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In this paper, we propose a two-stage transmission hardening and planning (TH&P) model that can meet the load growth demand of normal scenarios and the resilience requirements of hurricane-induced damage scenarios. To better measure the resilience requirements, the proposed TH&P model includes two resilience assessment indexes, namely, the load shedding (LS) under the damage scenario and the average connectivity degree (ACD) at different stages. The first-stage model, which aims to meet the load growth demand while minimizing the LS, is formulated as a mixed-integer linear program (MILP) to minimize the total planning and hardening cost of transmission lines, the operating cost of generators, and the penalty cost of wind power and load shedding in both normal and damage scenarios. The second-stage model aims to further improve the ACD when the ACD of the scheme obtained from the first-stage model cannot reach the target. Specifically, the contribution of each transmission line to the ACD is calculated, and the next hardened line is determined to increase the ACD. This process is repeated until the ACD meets the requirements. Case studies of the modified IEEE RTS-24 and two-area IEEE reliability test system-1996 indicate the proposed TH&P model can meet the requirements for both normal and damage scenarios.

This paper presents resilience-oriented transmission expansion planning (RTEP) with optimal transmission switching (OTS) model under typhoon weather. The proposed model carefully considers the uncertainty of component vulnerability by constructing a typhoon-related box uncertainty set where component failure rate varies within a range closely related with typhoon intensity. Accordingly, a min-max-min model is developed to enhance transmission network resilience, where the upper level minimizes transmission lines investment, the middle level searches for the probability distribution of failure status leading to max worst-case expected load-shedding(WCEL) under typhoon, and the lower level optimizes WCEL by economic dispatch (ED) and OTS. A nested decomposition algorithm based on benders decomposition is developed to solve the model. Case studies of modified IEEE 30-bus and 261-bus system of a Chinese region illustrate that: a) the proposed RTEP method can enhance resilience of transmission network with less investment than widely used RTEP method based on attacker and defender (DAD) model, b) the influence of OTS on RTEP is closely related with contingency severity and system scale and c) the RTEP model can be efficiently solved even in a large-scale system.

With the aggregation of renewable energy in the power system, the uncertainty caused by the renewable energy affects the planning and operation of power systems. Meanwhile, the existing planning models fail to consider renewable energy uncertainty methods, specifically concerning renewable energy confidence and future possible scenarios; thus, a confidence-based scenario cluster method is presented. A novel generator, network, load, and energy storage (GNLS) co-planning model is proposed in the paper. First, a confidence-based scenario cluster is built, which can reflect uncertainties by clustering and analyzing wind, solar, and load. Second, the proposed model focuses on load and energy storage co-planning, and in addition, relevant flexible indices are used to assess the model. Finally, the GNLS co-planning model is built as a bi-level stochastic model on continuous time scales. The model is solved using the Benders decomposition algorithm. The method in this paper is validated using an IEEE RTS 24-bus and a real test system in China to demonstrate the reduction in renewable energy curtailment and optimization of economic factors in power system planning.

Hardening planning is an effective way to enhance the ability of the transmission system against hurricane attacks and further improve the resilience of power systems. However, the existing hardening method gives little consideration to the risk of multiple failures under hurricanes which may underestimate the real post-disaster damage. To fill the research gap, this paper proposes a resilience index, i.e. fault chain risk expectation (FCRE), which can measure the risk of multiple failures under hurricanes. Then the FCRE-based resilient transmission hardening planning (RTHP) model is proposed to minimize hardening and load shedding penalty costs under different hurricane scenarios. In this paper, hurricane simulation is finished by critical parameters firstly, then the failure probability curve is adopted to obtain the spatial–temporal failure probability of different components, and finally, the corresponding contingency scenarios under simulated hurricanes are obtained by Monte Carlo Simulation (MCS) and k-means clustering algorithms. Meanwhile, the set of fault chains is constructed to calculate the FCRE for each line, and the corresponding constraint is formed to ensure that the system resilience reaches a target level. The proposed model is verified on the modified RTS 24-bus system and the results demonstrate the effectiveness of the proposed hardening planning method.

With the increase of inverter-based generators in the power system, the proportion of traditional generators is decreasing, and their voltage support ability to the power system is weakening, the power system operation is approaching to its voltage stability limit. It is of great significance to study on-line analysis of power system voltage stability under different control manners of inverter-based generators. Firstly, impedance matching theory and coupled single-port circuit theory are introduced. Secondly, coupled single-port method based voltage stability assessment method with inverter-based generators is proposed. Then, use the impedance matching condition and proposed method to analyze the influence of inverter-based generators on voltage stability in different control manners. The proposed method can reveal the voltage stability margin of power system with inverter-based generators in the current running state, and is suitable as an on-line voltage stability approach to evaluate the proximity of voltage collapse in real time. The various scenario simulations experiment validate the effectiveness and accuracy of the proposed method. Meanwhile, experimental analysis results show that different control manners of inverter-based generators not only affect voltage stability margin but also change the weakest bus of power system.

