Search

With the increasing penetration of Inverter-Based Resources (IBRs), power system stability constraints must be incorporated into the operational framework, transforming it into stability-constrained optimization. Currently, there exist parallel research efforts on developing the stability constraints within DC power flow-based unit commitment (UC) and AC Optimal Power Flow (OPF). However, few studies discuss how including such constraints can interact with each other and eventually impact grid stability. In this context, this work simulates a realistic power system decision making framework and provides a thorough analysis on the necessity of incorporating frequency nadir and small signal stability constraints into these sequentially connected two operation stages. The simulation results demonstrate that including both stability constraints in the UC is essential to maintain power system stability, while the inclusion in AC OPF can further improve the stability index.

Encoding frequency stability constraints in the operation problem is challenging due to its complex dynamics. Recently, data-driven approaches have been proposed to learn the stability criteria offline with the trained model embedded as a constraint of online optimization. However, random sampling of stationary operation points is less efficient in generating balanced stable and unstable samples. Meanwhile, the performance of such a model is strongly dependent on the quality of the training dataset. Observing this research gap, we propose a gradient-based data generation method via forward-mode automatic differentiation. In this method, the original dynamic system is augmented with new states that represent the dynamic of sensitivities of the original states, which can be solved by invoking any ODE solver for a single time. To compensate for the contradiction between the gradient of various frequency stability criteria, gradient surgery is proposed by projecting the gradient on the normal plane of the other. In the end, we demonstrate the superior performance of the proposed sampling algorithm, compared with the unrolling differentiation and finite difference. All codes are available at https://github.com/xuwkk/frequency_sample_ad.

Security and stability challenges in future power systems with high penetration Inverter-Based Resources (IBR) have been anticipated as one of the main barriers to decarbonization. Grid-following IBRs may become unstable under small disturbances in weak grids, while during transient processes, system stability and protection may be jeopardized due to the lack of sufficient Short-Circuit Current (SCC). To solve these challenges and achieve decarbonization, the future system has to be carefully planned. However, it remains unclear how both small-signal and transient stabilities can be considered during the system planning stage. In this context, this paper proposes a coordinated planning model of different resources in the transmission system, namely the synchronous condensers and GFM IBRs to enhance system stability. The system strength and SCC constraints are analytically derived by considering the different characteristics of synchronous units and IBRs, which are further effectively linearized through a novel data-driven approach, where an active sampling method is proposed to generate a representative data set. The significant economic value of the proposed coordinated planning framework in both system asset investment and system operation is demonstrated through detailed case studies.

With the growing penetration of Inverter-Based Resources (IBRs) in power systems, stability service markets have emerged to incentivize technologies that ensure power system stability and reliability. Among the various challenges faced in power system operation and stability, a prominent issue raised from the increasing integration of large-scale IBRs is the significant reduction of the Short-Circuit Current (SCC) level in the system, which poses a considerable threat to system voltage stability and protection. Thus, a proper market mechanism to incentivize the provision of SCC as a stability service is desired. However, the pricing of this service within the future stability market has not yet been fully developed, due to the nonconvex nature of SCC constraints and the locational property of SCC. To address these problems, this work aims to explore, for the first time, a pricing model for SCC service by incorporating a linearized SCC constraint into the Unit Commitment (UC) problem, to achieve the desired SCC level and extract the shadow price for SCC through different pricing methods.

With the increasing penetration of Inverter-Based Resources (IBRs) and their impact on power system stability and operation, the concept of stability-constrained optimization has drawn significant attention from researchers. In order to manage the parametric uncertainty due to inaccurate modeling that influences the system dynamics, this work proposes a distributionally robust stability constraint formulation. However, the uncertainty of system dynamic parameters influences the stability constraints indirectly through a nonlinear and implicit relationship. To address this issue, a propagation mechanism from the uncertainty of the system dynamic parameters to the stability constraint coefficients is established. Since these coefficients are connected to the uncertain parameters through highly nonlinear and implicit functions, an approximation approach utilizing Taylor expansion and the Delta method is developed to estimate the statistical moments of the stability constraint coefficients based on the first and second-order derivatives, with which an ambiguity set for the distributionally robust optimization can be formulated. The accuracy of the uncertainty propagation as well as the effectiveness of the distributionally robust stability constraints are demonstrated through detailed case studies in the modified IEEE 39-bus system.

To address the increasing vulnerability of power grids, significant attention has been focused on the attack detection and impact mitigation. However, it is still unclear how to effectively and quickly recover the cyber and physical networks from a cyberattack. In this context, this paper presents the first investigation of the Cyber Recovery from Dynamic load altering Attack (CRDA). Considering the interconnection among electricity, transportation, and cyber networks, two essential sub-tasks are formulated for the CRDA: i) Optimal design of repair crew routes to remove installed malware and ii) Adaptive adjustment of system operation to eliminate the mitigation costs while guaranteeing stability. To achieve this, linear stability constraints are obtained by estimating the related eigenvalues under the variation of multiple IBR droop gains based on the sensitivity information of strategically selected sampling points. Moreover, to obtain the robust recovery strategy, the potential counter-measures from the adversary during the recovery process are modeled as maximizing the attack impact of remaining compromised resources in each step. A Mixed-Integer Linear Programming (MILP) problem can be finally formulated for the CRDA with the primary objective to reset involved droop gains and secondarily to repair all compromised loads. Case studies are performed in the modified IEEE 39-bus power system to illustrate the effectiveness of the proposed CRDA compared to the benchmark case.

