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• A generalized integer linear programming model of the PMU placement is proposed. • Topology changes are considered to guarantee the observability with multiple topologies. • The effects of existing measurements and their relevance are covered. Distribution networks usually have a meshed structure but are operated radially to improve the operating efficiency and ensure the power supply under an emergency situation. It is of great significance to guarantee the observability of the entire system under the topology changes in operation. This paper proposes an optimal placement method of phasor measurement unit (PMU) for distribution networks. A generalized binary integer linear programming (ILP) model for PMU placement is proposed. The changes in topology are considered to guarantee the observability under any possible operation mode. The existence of zero injection nodes (ZINs), the existing measurements, and their relevance are also covered in the proposed method to reduce the installed PMU number. The objective of the ILP problem is weighted by the degree of the corresponding node to obtain a scheme with higher measurement redundancy. The correctness and effectiveness of the proposed method are verified via case studies on the IEEE 33-node test feeder, PG&E 69-node test feeder, and a medium voltage distribution network in Southern China. [ABSTRACT FROM AUTHOR]

• A novel PMU-based equivalent model for voltage sensitivity estimation is proposed. • The simplified observable network is obtained with PMUs configured arbitrarily. • Multitime slots of PMU measurements are used to estimate equivalent parameters. • A robust method is exploited to handle the noise and bad data in measurements. The access and application of phasor measurement units (PMUs) in distribution networks highly improve the system observability and further enhance the performance of operation control and energy management. A novel PMU-based estimation method of voltage-to-power sensitivity via network equivalent is proposed for distribution systems. An equivalent model is introduced to simplify the PMU-unobservable parts of the distribution network. The equivalent parameters are estimated with the PMU measurements on both sides. The original PMU-unobservable distribution network is simplified into a completely observable network with an arbitrary configuration of PMUs. The maximum correntropy Kalman filter (MCKF) is exploited in parameter estimation to handle the noise and bad data within the PMU measurements. The voltage-to-power sensitivity of the simplified system is then calculated according to the estimation of the equivalent network parameters. Case studies on the IEEE 33-node and the PG&E 69-node test feeders verify the correctness and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Highlights • An analytical framework for quantifying the flexibility of ADNs was proposed. • Flexibility of network transmission was analysed with the limits of physical network. • The benefits of controllable resources for flexibility improvement were explored. Abstract With the integration of high shares of distributed generators (DGs), it is increasingly difficult to cope with the various uncertainties and puts forward higher requirements for the operational flexibility in active distribution networks (ADNs). Controllability of ADNs has been significantly improved by the application of energy storage and power electronic devices. However, due to the difficulties in effective coordination of various controllable resources, the controllability cannot be fully translated into the system flexibility. In this paper, an analytical framework for quantifying the flexibility of ADNs is proposed, including the quantification of node flexibility, the matching of system flexibility, and the flexibility of network transmission. The proposed framework provides a novel perspective of flexibility to reinterpret operation issues of distribution networks. As the power imbalance and voltage deviation are even more severe caused by the high shares of DG integration, the indexes of flexibility from magnitude, frequency and intensity dimensions are deteriorated in ADNs operation. Through the spatial and temporal regulation of power flow, various controllable devices, such as soft open points (SOPs) and energy storage system (ESS), can effectively mitigate the power imbalance and voltage deviation to improve the indexes of system flexibility. Thus, under the unified analytical framework, the potential benefits of system controllability are fully utilized to provide effective countermeasures for the flexible operation of ADNs. Finally, case studies are performed on the modified IEEE 33-node system to quantify the operational flexibility of ADNs and verify the flexibility enhancement brought by controllable resources. [ABSTRACT FROM AUTHOR]

Highlights • A day-ahead scheduling strategy is proposed with detailed device modeling. • The effects of multiple thermal storage devices on flexibility are fully utilized. • The unit commitment constraints in practical operation are well considered. • The optimal scheduling model is transformed into a MILP formulation by linearization. Abstract The operation of community integrated energy systems (CIESs) is challenging because it is necessary to couple energy production, conversion and consumption on the end-user side. Multiple energy demands need to be fed simultaneously with the goal of economy and reliability. This paper formulates the optimal scheduling problem based on a real community integrated energy system in China. The system has multiple chillers (i.e. three ground source heat pumps, two conventional water-cooled chillers and two double-duty chillers) and two types of thermal storage devices (i.e. two cold water tanks and an ice-storage tank). Based on detailed device modeling, a community integrated energy system operation strategy considering unit commitment is proposed, and then is transformed into a mixed-integer linear programming model by linearization of nonlinear items. Case studies are conducted based on the data for a typical day in summer. The results show that the proposed strategy can utilize the flexibility of the energy storage devices and realize an economic and reliable operation of the community integrated energy system by coordinating various energy devices. The strategy can also reduce the startup/shutdown frequency of chillers significantly. [ABSTRACT FROM AUTHOR]

Highlights • A distributed network loss optimization approach is present to increase energy utilization. • A fully distributed voltage control method is proposed. • A topology simplification method with DPMU data at controllable DGs/loads is proposed. • The coordinated control system is based on incomplete measurements. Abstract This paper explores a distributed coordinated control algorithm for active distribution networks (ADNs) based on measurements of distribution phasor measurement units (DPMUs) that are only installed at a portion of network nodes. First of all, a network topology simplification method is proposed to deal with the lack of impedance and power information in ADNs. Specifically, sub-networks with unknown impedance and power information are transformed to simplified networks with known equivalent parameters that are derived from the measurements of DPMUs at the sub-network boundaries. After that, a fully distributed control strategy utilizing a multiple agent system (MAS) is employed to control voltage during voltage excursions in ADNs, and to optimize network losses if no voltage excursions occur. MAS achieves global voltage control through distributed decision-making according to the voltage-power sensitivities that are calculated by each agent based on local and neighbourhood measurements. MAS balances reactive power locally to reduce network active power losses. The convergence of the proposed distributed voltage control method is proved. Finally, the feasibility and effectiveness of the proposed method has been demonstrated on a modified IEEE 33-bus system. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • The real-time simulation framework for active distribution networks was built. • A multirate simulation method was proposed with high-accuracy and stability. • The detailed hardware design of the real-time simulator was presented. Abstract Real-time simulation of large-scale active distribution networks exhibiting a wide range of time-scales puts forward higher requirements for simulation accuracy and efficiency. This paper presents an extendable method and design for the real-time simulation of active distribution networks utilising high-performance hardware field programmable gate arrays. In the aspect of numerical algorithm, a high-accuracy and stable multirate simulation algorithm is proposed. The entire active distribution network is decoupled into different subsystems by their inherent time-scales and distinct time steps are used to solve the subsystems. Then root-matching method is adopted to form the exponential difference equations that represent the behaviours of the electric distribution network being modelled, which eliminates the truncation errors and thus provides a highly accurate time-domain solution. To handle the interface between the subsystems, a multirate interfacing method is proposed. The hardware design of the multirate interfaces is presented as well. With the multirate algorithm, a fully functional extendable real-time simulator based on field programmable gate arrays is designed and implemented. Two modified IEEE 33-node systems with photovoltaics and energy storage are simulated on the 4-field-programmable-gate-arrays-based real-time simulator. Simulation results are compared with the commercial simulation tool PSCAD/EMTDC to validate the correctness and effectiveness of the proposed method and design. [ABSTRACT FROM AUTHOR]

