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Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The frequency security issue has become more critical in recent decades for various reasons, especially the reduced and degraded primary frequency control (PFC) response of traditional participants based on the economic incentives of generation units to earn more profit in the energy market. Since frequency security is a dynamic phenomenon, incorporating it into an optimization problem such as scheduling is complicated, especially with realistic modeling assumptions. This difficulty can be solved using a variety of solutions ranging from simple and inaccurate static methods to complex and accurate dynamic approaches. This paper proposes a competitive mechanism among participants in real-time scheduling (hour-ahead) that integrates the dynamic frequency security in the economic optimization procedure, hence enhancing the frequency security. The proposed formulation is a rescheduling scheme based on optimal power flow (OPF) which clears the energy and reserve simultaneously and considers the network constraints. Also, this mechanism uses the accurate model of the governors by including all of the influential parameters on PFC. The cutting-plane model of the nadir frequency function is used to resolve the complexity of the optimization problem. In addition, a framework for multi-objective optimization has been developed that enables the policymakers to reconcile the frequency security with the rescheduling cost. Finally, the correctness and the efficiency of the proposed framework are demonstrated from the economic and technical perspectives based on the implementation of the IEEERTS. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper introduces an enhanced frequency aware microgrid scheduling (E-FAMS) model designed to achieve seamless islanding (SI) for microgrids after experiencing an unintentional islanding event (UIE). The model addresses uncertainties in load forecasting and demand-side resources’ (DSRs) frequency support, described using a Wasserstein-metric ambiguity set, through the distributionally robust chance constrained (DRCC) approach. It concurrently optimizes unit commitment, generation dispatch, reserve capacity, power exchange, and the frequency response of heterogeneous frequency support resources (HFSRs). A quadratic frequency (QF) approach is proposed to derive sufficient conditions for the maximum frequency deviation (MFD) constraints, which are then convexified using the piecewise linear of multivariable functions (PWL-MFs) technique and integrated into the proposed model. Case study results confirm the effectiveness of the proposed model, providing a novel solution for SI in microgrids.

With the large-scale use of wind turbines, the ability of the power system to resist frequency fluctuations has been greatly weakened, making the contradiction between frequency regulation supply and demand in the power system increasingly prominent. In order to ensure the frequency security of the power system, this paper conducts research on the primary frequency regulation (PR) backup configuration problem of a power system containing a high proportion of wind power. First, according to the dynamic properties of the speed regulator, a system frequency response model considering the limiting link is established. And the system frequency response model is transformed into a time-domain analytical function of PR reserve capacity and frequency maximum value. On this basis, a PR backup configuration model of a power system containing a high proportion of wind power is constructed with the optimization goal of minimizing system operating costs and taking into account the limiting link constraints. It is proposed to use the L-shape algorithm to decompose the model into main problems and sub-problems, which effectively reduces the solution complexity of the model. Finally, the correctness and effectiveness of this model are verified based on the improved IEEE 39-bus system. [ABSTRACT FROM AUTHOR]

Base station (BS) backup batteries (BSBBs), with their dispatchable capacity, are potential demand-side resources for future power systems. To enhance the power supply reliability and post-contingency frequency security of power systems, we propose a two-stage stochastic unit commitment (UC) model incorporating operational reserve and post-contingency frequency support provisions from massive BSBBs in cellular networks, in which the minimum backup energy demand is considered to ensure BS power supply reliability. The energy, operational reserve, and frequency support ancillary services are co-optimized to handle the power balance and post-contingency frequency security in both forecasted and stochastic variable renewable energy (VRE) scenarios. Furthermore, we propose a dedicated and scalable distributed optimization framework to enable autonomous optimizations for both dispatching center (DC) and BSBBs. The BS model parameters are stored and processed locally, while only the values of BS decision variables are required to upload to DC under the proposed distributed optimization framework, which safeguards BS privacy effectively. Case studies on a modified IEEE 14-bus system demonstrate the effectiveness of the proposed method in promoting VRE accommodation, ensuring post-contingency frequency security, enhancing operational economics, and fully utilizing BSBBs' energy and power capacity. Besides, the proposed distributed optimization framework has been validated to converge to a feasible solution with near-optimal performance within limited iterations. Additionally, numerical results on the Guangdong 500 kV provincial power system in China verify the scalability and practicality of the proposed distributed optimization framework.