In power systems with high penetration of power electronics, grid-forming control is proposed to replace traditional Grid-Following Converter (GFL) in order to improve the overall system strength and resist small-signal instability in weak grids by directly forming the terminal voltage. However, sufficient headroom of both active and reactive power must be made available for Grid-Forming Converter (GFM) to operate, potentially leading to sub-optimal operation in steady states. This presents a new research problem to optimally allocate between GFM and GFL to balance the ability of GFMs to improve the grid strength and the potential economic loss resulting from reserved headroom. An optimization framework under software-defined grids is proposed, for the first time, to dynamically determine the optimal allocation of GFMs and GFLs in power systems at each time step of system scheduling according to system conditions, which ensures both system stability and minimum operational cost. To achieve this, the system scheduling model is expanded to simultaneously consider the constraints related to active and reactive power reserves for GFMs, as well as the system level stability. Case studies conducted on the modified IEEE 30-bus system demonstrate significant economic benefits in that the optimal proportion of GFMs in the power system can be dynamically determined while ensuring power reserve and grid stability constraints.

Maintaining power system stability is becoming more and more challenging due to the ever-increasing inverter-interfaced renewable penetration in power systems. To ensure system stability during system operation and to provide appropriate incentives in the future market-based stability maintenance framework, it is essential to develop a comprehensive set of power system stability constraints which can be incorporated into system operation, market design and planning problems. In this paper, different system stability issues, including synchronization, voltage and frequency stability, are investigated and the corresponding stability conditions are analytically formulated as system operation constraints. A unified framework is further proposed to represent the stability constraints in a general form and enables effective reformulation of the impedance-based stability metrics. All the constraints are converted into linear or Second-Order-Cone (SOC) form, which can be readily implemented in any optimisation-based applications, such as system scheduling, planning and market design, thus providing significant value for multiple system stability enhancement and studies.

Multiple operational constraints of power system stability are derived analytically and reformulated into Second-Order Cone (SOC) form through a unification method in Part I of this paper. The accuracy and conservativeness of the proposed methods are illustrated in the second part. The validity of the developed constraints is tested against dynamic simulations carried out based on the modified IEEE 39-bus system. Furthermore, the developed power system stability constraints are applied to the optimal system scheduling model. The resulting stability-constrained system scheduling problem aims to achieve most economic system operation while ensuring different stability in power systems with high Inverter-Based Resources (IBR) penetration. Moreover, based on the stability-constrained optimization model, a novel marginal unit pricing scheme is proposed to quantify the stability services of different units appropriately according to their economic value in maintaining system stability, thus providing rational incentives to the stability service provider and insightful information for the stability market development.

Recently, frequency security is challenged by high uncertainty and low inertia in power system with high penetration of Renewable Energy Sources (RES). In the context of Unit Commitment (UC) problems, frequency security constraints represented by neural networks have been developed and embedded into the optimization problem to represent complicated frequency dynamics. However, there are two major disadvantages related to this technique: the risk of overconfident prediction and poor computational efficiency. To handle these disadvantages, novel methodologies are proposed to optimally design the neural network structure, including the use of asymmetric loss function during the training stage and scientifically selecting neural network size and topology. The effectiveness of the proposed methodologies are validated by case study which reveals the improvement of conservativeness and mitigation of computation performance issues.

The objective-based forecasting considers the asymmetric and non-linear impacts of forecasting errors on decision objectives, thus improving the effectiveness of its downstream decision-making process. However, existing objective-based forecasting methods are risk-neutral and not suitable for tasks like power system inertia management and unit commitment, of which decision-makers are usually biased toward risk aversion in practice. To tackle this problem, this paper proposes a generic risk-aware objective-based forecasting method. It enables decision-makers to customize their forecasting with different risk preferences. The equivalence between the proposed method and optimization under uncertainty (stochastic/robust optimization) is established for the first time. Case studies are carried out on a Great Britain 2030 power system with system operational data from National Grid. The results show that the proposed model with deterministic optimization can approximate the performance of stochastic programming or robust optimization at only a fraction of their computational cost.

Integrated with a high share of Inverter-Based Resources (IBRs), microgrids face increasing complexity of frequency dynamics, especially after unintentional islanding from the maingrid. These IBRs, on the other hand, provide more control flexibility to shape the frequency dynamics of microgrid and together with advanced communication infrastructure offer new opportunities in the future software-defined microgrids. To enhance the frequency stability of microgrids with high IBR penetration, this paper proposes an optimal scheduling framework for software-defined microgrids to maintain frequency stability by utilizing the non-essential load shedding and dynamical optimization of the virtual inertia and virtual damping from IBRs. Moreover, side effects of these services, namely, the time delay associated with non-essential load shedding and potential IBR control parameter update failure are explicitly modeled to avoid underestimations of frequency deviation and over-optimistic results. The effectiveness and significant economic value of the proposed simultaneous and dynamic virtual inertia and damping provision strategy are demonstrated based on case studies in the modified IEEE 33-bus system.