Highlights • A centralized parameter tuning model of local control curves was proposed for DGs. • The potential benefits of DG inverters were explored to realize voltage control. • A mixed-integer second-order cone programming (MISOCP) model was formulated. Abstract The increasing penetration of distributed generators (DGs) exacerbates the risk of voltage violations in active distribution networks (ADNs). The var capacity provided by DG inverters is a potential solution for voltage regulation. The conventional centralized control strategies limited by computation and communication burdens are difficult to meet the requirement of rapid voltage control. However, the local control strategies based on real-time measurements have a fast response to the frequent fluctuations of DG outputs. The performance of these local controllers depends on the tuning of the control parameters. This paper proposes a centralized-based method to determine the local voltage control strategies for DGs. A centralized parameter tuning model of control curves is built, in which Q - V and P curt - V curves of DG inverters are mathematically formulated based on piecewise linearization. The original mixed-integer nonlinear programming (MINLP) model is converted into an effectively solved mixed-integer second-order cone programming (MISOCP) model using convex relaxation. The potential benefits of DG inverters are explored to regulate both reactive and curtailed active power, based on local voltage measurements. Case studies on a modified PG&E 69-node distribution system are carried out to verify the effectiveness of the proposed method. Results show that power losses of ADNs are significantly reduced and voltage profiles are also improved. [ABSTRACT FROM AUTHOR]

With the integration of high shares of distributed generators (DGs), both volatile DGs and demand-side resources make it increasingly difficult to cope with the various uncertainties and put forward a higher requirement for the operational flexibility in active distribution networks (ADNs). The highly integrated distribution-level power electronic devices represented by soft open point (SOP) significantly benefit the operation of ADNs. Due to the accurate and rapid power flow control provided by SOP, various flexible resources can be coordinated in the spatial and temporal aspects, which effectively increases the DG penetration of ADNs. In this paper, the multi-dimensional characteristics of distribution system flexibility are analysed and the maximum DG hosting capacity is adopted as the index to evaluate the flexibility brought by SOP. The flexibility evaluation model is further proposed to quantify the benefits of SOP-based flexible resources, such as conventional SOP, multi-terminal SOP and SOP with energy storage. Then, the original non-convex nonlinear model is converted into an effectively solved second-order cone programming (SOCP) model using convex relaxation. To tighten the deviation of convex relaxation to the predefined accuracy, a difference-of-convex programming (DCP)-based approach is developed to solve the proposed model. Finally, case studies are performed on the modified IEEE 33-node system to verify the effectiveness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

With the increasing penetration of renewables, microgrid integration has been considered as one of the most promising approaches to enhance the utilizations of various types of energy resources in smart distribution systems. In the near future, with the higher levels of intermittent renewables are envisaged, the distribution network operators will face significant challenges to the control and operation of distribution networks dispersedly. Consequently, the development of effective and motivating ancillary service schemes in a decentralized way for executing real-time control and reducing calculation and communication burden is still in its infancy and needs to be researched. To address this issue, this paper explores an optimal voltage regulation method with the participants of multi-microgrids based on multiple agent systems. Without an arbitration agent, peer agents in the multiple agent system calculate voltage sensitivities by local and neighbourhood measurements only. In this paper, a bi-level game model is proposed for voltage control process. In the upper-level, the distribution network operator searches the reasonable incentive mechanism based on the Stackelberg game. In the lower-level, microgrids make voltage control strategies autonomously based on a static game among microgrids. In the proposed method, microgrids participate in voltage control in distribution networks as ancillary service providers while maximizing their own profits. Meanwhile, the distribution network operator reduces the infrastructure reinforcement and avoids unnecessary renewable energy curtailment. Finally, the feasibility and effectiveness of the proposed method has been demonstrated on a modified IEEE 33-bus system. [ABSTRACT FROM AUTHOR]

The integration of distributed generators (DGs) exacerbates the feeder power flow fluctuation and load unbalanced condition in active distribution networks (ADNs). The unbalanced feeder load causes inefficient use of network assets and network congestion during system operation. The flexible interconnection based on the multi-terminal soft open point (SOP) significantly benefits the operation of ADNs. The multi-terminal SOP, which is a controllable power electronic device installed to replace the normally open point, provides accurate active and reactive power flow control to enable the flexible connection of feeders. An enhanced SOCP-based method for feeder load balancing using the multi-terminal SOP is proposed in this paper. By regulating the operation of the multi-terminal SOP, the proposed method can mitigate the unbalanced condition of feeder load and simultaneously reduce the power losses of ADNs. Then, the original non-convex model is converted into a second-order cone programming (SOCP) model using convex relaxation. To tighten the SOCP relaxation and improve the computation efficiency, an enhanced SOCP-based approach is developed to solve the proposed model. Finally, case studies are performed on the modified IEEE 33-node system to verify the effectiveness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Soft open points (SOPs) are power electronic devices installed to replace normally open points in active electrical distribution systems. SOPs can provide active/reactive power flow control and voltage regulation under normal operating conditions as well as fast fault isolation and supply restoration under abnormal conditions. The application of SOPs can improve the controllability of distribution systems, thus further enhances the economy, flexibility and reliability of the grid. In this paper, considering the long-term operation characteristics of distributed generation, a mixed integer non-linear optimization problem is formulated to optimally determine the siting and sizing of SOPs based on the typical operation scenarios generated by Wasserstein distance. It is then transformed to and solved as a mixed integer second-order programming model. Finally, case studies on the IEEE 33-node system and Taiwan Power Company distribution system are used to verify the effectiveness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A novel two-level scheduling method was proposed in this paper, which helps an aggregator optimally schedule its flexible thermostatically controlled loads with renewable energy to arbitrage in the intraday electricity market. The proposed method maximizes the economic benefits of all the prosumers in the aggregation, and naturally helps balance intra-hour differences between supply and demand of the bulk power systems because the prices of the intraday electricity market reflects the need of the bulk power systems. In the proposed two-level scheduling, the upper level is a model predictive control optimization, of which the objective function is to minimize the sum of energy and capacity cost of imbalances and the constraints are thermal constraints based on a proposed energy-balanced model, while the lower level adopts the typical temperature priority list (TPL) control. Simulation results verified the validity of the proposed method and evaluated the effects of important influencing factors. In the base case, 41.64% imbalance cost was saved compared to the reference TPL-based control. Moreover, three further conclusions were drawn: (a) the proposed method mainly saves the imbalance cost by reducing imbalance peak, thus being suitable for places with high capacity price for imbalances; (b) parameter heterogeneity affects the performance of the proposed method, and average value method performs well only with low heterogeneity; (c) the performance of the proposed method worsens with the increase of forecast uncertainty, but keeps better than that of typical TPL-based control unless the forecast uncertainty gets very strong. [ABSTRACT FROM AUTHOR]

