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Time-of-use (TOU) is an effective price-based demand response strategy. A reasonable design of TOU strategy can effectively reduce the peak-valley difference, and then produce a lot of benefits (such as delaying power grid investment, reducing interruption cost, and improving reliability). However, changing peak-valley period has a great influence on the peak-valley difference and power supply reliability of power system. Therefore, this paper aims to investigate the optimal modification of peak-valley period considering reliability loss under multiple TOU schemes. Firstly, this paper presents a clustering model and algorithm of optimal load curve based on a minimum error iteration method. Secondly, an optimal modification of peak-valley period based on a dynamic load point method is proposed, and the traditional peak-valley difference is replaced by the global peak-valley difference to calculate the objective function. Thirdly, this paper establishes a load–reliability relation fitting model based on the back propagation neural network. Finally, the effectiveness and correctness of the proposed method are investigated by the Roy Billinton test system and reliability test system. [ABSTRACT FROM AUTHOR]

Load profile classification is very important in load forecast, planning and management. Although customers are generally grouped by utilities into residential, commercial classes and respective subclasses, there is a lack of systematic framework that can be used to characterize different classes with signatures that are both human-readable and machine-readable. The work presented in this paper attempts to formulate the theoretical framework for customer classification using the annual load profiles. This paper demonstrates how to extract characteristic attributes in frequency domain (CAFD) and use these CAFDs to formulate a hierarchy of load profiles that can be used as the systematic framework for customer load classification. As signatures for customer classes and subclasses, the CAFDs are obtained by using a data mining method called CART (classification and regression tree). The paper presents a load profile classification test to establish the efficacy of the proposed approach which is significant improvement over current practices that provide mostly qualitative labeling. [ABSTRACT FROM AUTHOR]

Aggregated loads of induction motors are often used in the study of power system dynamic stability. This paper reports the finding that aggregation of the same or similar induction motors may likely cause the dynamic instability. Theoretical analysis is presented in the paper to show that a group of N same induction motors in parallel connection is equivalent to N dynamic independent subsystems. Oscillation modes of one of the equivalent subsystems are affected by the number of induction motors. Hence, when the number of induction motors increases, it is possible that the oscillation modes of the group of induction motors may move toward the right on the complex plane, leading to the dynamic instability in the worst case. The analysis explains why aggregation of induction motors may possibly bring about the risk of power system dynamic instability. In this paper, case studies of an example power system with a cluster of induction motors are presented. Results of modal computation and simulation demonstrate that when the number of induction motors increases, aggregation of the same or similar induction motors leads to the dynamic voltage instability and growing low-frequency electromechanical power oscillations in the test case. [ABSTRACT FROM AUTHOR]

As the inverter-based generation replaces the conventional synchronous generators, it may also need to fill in the missing ancillary service support. One of these ancillary services is dynamic reactive power provision and voltage control. This paper analyzes optimal strategy of reactive and active fault-current support of the inverter-based generation leading to fast voltage recovery of the system. For the purpose of the analysis, new ramping active current controller able to emulate different behavior of active current injection is proposed. By optimizing its parameters for different case studies of the system, the conclusions about optimal behavior of the inverter based generation with respect to system parameters and operating conditions are drawn. It is observed that the optimal combination of active and reactive fault-current is the most sensitive to the dynamic load component penetration levels in the system. With the increasing penetration levels, the significance of active fault-current injection increases. The results show that with higher penetration levels of dynamic load component in the heavy load areas, the ramping down of the inverter-based generation active fault-current results in slower voltage recovery of the system. Following this conclusion, a recommendation on update of current European grid codes is proposed. [ABSTRACT FROM AUTHOR]

Extreme events can cause severe power system damage. Resilience-driven operation of networked microgrids (MGs) has been heavily studied in literature. There is, though, little research considering the influence of resilience on decision making for planning. In this paper, a three-level model is suggested to solve the optimal sizing problem of networked MGs considering both resilience and cost. In the first level, a meta-heuristic technique based on an adaptive genetic algorithm (AGA) is utilized to tackle the normal sizing problem, while a time-coupled AC OPF is utilized to capture stability properties for accurate decision-making. The second and third levels are combined as a defender-attacker-defender model. In the former, the suggested AGA is utilized to generate attacking plans capturing load profile uncertainty and contingencies for load shedding maximization, while a multi-objective optimization problem is suggested for the latter to obtain a trade-off between cost and resilience. Simulations considering meshed networks and load distinction into critical and non-critical are developed to demonstrate algorithm effectiveness on capturing resilience at the planning stage and optimally sizing multiple parameters. The results indicate that higher resilience levels lead to higher investment cost, while sizing networked MGs leads to decreased investment in comparison with standalone MGs sizing. [ABSTRACT FROM AUTHOR]

Economic dispatch with valve-point effect (EDVPE) considered is presented as a more accurate model of the real problem compared to the conventional economic dispatch model. It is basically a non-convex, non-differentiable, and multi-modal optimization model with many local minima. Part I of the paper focuses on the local minimum analysis of the EDVPE. The analysis indicates that a local minimum consists of the singular points, the small convex regions, and the output of a slack unit that is dispatched to balance the load demand. Two types of local minima are identified and the second type could be ignored. To verify the rationality of the analyses, a traverse search has been performed to solve the EDVPE with and without considering the transmission loss on different test systems. All the simulation results support the analysis given in the paper. To effectively solve the EDVPE on a large-scale power system, based on the analysis presented in this paper, a new method, dimensional steepest decline method, is proposed in Part II of the paper. [ABSTRACT FROM PUBLISHER]

