To quantify the level of power electronics integration in a distribution network, this paper proposes a universal definition and calculation method of flexibility degree for power-electronized distribution networks. First, a universal flexibility degree is defined. The term "universal" means that this definition and its calculation method include all power electronic devices currently used in distribution networks, covering medium-voltage, low-voltage, and AC/DC hybrid distribution networks. Second, a hierarchical and partitioned calculation method is proposed for the flexibility degree. Then, several cases are used to verify the proposed definition and method. Finally, some rules of power electronic devices on flexibility degree are revealed, and configuration principles for these devices are further suggested.

Distribution system security region (DSSR) has time-variant characteristics after considering flexible resources (FRs) such as energy storage systems and demand response. This paper conducts an in-depth study on the time-variance of DSSR for the first time, pointing out and addressing the problem it causes. Firstly, the existing DSSR model is introduced. The reason for the time-variance is analyzed: FR regulations are reflected in the region varying. The problem caused by the time-variance of DSSR is also analyzed, namely that the region-based method will lose its speed advantage in online security analysis. Secondly, a time-invariant DSSR model and its security analysis method are proposed, considering complete types of FRs and N-1 security. The key to addressing the time-variance of DSSR is to reflect FR regulations as the operating point movement. Finally, the proposed model and method are verified in a real case and a large case, and compared with the existing research. The comparison shows that the proposed model maintains the speed advantage of the region-based method in security analysis. This work establishes a link between time-variant DSSR and time-invariant DSSR, laying a key foundation for practical applications of DSSR in smart distribution networks.

The construction of a new-type power system is pivotal for China to achieve its 'dual carbon' goals. To address the current challenges of constrained renewable energy (RE) integration and low equipment utilization efficiency, this paper proposes a new development pathway for China's distribution networks. Firstly, existing development pathways for distribution systems are introduced, all of which are characterized by the requirement for extensive energy storage system deployment to achieve local balancing of source-load. Secondly, a wide-area balancing development pathway based on secure bidirectional power flow is proposed, in which secure reverse power flows are encouraged across wide geographical areas and voltage levels within distribution networks, rather than being restricted or balanced locally via energy storage systems. The wide-area balancing approach will break through the existing national regulations that the reverse load rate shall not exceed 80% and that power shall not be fed back to 220 kV side. The logics to propose the new pathway is that the spatiotemporal imbalance between renewable energy and load is natural, which is the value of distribution networks' existence. Furthermore, the evolutionary process and key technologies for the proposed pathway are illustrated. The proposed pathway is demonstrated and compared to the existing ones through a case study. The case study covers the complete distribution voltage levels (0.4 kV, 10 kV, 110 kV) and 220 kV; and steady-state power flow and transient voltage stability are analyzed. The comparison shows that the proposed pathway allows for high RE integration and keeps the system secure. It also greatly boosts the bidirectional efficiency of distribution networks. The proposed pathway requires small changes to the current situation, significantly reducing energy storage needs and lowering total investment costs. In summary, the proposed pathway is well-suited to China's practical conditions and represents a promising new direction for distribution systems.

Urban distribution networks span from 220 kV to 0.4 kV, forming a tightly coupled hierarchical structure through transformers. Existing distribution system security region (DSSR) methods are limited to a single voltage level. This paper proposes a decoupling and dimension reduction method for full voltage level hierarchical and partitioned distribution networks. The security region is extended to a four level architecture (220/110/10/0.4 kV), with explicit formulations for internal and cross level coupling DSSRs. The DSSR dimension is defined as the maximum number of coupled components, easily derived from a correlation matrix. By partitioning the full system correlation matrix and identifying all ones block matrices, the high dimensional security region is decomposed into lower dimensional sub regions. A case study shows the network can be naturally partitioned into four levels, with dimensions increasing from about 2 to over 9, achieving hierarchical decoupling. The method provides a basis for decentralized security analysis of full voltage level networks.

This paper presents a novel observation approach for distribution systems based on the visualization of their security region. First, the concept of distribution system security region (DSSR) is introduced. Second, a full-dimensional visualization method for DSSR is proposed, which can visualize the entire DSSR by considering all dimensions and reveal new topological characteristics, such as collapses. Building on this, a DSSR-based observation approach for distribution systems is developed, enabling global scanning and detailed local inspection of system security. Moreover, schemes for integrating the proposed DSSR-based approach into DMS and planning platforms are presented. Finally, an IEEE RBTS test system with DGs is used to verify the proposed approach and demonstrate its applications in planning and operation. Compared with existing research, the proposed approach provides a new perspective for observing distribution system security and can identify differences that existing approaches cannot; the proposed method can reduce the complexity and time required for visualizing the entire DSSR. This work provides a new analysis tool for distribution systems, which offers methodological reference for foundational research in other energy systems.