As the proportion of renewable energy (RE) increases, the inertia and the primary frequency regulation (FR) capability of the power system decrease. Thus, ensuring frequency security in the scheduling model has become a new technical requirement in power systems with a high share of RE. Due to a shortage of conventional synchronous generators, the frequency support of multi-source converters has become an indispensable part of the system frequency resources, especially variable-speed wind turbine generation (WTG) and battery energy storage (BES). Quantitative expression of the FR capability of multi-source converters is necessary to construct frequen-cyconstrained scheduling model. However, the frequency support performance of these converter-interfaced devices is related to their working states, operation modes, and parameters, and the complex coupling of these factors has not been fully exploited in existing models. In this study, we propose an integrated frequency-constrained scheduling model considering the coordination of FR capabilities from multi-source converters. Switchable FR control strategies and variable FR parameters for WTG with or without reserved power are modeled, and multi-target allocation of BES capacity between tracking dispatch instruction and emergency FR is analyzed. Then, the variable FR capabilities of WTG and BES are embedded into the integrated frequency-constrained scheduling model. The nonlinear constraints for frequency security are precisely linearized through an improved iteration-based strategy. The effectiveness of the proposed model is verified in a modified IEEE 24-bus standard system. The results suggest that the coordinated participation of BES and WTG in FR can effectively reduce the cost of the scheduling model while meeting frequency security constraints.

The ever-growing proportion of renewable energy results in the decrease of frequency regulation capability of the multi-power system. Hence, to ensure the stability of the multi-power system with a high proportion of renewable energy, a novel day-ahead scheduling approach is proposed considering the frequency security constraint. Firstly, the dynamic changing process of frequency due to the power disturbance is analyzed. Secondly, a frequency security constraint considering the dynamic process is modeled and incorporated into the scheduling model of the multi-power system. The proposed scheduling model ensures that the maximal frequency deviation of the dynamic process is kept within the permitted range. Next, to ensure the stable operation of the system and make full use of renewable energy, the proposed scheduling model aims at minimizing the net load fluctuation and intermittent new energy curtailment. Finally, simulation results show that the proposed optimal scheduling model considering dynamic frequency security constraint can maintain the stability and frequency security of the multi-power system under power disturbance.

Under the background of the accelerated transformation of the modern power system, renewable energy will gradually replace the role of traditional energy in the power system. Because of the randomness, uncertainty, and low inertia of renewable energy, the power system frequency security assessment is becoming a serious issue under the influence of large-scale renewable energy integrations. To achieve the rapid assessment of power system frequency security, a resnet-based frequency security assessment method considering frequency spatiotemporal distribution characteristics is proposed. In this paper, to provide more comprehensive frequency response information, the spatiotemporal characteristics of frequency are introduced and integrated into the input feature set. At the same time, the Resnet network and multi-task-learning framework are applied to construct a frequency security assessment model. Based on the experimental results on the modified IEEE39 bus system, the assessment accuracy is higher than 99%, which shows the excellent assessment performance of the proposed model.

The large-scale integration of renewable energy and the increasing access to power electronic equipment lead to the low inertia of power grid, which raises severe challenges to frequency security. The low inertia makes power system more sensible to power disturbances, and therefore, evaluating frequency stability is crucial. To address this issue, a fast frequency security assessment method for power grid based on the extended SFR (system frequency response) model is proposed. In this method, an extended SFR model is established based on the characteristics of future new power systems, which are comprised of multiple frequency response sources, including induction motor load, renewable energy, and other asynchronous resources. To obtain the parameters of the proposed model, the principle and applicability of model parameter aggregation methods are explained. Considering the difficulty of obtaining all the required information in real-world situations, the parameters are obtained by parameter identification method through optimization algorithms. Finally, the effectiveness of the proposed extended SFR model is verified in the WSCC-9 bus system and the parameter identification method is validated in a regional power grid. The calculation time is less than 0.03s and the accuracy is more precise than conventional SFR. The results demonstrate that the proposed extended SFR model and parameter identification method show characteristics of both rapidity and accuracy in judging the security of power systems.