This paper investigates systemwide short-term voltage stability concerns of power systems due to the multiple parametric uncertainties in the dynamic load model. The impact of regional load model uncertainty can be widespread and may mislead the whole system analysis and subsequent measures, if not properly addressed. This research discloses that the systemwide impact is related to the voltage weak areas through voltage stability modal analysis, and suggests that the impact of uncertain parameters needs to be assessed from a systems perspective, which has rarely been done in the existing practices. We thus present a three-step methodology for evaluating the systemwide uncertainty impacts: Firstly, it screens possible trajectories of all buses. The second step verifies whether the screened trajectories comply with the defined criteria, and determines the necessity of the final step. The final detailed analysis is conducted for those selected scenarios. Comprehensive studies for both the IEEE test and real Korea power systems consistently confirm the observations and demonstrate the efficacy and validity of the proposed method. [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]

This two-part paper considers the coordination of a population of thermostatically controlled loads (TCLs) with unknown parameters to achieve group objectives. The problem involves designing the bidding and market clearing strategy to motivate self-interested users to realize efficient energy allocation subject to a peak energy constraint. The companion paper (Part I) formulates the problem and proposes a load coordination framework using the mechanism design approach. To address the unknown parameters, Part II of this paper presents a joint state and parameter estimation framework based on the expectation maximization algorithm. The overall framework is then validated using real-world weather data and price data, and is compared with other approaches in terms of aggregated load response. Simulation results indicate that our coordination framework can effectively improve the operational efficiency of the distribution system and reduce power congestion at key times. [ABSTRACT FROM AUTHOR]

This paper presents parameter values and ranges of static load models used in a power system analysis for the representation of both individual electrical devices and aggregate system loads. The paper discusses and correlates load models and their parameters following statistical processing of the responses of around 100 transmission system operators and utilities around the world, who participated in a survey initiated by CIGRE Working Group C4.605, with the corresponding information on load models and their parameter values from the existing literature. According to the survey, the most frequently used static load models are voltage dependent, and voltage and frequency dependent exponential load models. The identified typical parameter values and ranges of these static load models, both for low voltage devices and for aggregate loads at higher voltage levels, are results of the analysis of a large number of data. Based on these results, the paper provides recommendations for their further use in power system studies and also introduces a novel method for obtaining the mean values and ranges of parameters of the aggregate system load models. [ABSTRACT FROM AUTHOR]

Renewables, such as solar and wind generation, combined with storage are becoming a key part of modern grid. This paper develops probabilistic tools for analysis of grid reliability with such variable generation resources. The developed tools improve speed and accuracy of the reliability analysis compared to usual Monte Carlo methods. This is achieved by using an extension of well known convolution method applicable to interdependent variables. The interdependent distributions are obtained from historical data using Machine Learning of quantile models. The paper presents a novel approach to the analysis of reliability contribution of storage based on these models and related to Information Theory. The developed tools are demonstrated in several example scenarios for ISO-New England service area. [ABSTRACT FROM AUTHOR]

A suitable probabilistic scenario set of load demand and natural characteristics of renewable energy is becoming a crucial issue in power system planning studies. Properly addressing the impact of potentially thousands of residential PV plants on the resilience and reliability needs of substations necessitates the representation of inherent relations between photovoltaics and the load throughout the long-term planning period. The optimal planning of substation expansions is achievable through proper modeling of input parameters which describes the characteristics of the service areas. In this paper, the co-existence of PV plants and the load in a service area under three different states such as daytime with clear-sky and no-fault, daytime with abnormal events, and nighttime are incorporated into the stochastic dynamic optimization problem by using scenario-based approach. The scenario tree of the problem is branched from three different bases simultaneously instead of only one as in conventional approach. This paper also combines the risk-constrained stochastic dynamic SEP problem and Mixed Integer Linear Programming (MILP) framework under one roof. The comparison between integrating inherent characteristics of PV plants with and without considering abnormal events into the optimization is performed to show the impact of suitable probabilistic model on dynamic nature of investment decisions. [ABSTRACT FROM AUTHOR]

The increasing prevalence of technologies such as advanced metering and controls and continuously variable power electronic devices are enabling a radical shift in the way frequency regulation is performed in the bulk power system. This is a welcome development in light of the increase of unpredictable and variable generation. The idea of active participation of loads in frequency markets is not new, but the rapidly changing landscape of the power grid requires new techniques for successful integration of new types of resources; this paper works towards that end. Previously, it has been shown that residential HVAC systems can be aggregated and used to provide frequency regulation by utilizing their thermal energy capacity and flexibility of energy consumption. The virtual battery model—a first-order linear dynamical model—was analytically shown to be an accurate and simple model to capture the flexibility of residential HVAC systems. This paper presents a technique for creating the same battery-type models for many other types of systems, which can be much more complex. Our technique is based on stress testing detailed software models of physical systems. A realistic case study involving the terminal building of a small airport is presented as evidence of the effectiveness of the proposed techniques. [ABSTRACT FROM PUBLISHER]

Due to the statistical uncertainty of loads and power sources found in smart grids, effective computational tools for probabilistic load flow analysis and planning are now becoming indispensable. In this paper, we describe a unified simulation framework that allows quantifying the probability distributions of a set of observation variables as well as evaluating their sensitivity to potential variations in the power demands. The proposed probabilistic technique relies on the generalized polynomial Chaos algorithm and on a regionwise aggregation/description of the time-varying load profiles. It is shown how detailed statistical distributions of some important figures of merit, which includes voltage unbalance factor in distribution networks, can be calculated with a two orders of magnitude acceleration compared to standard Monte Carlo analysis. In addition, it is highlighted how the associated sensitivity analysis is of guidance for the optimal allocation and planning of new loads. [ABSTRACT FROM AUTHOR]