This paper proposes a robust scheduling strategy to manage a building energy system with solar power generation system, multi-chiller system and ice thermal energy storage under prediction uncertainty. The strategy employs a two-stage adjustable robust formulation to minimize the system operation cost, wherein a parameter is introduced to adjust the level of conservatism of the robust solution against the modeled uncertainty. Then a column and constraint generation algorithm with modified initialization strategy is adopted to solve this optimization model along with mixed-integer linear programming. Further, we evaluate the performance of the proposed strategy by hourly simulating the system operation of a practical project with Monte Carlo simulation. Numerical results show that the robust scheduling with a proper parameter can be superior to the deterministic strategy in all the studied cases. Additionally, the proposed strategy has similar results with the model-based predictive control strategy while the former only needs to be implemented once. Even in the highest load case, the relative deviation between the two strategies is less than 2%. [ABSTRACT FROM AUTHOR]

Abstract: With the various detail pricing schemes designed by utilities and the development of the smart grid technologies, consumers are motivated and enabled to schedule their home appliances to save energy, reduce cost and help grid operation. This paper presents a novel Traversal-and-Pruning (TP) algorithm which schedules thermostatically controlled household loads to meet an optimization objective considering both payment and comfort settings. The novel TP algorithm is robust and a flexible method is developed to balance the optimality and speed of the algorithm. Simulation results show that an improved load schedule is obtained by the novel TP algorithm compared to an existing algorithm. [Copyright &y& Elsevier]

• Solved the profit distribution and optimal scheduling problem of multi-operator VPP. • A bi-level multi-time scale scheduling method based on bidding is proposed. • Proposed bidding and price formation methods considering fluctuation cost. • Established a multi-time scale scheduling model including default penalty mechanism. With the development of energy internet and power market, the operation regulation and pricing mechanism of traditional virtual power plants are improved to adapt to the new environment. In this paper, a bi-level multi-time scale scheduling method based on bidding for multi-operator virtual power plant is proposed to provide a framework for solving the interest distribution between operators and optimal scheduling problems of multiple-operator virtual power plant. An operator power allocation and internal electricity price formation method based on bidding equilibrium is proposed in the upper level, which introduces the fluctuation cost coefficient to express the influence of the uncertainty of renewable energy power generation on the bidding process. A multi-time scale optimal scheduling method combining scheduling model and adjustment strategy is established in the lower level. A default penalty mechanism in the scheduling model is used to ensure that operators provide the electricity allocated from the bidding process and considering the influence of demand response based on internal electricity price on adjustment strategy. Simulation results show that the proposed method can realize the optimal distribution of operators' power generation and form the internal electricity price that reflects the internal supply and demand level of virtual power plant. Besides, it can reduce the impact of uncertainty on dispatching results and improve the application range of virtual power plant to enhance the competitiveness of virtual power plant in market transactions. [ABSTRACT FROM AUTHOR]

Highlights • An interactive mechanism is proposed for smart distribution networks with microgrids. • The interaction process is formulated as Stackelberg game under a market framework. • The uncertainty of microgrids is handled by two-stage robust method. • A collaborative strategy is established to promote the trading among microgrids. Abstract This paper proposes a two-level interactive mechanism to address the day-ahead scheduling optimization of smart distribution networks with multi-microgrids. Each microgrid realizes the economic dispatch in the lower level interactive model, where the uncertainties caused by renewable energy integration and loads as well as the coordination of controllable distributed generator, energy storage and demand response are handled through a two-stage robust model. In the upper level interactive model, the distribution network operator (DNO) guarantees the operational quality by considering the power flow constraints and decides the transaction price and quantity with each microgrid based on the solutions of the lower level problem, to minimize the operation cost. The interaction process is formulated as a Stackelberg game, in which the trading strategies of coupled microgrids, acted as followers, are influenced by price incentive mechanism of DNO and affect the decision of DNO in turn. A collaborative strategy promoting the internal power trading among microgrids is also presented to deal with the market power of DNO, such that the participating microgrids can benefit from the internal trading and further reduce the cost. Numerical cases on an improved IEEE 33-bus system show the effectiveness of the proposed model and solution strategy. [ABSTRACT FROM AUTHOR]

Long-term energy storage (LTES), such as hydrogen storage, has attracted significant attention due to its outstanding performance in storing energy over extended durations and seasonal balancing of power generation and consumption. However, planning for LTES usually necessitates the comprehensive coverage of its whole operation cycle, spanning from days to months, making the issue complex and intractable. To simplify the planning of a community integrated energy system (CIES) with LTES, this study proposes a time horizon compression (THC) method and formulates a concise long-term planning model for CIES with compressed time horizons. Then, robust optimization method with a budget uncertainty set is employed to develop a robust THC model, aimed at addressing data uncertainties in CIES planning. The proposed robust THC model is implemented in the planning of a CIES with high penetration of renewable energy sources, with the objective of minimizing the total annual cost. The results demonstrate that the proposed model can efficiently solve the complex CIES planning problem, resulting in a 42.77% acceleration in optimization speed. Additionally, the diversity and differentiation in THC configurations is investigated to enhance the implementation of THC in long-term CIES planning. The effectiveness of solution robustness and the significant effects of LTES on CIES are analyzed and validated in the case study. • A compact time horizon compression (THC) method is proposed for CIES planning. • Long-term energy storage is planned and investigated for seasonal energy balance. • Robust optimization is used for robust CIES designs with a budget uncertainty set. • The results indicate that THC reduces 42.77% solving time while keeping accuracy. • Applied conditions are analyzed and proposed for appropriate THC implementation. [ABSTRACT FROM AUTHOR]

