secure. This paper proposes using a sparse weighted oblique decision tree to learn accurate, understandable, and embeddable security rules that are linear and can be extracted as sparse matrices using a recursive algorithm. These matrix rules can then be easily embedded as security constraints in power system economic dispatch calculations using the Big-M method. Tests on several large datasets with high renewable energy penetration demonstrate the effectiveness of the proposed method. In particular, the sparse weighted oblique decision tree outperforms the state-of-art weighted oblique decision tree while keeping the security rules simple. When embedded in the economic dispatch, these rules significantly increase the percentage of secure states and reduce the average solution time. [ABSTRACT FROM AUTHOR]

Data-driven models analyze power grids under incomplete physical information, and their accuracy has been mostly validated empirically using certain training and testing datasets. This paper explores error bounds for data-driven models under all possible training and testing scenarios drawn from an underlying distribution, and proposes an evaluation implementation based on Rademacher complexity theory. We answer critical questions for data-driven models: how much training data is required to guarantee a certain error bound, and how partial physical knowledge can be utilized to reduce the required amount of data. Different from traditional Rademacher complexity that mainly addresses classification problems, our method focuses on regression problems and can provide a tighter bound. Our results are crucial for the evaluation and application of data-driven models in power grid analysis. We demonstrate the proposed method by finding generalization error bounds for two applications, i.e., branch flow linearization and external network equivalent under different degrees of physical knowledge. Results identify how the bounds decrease with additional power grid physical knowledge or more training data. [ABSTRACT FROM AUTHOR]

The power system inertia is gradually decreasing with the growing share of variable renewable energy (VRE). This may jeopardize the frequency dynamics and challenges the secure operation of power systems. In this paper, the concept of frequency security margin is proposed to quantify the system frequency regulation ability under contingency. It is defined as the maximum power imbalance that the system can tolerate while keeping frequency within the tolerable frequency range. A frequency constrained unit commitment (FCUC) model considering frequency security margin is proposed. Firstly, the analytical formulation of system frequency nadir is derived while considering both the frequency regulation characteristics of the thermal generators and the frequency support from VRE plants. Then, the frequency security margin is analytically formulated and piecewise linearized. A novel FCUC model is proposed by incorporating linear frequency security constraints into the traditional unit commitment model. Case studies on a modified IEEE RTS-79 system and HRP-38 system are provided to verify the effectiveness of the proposed FCUC model. The impacts of VRE penetration on system frequency security are analyzed using frequency security margin. [ABSTRACT FROM AUTHOR]

The technical virtual power plant (TVPP) is a promising paradigm to facilitate the integration of distributed energy resources (DERs) while incorporating operational constraints of both DERs and networks. Due to the volatility and limited predictability of DER generation and electric loads, the output capability of the TVPP is uncertain. In this regard, this paper proposes the robust capability curve (RCC) of the TVPP, which explicitly characterizes the allowable range of the scheduled power output that is executable for the TVPP under uncertainties. Implementing the RCC can secure the scheduling of the TVPP against unexpected fluctuations of operating conditions when the TVPP participates in the transmission-level dispatch. Mathematically, the RCC is the first-stage feasible set of an adjustable robust optimization problem. An uncertainty set model incorporating the variable correlation and uncertainty budget is employed, which makes the robustness and conservatism of the RCC adjustable. A novel methodology is proposed to estimate the RCC by the convex hull of several points on its perimeter. These perimeter points are obtained by solving a series of multi scenario-optimal power flow problems with worst-case uncertainty realizations identified based on a linearized network configuration. Case studies based on the IEEE-13 test feeder validate the effectiveness of the RCC to ensure the scheduling feasibility while hedging against uncertainties. The computational efficiency of the proposed RCC estimation method is also verified based on larger-scale test systems. [ABSTRACT FROM AUTHOR]

The computational efficiency of large-scale unit commitment (UC) is still a critical issue in power system and electricity market operations. To reduce the computation time of UC, relaxation-based neighborhood search (RBNS) and improved relaxation inducement (IRI) are proposed in this article. RBNS explores the neighborhood of the linear program (LP) relaxation optimal solution for a high-quality feasible solution. A new distance function, termed relaxation distance (RD), is proposed to measure the distance between the current solution and the tendency of the LP relaxation optimal solution. RBNS can substantially reduce the optimization space, and thus improve the efficiency. IRI has been developed to effectively induce binary variables towards the tendency of the relaxed solution. In contrast to a conventional relaxation inducement method, the binary variables are symmetrically and bi-directionally induced. The ratio between the inducing functions and the original objective function is optimized. IRI can induce more binary variables to integrality, and fewer binary variables need to be branched. Therefore, the size of the branch-and-bound tree can be reduced significantly. Modified IEEE-300 bus system and Polish 2746 bus system are used to demonstrate the effectiveness and performance of the proposed RBNS and IRI methods. [ABSTRACT FROM AUTHOR]