Cold load pick-up (CLPU) has been a critical concern to utilities. Researchers and industry practitioners have underlined the impact of CLPU on distribution system design and service restoration. The recent large-scale deployment of smart meters has provided the industry with a huge amount of data that are highly granular, both temporally and spatially. In this paper, a data-driven framework is proposed for assessing CLPU demand of residential customers using smart meter data. The proposed framework consists of two interconnected layers: 1) At the feeder level, a nonlinear autoregression model is applied to estimate the diversified demand during the system restoration and calculate the CLPU demand ratio. 2) At the customer level, Gaussian mixture models and probabilistic reasoning are used to quantify the CLPU demand increase. The proposed methodology has been verified using real smart meter data and outage cases. [ABSTRACT FROM AUTHOR]

This paper proposes an approach to obtain dynamic versions of static distribution factors, such as power-transfer, line-outage, and outage-transfer distribution factors. With the proposed dynamic distribution factors (DDFs), one can predict line flows over the post-contingency transient period with the same computational effort as obtaining static distribution factors. Our development centers on deriving closed-form expressions that approximate generator outputs through the post-contingency transient period with a reduced-order aggregate dynamical model to recover dynamic generator participation factors. The full suite of DDFs can then be derived by combining these dynamic generator participation factors with injection shift factors, i.e., static linear sensitivities of line active-power flows with respect to nodal active-power injections, computed at the pre-disturbance steady-state operating point. We illustrate the accuracy and computational benefits of the proposed DDFs via numerical case studies involving the New England test system. [ABSTRACT FROM AUTHOR]

Load forecasting is one of the most important and studied topics in modern power systems. Most of the existing research on day-ahead load forecasting try to build a good model to improve the forecasting accuracy. The forecasted load is then used as the input to generation scheduling with the ultimate goal of minimizing the cost of generation schedules. However, existing day-ahead load forecasting models do not consider this ultimate goal at the training/forecasting stage. This paper proposes a task-based day-ahead load forecasting model labeled as LfEdNet that combines two individual layers in one model, including a load forecasting layer based on deep neural network (Lf layer) and a day-ahead stochastic economic dispatch (SED) layer (Ed layer). The training of LfEdNet aims to minimize the cost of the day-ahead SED in the Ed layer by updating the parameters of the Lf layer. Sequential quadratic programming (SQP) is used to solve the day-ahead SED in the Ed layer. The test results demonstrate that the forecasted results produced by LfEdNet can lead to lower cost of day-ahead SED at the expense of slight reduction in forecasting accuracy. [ABSTRACT FROM AUTHOR]

Thermostatically controlled loads (TCLs) are regarded as one of the promising resources for suppressing power fluctuations due to renewable energy (RENs). However, due to the great burdens of fully considering each users’ characteristics, it is difficult to achieve unity of the individual optimal decisions and global optimum in demand-side management (DSM). This paper proposes a game-theoretic DSM that can optimize the global power consumption schedule by individual TCL user's optimization. By integrating the prediction of REN outputs into the pricing mechanism, the proposed DSM can guide the users to make their best power consumption schedules along with intermittent REN generations, thus to smooth the tie-line power of microgrids. In this paper, a novel pricing mechanism is firstly developed based on the concave N-person game theory, which is more adaptive and flexible compared with existing game-theoretic DSM. Then, an individual's power consumption optimization and its simplified model are developed considering the constraints of the TCL model and personal preferences. The simplified model can be easily solved and achieve a fast solution in the power consumption game. An implementation framework of the proposed DSM is further developed for practical application. Finally, numerical studies verify the effectiveness of the proposed models and methods. [ABSTRACT FROM AUTHOR]

This paper presents a new non-deterministic approach for multiyear distribution network reinforcement planning (DNRP) considering the uncertainty sources pertaining to loads, electricity prices, investment costs, and operation costs. Accordingly, the underlying idea of the information-gap decision theory (IGDT) is used to obtain a robust solution protected against different realizations of each uncertain variable lying in its robust region. The proposed model is capable of adjusting the robustness of the optimal solution in terms of a specific parameter designated as the budget of uncertainty. As the uncertain loads, investment and operation costs competitively tend to maximize their robust regions for a particular value of the budget of uncertainty, the normalized normal constraint (NNC) method as a proficient multi-objective optimization method is exploited in this paper to solve the proposed multiobjective IGDT-based DNRP (IGDT-DNRP) model. Mainly, the NNC method presents a set of Pareto optimal solutions rather than a single optimal solution. Accordingly, a posteriori out-of-sample analysis is introduced in this paper to find the best solution among the set of Pareto optimal solutions. The proposed IGDT-DNRP model is implemented on the IEEE 33-bus distribution network under different circumstances. Simulation results illustrate the effectiveness of the proposed nondeterministic approach. [ABSTRACT FROM AUTHOR]

Service restoration is one of the critical functions to enable the future self-healing distribution system. To restore the distribution system in a timely and reliable manner, the realistic system operating conditions need to be accurately characterized. In this paper, two main factors that have great impacts on distribution system restoration (DSR) in practice are investigated. First, cold load pickup (CLPU), generally caused by thermostatically controlled loads (TCLs), is a common phenomenon after an outage and shaped by the outage duration. However, the time-dependent behaviors of CLPU are rarely considered in literature. In this paper, the operating state evolution of TCLs after an outage is analyzed to characterize time-dependent CLPU. And the time-dependent CLPU is analytically embedded in DSR to accurately represent the actual behaviors of the restored loads. Second, it is difficult to predict loads that fluctuate during DSR due to the lack of real-time measurement data. Accordingly, a robust DSR based on the information gap decision theory (IGDT) is proposed to address this challenge, fully considering the uncertainty of CLPU. The proposed models are tested in IEEE 13-node and 123-node test feeders. Simulation results demonstrate that the time-dependent CLPU model and the uncertainty modeling of CLPU can accurately capture the actual behaviors of loads with TCLs after an outage, which greatly improves DSR decisions in practice. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive scheduling framework for residential demand response (DR) programs considering both the day-ahead and real-time electricity markets. In the first stage, residential customers determine the operating status of their responsive devices such as heating, ventilation, and air conditioning (HVAC) systems and electric water heaters (EWHs), while the distribution system operator (DSO) computes the amount of electricity to be purchased in the day-ahead electricity market. In the second stage, the DSO purchases insufficient (or sells surplus) electricity in the real-time electricity market to maintain the supply-demand balance. Due to its computational complexity and data privacy issues, the proposed model cannot be directly solved in a centralized manner, especially with a large number of uncertain scenarios. Therefore, this paper proposes a combination of stochastic programming (SP) and the alternating direction method of multipliers (ADMM) algorithm, called SP-ADMM, to decompose the original model and then solve each sub-problem in a distributed manner while considering multiple uncertain scenarios. The simulation study is performed on the IEEE 33-bus system including 121 residential houses. The results demonstrate the effectiveness of the proposed approach for large-scale residential DR applications under weather and consumer uncertainties. [ABSTRACT FROM AUTHOR]