As a low-cost and high-efficiency distributed energy storage resource, electric vehicles (EVs) play an increasingly prominent role in power system regulation. Since EVs are the regulation resources on the demand side, EVs should return to the initial states as soon as possible after completing the grid regulation task to avoid affecting the charging demand. Although EVs can provide a more flexible response to under-frequency load shedding (UFLS) than load shedding, the disorderly recharging of EVs during the load restoration stage may cause a significant second disturbance to the system frequency after UFLS. To ensure frequency stability and simultaneously restore the power supply, a multi-stage sequential load restoration method for UFLS with EVs participation is proposed to coordinate the priority and sequential restoration between the shedding load and recharging power of EVs. In the proposed method, the restoration willingness of EVs is quantified by the membership function, and the EV recharging optimization model with the objective function of maximizing the user’s restoration willingness satisfaction is established based on a two-stage robust under-frequency load shedding framework. Simulation results show that the proposed method can ensure system frequency stability and complete the load restoration quickly, effectively avoiding the secondary frequency drop caused by the disorderly recharging of EVs.

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

With the large-scale use of wind turbines, the ability of the power system to resist frequency fluctuations has been greatly weakened, making the contradiction between frequency regulation supply and demand in the power system increasingly prominent. In order to ensure the frequency security of the power system, this paper conducts research on the primary frequency regulation (PR) backup configuration problem of a power system containing a high proportion of wind power. First, according to the dynamic properties of the speed regulator, a system frequency response model considering the limiting link is established. And the system frequency response model is transformed into a time-domain analytical function of PR reserve capacity and frequency maximum value. On this basis, a PR backup configuration model of a power system containing a high proportion of wind power is constructed with the optimization goal of minimizing system operating costs and taking into account the limiting link constraints. It is proposed to use the L-shape algorithm to decompose the model into main problems and sub-problems, which effectively reduces the solution complexity of the model. Finally, the correctness and effectiveness of this model are verified based on the improved IEEE 39-bus system.

The continuous increase in the penetration rate of renewable energy has led to a decrease in the system's frequency response capability, which presents great challenges to the safety and stability of the power system. In order to ensure the safe operation of the power system, online frequency safety assessment has become necessary. However, the time-varying characteristics of the virtual inertia HNE of renewable energy stations make it more difficult to accurately predict the lowest point of the system frequency after a disturbance. Based on the general average system frequency (G-ASF) model, this paper proposes a G-ASF-H model that considers the time-varying characteristics of the virtual inertia of renewable energy stations, accurately predicts the lowest frequency point after a system disturbance, and realizes the online frequency safety assessment of the system. Firstly, a unified virtual synchronous generator model is established to identify the virtual inertia time constant of the renewable energy station in real time; then, under the pre-defined frequency safety verification event, the maximum deviation of the system frequency is periodically calculated and judged based on the G model to realize the online frequency safety assessment. The example analysis on the IEEE 10-machine 39-node system shows that the model has a high calculation speed and accuracy under different disturbances or daily load level scenarios and can be used for the online security assessment of new power systems with time-varying virtual inertia characteristics. [ABSTRACT FROM AUTHOR]