The wide utilization of network reconfiguration brings new challenges to domestic peer-to-peer (P2P) energy market. Specifically, flexible and changeable system topology has a profound impact on electricity distance-based network charges which increases the difficulty in market participants' decision-making. To address this issue, the authors propose a hierarchical P2P energy market framework which integrates network reconfiguration and virtual P2P power flow-based network usage fee (NUF) mechanism. Then, this framework is modelled as a bi-level nonlinear programming which reflects the complex interation between system topology, network charges and stakeholders' strategies. In the upper-level, distribution system operator (DSO) aims to maximize its economic benefits and ensure network security through network reconfiguration. In the lower-level, prosumers form a cooperative coalition to obtain their own optimal strategies (i.e., join in P2P trading or transact with DSO) under network charge mechanism. Furthermore, a model formulation method and a sample-based algorithm are presented to clear the domestic P2P energy market and ensure the convergence. Numerical results demonstrate that the proposed market achieves a win-win situation for both prosumers and DSO. Meanwhile, the proposed reformulation method and solution algorithm not only guarantee the global optimality under finite iterations, but also possess high computational efficiency. • A virtual P2P power flow-based network usage fees calculation method is designed for the hierarchical P2P market. • A bilevel nonlinear mathematical model is proposed to integrate the influence of changeable topology and network usage fees. • An exact algorithm with finite convergence is presented to solve the proposed nonconvex model. [ABSTRACT FROM AUTHOR]

Due to the proliferation of distributed renewable energy, bidirectional electricity and carbon interaction appears in the coordinated transmission and distribution network and increases complexity in entities' decision-making. To address the issues, this paper develops a hierarchical market framework integrated with electricity and carbon trading. Specifically, an electricity market which combines locational marginal price (LMP) and peer-to-peer (P2P) trading is established considering transmission and distribution coordination. Meanwhile, based on carbon emission flow and P2P trading, a hierarchical coordinated carbon market is also designed to precisely measure and price carbon responsibility and contribution from prosumers. In addition, a hierarchical distributed algorithm is developed to clear the proposed market with privacy protection. Numerical results authenticate the necessity for transmission and distribution coordination, benefits of distribution electricity P2P trading as well as superiority in carbon measurement and pricing method. • An LMP-based electricity P2P market is designed for transmission and distribution network. • A systematic method is proposed to precisely price prosumers' carbon responsibility and contribution. • A hierarchical distributed algorithm is proposed to clear the P2P market under TSO-DSO-prosumer coordination. [ABSTRACT FROM AUTHOR]

Operational flexibility is to depict the ability of a power system in guaranteeing a secure and high-performance system operation, which is essential for distribution systems (DSs) with high renewable energy generation (REG) penetration. However, due to the dispersed integration of energy storage systems and uncertain REGs, the available regulation capability exhibits spatio-temporal coupling. It poses a challenge to quantify flexibility considering multiple locations and time periods. This paper proposes a novel analytical region-based method to characterize the flexibility considering spatio-temporal coupling, where the total dispatch budget and carbon emission constraints are considered to guarantee economic and environmental benefits. Leveraging the basic feasible solution theory, we derive an analytical formulation of the flexibility region, expressed as a set of linear inequalities. Note that no inner or outer approximation techniques are employed in the deduction procedure. The effectiveness and scalability of the proposed method are validated on test systems. Case studies demonstrate that the proposed method enables precise quantification and visualization of operational flexibility for DSs. The derived flexibility region is a closed polyhedron in a high-dimensional space, signifying the maximum ranges of uncertainties that can be accommodated. • A region-based method is developed for quantification and visualization of operational flexibility in distribution systems. • An analytical expression of the flexibility region under spatio-temporal coupling is derived from the dispatch model. • Total dispatch budget and carbon emission constraints are considered in flexibility quantification. [ABSTRACT FROM AUTHOR]

• Solved the optimal operation problem for IMS in market environment with uncertainty. • Established a hierarchical distributed framework for cloud-edge coordination. • Proposed a bi-level distributed optimization model with fair price mechanism. • Analytical target cascading and augment Lagrange method are integrated. • The diagonal quadratic approximation is employed for parallel solution. The interconnected microgrid system (IMS) is a promising solution for the problem of growing penetration of renewable-based microgrids into the power system. To optimally coordinate the operation of microgrids owned by different owners while considering uncertainties in market environment, a bi-level distributed optimized operation method for IMS with uncertainties is proposed in this paper. A hierarchical and distributed operational communication architecture of IMS is first established. A bi-level distributed optimization model was built for IMS, where at the upper level, the IMS operates purchase-sale mode or demand response mode with the distribution network operator and optimizes the trading power with microgrids to maximize revenue. At the lower level, the chance constraint programming is used to describe and deal with the uncertainty of renewable energy and loads and optimize the output and energy storage of distributed energy with the goal of minimum cost. The analytical target cascading and augmented Lagrange method are combined to decouple and reconstruct the bi-level model for distributed solution and establishing a fair price mechanism. The optimal solutions of the problem are obtained through parallel iteration, in which the price signal plays a coordinated role in the distributed iterative optimization process. Abundant case studies verify the advantages of the model and the performance of the proposed method. [ABSTRACT FROM AUTHOR]

• An error correction method based on dynamic mode decomposition is proposed. • Developed an extreme value constraint method to further correct outliers. • The proposed method does not depend on any previous assumptions. • The proposed method can improve the prediction accuracy of different models. Accurate short-term load forecasting (STLF) is an important basis for daily dispatching of the power grid, but the non-stationary characteristics of the load series add to the challenge of this task. Many researchers have been working to improve the accuracy and speed of forecasting models, but stability is equally important. This paper develops a forecasting method based on error correction using dynamic mode decomposition (DMD) for STLF, including data selection, error forecasting, and error correction. In the data selection stage, three types of data are selected as input data of the model, including previous day data, same day data in previous week and similar day data obtained by grey relational analysis (GRA). In the error forecasting stage, the data driving characteristics of the DMD algorithm is used to capture the potential spatiotemporal dynamics of error series, thereby realizing the error forecasting. In the error correction stage, on the basis of combining the forecasting results of load and error, an extreme value constraint method (EVCM) is developed to further correct the load demand series. Based on the load data of different regions, this paper selects different performance indicators, such as MAPE, MAE, RMSE, Variance and direction accuracy (DA), to prove that the proposed method has the advantages of accuracy and stability. [ABSTRACT FROM AUTHOR]