To ensure the power supply of critical loads under intentional attacks, this study investigates the survivability of stand-alone microgrids in terms of its definition, indicators, and assessment. First, based on a comprehensive review of existing definitions of survivability, a survivability definition for SAMG is proposed. Second, a survivability indicator hierarchy and evaluation method are developed. Third, four network topologies for highsurvivability SAMG are designed, along with configuration principles for power sources, energy storage, loads, and secondary systems. Finally, case studies are conducted to validate the proposed definitions and methods. The survivability of different typical configurations is compared, and a recommended configuration is presented. This work provides guidance for planning SAMG under extreme scenarios of intentional attacks.

The total accommodation capability curve (TAC curve) can completely describe the DG accommodation capability of a distribution network. The urban distribution network generally adopts the security constraints under N-1 criterion, but the formulation of the TAC curve in the existing studies only considers the network constraints under normal operation conditions considering N-0 criterion. To fill this gap, this paper develops a TAC curve model considering security constraints under N-1 criterion in distribution networks. The model is based on alternating current (AC) power flow because the problem of voltage override after DG integration cannot be ignored. Then, the solution and plotting method of the TAC curve are proposed. The method is based on the DC power flow model combined with voltage calibration correction, which is easy to solve and accurate. Finally, test systems are used to verify the proposed model and method. The rules between the N-1 TAC curve and the N-0 TAC curve and the main factors affecting the TAC curve are analyzed. The application of the TAC curve to planning is also provided.

The calculation speed is critical for the practical application of the distribution system security region (DSSR). This paper proposes a new method to accelerate DSSR calculation. Firstly, the DSSR models are briefly introduced. Secondly, the influence mechanism of the main transformer capacity on the DSSR is observed and analyzed, forming the theoretical basis for simplifying the computation. Thirdly, a speed-up method based on neglecting the main transformer constraints is proposed. The method includes the calculation formula of the main transformer active capacity, forming main transformer active capacities for common distribution systems in China, and a convenient lookup table-based speed-up process. When the main transformer reaches or exceeds this active capacity condition, it is determined that the main transformer constraints can be ignored in the DSSR modeling, thereby simplifying the model and improving calculation speed. Finally, the proposed method is verified by an extended IEEE-RTBS-BUS4 case and a real distribution system case. The proposed method can accelerate the DSSR calculation by 701 times when it is individually used. The method is further integrated with another method, which combines two speed-up methods for the first time. As a result, the solving efficiency is improved by 6.02 times and 7.43 times, respectively, compared to using the two methods individually, which has achieved the best speed-up effect so far. This study finds that common distribution systems in China mostly satisfy the speed-up condition.

Stand-alone microgrids (SAMG) lack the support of the main grid. The large-scale integration of distributed generators and their randomness and volatility in output increase the risk of secure and stable operation of the system. To enhance the security level of SAMG operation, the concept of security region for SAMG is introduced for the first time. Initially, this paper introduces the basic concepts of SAMG and security, and provides security verification methods under the N-0 and N-1 security criteria. Subsequently, the definitions and models of security region for SAMG are proposed under the N-0 and N-1 security criteria; furthermore, based on the security distance, a security assessment and preventive control method are presented. Finally, the effectiveness of the proposed models and methods is verified through a specific case. Compared with existing methods, this paper provides more comprehensive security information such as explicit security levels, violation components, violation degree, complete N-1 fault scenarios, visual observation, and a preventive control method. The method in this paper firstly depicts the security operating range of SAMG and establishes a theoretical foundation for implementing online security functionalities.

The convex hull method is a common approach for the solution of the distribution system security region (DSSR). For the first time, this paper identifies that this method is not applicable to solve many DSSRs. Firstly, the model of the DSSR and the convex hull based solving method for the DSSR are briefly introduced. Secondly, the concepts of the concave region and convex region in the DSSR are presented. Thirdly, theoretical analyses are separately conducted for concave and convex regions, which result in two theorems and one corollary, leading to the following conclusions: (1) The convex hull method is not suitable for solving concave regions, while concave regions are widely present in real-world distribution networks. (2) Error may also be produced by the convex hull method when solving convex regions. For the convex region, the condition for an error-free solution is proven, the error causes are analyzed, and error reduction measures are proposed. Finally, the theoretical analyses are validated through case studies. The validation shows that when solving concave regions, the convex hull method can produce significant error and thus cannot satisfy the requirements for a security analysis. When solving convex regions, measures should be taken to minimize or remove error. This paper has significant value in enhancing the fundamental theory of the DSSR and applying it correctly in practice.