• An enhanced frequency aware microgrid scheduling model aimed at providing a solution for seamless islanding in microgrids is proposed. • A quadratic frequency approach is proposed to derive sufficient conditions for the maximum frequency deviation constraints. • Modeling and coordinated optimization of heterogeneous resources to enhance economic efficiency and frequency security. • The uncertainty of load and demand-side frequency regulation resources is addressed using DRCC approach. This paper introduces an enhanced frequency aware microgrid scheduling (E-FAMS) model designed to achieve seamless islanding (SI) for microgrids after experiencing an unintentional islanding event (UIE). The model addresses uncertainties in load forecasting and demand-side resources' (DSRs) frequency support, described using a Wasserstein-metric ambiguity set, through the distributionally robust chance constrained (DRCC) approach. It concurrently optimizes unit commitment, generation dispatch, reserve capacity, power exchange, and the frequency response of heterogeneous frequency support resources (HFSRs). A quadratic frequency (QF) approach is proposed to derive sufficient conditions for the maximum frequency deviation (MFD) constraints, which are then convexified using the piecewise linear of multivariable functions (PWL-MFs) technique and integrated into the proposed model. Case study results confirm the effectiveness of the proposed model, providing a novel solution for SI in microgrids. [ABSTRACT FROM AUTHOR]

The inertia of the power system currently lies in a relatively narrow range. However, the increasing penetration of distributed energy resources (DERs) will significantly reduce the inertia level, meanwhile increasing its volatility. This will affect the system’s ability to contain the maximum frequency excursion and recover from large frequency disturbances. In order to maintain system frequency security and stability, a common practice is to incorporate frequency security constraints into the unit commitment (UC) model, so a concern is how the volume and volatility of system inertia impact system operation costs and energy clearing prices. Furthermore, inertia forecasting is often required when performing day-ahead UC with frequency security constraints. Therefore, this paper aims to evaluate the impact of system inertia on system operation costs and energy clearing prices. The experiment is designed under scenarios with different inertia volume, inertia volatility, and inertia forecasting errors. The results show that: 1) Increasing the system inertia volume can effectively reduce the system operation costs and energy clearing prices. 2) Increasing the inertia volatility will lead to an increase in system operation costs and energy clearing prices. 3) The increment of system operation cost caused by positive or negative errors of inertia forecasting is asymmetric.

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The integrated electricity-heat microgrid (IEHM) is characterized by low inertia and a high share of renewable generation. Although sector coupling in the IEHM enhances energy efficiency, the integration of electricity and heat systems restricts the primary frequency regulation (PFR) ability of coupling equipment, further threatening frequency security. This paper presents a frequency-secured planning method for virtual inertia suppliers and combined heat and power (CHP) units in the IEHM. First, we examine the PFR in IEHMs from both device and system perspectives. We develop steady-state models for sector-coupled equipment, specifically CHP units and large-scale heat pumps, for PFR and sizing purposes. To describe the system's frequency response under emergency conditions, we explicitly derive frequency constraints that account for varying system inertia of heterogeneous resources. Furthermore, we conduct a comprehensive analysis of the impact of PFR on heating systems within the IEHM. Second, we propose a frequency-constrained planning model for IEHMs based on the aforementioned modeling framework. This model balances the power supply, heating supply, and PFR reserves deployment of IEHM by properly sizing the regulation resources. It also leverages distributionally robust (DR) chance constraints to address uncertain wind power generation. To improve the tractability of this model, we introduce a well-tailored reformulation approach that handles the nonconvexity of system inertia and DR chance constraints. Case studies conducted on two test systems demonstrate the effectiveness of the proposed method in securing frequency stability while improving the economic performance of IEHM. This method ensures both dynamic and static frequency security across 100% of time steps by optimally deploying system inertia and PFR reserves. Moreover, by coordinating heterogeneous PFR resources with time-varying system inertia, the proposed approach yields superior economic performance, achieving over a 9% reduction in total capacity compared to average benchmarks. • This paper derives the frequency constraints with time-varying system inertia of IEHMs from the planning aspect. • Steady-state models of large-scale heat pumps and extraction-condensing CHP units are developed. • A well-tailored solution algorithm convexifies the intractable system inertia and DR chance constraints. • The proposed method effectively secures the frequency security of IEHM while improving the economy. [ABSTRACT FROM AUTHOR]