• PV hosting capability for multiple locations is modeled as a feasible region. • The uncertainty of PV output is addressed by data-driven WDRCC. • Active management with limited budget is used to improve the hosting capability. • A systematic solution procedure is proposed to observe the feasible region. • Each PV integration request in the feasible region is a feasible request. The increasing integration scale of photovoltaic (PV) systems brings enormous challenges on distribution networks (DNs). To provide an explicit boundary of feasible PV integration capacity (PVIC) associated with each integration location, this paper proposes a novel depiction of PV hosting capability, which is the feasible region for PVIC in high-dimensional space. Next, a multi-objective optimization model based on information gap decision theory (IGDT) is proposed to observe the feasible region, where active distribution network management (ADNM) schemes with a limited budget are deployed to improve PV hosting capability. The impact of PV output uncertainty on security constraints is addressed by data-driven Wasserstein-distance-based distributionally robust chance constraints (WDRCCs). Finally, a systematic procedure is developed to solve the proposed model. Note that the exact power flow model associated with a new equivalent WDRCC reformulation method is deployed so as to guarantee the accuracy of the assessment. The effectiveness, solution accuracy, computational efficiency, and scalability of the proposed model and method are verified with the 4-bus system, the IEEE 33-bus system, and the IEEE 123-bus system. The output of the common method based on the linearized power flow deviates by more than 10% from the output of the proposed method based on the exact power flow in the 33-bus system. Each multi-location PV integration request is feasible as its locations and capacities belong to the proposed region. It implies that this region can provide guidance for PV allocation. [ABSTRACT FROM AUTHOR]

• The flexibilities of multiple links are utilized with economic performance improved. • The adaption to uncertainties is enhanced by the MPC-based rolling optimization. • The scheduling strategy with reservation margins is robust for real-time errors. Community integrated energy system (CIES) couples multiple energy forms and links, it is important to cope with the inadequacy of flexibility for realizing efficient utilization and reliable supply. Based on the detailed modeling of central energy station, district heating network (DHN) and building loads, a unified scheduling model is established by fully considering the coupling characteristics of the sources, the networks, and the loads. Meanwhile, the flexibilities from adjustable capacity of thermal storage device and the indoor temperature on the demand side, as well as the energy storage of DHN, are utilized to improve the economy. Furthermore, a model predictive control (MPC) based robust scheduling strategy is proposed to maintain and utilize CIES flexibility for enhancing the uncertainty adaptability. The scheduling framework consists of rolling optimization and robust constraint generation. The rolling optimization schedules the system with a better adaptation to flexibility demands, and the robust constraints generate adjustable margin for building demands by modifying the upper/lower and ramping limits. After the linearization of nonlinear terms in the model, case studies are conducted based on the data of a typical day in summer. The results show that the unified source-network-load scheduling strategy can give full play to the flexibilities of different energy links with a better operation economy. Additionally, the MPC-based optimization can well adapt to the rolling forecasting uncertainties, and the schedule generated by advance reserving means has stronger robustness for real-time errors. [ABSTRACT FROM AUTHOR]

Relationship between restored loads and chance level at different fault time. • The uncertainties of islanding operation in ADNs were modelled. • A chance-constrained programming based model was built for islanding partition. • The effects of the chance level on the islanding partition strategies were explored. With the high integration of uncontrollable distributed generators (NDGs) comprising photovoltaic arrays (PVs) and wind turbines (WTs), many technical issues have become increasingly prominent in the islanding operation of active distribution networks (ADNs). Such problems including branch overloading and voltage violations threaten the secure operation of distribution systems and a continuous power supply. To address the uncertainties of NDG outputs when implementing islanding partition strategies, this paper proposes a new method of the islanding partition of ADNs based on chance-constrained programming. First, power generation scenarios and probability distributions for these scenarios are generated according to historical data considering the time series characteristics and uncertainties of NDGs. Then, the chance-constrained description of islanding operation is expanded to consider the effect of uncertainties related to NDGs. Moreover, an islanding partition model of ADNs based on chance-constrained programming is established. By applying convex relaxation and introducing auxiliary variables, the model is converted to a mixed-integer quadratically constrained programming model that can be effectively solved. Finally, case studies involving the modified IEEE 33-node system, IEEE 123-node system and an actual distribution system are conducted to verify the effectiveness and scalability of the proposed method. [ABSTRACT FROM AUTHOR]

Highlights • A combined decentralized and local voltage control strategy of SOPs was proposed. • Decentralized regulation was used for the power transmission of SOPs among areas. • The local reactive power curve of SOPs was optimally tuned in each area. • The potential benefits of SOPs were fully explored to realize fast voltage control. Abstract With the integration of high shares of distributed generators (DGs), it is increasingly difficult to cope with the voltage violations and puts forward a higher requirement for the operational flexibility in active distribution networks (ADNs). Soft open point (SOP) can realize accurate power flow control and continuous voltage regulation, which is usually operated by the centralized control strategy. However, the heavy burden of communication and complex global optimization process hinder its application on fast voltage control. This paper proposes a combined decentralized and local voltage control strategy of SOPs to rapidly cope with the frequent voltage fluctuations. Based on the dynamic network partition results, the decentralized optimization is applied to regulate active power transmission of SOPs among the connected areas. The Q - V control curve is optimally tuned to locally regulate the reactive power outputs of SOPs by using the intra-area information. Compared to the widely-used centralized strategy, the proposed combined control strategy of SOPs can effectively reduce the communication and computational burden with acceptable voltage control performance. Finally, the effectiveness of the proposed control strategy of SOPs is validated on the modified PG&E 69-node distribution system and modified IEEE 123-node distribution system. [ABSTRACT FROM AUTHOR]

Highlights • The adaptive droop method is used to design the primary control for each unit. • Only the local electrical parameters are used for droop control. • The coordination strategy is proposed for the multi group energy storage. • The typical mode transition scenarios are tested by the designed supervisory control. • The play and plug can be satisfied and accurate load power is realized. Abstract The hierarchical control strategy is proposed for DC microgrid with distributed generators, energy storage systems and loads. In order to maintain power balance and smooth bus voltage fluctuation during system operation due to dynamic load and resource variation, the designed hierarchical control is divided into two layers. In the primary layer, the novel adaptive droop controller with voltage feedback compensation is constructed for distributed generators and energy storage systems by taking advantage of local electrical parameters, which can realize the dynamic load power sharing and reduce bus voltage deviation. The distributed generators may operate between maximum power point tracking mode and droop control mode by bus regulation units when power supply is larger than the loads demand and the charging capacity of energy storage systems. The state of charge can also be adjusted for energy storage through the designed adaptive droop scheme. On the other hand, the secondary supervisory control is designed to reduce power exchange and improve the system stability. Using the designed hierarchical control, the DC microgrid can operate in four different modes according to which source responsible for the bus voltage stabilization. Simulation and comparison results validate that the proposed strategy may smooth the bus voltage fluctuation and realize the dynamic power sharing. [ABSTRACT FROM AUTHOR]