The wide implementation of information and communication technologies (ICT) cause power system operations exposed to cyber-attacks. Meanwhile, the tendency of integrated multi energy vectors has worsened this issue with multiple energy coupled. This paper proposes a two-stage risk-averse mitigation strategy for water-energy systems (WESs), incorporating power, natural gas and water systems against false data injection attacks (FDIA) under water-energy nexus. The FDIA on individual sub-systems is modelled through hampering false data integrity to the systems. An innovative two-stage risk-averse distributionally robust optimization (RA-DRO) is proposed to mitigate uneconomic operation and provides a coordinated optimal load shedding scheme for the nexus system security. A coherent risk measure, Conditional Value-at-Risk is incorporated into the RA-DRO to model risk. A Benders decomposition method is used to solve the original NP-hard RA-DRO problem. Case studies are demonstrated on a WES under water-energy nexus and results show that the effectiveness of the method to mitigate risks from potential FDIA and renewable uncertainties. This research provides WES operators an economic system operation tool by optimally coordinating energy infrastructures and implementing reasonable load shedding to enhance cybersecurity. [ABSTRACT FROM AUTHOR]

Ensuring long-term voltage stability is critical for reliable operations of power grids. High share of distributed energy resources (DERs) can create complicated system operation modes that may invalidate the traditional long-term voltage stability analysis based on typical operation modes. To address this challenge, this paper investigates how to compute the shortest path to the voltage stability boundary in the DER aggregated load space with large dispersion. Instead of working in the Euclidean space, we establish the analysis and computations on the algebraic power flow manifold to better capture the curvature change of the shortest path along the direction of losing stability. A modified optimal control framework is presented for obtaining the ground-truth of the smooth shortest path on the manifold. To efficiently and accurately solve for the shortest path, we further leverage the geometric features of the power flow manifold and propose a tri-sectional approximation model that is scalable for large-scale systems. Several numerical examples, up to the 1354-bus system, with different DER penetration levels and high dimensional renewable power injection variations are evaluated. The simulation results demonstrate that the tri-sectional approximation achieves high accuracy and efficiency to approximate the shortest path to the voltage stability boundary. [ABSTRACT FROM AUTHOR]

In many power systems, the increased penetration of inverter-based renewable generation will cause a decrease in kinetic energy storage, leading to higher frequency excursions after a power disturbance. This is the case of the future Nordic Power System (NPS). The look-ahead study reported in this paper shows that the chosen units participating in Frequency Containment Reserves (FCR) cannot keep the frequency above the prescribed threshold following the outage of the largest plant. This analysis relies on a detailed model of the Northern European grid. The latter is compared to the classical single-mass equivalent, and the impact of voltage-dependent loads is assessed in some detail. Next, the paper focuses on emergency power control of the HVDC links that connect the NPS to the rest of the European grid, which can supplement or even replace part of the FCR. The proper tuning of that control is discussed. Finally, the analysis is extended to the HVDC links connecting the future North Sea Wind Power Hub under two configurations, namely low and zero inertia. The impact of outages in the latter sub-system is also assessed. The material to simulate the system with industrial software is made publicly available. [ABSTRACT FROM AUTHOR]

The wide variety of inverter control settings for solar photovoltaics (PV) causes the accurate knowledge of these settings to be difficult to obtain in practice. This paper addresses the problem of determining inverter reactive power control settings from net load advanced metering infrastructure (AMI) data. The estimation is first cast as fitting parameterized control curves. We argue for an intuitive and practical approach to preprocess the AMI data, which exposes the setting to be extracted. We then develop a more general approach with a data-driven reactive power disaggregation algorithm, reframing the problem as a maximum likelihood estimation for the native load reactive power. These methods form the first approach for reconstructing reactive power control settings of solar PV inverters from net load data. The constrained curve fitting algorithm is tested on 701 loads with behind-the-meter (BTM) PV systems with identical control settings. The settings are accurately reconstructed with mean absolute percentage errors between 0.425% and 2.870%. The disaggregation-based approach is then tested on 451 loads with variable BTM PV control settings. Different configurations of this algorithm reconstruct the PV inverter reactive power timeseries with root mean squared errors between 0.173 and 0.198 kVAR. [ABSTRACT FROM AUTHOR]