Test systems are important tools and benchmark for power system research. Currently, there is a lack of standard test systems for modern transmission expansion planning (TEP) research, especially under high variable renewable energy (VRE) penetrations. This article describes a 38-bus test system named the HRP-38 system dedicated to TEP. “HRP” stands for high renewable penetration. The objective of establishing such a system is to provide a consistent platform for different TEP methods to be tested and compared. The test system considers high VRE penetration of more than 30% energy share, which will be an important feature in many power systems in the future. Both AC and DC candidate lines are given to provide sufficient transmission planning alternatives. The complexity of the test system is well balanced considering calculation tractability and the ability to test the performance of the TEP planning model. The network topology, generation mix and load characteristics are described in detail. Year-round time series of VRE (wind power and PV) output and load curves for each bus are provided to facilitate a detailed evaluation of the transmission grid configuration under high VRE penetration. Finally, four benchmark results with different optimization settings are provided for the HRP-38 system. [ABSTRACT FROM AUTHOR]

Renewable energy will become a normal energy source and will be required to participate in the market. The renewable portfolio standards (RPS) together with tradable green certificates (TGC) are considered as an appropriate market mechanism to help recover renewable energy investments. The strategic offering behaviors of renewable energy should be carefully studied, especially with the introduction of TGC. This paper proposed a market equilibrium model with joint consideration on energy and TGC. The model includes two-stages of day-ahead and real-time analysis, to formulate the complex decision processes of strategic renewable energy. The model is built in a bilevel format, with multiple-scenario settings to consider the uncertainty of renewable power output within a day. Then, the bilevel model is reformulated as a single-level nonlinear problem based on KKT theorems. Then, the nonlinearities are linearized based on the strong duality theorem and a binary expansion method. The model has been finally transformed as a mix integer linear problem. Finally, an illustrative example is proposed to analyze the strategic offering behaviors of renewable energy under various market situations. [ABSTRACT FROM AUTHOR]

High renewable energy penetration profoundly increases the diversity of operating statuses for the power system. Therefore, massive operating scenarios need to be considered in transmission expansion planning (TEP) to fully reflect the impact of renewable energy on power system operation. Usually, representative scenarios need to be selected to reduce the computational burden of TEP. However, the impact of abandoning many scenarios is unclear because investment decisions are highly non-linear with respect to the input scenarios. In this paper, we propose a TEP model to effectively consider massive scenarios without reduction. We use Benders decomposition to divide the TEP problem into an investment master problem and many operation subproblems. Multiple parametric linear programming (MPLP) is applied to cluster the operation subproblems in each iteration. Here, only one operation subproblem needs to be solved in each cluster, and the results of other subproblems in the same cluster can be analytically obtained. The clustering process is objective-based and self-updated dynamically during each iteration so that the effects of all the scenarios on investment decisions are considered. The efficiency improvement and effectiveness of the proposed method are illustrated through case studies on the modified Garver's 6-bus, IEEE RTS-79, IEEE RTS-96, and realistic-sized test system. [ABSTRACT FROM AUTHOR]

Improved coordination between power and district heating systems (DHSs) can play a vital role in accommodating more wind power. However, the dynamics of district heating networks (DHNs) have not yet been fully described for large transfer delays, which remains an obstacle for optimal electricity-heat coordination. This paper solves this problem by proposing a uniform framework in the Laplace domain by modeling heat losses and transfer delays from an electrical-analog perspective. Based on this framework, an equivalent representation of DHNs is proposed, showing the explicit “end-to-end” relationship between heat power generation and demand. The model is applied in combined electricity and heat operation, in which the black-box model is provided by DHS operators for power system operators without revealing the detailed network information. A case study of an integrated electricity-heat system demonstrates the effectiveness and simplicity of the proposed model. [ABSTRACT FROM AUTHOR]

The high penetration of renewable energy will substantially change the power system operation. Traditionally, the annual operation of a power system can be represented by some typical operation modes and acts as the basis for the power-system-related analysis. The introduction of highly penetrated renewable energy will make the power system operation mode highly diversified and variable. These modes may not follow traditional empirical patterns. In this paper, we propose a data-driven method based on high-dimensional power system operation data (including power flow, unit generation, and load demand) to identify the pattern of the operation modes and analyze the impact of high renewable penetration. Specifically, the proposed data-driven method is composed of simulation, preprocessing, clustering, dimension reduction, and visualization with the aim to provide an intuitive understanding of the operation mode variety under high renewable penetration. In addition, several indices are introduced to quantify the space dispersion, time variation, and seasonal consistency of operation modes. A case study on actual Qinghai provincial power system in China validates the effectiveness of the proposed data-driven method and indicates that the dispersion and time variation of operation mode will significantly increase in the beginning and then saturate with the increase in renewable penetration level. The operation mode is also less correlated with seasons in renewable energy dominated power system. [ABSTRACT FROM AUTHOR]