The distribution system is demanded to be more efficient, more flexible and more intelligent due to the continued growth of the electricity loads, the high efficiency of energy utilization and the environmental protection. The traditional distribution systems are facing the challenge of evolving from passive networks to the active distribution networks (ADN) with the integration of multiple controllable resources. This paper presents an optimal operation and schedule model of the ADN, considering a variety of controllable resources such as distributed generations, battery storages and interruptible loads. To solve the optimization problem, a modified fuzzy adaptive PSO assisted by Kriging model (KMA-MFAPSO) is developed in this paper. In KMA-MFPSO, a novel constraint handling technique (CHT) based on the PSO is proposed to handle the constraints effectively. In addition, under the premise of ensuring the accuracy of the calculation, the Kriging model is used in KMA-MFAPSO to calculate the power flow the ADN approximately, which greatly speeds up the solving process. Finally, the effectiveness of the proposed algorithm is tested on a modified IEEE-123 system. The optimal results obtained by the proposed method are compared with the results obtained by using other solving algorithms. The simulation results indicate that KMA-MFAPSO is very robust and fast to solve the optimization problem so that it can be used in practical systems. [ABSTRACT FROM AUTHOR]

• Wasserstein ambiguity sets are utilized to depict the uncertain locational marginal price and nodal carbon intensity from the main grid and variable renewables in the distribution network. • A carbon-oriented Wasserstein distributionally robust scheduling model is proposed for the flexible interconnected distribution system with different price and carbon signals from the main grid. • Calculation and decomposition methods of DLMPs are presented for the flexible interconnected distribution system to measure the marginal cost of energy consumption in different nodes. • A novel equivalent DLMP (EDLMP) mechanism is also developed for the flexible interconnected distribution system to measure the actual cost of energy consuming in different nodes. Nowadays, distribution locational pricing mechanism has been widely used in the radial distribution network to guide the energy consumption and promote the renewables utilization. Aiming to explore the reasonable pricing policy which is applicable to the merging flexible interconnected distribution system (FIDS), this paper develops two different distribution locational pricing mechanisms for distribution lines interconnected by soft open points (SOPs). First, based on the Wasserstein ambiguity sets for uncertainties from the main grid and distribution network, a carbon-oriented distributionally robust economic dispatch model is constructed for FIDS considering different price and carbon signals from the main grid. Then, by leveraging the optimal scheme from economic scheduling model, distribution locational marginal prices (DLMPs) and equivalent DLMPs (EDLMPs) are presented to measure the marginal cost and actual cost for energy consumption in the FIDS respectively. The calculation and decomposition methods of these price signals are also developed. In case studies, a practical 63-node FIDS is chosen to verify the effectiveness of the proposed methods. Numerical results illustrate the characteristics of DLMPs and EDLMPs in FIDS under multiple uncertainties. Comparing to DLMPs, EDLMPs are more appropriate to FIDS because this pricing mechanism can reflect the lower generation cost of renewables for each consumer. [ABSTRACT FROM AUTHOR]

• A peer-to-peer trading mechanism is proposed for electricity-carbon integrated market on basis of Stackelberg game, which allows prosumers to change the roles between buyers and sellers flexibly. • The existence and uniqueness of Stackelberg equilibrium is demonstrated for the established electricity-carbon integrated market. • Both centralized analytical algorithm and decentralized iterative algorithm are expounded to solve the game model. • A two-stage peer-to-peer trading framework is extended to the electricity-carbon integrated market to support the transactive results of electricity and carbon allowance. The emergence of prosumers with considerable renewables promotes the lower-carbon operation of distribution network. However, prosumers' flexible roles also bring new challenges to establish a fairness distribution-level transactive market and ensure the security in distribution network. To address this issue, this paper presents a network-secure peer-to-peer (P2P) market with two-stage framework. In the first stage, a multi leaders multi followers (MLMF) Stackelberg game is utilized to establish the P2P electricity-carbon integrated market, which considers stakeholders' changeable roles between producer and consumer in the energy and carbon allowance transaction. The existence and uniqueness of the market equilibrium are also verified. In the second stage, network reconfiguration is taken into consideration to support the transactive results and avoid the restriction on node injected power to the largest extent. Numerical results show that the established P2P electricity-carbon integrated market can reduce carbon emissions by over 6% without harming prosumers' total revenues. [ABSTRACT FROM AUTHOR]

The increasing penetration of photovoltaics and electric vehicles exacerbates uncertainties of distribution networks, resulting in serious challenges to secure operation. To tackle the volatility caused by renewable generators and charging loads, a critical uncertain factors identification method is proposed to guide the allocation of flexible resources in this paper. First, diverse uncertainties in distribution networks are quantified and the low-rank approximation (LRA) approach is proposed to evaluate system voltage risk with the consideration of multivariate uncertainties. Then, global sensitivity analysis (GSA) is put forward to identify the critical uncertain factors under independent or correlated circumstances. The guidance for flexible resource allocation is further formulated based on the rank of global sensitivities. Numerical studies on the modified IEEE 33-node and IEEE 123-node systems indicate that the proposed method can effectively deal with the high-dimensional and non-Gaussian randomness in distribution networks. The system voltage risk can be alleviated through var capacity allocation of inverters in an economic manner. In addition, the proposed method has a light computational burden compared with Monte Carlo simulation and the polynomial chaos expansion method. • Diverse uncertainties in distribution networks are quantified. • LRA is proposed to calculate the probabilistic characteristics of system states. • Critical uncertain factors are identified based on global sensitivity analysis. • Guidance for flexible resource allocation is formulated. • System voltage risk is effectively alleviated in an economic manner. [ABSTRACT FROM AUTHOR]

• Compact shifted-frequency analysis models transferred readily from the time-domain models. • Flexible simulation model switching method that accelerates the multi-timescale simulations. • Flexible discontinuity treatment that exploits inherent phase information of the shifted-frequency analysis provides high accuracy during the discontinuities. The growing proportion of distributed generators in active distribution networks highlights the importance of multi-timescale system dynamics. The electromagnetic transient simulators with detailed modeling have been widely used for high-fidelity simulations, which leads to a contradiction between the efficiency and accuracy in the studies of the multi-timescale property of the ADNs. The shifted-frequency analysis method integrated with state-space based exponential integration is introduced in this paper, which possesses both high accuracy of exponential integration and the advantage of system-level modeling. It accurately simulates the networks considering the nonlinearities with the advantage that allows large time-steps in the simulations wherein the signals have a small bandwidth around the fundamental frequency. A model-switching method based on the integral transformation of the shifted-frequency models is designed to address the inefficiency of multi-timescale simulations. In addition, a flexible discontinuity treatment in the shifted-frequency domain is introduced for the reduction of the errors brought by the detections and interpolations of discontinuities in the time-domain. Numerical studies are conducted considering the distributed generations, the shifted-frequency models are generated integrally from the original time-domain models. The results of the multi-timescale simulations with model-switching in different domains show the high efficiency of the proposed method, and the discontinuity treatment presents higher accuracy compared with the time-domain solution. Those combined advantages compose the flexible shifted-frequency analysis for the multi-timescale simulations of active distribution networks. [ABSTRACT FROM AUTHOR]