With the new feature of multi-energy coupling and the advancement of the energy market, Energy Internet (EI) has higher requirements for the efficiency and applicability of integrated energy response. This paper proposes an indirect multi-energy transaction (IMET) to promote multi-energy collaborative optimization in local energy market (LEM) and improve energy utilization through personalized responses from We-Energies (WEs). Firstly, an indirect customer-to-customer multi-energy transaction is modeled for local multi-energy coupling market which can satisfy privacy, preference and autonomy of users. The efficiency of energy matching can be promoted through the participation of conversion devices. In addition, multi-time scale hybrid trading mechanism is constructed with the consideration of the transmission speed of different energy sources. Meanwhile, energy transaction process is built as a Markov decision process (MDP) with deep reinforcement learning algorithm so that the system modeling error can be successfully avoided. Furthermore, a distributed training structure is utilized to obtain more experience for a wider range of scenarios. The results of numerical simulations demonstrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel contribution factor (CF) approach to predict diversified daily peak load of low voltage (LV) substations. The CF for each LV template developed in part I of the paper is determined by a novel method—clusterwise weighted constrained regression (CWCR). It takes into account the contribution from different customer classes to substation peaks, respecting the natural difference in time and magnitude between LV substation peaks and the variance within the templates. In CWCR, intercept and coefficients are constrained to ensure that the resultant coefficients do not lead to reverse load flow and can respect zero-load substations. Cross validation is developed to validate the stability of the proposed method and prevent over fitting. The proposed method shows significant improvement in the accuracy of peak estimation over the current status quo across 800 substations of different mixes of domestic, industrial and commercial (I&C) customers. The work in the two parts of the paper is particularly useful for understanding the capabilities of LV networks to accommodate the increasing penetration of low carbon technologies without large-scale monitoring. [ABSTRACT FROM PUBLISHER]

This paper presents a multi-period active distribution network planning (ADNP) with distributed generation (DG). The objective of the proposed ADNP is to minimize the total planning cost, subject to both investment and operation constraints. The paper proposes a multi-stage stochastic optimization model to address DG uncertainties over several periods, in which the decisions are made sequentially by only using the present-stage information. A nested decomposition method is proposed which applies the stochastic dual dynamic integer programming (SDDIP) method to address computational intractabilities of the proposed ADNP approach. The presented numerical results and discussions on a 33-bus distribution system and a large-scale 906-bus system verify the effectiveness of the proposed ADNP method and its solution method. [ABSTRACT FROM AUTHOR]

In a multi-regional interconnected grid, the probabilistic load flow (PLF) of any region cannot be calculated individually but should consider the uncertainties introduced in other areas. Accordingly, the topologies, loads, and generations of every region are needed. Although the renewable generation data could be assumed as publicly known, some regional independent system operators (ISOs) still would not share important parameters with others. This motivates the development of a privacy-preserving distributed (PPD) PLF method. The challenge is to identify the mapping between the regional flows and uncertain power injections across regions without full information about the entire grid. The main idea of this paper is to respectively calculate the coefficient matrix and constant vector of the mapping: for the former, a PPD accelerated projection-based consensus algorithm is proposed; for the latter, a privacy-preserving accelerated average consensus algorithm is leveraged. Consequently, a PLF method is derived for each ISO to analytically obtain its regional joint PLF in a distributed way without sharing parameters — the key contribution of this paper. Experiments on the 118- and 1354-bus systems demonstrate that this method can generate the same results as the corresponding centralized method, and has satisfactory accuracy compared with frequently used PLF methods. [ABSTRACT FROM AUTHOR]

Synthetic power systems that imitate functional and statistical characteristics of the actual grid have been developed to promote researchers’ access to public system models. Developing time series to represent different operating conditions of these synthetic systems will expand the potential of synthetic power systems applications. This paper proposes a methodology to create synthetic time series of bus-level load using publicly available data. Comprehensive validation metrics are provided to assure that the quality of synthetic time series data is sufficiently realistic. This paper also includes an example application in which the methodology is used to construct load scenarios for a 10,000-bus synthetic case. [ABSTRACT FROM AUTHOR]

In this paper, previous theory and results regarding Low-Voltage (LV) distribution losses are validated through power-flow simulation using real load data with standard metering resolution. The validated results are then used to build a generalized loss prediction model for arbitrary grid topologies and metering resolutions. The paper provides the theoretical background to build and generalize a loss prediction model based on load variances together with an approach to estimate such variances. The prediction model uses as explanatory variables the variances of the loads. Yet, such variances are usually unknown for the higher metering resolutions, so the model also proposes a method to predict the higher resolution variances based on the standard metering ones. Results are presented to illustrate the approach proposed and to estimate the increase in losses expected for typical LV grids. [ABSTRACT FROM AUTHOR]

Distribution power systems (DPSs) are generally unbalanced, and their loads may have notable static voltage characteristics (ZIP loads). Hence, although many papers have focused on linear single-phase power flow models, it is still necessary to study linear three-phase distribution power flow models. This paper proposes a data-driven-aided linear three-phase power flow model for DPSs. We first formulate how to amalgamate data-driven techniques into a linear power flow equation to establish our linear model. This amalgamation makes our linear model independent of the assumptions commonly used in the literature (e.g., nodal voltages are nearly 1.0 p.u.); therefore, our model is characterized by relatively high accuracy, even when the assumptions become invalid. We then demonstrate how to apply our model to DPSs with ZIP loads. We also show that with the Huber penalty function employed, the adverse impact of bad data on our model's accuracy is significantly reduced, rendering our model robust to poor data quality. Case studies demonstrate that our model is generally more accurate, with 2- to 100-fold smaller errors, than most existing linear models, and remains fairly accurate even under poor data conditions. Our model also contributes to a rapid solution to DPS analyses and optimization problems. [ABSTRACT FROM AUTHOR]

Emergency frequency control is one of the most critical approaches to maintain power system stability after major disturbances. With the increasing number of grid-connected renewable energy sources, existing model-based methods of frequency control are facing up with challenges of computational speed and scalability for large-scale systems. In this paper, the emergency frequency control problem is formulated as a Markov Decision Process and solved through a novel distributional deep reinforcement learning (DRL) method, namely the distributional soft actor critic (DSAC) method. Compared with other reinforcement learning methods that only estimate the mean value, the proposed DSAC model estimates the distribution of value function over returns. This advancement can lead to more insights and knowledge for the agent, with the benefit of a much faster and more stable learning process, and the improved frequency control performance. The simulation results on IEEE 39-bus and IEEE 118-bus systems demonstrate the effectiveness and robustness of proposed models, as well as the advantage compared to other state-of-the-art DRL algorithms. [ABSTRACT FROM AUTHOR]