Most urban distribution networks in China are now characterized by limited construction land and low load growth. This paper proposes a planning method that considers the total supply capability (TSC), which can enhance the efficiency of active distribution network. Firstly, the TSC planning method is introduced from two perspectives: planning measures and planning processes. Secondly, a model for load and distribution generation (DG) allocation is established, ensuring the maximum accommodation of load under the premise of all DG allocation. If there is any load or DG that cannot be connected, the corresponding feeder capacity is increased, and the problem is resolved until all loads are connected. Thirdly, balancing of the feeder netload is conducted to further optimize the planning scheme. In addition, the location of new loads and DGs is concurrently considered for the first time, aligning more closely with the practical need of urban networks with multiple feeders sharing the same path. Finally, case study is conducted to verify the effectiveness of the proposed planning method. Compared to existing method, the proposed method prioritizes utilizing the distribution network's power supply potential through TSC calculations, which delays the upgrade of substation main transformers and feeders.

Existing methods plan the distribution network and sub-transmission network separately. This paper proposes a collaborative renewable energy resource siting and sizing planning method for distribution and sub-transmission networks to increase the renewable energy ratio in high-load density industrial parks and promote the hosting capacity of the power grid. First, to accurately measure planning effectiveness, a renewable energy ratio calculation method is proposed, which comprehensively considers the contributions of green electricity from the power grid and renewable energy generation inside and outside the industrial park. Second, a collaborative planning model is proposed, which optimizes access points and access capacity in the distribution and sub-transmission networks for renewable energy around the park. The net load is better matched with the output of renewable energy outside the park through demand response, thereby maximizing the utilization of the park load to host more renewable energy. Finally, the proposed method is verified in a real industrial park. The method outperforms traditional planning methods in terms of renewable energy ratio in the park and renewable energy hosting capacity outside the park.

Solving optimization problems plays a vital role in ensuring the secure and economic operation of distribution systems. To enhance computational efficiency, this paper proposes a general simplification and acceleration method for distribution system optimization problems. Firstly, the capacity boundary and voltage boundary model of distribution systems are established. The relative position between the two boundaries reflects the strength of capacity and voltage constraints, leading to the definition of two critical feeder lengths (CFLs) to quantify these strengths. Secondly, simplification criteria and an acceleration method are proposed. Given a distribution system, if the distance from the end load/DG node to the slack bus is less than the corresponding CFL, we can conclude that the capacity constraints are stricter than the voltage constraints. Then, the distribution system can be simplified by adopting DC power flow model or disregarding the voltage constraints. After that, the reference value tables of CFL are presented. Finally, the effectiveness of the proposed method is verified by exemplifying the method in network reconfiguration and reactive power optimization problems. By implementing the proposed acceleration method, a significant reduction in computation time is achieved while ensuring accuracy. This method applies to most urban distribution systems in optimization problems involving power flow equations or voltage constraints.

Measuring the coupling degree of heterogeneous energy is a fundamental task of integrated energy system (IES). To describe the energy coupling, this paper proposes new indicators and observes IES energy coupling phenomena with the proposed indicators. Firstly, a set of energy coupling indicators is proposed. The proposed indicators not only measure the coupling degree of IES and its subsystems, but also distinguish among power coupling, energy coupling, and capacity coupling. Secondly, the proposed indicators are compared with existing indicators. It is demonstrated that the proposed indicators are more accurate and comprehensive in measuring the coupling degree of IES. Thirdly, by observing the variation law of the operational region of IES in different coupling degrees, four phenomena have been discovered. The influence mechanism of coupling degree on the operational region of IES is revealed. The proposed indicators are verified by typical electricity-gas-heat-hydrogen cases and a real case, demonstrating good universality and applicability.

Exergy is the quantification of the work capability of energy. Accurately characterizing the limits and scope of the work potential within an integrated energy system (IES) is a crucial foundation for achieving energy-quality matching, hierarchical utilization, and enhancing the level of energy utilization. Based on the "region" method, this paper first establishes a work region model for the IES. It demonstrates a linear mapping relationship between the operating point of the work region and that of the operation region, and proves the isometric, similarity, and nonlinear geometric transformation relationships between the work region and the operation region in a multi-dimensional space. Furthermore, an improved dichotomy method is proposed as a solution for determining the security boundary of the work region, balancing both computational accuracy and efficiency. Subsequently, a model for the maximum total work capability (TWC) and the TWC curve of the IES is established. Based on the mathematical relationship between TWC and total supply capability (TSC), three methods for calculating the maximum TWC are proposed. Finally, through three typical case studies, the operation region and TSC were used as comparison benchmarks to validate the accuracy and superiority of the proposed model and method, revealing the phenomenon of local work capability decay under different operating conditions. The research presented in this paper contributes to the collaborative development of energy quantity and quality in IES, providing essential theoretical and technical support for the planning, operation, and energy market transactions of IES.