To reduce the consumption of fossil fuel and greenhouse gas (GHG) emissions, incentive-based policies are used to encourage end-users to utilize more clean energy. Hydrogen energy is an ideal clean energy that can be integrated into the next generation power grid. Deferrable electrolyzers (DEs), as a typical electricity-to-hydrogen conversion devices and capable of modulating power consumption, can convert excessive power to store electricity as hydrogen. Therefore it can be used as a method for load management. The main contribution of this paper is to propose an energy-constrained state priority list (ECSPL) model, for analyzing the charging response of aggregated loads consisting of DE units. The typical hysteresis control of DEs as a load management mechanism is first discussed. A characteristic parameter, i.e. the energy state of DE charging load, is used to group and prioritize the DE units. The proposed ECSPL model optimally determines the operating status of DE charging and standby process, and it maintains the user-desired DE charging trajectory considering customer-constraints. The proposed model maintains the diversity of operating status of DE charging and standby process to prevent unexpected synchronization phenomenon for operating status. To evaluate the performance of the proposed method, an estimated baseline of the aggregated DE charging loads is obtained based on natural hysteresis control. The ECSPL control method of DE units for intra-hour load balancing is then evaluated. The effects of different energy-constraints, deadbands of sampled end-use state comparison, error associated with the charging-trajectory measurements are modeled to evaluate the performance of controlled DE group. The ECSPL model is described and demonstrated by the modeling results of investigated DE units. [ABSTRACT FROM AUTHOR]

Soft Open Points (SOPs) are power electronic devices installed in place of normally-open points in electrical power distribution networks. They are able to provide active power flow control, reactive power compensation and voltage regulation under normal network operating conditions, as well as fast fault isolation and supply restoration under abnormal conditions. A steady state analysis framework was developed to quantify the operational benefits of a distribution network with SOPs under normal network operating conditions. A generic power injection model was developed and used to determine the optimal SOP operation using an improved Powell’s Direct Set method. Physical limits and power losses of the SOP device (based on back to back voltage-source converters) were considered in the model. Distribution network reconfiguration algorithms, with and without SOPs, were developed and used to identify the benefits of using SOPs. Test results on a 33-bus distribution network compared the benefits of using SOPs, traditional network reconfiguration and the combination of both. The results showed that using only one SOP achieved a similar improvement in network operation compared to the case of using network reconfiguration with all branches equipped with remotely controlled switches. A combination of SOP control and network reconfiguration provided the optimal network operation. [ABSTRACT FROM AUTHOR]

Soft Open Points (SOPs) are power electronic devices installed in place of normally-open points in electrical power distribution networks. They are able to provide active power flow control, reactive power compensation and voltage regulation under normal network operating conditions, as well as fast fault isolation and supply restoration under abnormal conditions. Two control modes were developed for the operation of an SOP, using back-to-back voltage-source converters (VSCs). A power flow control mode with current control provides independent control of real and reactive power. A supply restoration mode with a voltage controller enables power supply to isolated loads due to network faults. The operating principle of the back-to-back VSCs based SOP was investigated under both normal and abnormal network operating conditions. Studies on a two-feeder medium-voltage distribution network showed the performance of the SOP under different network-operating conditions: normal, during a fault and post-fault supply restoration. During the change of network operating conditions, a mode switch method based on the phase locked loop controller was used to achieve the transitions between the two control modes. Hard transitions by a direct mode switching were noticed unfavourable, but seamless transitions were obtained by deploying a soft cold load pickup and voltage synchronization process. [ABSTRACT FROM AUTHOR]

• The mathematical model of different uncertainties is presented. • The multi-objective stochastic-information gap decision model is developed considering multiple uncertainties in the SOP planning. • The general and systematic solving method of the multi-objective stochastic-information gap decision model is proposed. • The interaction between the power fluctuation and the growth uncertainty can be analyzed by means of the multi-objective stochastic-information gap decision model. Recently, soft open points (SOPs) attract much attention due to providing power flow control and voltage regulation to the distribution system (DS). However, multiple uncertainties and expensive capital cost are referred to as thorny issues in the SOPs planning. In this paper, a multi-objective stochastic-information gap decision (MS-IGD) model is presented to alleviate multiple uncertainties with the limited budget. First, a deterministic SOP planning model is built to minimize the comprehensive cost of distributed system operator (DSO). Then, a MS-IGD model is formulated considering power fluctuation and growth uncertainty in distributed generators (DGs) and loads. To solve this model effectively, it is transformed to a mixed integer linear programming (MILP) by the polyhedron linearization technology, linear programming theory and ε constraint algorithm. In case studies, based on a prospective DS from northern China, the SOPs planning scheme with corresponding accommodation range of multiple uncertainties is presented. Numerical results not only authenticate that the worst-case envelope bound should not be decided in advance because of the complicated relationship between multiple uncertainties and investments, but also demonstrate the negative correlation between the deviation of power fluctuation and growth uncertainty under the same budget. [ABSTRACT FROM AUTHOR]

• A modified third-order quantized state system (MQSS3) simulation method is proposed. • An event-driven framework is developed for the co-simulation of EH-IES using MQSS3. • Better performance is achieved in simulations of EH-IES with continuous-discrete properties. • Detailed dynamics can be derived to support the precise operation analysis of EH-IES. Effective simulation methods are becoming critically essential for the analysis of integrated energy systems (IESs) to reveal the interactions of multiple energy carriers. The incorporation of various energy technologies and numerous controllers make the IES a heterogeneous system, which poses new challenges to simulation methods. This paper focuses on the simulation of an IES with hybrid continuous-discrete properties and heterogeneous characteristics. First, a modified third-order quantized state system (MQSS3) method is proposed for the simulation of district heating systems (DHSs), in which quantized state system (QSS) and time-discretized integration are integrated to efficiently manage numerous discrete control actions. Second, an event-driven framework is established to integrate MQSS3 into the simulation of the electricity-heat integrated energy system (EH-IES). This framework enables the adoption of the most suitable models and algorithms for different systems to accommodate the heterogeneous properties of an IES. Case studies of an EH-IES with maximum 80% PV penetration and 210 buildings demonstrate that the dynamic interactions between the DHS and the power distribution network are accurately illustrated by the proposed simulation methods, in which MQSS3 indicates the highest simulation efficiency. It is also demonstrated in the simulation results that the flexibility from DHS can be utilized as demand-side resource to support the operation of power distribution network in aspects such as consuming the surplus PV generations. [ABSTRACT FROM AUTHOR]