In order to reduce the dependence on accumulated experience that is difficult to replicate for the human dispatchers to make power generation scheduling more automatically, quickly, and intelligently, higher requirements are placed on the level of the auxiliary decision-making system. In this paper, a short-term scheduling problem was treated as a regression task that concentrates on how to learn a reliable statistic model that concludes the intrinsic logic of the dispatching policy from extensive historical dispatching experience. In this way, since Kullback-Leibler distance can better measure the distance between two distributions, we designed a novel GAN-based learning method for the scheduling task. Also, we proposed a feasible framework that combines the stage of learning, decision-making, and deployment to support the practical implementation of the proposed algorithm. In the experiment, a real case that takes short-term scheduling tasks on a regional large-scale power system is considered in our experiments. As a result, the comparison of several methods further shows the superiority of the proposed GAN-based method under our implementations. [ABSTRACT FROM AUTHOR]

Short-term load forecasts are needed for the efficient management of power systems. Although weather-based modeling is common, univariate models can be useful when the lead time of interest is less than one day. A class of univariate methods that has performed well with intraday data is exponential smoothing. This paper considers five recently developed exponentially weighted methods that have not previously been used for load forecasting. These methods include several exponential smoothing formulations, as well as methods using discount weighted regression, cubic splines, and singular value decomposition (SVD). In addition, this paper presents a new SVD-based exponential smoothing formulation. Using British and French half-hourly load data, these methods are compared for point forecasting up to one day ahead. Although the new SVD-based approach showed some potential, the best performing method was a previously developed exponential smoothing method. A second empirical study showed the better of the univariate methods outperforming a weather-based method up to about five hours ahead, with a combination of these methods producing the best results overall. [ABSTRACT FROM PUBLISHER]

In this paper, a new systematic method is proposed to analyze the system frequency in power systems under uncertain variability (UV). UV gradually increases in power systems, which originates from the renewable energy generation, random loads, frequency measurement, and communication channels, exerting noteworthy impacts on dynamic system frequency. The UV is modeled as a stochastic process in this paper. Then, the stochastic differential equations are used to describe the dynamic system frequency response (SFR) of a power system under UV, which is based on the SFR model. To assess system frequency dynamics under UV, an index of intra-range probability is put forward. Based on stochastic analysis theory, an analytic method is proposed to analyze the system frequency under UV, by which the intra-range probability can be analytically solved. Compared with Monte Carlo simulation in a typical SFR case and the Iceland electricity transmission network, the proposed method shows almost the same results using much less computation resource. Finally, insights for improving the SFR under UV are provided. The proposed method can be used to quickly verify whether the system frequency could withstand the UV and stay in the security range. [ABSTRACT FROM AUTHOR]

Time-domain simulation is the basis of dynamic security assessment for power systems. Traditionally, numerical integration methods are adopted by simulation software to solve nonlinear power system dynamics for any given contingency under a specific operating condition. An alternative simulation approach promising for online applications is to offline derive a semi-analytical solution (SAS) for power system differential equations and then online evaluate the SAS over consecutive time windows regarding the operating condition and contingency until the simulation result over a desired period is obtained. This paper proposes a general semi-analytical approach that derives and evaluates an SAS in the form of a power series in time to approximate the true solution. This paper provides an error-rate upper bound of the SAS for reliable use of adaptive time windows in evaluation of the SAS. To extend the semi-analytical approach for solving general power system differential-algebraic equations, this paper also proposes a dynamic bus method to efficiently link the SAS for dynamic components with the numerical solution of the network algebraic equations. Case studies on the New England 39-bus system and the Polish 2383-bus system test the performance of the proposed approach, compare it with other methods, and show the potentials of the proposed semi-analytical approach for online simulation. [ABSTRACT FROM AUTHOR]

To uncover the mechanism by which voltage-dependent loads (VDLs) influence electromechanical dynamics, this paper mathematically deduces the damping torque induced by VDLs based on a single machine infinite bus system. Moreover, by continuously regulating the terminal voltage of a typical large-scale VDL, i.e., the aluminum electrolysis load, this paper proposes a novel load damping control architecture to dynamically modulate the power consumption of controlled loads so as to eliminate interarea oscillations in power systems. Specifically, the decentralized load damping controllers (LDCs) used in this architecture are designed by a proposed multistage mixed ${{{H}}_{2}} / {{{H}}_\infty }$ control approach to guarantee robustness against uncertainties (e.g., tie-line outages and wind generation fluctuations) as well as to ensure reasonable control efforts of controlled VDLs. Simulation results on the modified New England and New York interconnected system validate the method for analysis of VDLs’ effects on interarea oscillations and show the proposed load damping control strategy can satisfactorily damp interarea oscillations over multiple operating points. [ABSTRACT FROM AUTHOR]

This paper proposes a novel comprehensive model of a rectifier-controlled induction motor drive for use in positive-sequence transient stability simulation (PSTSS) programs. The model is implemented to approximately capture the behavior of the point-on-wave drive model, and applied to investigate the dynamic performance of the advanced drive loads in system-level simulations. This positive-sequence drive model is systematically developed by reducing the detailed three-phase electrical and control representations into $dq$ axes positive-sequence formulations. For the positive-sequence model, the line-side rectifier is interfaced to the grid through a voltage source with separate $dq$ axes controls to regulate the active and reactive power of the drive. The machine-side inverter control system is represented based on rotor flux oriented control. The dc-link of the drive converter is implemented by employing the average model of the pulse width modulated converter, and is utilized to integrate the line-side rectifier and machine-side inverter. The proposed motor drive model is validated by comparing the performance with the electromagnetic transient point-on-wave drive model. The VAr support capability of the drive load model is investigated by incorporating the developed model into a composite load structure in PSTSS programs. Multiple units of the developed drive models are represented in large-scale transmission systems to examine the system-level responses of drive loads. [ABSTRACT FROM AUTHOR]