Copyright of Electric Power Automation Equipment / Dianli Zidonghua Shebei is the property of Electric Power Automation Equipment Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The rotational inertia and primary frequency response capabilities of power systems are declining as synchronous generators (SGs) are replaced by inverter-based variable renewable energy (VRE) resources. Therefore, when a high VRE proportion is present, it becomes essential to include frequency security constraints in power system planning. Under this circumstance, the decline in SGs would deteriorate the system frequency response performance; thus, inverter-based resources are supposed to provide frequency response support. This paper presents a frequency-constrained stochastic planning method for high VRE share systems. Frequency response support from wind farms is considered in the planning process for the first time, and the unique characteristics of wind power support are addressed. Specifically, the uncertainty of and variations in wind power support capabilities are modeled from the field-measured data, and the optimal combination of various support schemes can be determined by introducing binary variables with novel linear constraints into the planning process. Moreover, the nonlinear frequency constraints are transformed and embedded in the planning model by the proposed computationally efficient adaptive piecewise linearization method. The planning is formulated as a stochastic optimization model to consider the VRE power uncertainty. Finally, case studies on the IEEE 30-bus system validate the proposed method, with results indicating time savings of 22%. Further, compared with the case that only SGs provide frequency support, the results based on the East China system demonstrate that considering wind power support can improve the VRE share from 49.5% to 79.7%. [ABSTRACT FROM AUTHOR]

Summary: Small size of microgrids (MGs), low inertia, and small scale of distributed generations, and high intermittent energy delivery of renewable generations, make the frequency security an important issue in the islanded multi‐microgrids (IMMG) systems which should be considered subject to the techno‐economic constraints of MGs. Motivated by this need, this article proposes a two‐stage stochastic optimization model for day‐ahead energy and reserve scheduling of IMMG systems. The objective of the proposed model is to minimize total operation cost of IMMG while the frequency security of system is preserved within a predefined range. To this end, the hierarchical frequency structure of IMMG system including primary, secondary, and tertiary control levels are precisely formulated in mixed‐integer linear programming format which can be efficiently solved by optimization software package. Meanwhile, to promote the proposed model, responsive loads and energy storage systems are considered in the energy and reserve scheduling problem. The proposed model is applied to a typical IMMG system to optimize energy and reserve scheduling over 24‐hr horizon. The obtained results verify that through the proposed model, the operation costs of MGs are minimized while frequency security of the system is preserved in a cost‐effective manner. [ABSTRACT FROM AUTHOR]

Frequency security is one of the most critical factors for ensuring the safe and stable operation of power systems. In wind-photovoltaic-hydro-thermal multi-power systems (WPHTMPS), the increase in new energy share and the water hammer effect weaken the frequency modulation (FM) capability, threatening the frequency security of the power system. To address this issue and ensure the frequency security of WPHTMPS under the trend of large-scale development of wind and photovoltaic (PV) power, this paper proposes a novel expansion planning method for wind and PV power in WPHTMPS that considers FM capability in the planning stage. The method realizes the coordinated optimization of long-term planning and short-term operation while adhering to the frequency security constraints. The constraints are derived from the multi-power system frequency response model (MPSFR) which integrates virtual inertia, synchronous inertia, and the water hammer effect. However, due to the high-order characteristic of the MPSFR model, the frequency security constraints cannot be expressed explicitly to be embedded in the planning model by current study. Therefore, the boundary equivalence method is proposed to deal with this problem, which is effective to convert the frequency security constraints into inertia constraints and embed them in the planning model according to their relationship with installed capacity and unit commitment. Finally, simulation for a power system in Southwest China validates the proposed method, with results indicating that around 13% more capacity of new energy is needed to provide adequate FM reserve and power supply. Furthermore, it is demonstrated that the FM capability of new energy can improve the installed share of new energy from 46.5% to 70% while effectively ensuring frequency security. • The frequency modulation capability is necessary in generation expansion planning. • An integrated system frequency response model with multiple power sources is built. • A two-layer model optimizing long-term planning and short-term operation is built. • The frequency security constraint is linearized by the boundary equivalence method. [ABSTRACT FROM AUTHOR]