This paper presents a novel model for transmission expansion planning (TEP) with optimal transmission switching (OTS) considering uncertain N-k contingency, renewables and loads. In the proposed approach, ambiguity set and budget uncertainty set are utilized to simultaneously characterize three types of uncertainties in power system: (1) wind power output; (2) load demands; (3) the status and probability distribution of generation and transmission N-k contingency. Accordingly, the optimal expansion plan and OTS can be obtained through a three-level model to guarantee the safety and economy of power system in the worst-case of wind power, load demand and N-k contingency. A decomposition algorithm based on benders decomposition is developed to efficiently solve the model. Cases studies on the revised IEEE 30-bus test system demonstrate that (1) the optimal expansion plan can be greatly affected by the proposed uncertainty sets, (2) the total costs can be effectively reduced by considering optimal transmission switching and (3) the decomposition method can efficiently solve the proposed TEP model.

A quasi-linear relationship between voltage angles and voltage magnitudes in power flow calculation is presented. An accurate estimation of voltage magnitudes can be provided by the quasi-linear relationship when voltage angles are derived by classical DC power flow. Based on the quasi-linear relationship, a novel extended DC power flow (EDCPF) model is proposed considering voltage magnitudes. It is simple, reliable and accurate for both distribution network and transmission network in normal system operation states. The accuracy of ED-CPF model is verified through a series of standard test systems.

Large-scale renewable energy integration decreases the system inertia and restricts frequency regulation. To maintain the frequency stability, allocating adequate frequency-sup-port sources poses a critical challenge to planners. In this context, we propose a frequency-constrained coordination planning model of thermal units, wind farms, and battery energy storage systems (BESSs) to provide satisfactory frequency supports. Firstly, a modified multi-machine system frequency response (MSFR) model that accounts for the dynamic responses from both synchronous generators and grid-connected inverters is constructed with preset power-headroom. Secondly, the rate-of-change-of-frequency (ROCOF) and frequency response power are deduced to construct frequency constraints. A data-driven piecewise linearization (DDPWL) method based on hyperplane fitting and data classification is applied to linearize the highly nonlinear frequency response power. Thirdly, frequency constraints are inserted into our planning model, while the unit commitment based on the coordinated operation of the thermal-hydro-wind-BESS hybrid system is implemented. At last, the proposed model is applied to the IEEE RTS-79 test system. The results demonstrate the effectiveness of our co-planning model to keep the frequency stability.

In this paper, a novel contingency-aware method for $N-2$ security-constrained transmission expansion planning is proposed. To ensure that the transmission construction plan satisfies the $N-2$ security criterion, the proposed method takes advantage of the adjustable robust optimization (ARO) framework and upgrades it. We construct a discrete uncertainty set in which component failures are treated as uncertain events that are handled as binary variables. In addition to the failure of existing lines and generators, we explicitly model the failure of candidate lines. The proposed model comprises a master problem that makes the transmission construction decision, and a series of subproblems that can detect not only the worst contingency, but also the potential contingencies. Computational studies on the IEEE RTS 24-bus and IEEE 118-bus test systems are carried out to validate the effectiveness of the proposed method. Compared with the deterministic method and ARO method in the literature, the proposed method has higher computational efficiency.

Integrated energy system (IES) has the advantages of improving the efficiency of energy utilization and promoting the consumption of renewable energy. It is of great importance to evaluate the reliability of an IES. This paper proposes a novel reliability evaluation method for the electricity-heat IES with heat pump. First, the load-point reliability indices and system-level reliability indices are defined according to the characteristics of electricity-heat IES. Second, the model of maximum output heat power of heat pump at the user-side considering the safety criterion of distribution network is established, and the step-varied repeated power flow method is applied to solve the model. Third, the reliability evaluation procedure of electricity-heat IES with heat pump based on the Monte Carlo simulation is presented. Case studies are carried out on the electricity-heat IES of an industrial park, and the results show that the configuration site, capacity and coefficient of performance of heat pump as well as the security constraints of distribution network can significantly affect the reliability indices.

The distributed generation (DG) plays an important role in the context of the environmental problems and sustainable development throughout the world. This paper proposes a DG siting and sizing model in an active distribution network (ADN). The objective is to minimize the total cost, including investment, operation and maintenance costs. The proposed model is transferred to a Mixed Integer Second-Order Cone Programming (MISOCP) model based on a distribution network forward backward-sweep power flow and constraint relaxation. The CVX platform and GUROBI solver are used for the solution. The scenario analysis is used for the uncertainties of load and DG. Different numbers of operational scenarios are considered in order to analyze the effect of a non-network solution to the final planning result and total investment. The planning results with and without consideration of active managements, and the planning results with and without taking environmental profits into consideration, are compared and analyzed. The proposed methodology is verified with a modified IEEE 33 example.