This paper summarizes simulation based technical feasibility and cost benefit analyses of a range of off-the-shelf electrical losses reduction intervention solutions in the Isle of Wight (IoW) 11 kV distribution network in the United Kingdom (UK), assessed over a period of 45 years. Based on presented results, the paper provides a brief commentary on the merits, drawbacks, risks and recommendations associated with each considered network intervention. Among considered network interventions, the transformer auto stop-start scheme, where one of the transformers among a pair at a primary substation would be switched depending on the substation's varying load, was found to be the optimal solution, i.e., in reducing technical losses significantly and may also have a reasonable Net Present Value (NPV) with a good rate of Return on Investment (RoI) when fully implemented. [ABSTRACT FROM PUBLISHER]

Due to the increasing penetration of large-scale renewable energy generation at transmission level, hybrid AC/DC transmission expansion is becoming more relevant by the day, especially if the considered renewable generation is far away from existing AC grid infrastructure. This paper presents a multi-period hybrid AC/DC network expansion planning model that incorporates node voltages, reactive power and network losses. Since the operation of a high voltage DC link is influenced considerably by the converter stations, converter transformer, filter, and phase reactor are modeled in each converter station. Since the AC power flow equations render a non-convex problem whose solution algorithms do not always guarantee convergence or optimality, a second-order conic relaxation is utilized. The resulting model is a mixed-integer convex problem with a convergence guarantee that embodies a better approximation of system operation than its DC linear counterpart. Three case studies are considered to illustrate the proposed model. [ABSTRACT FROM AUTHOR]

This paper proposes a new deep learning (DL) based model-free robust method for bulk system on-line load restoration with high penetration of wind power. Inspired by the iterative calculation of the two-stage robust load restoration model, the deep neural network (DNN) and deep convolutional neural network (CNN) are respectively designed to find the worst-case system condition of a load pickup decision and evaluate the corresponding security. In order to find the optimal result within a limited number of checks, a load pickup checklist generation (LPCG) algorithm is developed to ensure the optimality. Then, the fast robust load restoration strategy acquisition is achieved based on the designed one-line strategy generation (OSG) algorithm. The proposed method finds the optimal result in a model-free way, holds the robustness to handle uncertainties, and provides real-time computation. It can completely replace conventional robust optimization and supports on-line robust load restoration which better satisfies the changeable restoration process. The effectiveness of the proposed method is validated using the IEEE 30-bus system and the IEEE 118-bus system, showing high computational efficiency and considerable accuracy. [ABSTRACT FROM AUTHOR]

New resource mix, e.g., renewable resources, are imposing operational complexities to modern power systems by intensifying uncertainty and variability in the system net load. This issue has motivated independent system operators (ISOs), e.g., California ISO (CAISO), to add flexible ramping products (FRPs) to their day-ahead (DA) market models. Such structural changes in the DA market formulation require further analyses and detailed design to ensure adequate operational flexibility, market efficiency, and reliability. This paper conducts a comprehensive study to: (a) augment existing DA market models with enhanced FRP design to schedule ramp capabilities that are more adaptive with respect to the real-time (RT) 15-min net load variability and uncertainty, and (b) design corresponding market payment policies that accurately reflect the value of the added flexibility through enhanced FRP design. The proposed FRP design can be implemented in present-day system operations with minimal disruption to existing DA market models. Performance of the proposed DA market model, which includes the enhanced FRP design, is compared against the DA market model with existing FRP design through a validation methodology based on RT unit commitment model. This validation methodology mimics fifteen-minute markets of CAISO. The proposed method is tested on an IEEE 118-bus test system. [ABSTRACT FROM AUTHOR]

This paper proposes a novel real-time adaptive under voltage load shedding (UVLS) method by using optimized fuzzy logic controllers to address fault-induced delayed voltage recovery (FIDVR) and short-term voltage instability (STVIS) problems. An intelligent multi-input multi-output fuzzy logic load shedding controller is developed based on a short-term voltage recovery criterion (STVRC). For the controller, the magnitude deviation and the recovery time deviation of voltage trajectory are extracted as inputs, while the load shedding amount at the current load shedding stage and the time delay of the next stage are taken as outputs. Particle swarm optimization (PSO) technique is further employed for the tuning of the controller parameters to realize the voltage recovery requirement at the lowest cost of load shedding. The proposed UVLS method is formed by a group of the fuzzy logic controllers deployed at the load buses, each monitoring its own bus voltage and shedding load in closed-loop. Responding to the severity of voltage variations, the proposed method is able to adaptively determine the location, time and amount of load shedding in real-time to make the voltage satisfy the STVRC. The effectiveness of the proposed method compared to other methods is testified by simulations on the Nordic test system. [ABSTRACT FROM AUTHOR]

This paper considers an event-triggered mechanism (ETM) for multiple frequency services of electric vehicles (EVs) in smart grids (SGs). A new model of a SG with an ETM and multiple agents of EVs is introduced. ETM is deployed to reduce the load on network bandwidth. EVs are incorporated in both secondary and primary frequency services to suppress frequency fluctuations in the system. The behaviours of EV owners are also considered by using batteries SOC controls. Then, a mathematical model of the system is derived which contains parametric uncertainties due to the incorporation of SOC control, an ETM variable arising from ETM control, and a time-varying delay in both the state and control input vectors. We derive new Lyapunov stability and stabilizability conditions to ensure robust $H_{\infty }$ performance of the closed-loop system. The conditions are derived based on various mathematical tools including relaxed Jensen inequality, free weighting matrix technique, reciprocally convex approach, and matrix inequality for uncertainties. An effective procedure is proposed based on an approach using the state transformation and tractable linear matrix inequalities to synthesis robust static output feedback controller gains. Extensive simulations of a SG with three agents of EVs are undertaken to validate of our proposed control scheme. [ABSTRACT FROM AUTHOR]