Optimal power flow (OPF) minimizes the production cost, while satisfying the constraints on the system, such as real and reactive power balance, equipment capability constraints, and voltage limits. This article presents a method of incorporating a frequency security constraint within the framework of the OPF problem. Increasing displacement of conventional generation by renewable resources that contribute little or no frequency regulation capability may necessitate the enforcement of such a constraint to meet frequency security requirements. The system frequency is required to be maintained within a safe limit, thus indicating the balance between generation and consumption. Hence, the solution for optimization of power flow should not only present a minimum cost of generation within the operating conditions, but also ensure frequency stability. In order to obtain this solution, the requirement of frequency stability is introduced as a new constraint of the power dispatch problem and is represented by the maximum frequency deviation limit. This new constraint is constructed as a nonlinear function of system inertia and the frequency regulation constant, since frequency deviation is highly sensitive to these factors. It is shown that the inclusion of this constraint causes the OPF to preferentially select higher inertia generators as necessary, to satisfy the frequency security requirement. A genetic algorithm is utilized as the optimization tool in this article. The IEEE RTS-79 test system is used to demonstrate efficacy of the proposed method. [ABSTRACT FROM AUTHOR]

The integration of wind power into the grid causes numerous stability and reliability issues due to its low inertia and intermittent nature. To ensure system stability, wind power production has to be restricted, which implies that the system cannot absorb the entire output available from wind generation, especially if the output is high. Consequently, the reliability of the integrated system is adversely affected. In order to improve the system reliability, energy storage can be used, which is emerging as a prominent solution for enhancing supply continuity. Complete utilization of an energy storage device can be achieved if it is properly coordinated with wind and conventional generation. This paper proposes a new method to coordinate energy storage with the existing system to improve the system reliability while maintaining the system frequency security. The effectiveness of the model is demonstrated on the IEEE RTS-79 system. [ABSTRACT FROM AUTHOR]

The low-carbon transition of the power industry plays a critical role for China in achieving carbon neutrality. Technical retrofitting for coal-fired power plants improves their flexibility and reduces carbon emissions. China has a large stock of coal-fired power plants, and the retrofit planning of existing coal-fired power plants is an important part of the decarbonizing power system. In this study, a decision support tool that provides coal-fired power plant retrofit investment decisions in low-carbon power system transition is proposed. First, three retrofit paths are investigated. In addition to flexibility reformation, carbon capture utilization and storage reformation, a novel scheme is introduced to transform retired or aged coal-fired power plants into a Carnot battery, also known as a thermal storage power plant. Then, a multipath retrofit planning model for coal-fired power plants is proposed, in which the embedded operational problem is a unit commitment problem considering flexibility and frequency security constraints. Therefore, the problem of frequency safety and uncertainty caused by the high share of variable renewable energy in the power system is solved. The planning model is solved by hyperplane piecewise linearization and the chance-constrained deterministic transformation method. Finally, based on the Shanxi Provincial power system, the roles of flexibility reformation, carbon capture utilization and storage reformation, and Carnot battery reconstruction are analysed, and coal-fired power plant retrofit planning suggestions for the Shanxi power system are provided in this study. • A novel Carnot battery reconstruction is applied to coal-fired power plant's retrofit. • A multi-path retrofit planning model for coal-fired power plants is established. • The roles of different retrofit technologies to coal-fired power plants are compared. • The retrofit decision for coal-fired power plants for the Shanxi power system is given. [ABSTRACT FROM AUTHOR]