Effective security early warning and alarm technology can provide comprehensive information such as the security levels, violation components, and the security trend of the system before a fault occurs. The core early warning and alarm information provided by existing methods is insufficient. To fill these gaps, this paper proposes an early warning and alarm method to monitor the security state of regional integrated energy system (RIES). Firstly, the security boundary and fuzzy theory are introduced. Secondly, the assessment methods of geometric security distance, overload and node parameter violation are further given, respectively. Thirdly, a two-stage early warning and alarm method is proposed, which can analyze the system operating state and determine the security level. The first stage can preliminarily classify the operating state of RIES through AC security boundary, including normal state, alert state and emergency state, and then send out signals correspondingly. The second stage can calculate the final security levels based on fuzzy inference and fuzzy comprehensive evaluation. For interconnected RIES, the security levels include I, IIa IId and IIIa IIId. For radial RIES, the security levels include I and IIIa IIId. Fourthly, the comprehensive and detailed early warning and alarm information is given. The overload components and N -1 components are located by DC security boundary analysis; the violation degree and parameters violation locations are further given based on energy flow calculation; the security trend is also predicted by the average value of the geometric security distance of the time series operating points. Finally, the correctness and effectiveness of proposed method are tested on typical cases. The results show that there are indeed five security levels: III, IIc, Ia, Ic and Id, the violation components and corresponding violation degrees can be obtained accurately, and the downward trend of N-0 and N - 1 security for RIES can be predicted further. Compared with existing methods, this paper provides more complete early warning and alarm information such as detailed security levels, violation components, violation degree and security trend. The time complexity of online early warning and alarm is only O(rt), and the online computational time is reduced by 2 orders of magnitude compared with the existing method. The detailed information provided by the proposed mothed can help RIES dispatchers assess security levels and make decisions timely.

The integration of multiple flexible resources in the distribution system calls for updated security analysis, especially considering flexible resource power regulating. This paper proposes the flexible resource security regulating capability (SRC) for distribution systems. First, the flexible resource SRC is defined as the feasible maximum power regulation amount at a given time within a certain area that meets the system security demand direction and can last longer than the security demand time. Several specific SRCs are proposed, including the node SRC, feeder SRC, available SRC, and priority SRC. The node SRC uniformly quantifies the SRC of different flexible resources. The feeder SRC provides the flexible resource SRC at the feeder level. Second, the calculation methods of the SRCs are presented. Third, the application of SRC is explored, in which a real-time security monitoring, warning, and emergency control method with SRC is proposed. Moreover, the scheme of integrating SRC-related functionalities into the DSCADA and DMS is presented. Finally, the proposed SRCs are verified in the case study. Compared with existing researches, SRC is suitable for security analysis while other metrics are not. SRC can provide better compatibility with diverse flexible resources and faster security emergency control.

The high penetration of distributed energy resources (DERs) in distribution systems calls for advanced security management techniques. Hence, this paper proposes the model of the distribution system security region with energy storage systems (DSSR-ESS). The N-1 secure operation range of distribution systems integrating ESS is characterized. Further research reveals the effect and mechanism of ESS on the DSSR properties. Firstly, the ESS in distribution systems is clarified from the perspective of security, and the security service time and real-time security service capability are defined. Secondly, the DSSR-ESS model is formulated by: 1) selecting load and distributed generation (DG) as the state variables, 2) identifying the normal operation security and N-1 security scenarios, and 3) determining the complete security constraints. Then, to solve the time-varying and nonlinear N-1 DSSR-ESS model, an algorithm is developed. The analytical expressions of the region boundaries considering voltage constraints, line loss, and ESS SOC are further obtained. Finally, a modified IEEE-RBTS-BUS4 system and its expanded 104-node test system are used to verify the proposed model. Comparing with the existing research, the proposed DSSR-ESS model considers ESS. This paper concludes that ESS bidirectionally adjusts the power flow of its upstream branches, thereby expanding the security region both in positive and negative directions. But limited by state space boundaries and security boundaries unaffected by ESS, increasing ESS capacity may not lead to DSSR-ESS expansion. Based on this discovery, a sitting strategy for ESS is developed to expand the security region, which demonstrates the practical application of DSSR-ESS in the security management of distribution systems.

The total supply capability (TSC) quantities load supply capability of a distribution network under specific security criteria. This paper develops and utilizes several quantitative tools, including the TSC curve, active transformer capacity, and boundary decomposition, to investigate the impact of transformers on TSC. It is found that the TSC curve remains unchanged if the transformer capacity is no less than the active transformer capacity, with only the feeder boundary taking effect. Otherwise, the TSC curve decreases due to the binding mixed boundaries, becoming deeper as the transformer capacity decreases. These rules and mechanisms are validated through case studies on urban distribution networks, enhancing the theoretical foundation of TSC and holding practical significance for security analysis. For instance, if the substation transformer capacity is larger than the defined threshold, security analysis can be simplified by ignoring transformer capacity constraints, and the transformer upgrade can be deferred in practice.