Large-scale Load-Altering Attacks (LAAs) against Internet-of-Things (IoT) enabled high-wattage electrical appliances (e.g., wifi-enabled air-conditioners, electric vehicles, etc.) pose a serious threat to power systems' security and stability. In this work, a Cyber-Resilient Economic Dispatch (CRED) framework is presented to mitigate the destabilizing effect of LAAs while minimizing the overall operational cost by dynamically optimizing the frequency droop control gains of Inverter-Based Resources (IBRs). The system frequency dynamics incorporating both LAAs and the IBR droop control are modeled. The system stability constraints are explicitly derived based on parametric sensitivities. To incorporate them into the CRED model and minimize the error of the sensitivity analysis, a recursive linearization method is further proposed. A distributionally robust approach is applied to account for the uncertainty associated with the LAA detection/parameter estimation. The overall performance of the proposed CRED model is demonstrated through simulations in a modified IEEE reliability test system.

With the increasing penetration of renewable energy sources, power system operation has to be adapted to ensure the system stability and security while considering the distinguished feature of the Power Electronics (PE) interfaced generators. The static voltage stability which is mainly compromised by heavy loading conditions in conventional power systems, faces new challenges due to the large scale integration of PE-interfaced devices. This paper investigates the static voltage stability problem in high PE-penetrated system. The analytic criterion that ensures the voltage stability at the Inverter-Based Generator (IBG) buses are derived with the interaction of different IBGs being considered. Based on this, an optimal system scheduling model is proposed to minimize the overall system operation cost while maintaining the voltage stability during normal operation through dynamically optimizing the active and reactive power output from IBGs. The highly nonlinear voltage stability constraints are effectively converted into Second-Order-Cone (SOC) form, leading to an overall Mixed-Integer SOC Programming (MISOCP), together with the SOC reformulation of AC power flow and frequency constraints. The effectiveness of the proposed model and the impact of various factors on voltage stability are demonstrated in thorough case studies.

In order to prevent the potential frequency instability due to the high Power Electronics (PE) penetration under an unintentional islanding event, this paper presents a novel microgrid scheduling model which explicitly models the system frequency dynamics as well as the long/short term uncertainty associated with renewable energy resources and load. Synthetic Inertia (SI) control is applied to regulating the active power output of the Inverter-Based Generators (IBGs) to support the post-islanding frequency evaluation. The uncertainty associated with the noncritical load shedding is explicitly modeled based on the distributionally robust formulation to ensure resilient operation during islanding events. The resulted frequency constraints are derived analytically and reformulated into Second-Order Cone (SOC) form, which are further incorporated into the microgrid scheduling model, enabling optimal SI provision of Renewable Energy Sources (RESs) from the micorgrid perspective. With the SOC relaxation of the AC power flow constraints, the overall problem is constructed as a mixed-integer SOC Programming (MISOCP). The effectiveness of the proposed model is demonstrated based on modified IEEE 14-bus system.

Inverter Based Generators (IBGs) have been increasing significantly in power systems. Due to the demanding thermal rating of Power Electronics (PE), their contribution to the system Short Circuit Current (SCC) is much less than that from the conventional Synchronous Generators (SGs) thus reducing the system strength and posing challenges to system protection and stability. This paper proposes a Unit Commitment (UC) model with SCC constraint in high IBG-penetrated systems to ensure minimum operation cost while maintaining the SCC level at each bus in the system. The SCC from synchronous generators as well as the IBGs are explicitly modeled in the formulation leading to an SCC constraint involving decision-dependent matrix inverse. This highly nonlinear constraint is further reformulated into linear form conservatively. The influence of the SCC constraint on the system operation and its interaction with the frequency regulation are demonstrated through simulations on IEEE 30- and 118-bus systems.

The undergoing transition from conventional to converter-interfaced renewable generation leads to significant challenges in maintaining frequency stability due to declining system inertia. In this paper, a novel control framework for Synthetic Inertia (SI) provision from Wind Turbines (WTs) is proposed, which eliminates the secondary frequency dip and allows the dynamics of SI from WTs to be analytically integrated into the system frequency dynamics. Furthermore, analytical system frequency constraints with SI provision from WTs are developed and incorporated into a stochastic system scheduling model, which enables the provision of SI from WTs to be dynamically optimized on a system level. Several case studies are carried out on a Great Britain 2030 power system with different penetration levels of wind generation and inclusion of frequency response requirements in order to assess the performance of the proposed model and analyze the influence of the improved SI control scheme on the potential secondary frequency dip. The results demonstrate that the inclusion of SI provision from WTs into UC can drastically impact the overall system costs., Comment: 10 pages, accepted by IEEE Transaction on Power System