Emergency control is an important measure for prevention of power system blackouts. This paper presents a new event-driven emergency load-shedding scheme that minimizes load shedding while meeting constraints on transient angle stability, voltage/frequency deviation security, and availability of load to be shed at any bus. The evaluation of these constraints is based on time domain trajectories provided by numerical simulations. The optimal event-driven load-shedding (OEDLS) model was created to minimize the total load-shedding cost. By analyzing the characteristics of the optimal solution of this model, a trajectory sensitivity based solution approach is presented. It linearizes the nonlinear OEDLS model through trajectory sensitivity and iteratively converges to the optimal solution. To accelerate the problem solving process, a parallel computation scheme is implemented for obtaining the trajectory sensitivities. The validity of the proposed algorithm and parallel computation scheme was tested and verified using two different power systems. [ABSTRACT FROM AUTHOR]

A DC power support strategy utilizes the flexibility of a High-voltage direct-current (HVDC) system in power modulation to optimize the operating point or compensate the power imbalance caused by a disturbance. The major impediment to the strategy is the difficulty in maintaining DC voltage values at converter stations during the process of DC power support. To overcome the difficulty, a coordinated DC power support strategy for multi-infeed HVDC systems is proposed in this paper. Synchronous condensers are employed to provide dynamic reactive power compensation in sustaining DC voltage values at converter stations. Models are built for the optimal leading phase operation and adjusting excitation voltage reference value of synchronous condensers. Multiple HVDC links are coordinated to participate by using the DC power support factor to rank and select the links. Optimal DC power support values of the participating HVDC links are obtained with a comprehensive stability margin index that accounts for transient stability of the sending-end systems and frequency security of the receiving-end systems. An optimal load shedding model is used to ensure the frequency security of receiving-end systems. Case study results of a provincial power system in China demonstrate the effectiveness and performance of the proposed DC power support strategy.

• Combination of Markov Chain Monte Carlo and Generative Adversarial Networks for future scenario generation. • Assessment model retraining with Domain Adaptation Metric Learning and transitive closure based constraint propagation clustering approach. • Frequency security early warning grading with risk assessment method. • Comparing results of provincial power grid of China. Loss of massive generation caused by HVDC blocking or tripping large power plants is a severe threat to receiving-end grids' frequency security, especially those with a high penetration level of renewable generation. Frequency security early warning is necessary to send warning messages in time. With the warning messages, appropriate measures can be taken in advance to minimize possible losses. In this paper, a machine learning-based frequency security early warning method considering the uncertainty of renewable generation is proposed. It includes three core parts: future scenario generation, assessment model establishment, and early warning indicator establishment. In the future scenario generation part, Markov Chain Monte Carlo (MCMC) is combined with Generative Adversarial Networks(GAN) for generating numerous future scenarios reflecting possible future operation modes of the system, considering the uncertainty of renewable generation and loads. In the assessment model establishment part, the assessment model with clustering based on metric learning is applied to establish the machine learning-based frequency security assessment model. The model is continuously retrained with Domain Adaptation Metric Learning (DAML) and a transitive closure-based constraint propagation clustering approach to improve assessment accuracy. Future frequency security risk indicators are established in the early warning indicator establishment part based on future scenarios' assessment results. According to the risk indicators, future frequency security is classified into different early warning levels. The future frequency security can be expressed clearly and intuitively with the early warning levels. A simplified provincial power system of China is adopted as an example to verify the validity of the proposed early warning method. [ABSTRACT FROM AUTHOR]

In island grids and weakly interconnected power systems, a loss of alarge proportion of generation will cause the system frequency to fall dramatically. In order to ensure a stable operation with the lowest impact on the system, the disturbed power balance must be equalizedwithin a short specified time by activating the seconds reserve of on-line units or by load shedding or both. This paper presents a frequency security constrained short-term scheduling. The procedure commits and optimizes units, calculates necessary seconds reserve capability, and allocates them among the available on-line units to provide emergent frequency regulation following a loss of generation. By means of the low-pressure pre-heater interruption (LPHI) implemented into thermal power plants, seconds reverse provision is increased. Thus, load shedding caused by insufficient availability of seconds reserve can be avoided. A case study on typical island systems with a large number of different units is demonstrated using the proposed procedure. Results from the study validated robust performance of the proposed procedure that minimizes fuel costs while maintaining frequency security condition. [ABSTRACT FROM AUTHOR]