The stochastic and intermittent nature of renewable energy resources (RERs) poses great challenges to the energy scheduling of microgrids. The hybrid energy storage system (HESS), such as a combination of the battery (BA) and ultracapacitor, is considered as an effective way to cope with such challenges. In this paper, a hierarchical energy scheduling framework is proposed for the microgrid with HESSs to optimize the operation under the uncertainty of RERs and loads. The framework consists of two stages of scheduling: hour-ahead scheduling and real-time scheduling. In hour-ahead scheduling, a deterministic optimization model is formulated to minimize the operation cost of microgrids, and to guarantee the operation safety. Subsequently, a decomposition-based method is presented to solve the proposed model. In real-time scheduling, a control strategy of HESSs is developed to accommodate the imbalanced power mainly due to the uncertainty of RERs and loads, while extending the lifetime of BAs. The methodology is tested on a seven-bus microgrid system. Simulation results validate the effectiveness of the formulated model and the developed strategy.

Reactive power reserve (RPR) management is a critical issue to power system voltage stability. Two RPR definitions are first proposed in this paper to evaluate the levels of RPR and improve voltage stability, namely long-term voltage stability-related RPR (LVRPR) and short-term voltage stability-related RPR (SVRPR). Both definitions consider two factors: 1) the RPR of each online generator and 2) the relative contribution of the RPR to voltage stability varying with location and scenario. For LVRPR, the generator participation factor is used to describe the contributions of RPR. For SVRPR, an voltage support coefficient considering the generator's dynamics is proposed to evaluate the RPR's contribution. In normal condition, short-term voltage stability is expected to be improved by the optimization of SVRPR, ensuring enough longterm voltage stability margin. A bi-objective optimization model that coordinates LVRPR and SVRPR is formulated to enhance longand short-term voltage stabilities simultaneously. The proposed model is solved using the normal boundary intersection technique. The proposed method is performed using an IEEE39-bus system, and the results show that the optimal solution improves both longand short-term voltage stabilities by optimizing the trade-off between LVRPR and SVRPR.

Abstract In recent years, failure recovery after faults is concerned and discussed worldwide as an important and hot topic. Facing the challenge of heavy loads and ultra-high voltage transmission, it’s urgent to propose some solutions to enhance transient voltage stability for failure recovery. Therefore, a novel dynamic volt ampere reactive (VAR) planning methodology is proposed in this paper to help failure recovery and improve transient voltage stability after contingencies. First, a transient voltage fluctuation (TVF) index is proposed to evaluate transient voltage condition after faults. Then dynamic compensation sensitivity is presented for searching the best candidate locations. Following that, the dynamic VAR planning methodology based on an improved Tent chaos multi-objective algorithm is discussed in detail. There are two optimization objects in the optimization. One is to minimize TVF to enhance transient voltage stability for failure recovery. And the other optimization is to minimize dynamic VAR investment cost and operation cost. Finally, IEEE 39 power system and a practical power system are analyzed and discussed. The proposed dynamic VAR planning methodology can support enough reactive power for failure recovery. With the least SVC planning amount and the power loss cost, it can greatly decrease the system TVF index and enhance the transient voltage stability. It’s proved that the proposed dynamic VAR planning optimization is effective and helpful for safety operation of power system.

The uncertainties of the predicted load demand and N-K contingencies are very significant aspects to composite generation and transmission expansion planning (CGTEP). In this paper, multi-contingency constrained CGTEP with load uncertainty was analyzed from stringent mathematical view and formulated as a tri-level optimization model. To effectively solve the tri-level optimization, the entire problem is formulated as two problems using Benders' decomposition: master problem with expansion planning and the sub-problem with the worst case load shedding. The sub-problem is a bi-level optimization problem which can be solved mathematically using strong duality theory and linearization method. CGTEP with the tri-level optimization can endure the disturbances of interval load and N-K contingencies. A benchmark test system is simulated to validate the effectiveness of the proposed approach. Furthermore, for Bender's decomposition with many sub-problems of worst load shedding, the numerically comparable results of a special case demonstrate that all sub-problems of composite contingencies must be validated at each iteration even if certain contingency meets the standard of load shedding at the previous iteration.