Accurate load modeling is critical for credible power system stability analysis. Because of the increasing complexity in modern system load, establishing a more comprehensive load model and performing accurate parameter estimation are the two biggest challenges in composite load modeling. In this paper, an induction motor with variable frequency drive (IM-VFD) together with the traditional ZIP+IM model is utilized to describe the dynamic characteristics of the system load. We estimate the time-varying probabilistic distributions of all states and parameters to describe their stochastic characteristics, thereby representing the real-time varying features of an actual load. The Fokker-Planck operator is applied to linearize the updated load model in tensor format. We then use tensor decomposition to reduce the computational and storage costs for calculating load model parameters. A sensitivity indicator is used to analyze the sensitivities of the estimated parameter distributions for subsequent model reduction. Simulations demonstrate that the updated load model has better performance than the traditional ZIP+IM model. [ABSTRACT FROM AUTHOR]

Microgrids incorporate an increasing number of distributed energy resources (DERs), which induce a higher variability and faster dispatch capabilities in power systems. This paper proposes a two-layer real-time scheduling model for microgrids, based on approximate future cost function (AFCF), where the future cost represents the opportunity cost for the microgrid operation in subsequent periods. At the upper layer, the look-ahead rolling scheduling is adopted to optimize microgrid operations, in which the future cost function (FCF) in deterministic and stochastic scenarios is approximated by a piecewise linear function. At the lower layer, a real-time parameter updating strategy based on real-time data is proposed. In this case, the real-time scheduling readjusts the look-ahead schedule using the immediate cost in the current period and the future cost calculated by the updated AFCF. The proposed two-layer real-time scheduling model uses an offline optimization, in which most of the computation tasks are completed at the upper layer, and applies a real-time optimization, in which the time-consuming problem is avoided at the lower layer. The effectiveness of the proposed two-layer real-time scheduling model of microgrids is validated by using a grid-connected microgrid system. For comparison, other existing real-time scheduling methods are also implemented in the same microgrid system. [ABSTRACT FROM AUTHOR]

This paper emphasizes the importance of including unbalanced distribution systems for voltage stability studies in power systems. The paper aims to: discuss the various simulation methods for power system analysis; highlight the need for modeling unbalanced distribution system for accurate load margin assessment; demonstrate the influence of net-load unbalance (NLU) on voltage stability margin (VSM). We also share a T&D co-simulation interface with commercial power system solvers. The distribution system is evolving rapidly with high proliferation of distributed energy resources (DERs); these are not guaranteed to proliferate in a balanced manner and uncertainty resulting due to these DERs is well acknowledged. These uncertainties cannot be captured or visualized without representing the distribution system in detail along with the transmission system. We show the impact of proliferation of DERs in various 3-phase proportions on voltage stability margin through T&D co-simulation. We also study the impact of volt/VAR control on voltage stability margin. This analysis is only possible by representing the distribution system in detail through T&D co-simulation. Higher percentage of net-load unbalance (NLU) in distribution system aggravates the voltage stability margin of the distribution system, which can further negatively influence the overall voltage stability margin of the system. [ABSTRACT FROM AUTHOR]

Wide-area data and algorithms in large power systems are creating new opportunities for implementation of measurement-based dynamic load modeling techniques. These techniques improve the accuracy of dynamic load models, which are an integral part of transient stability analysis. Measurement-based load modeling techniques commonly assume response error is correlated to system or model accuracy. Response error is the difference between simulation output and phasor measurement units (PMUs) samples. This paper investigates similarity measures, output types, simulation time spans, and disturbance types used to generate response error and the correlation of the response error to system accuracy. This paper aims to address two hypotheses: 1) can response error determine the total system accuracy? and 2) can response error indicate if a dynamic load model being used at a bus is sufficiently accurate? The results of the study show only specific combinations of metrics yield statistically significant correlations, and there is a lack of pattern of combinations of metrics that deliver significant correlations. Less than 20% of all simulated tests in this study resulted in statistically significant correlations. These outcomes highlight concerns with common measurement-based load modeling techniques, raising awareness to the importance of careful selection and validation of similarity measures and response output metrics. Naive or untested selection of metrics can deliver inaccurate and misleading results. [ABSTRACT FROM AUTHOR]

Low frequency electromechanical oscillations can pose a threat to the stability of power systems if not properly addressed. This paper proposes a novel methodology to damp these inter-area oscillations using loads, the demand side of the system. In the proposed methodology, loads are assigned to an aggregated cluster whose demand is modulated for oscillation damping. The load cluster control action is obtained from an optimal output feedback control (OOFC) strategy. The paper presents an extension to the regular OOFC formulation by imposing a constraint on the sum of the rows in the optimal gain matrix. This constraint is useful when the feedback signals are generator speeds. In this case, the sum of the rows of the optimal gain matrix is the droop gain of each load actuator. Time-domain simulations of a large-scale power system are used to demonstrate the efficacy of the proposed control algorithm. Two different cases are considered: a power imbalance and a line fault. The simulation results show that the proposed controllers successfully damp inter-area oscillations under different operating conditions and with different clustering for the events considered. In addition, the simulations illustrate the benefit of the proposed extension to the OOFC that enable load to provide a combination of droop control and small signal stability augmentation. [ABSTRACT FROM AUTHOR]