Decarbonization of electricity systems drives significant and continued investments in distributed energy sources to support the cost-effective transition to low-carbon energy systems. However, the rapid integration of distributed photovoltaic (PV) generation presents great challenges in obtaining reliable and secure grid operations because of its limited visibility and intermittent nature. Under this reality, net load forecasting is facing unprecedented difficulty in answering the following question: How can we accurately predict the net load while capturing the massive uncertainties arising from distributed PV generation and load, especially in the context of high PV penetration? This paper proposes a novel probabilistic day-ahead net load forecasting method to capture both epistemic uncertainty and aleatoric uncertainty using Bayesian deep learning, which is a new field that combines Bayesian probability theory and deep learning. The proposed methodological framework employs clustering in subprofiles and considers residential rooftop PV outputs as input features to enhance the performance of aggregated net load forecasting. Numerical experiments have been carried out based on fine-grained smart meter data from the Australian grid with separately recorded measurements of rooftop PV generation and loads. The results demonstrate the superior performance of the proposed scheme compared with a series of state-of-the-art methods and indicate the importance and effectiveness of subprofile clustering and high PV visibility. [ABSTRACT FROM AUTHOR]

Inter-regional power trading plays a crucial role in optimal resource utilization. However, intra-regional operation constraints are currently not well considered in practical implementation, which may lead to internal congestions and economic loss. In this paper, a non-iterative tie-line scheduling framework taking account of both intra- and inter-regional network constraints is proposed. Based on projection theory, admissible set of tie-line injections (ASTI) is defined as the allowable range of tie-line power injections that can be met by a regional system. Then, the ASTI is implemented in tie-line scheduling to ensure the feasibility of the tie-line schedule result for each region. Requirements for practical algorithms that calculate the ASTI in power system applications are analyzed, and a novel vertex-oriented projection algorithm is proposed to efficiently calculate the ASTI. Case studies based on several IEEE and Polish test systems verify the validity and efficiency of the proposed projection algorithm. Simulations based on a four-region system demonstrate the effectiveness of the proposed tie-line scheduling framework. [ABSTRACT FROM AUTHOR]

Market power has been a problematic issue for fair and transparent trades in various electricity markets. To deal with the problems of existing market power mitigation methods, such as complicated judgment criteria, excessive supervision probability, impersonal cost data accounting, and the requirements on perfect information circumstances, a novel spot market power mitigation clearing mechanism (MPMCM) is proposed, which manages to limit potential market power execution while avoiding overregulation and maintaining a real market supply–demand situation. The MPMCM consists of three processes, namely, market power evaluation, bidding capacity division, and bidding capacity constraint. The MPMCM is transformed into a set of bidding constraints and properly integrated in the common market clearing procedure. A bilevel mathematical problem with equilibrium constraints market equilibrium model is proposed to formulate the MPMCM for market simulation, and the mixed integer linear problem reformulation of the bilevel model is derived. Finally, an illustrative example is proposed to observe the strategic behaviors under various situations, thereby proving the validity and effectiveness of the MPMCM. A large-scale numerical example based on a modified IEEE 200-node system is proposed to prove the adaptivity of the MPMCM. [ABSTRACT FROM AUTHOR]

With substantially increasing penetration levels of wind power, electric power system flexibility is needed to address the variability and uncertainty of wind power output. Thus, it has become an urgent issue to obtain an optimal tradeoff between economics and reliability, and to price system uncertainties. This paper proposes a new electricity market-clearing mechanism based on locational marginal prices (LMPs) for pricing uncertain generation and load. The uncertainty contained locational marginal price (U-LMP) is derived from a distributionally robust chance-constrained optimal power flow model in which only the first-order and second-order moments of the uncertain sources’ probability distribution are needed. Compared with traditional LMPs, the proposed U-LMP formulation includes two new uncertainty components: transmission line overload uncertainty price and generation violation uncertainty price. These LMP uncertainty components are the price signals reflecting the system costs as a result of wind generation and demand uncertainty at different locations. Finally, using parametric case studies, the relationship among uncertainty levels, system generation cost, and LMP uncertainty components are established. Case studies performed on the PJM 5-bus and IEEE 118-bus systems verify the proposed U-LMP method. [ABSTRACT FROM AUTHOR]