During the operation of the integrated energy system (IES), the dynamic behaviour of heat loads can affect the optimal operation strategy. This study proposes a novel optimal day-ahead operation method of user-level IES considering the dynamic behaviour of heat loads. Firstly, based on the energy hub, the model of heat loads with dynamic behaviour is added into IES. The dynamic behaviour is embodied by water temperature which can be represented by differential equations. Then, the optimal day-ahead operation model aimed at minimising the energy purchase cost is proposed. Piecewise linearisation is utilised to simplify the temperature constraints which can transform the initial non-convex and non-linear optimisation into a linear programming problem. Finally, case studies are carried out on a practical case, and the results indicate that with the consideration of dynamic behaviour of heat loads, the energy purchase cost can be reduced by 5.6%.

The curtailment of wind power has caused huge economic losses and needs to be considered on the stage of transmission expansion planning (TEP). Based on the superquantile theory, the authors use the buffered failure probability to handle the events of wind power curtailment. This new measurement offers several advantages including clear concept, simple calculation, and flexibility. Moreover, the authors form a novel convex relaxation model of the TEP problem. A tri-level approximation algorithm is developed to solve the proposed probability constrained model. The numerical study verifies the performance of the proposed algorithm and demonstrates the advantages of the proposed model over deterministic TEP. Sensitivity analysis is performed to identify the influence of different thresholds in probability constrained TEP problem.

with the onboard diesel generators and energy storage system to meet the propulsion and service load, the all-electric ship (AES) can be viewed as a ‘mobile microgrid’. Nowadays, photovoltaic (PV) generation is gradually integrated into the AES for a ‘greener’ voyage. To fully utilise the PV energy, this paper proposes a joint generation and voyage scheduling method for the PV integrated AES. The overall model is formulated as a bi-level programming problem and solved by column-and-constraint generation method. The simulation results manifest that, the integration of PV into AES leads to reductions on both the fuel consumption and CO2 emission.

High-penetration renewable energy and AC/DC hybrid network are two main basic characteristics of future power systems. Evaluating different networks' structure adaptability is extremely important for the power system to keep economical, safe, reliable and flexible. Firstly, the basic characteristic and the definition of network structure adaptability are given under the background of strong randomness. On this basis, several probable indexes of structure adaptability are proposed. After that, a practical calculation method is put forward, in which the Monte Carlo simulation method and the optimal economic dispatch model are used. Case studies are carried out on the modified IEEE 30-bus system, and the simulation results show that the proposed indexes can effectively reflect the adaptability of different network structures with the integration of high-penetration renewable energy.

This study presents a multi-objective operation optimisation model for urban power grids with flexible switching (FS) stations to comprehensively improve system security and reliability. In the proposed model, uncertainties associated with load variation and component failures are considered. Moreover, constraints after a feeder or transformer N − 1 contingency are preliminarily formulated. The operation problem optimises the apparent power of feeder section loading. The combination of normal boundary intersection and sequential quadratic programming is employed to solve the non-linear optimisation model. A case study carried out on a test 75-feeder distribution grid with FS stations demonstrates the effectiveness of the proposed model and solving method. Compared with conventional distribution loadability, the optimal load distribution solution obtained in this study provides a trade-off between system security and reliability. The coordinated operation optimisation method is suitable for urban smart distribution grids featured by distribution automation and large-scale interconnections.

This study proposes a novel optimal day-ahead operation method for the user-level integrated energy system (IES), which can take into account the dynamic behaviour of heat loads and customers' heat satisfaction. First, based on the energy hub, the dynamic model of heat loads is added into IES. Additionally, the customers' heat satisfaction model is constructed by the variance of water temperature and punishment coefficient. Then, the optimal day-ahead operation model aimed at minimising the total cost is proposed. Constraints of energy purchase, operation of energy converters, loads, temperature and the variation of temperature are all contained. Piecewise linearisation and a standard modelling method are utilised to simplify the initial non-convex and non-linear problem to a quadratic programming problem. Finally, case studies are carried out on a practical calculation example. Results indicate that the total cost can be reduced by 5.6% when considering the dynamic behaviour of heat loads. Also, customers' heat satisfaction exerts a remarkable influence on the total cost.

This paper investigates the stochastic optimal operation of microgrid considering the influence of energy storage system (ESS). The uncertain factors related to renewable energies are also fully considered. Monte Carlo simulation (MCS) and scenario reduction technique are used to capture the randomness of renewable energy output. The objective is to minimize the operation cost and pollutant treatment cost of the microgrid system. Then, the multi-objective optimization problem is transformed to a single-objective problem by a line weighted sum method. A nonlinear programming tool—General Algebraic Modeling System (GAMS)—is adopted to solve the single-objective problem. Simulation results indicate that the total cost of the microgrid system can be reduced effectively when considering the effect of ESS and verify the correctness of the proposed strategy.