Highlights: [•] The Spatial Temporal model (STM) runs based on systematic integration of power system analysis and transportation analysis. [•] For the first time Origin–Destination analysis was used to model the spatial and temporal characteristics of EV charging load. [•] The STM can provide both average and probabilistic values and can identify the critical network components to upgrade. [•] Compared with the previous studies in this area, the STM shows more comprehensive and accurate evaluation results. [Copyright &y& Elsevier]

• The modeling of IT equipment is formulated based on piecewise linearization. • The spatio-temporal dispatch strategies for workload are proposed. • An operational flexibility analysis model with data centers is established. • The potential of data centers is explored to improve the system flexibility. With the development of information technology, the scale and quantity of internet data centers (IDCs) are expanding rapidly. IDCs have emerged as the major electricity consumers in active distribution networks (ADNs), which dramatically increase the electricity load and have a significant impact on the operational flexibility of ADNs. Geographically distributed IDCs can participate in the operation of ADNs with the potential for spatio-temporal load regulation. This paper proposes flexible dispatch strategies of data centers to improve the operational flexibility of ADNs. First, a data-power model of IT equipment is proposed based on piecewise linearization to describe the power consumption characteristics of data centers. The flexible dispatch strategies for the delay-tolerant workload are further proposed from two aspects of temporal transfer and spatial allocation. Then, considering the potential for spatio-temporal load regulation, the operational flexibility analysis model with data centers is formulated to adapt to the operational requirements of ADNs in complex environments. Case studies show that through the spatio-temporal regulation of workload, the energy efficiency of IDCs can be effectively improved. The flexible dispatch of IDCs can also reduce the voltage violation and feeder load imbalance of ADNs, which can facilitate providing the high-quality power supply for IDCs. [ABSTRACT FROM AUTHOR]

• Propose an optimal scheduling method to deal with multi-energy and multi-uncertainty. • Combine deep learning and clustering algorithm to deal with load-side uncertainty. • Adjusting robust coefficients can obtain scheduling schemes under different risk. • The proposed method can reduce the overall scheduling cost. In recent years, with the rapid development of the energy Internet and the deepening of the complementary coupling of various energy sources, the concept of multi-energy virtual power plant comes into being. At the same time, insufficient research on optimal scheduling of multi-energy virtual power plants under multiple uncertainties. Here we propose a robust stochastic optimal dispatching method to solve the scheduling problem under multiple uncertainties. For the source side uncertainties, the uncertain set of cardinalities with a robust adjustable coefficient is adopted to describe the output of wind turbines and photovoltaics. For the load side uncertainties, the Wasserstein generative adversarial network with gradient penalty is used to generate electric, thermal, cooling, and natural gas load scenarios, and the K-medoids clustering is used to get typical scenes. A two-stage robust stochastic optimal model of the min-max-min structure was established. Based on the dual transformation theory and the column constraint generation algorithm, the original model was solved alternately. Finally, the effectiveness of the proposed model and algorithm is verified by simulation analysis. The proposed method can get the scheduling scheme with the lowest operating cost in the worst scenario and is conducive to reducing the overall scheduling cost of the system. [ABSTRACT FROM AUTHOR]

• A novel typical day selection method is proposed. • The typical day selection process is formulated as a MIMLP problem. • Better performance on key information extraction of the original data is realized. • A robust planning scheme can be obtained based on the MIMLP method. Focusing on the problem of capacity planning for a stand-alone wind-photovoltaic-diesel-battery microgrid, this paper constructs a novel evaluation index system of typical day selection with comprehensive consideration of statistical information, typicality, and extreme scenarios information of the original data. The novel typical day selection method is formulated as mixed integer multi-objective linear programming (MIMLP) problem and the extreme indicators are considered as flexibility constrains in the MIMLP model to address the robustness of the planning scheme. The proposed MIMLP problem is converted into a series of single objective problems and solved via the two-stage fuzzy programming method to balance the performance of each objective. Based on the proposed method, a bilevel programming model is established to achieve the optimal capacity design of stand-alone wind-photovoltaic-diesel-battery microgrid. The advantages of the proposed MIMLP model are verified via comprehensive comparison with traditional k-means clustering method and a linear programming method of typical day selection based on actual data of northwestern China. [ABSTRACT FROM AUTHOR]

• A distribution network partitioning method for DSE is developed. • An optimal PMUs and communication links placement model for DSE is proposed. • Both the bandwidth cost and length cost of communication links are considered. With the expansion in scale and complexity of distribution networks, distributed state estimation (DSE), a real-time database for other on-line applications, is becoming popular for large-scale active distribution networks (ADN). Measurements from phasor measurement units (PMUs) with the same time stamp can assist DSE to obtain faster and more accurate estimation; however, the configuration of PMUs and communication links should be updated to support data collection and transmission. This paper proposes an optimal PMUs and communication links placement method for DSE in distribution networks. A network partitioning method is presented with the aim of balancing calculation times among subareas. Then, a binary integer linear programming model that simultaneously considers the optimal placement of PMUs, phasor data concentrators (PDCs) and communication links is proposed. The economy of the configuration scheme is guaranteed on the premise that the network is fully observable. Finally, case studies on the IEEE 33-node, PG&E 69-node and IEEE 123-node systems verify the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

• Typical configuration and four operation modes of DC Microgrid. • Power sharing control in hierarchical control for energy storage units. • Power balance control in hierarchical control for balance state of charge. • Virtual inertia control for power generation and Load Side Control for load consumption. • The autonomous operation of isolated DC microgrid can be realized without communication. In the DC microgrid, renewable energy sources are increasingly applied as distributed generations to replace the traditional energy at remote locations. Meanwhile, energy storage system needs to be employed to maintain the balance between fluctuated power generation and load consumption. In this paper, the coordinated control strategy is proposed for the stability operation of isolated DC microgrid. In order to avoid over-charging or deep-discharging for certain energy storage units, the novel hierarchical droop control scheme is introduced to balance state of charge among energy storage units to. Additionally, the virtual inertia control is designed to adjust the output power of renewable energy generation, and the fuzzy iterative method is added to reduce the voltage deviation induced by droop control. According to the bus voltage variation and the preset value of threshold, the load side control is constructed to guarantee the stability operation of high-priority loads. Finally, the autonomous operation of isolated DC microgrid can be realized without relying on communication. Comprehensive cases based on real-time digital simulator are provided to demonstrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]