We propose a two-stage scenario-based stochastic optimization problem to determine investments that enhance power system resilience. The proposed optimization problem minimizes the Conditional Value at Risk (CVaR) of load loss to target low-probability high-impact events. We provide results in the context of generator winterization investments in Texas using winter storm scenarios generated from historical data collected from Winter Storm Uri. Results illustrate how the CVaR metric can be used to minimize the tail of the distribution of load loss and illustrate how risk-Aversity impacts investment decisions.
In the face of increasing natural disasters and an aging grid, utilities need to optimally choose investments to the existing infrastructure to promote resiliency. This paper presents a new investment decision optimization model to minimize unserved load over the recovery time and improve grid resilience to extreme weather event scenarios. Our optimization model includes a network power flow model which decides generator status and generator dispatch, optimal transmission switching (OTS) during the multi-time period recovery process, and an investment decision model subject to a given budget. Investment decisions include the hardening of transmission lines, generators, and substations. Our model uses a second order cone programming (SOCP) relaxation of the AC power flow model and is compared to the classic DC power flow approximation. A case study is provided on the 73-bus RTS-GMLC test system for various investment budgets and multiple hurricane scenarios to highlight the difference in optimal investment decisions between the SOCP model and the DC model, and demonstrate the advantages of OTS in resiliency settings. Results indicate that the network models yield different optimal investments, unit commitment, and OTS decisions, and an AC feasibility study indicates our SOCP resiliency model is more accurate than the DC model.
This paper presents a preliminary investigation on controlling the existing high voltage dc (HVDC) links connecting the North American western interconnection (WI) to the other interconnections, to provide damping to inter-area oscillations. The control scheme is meant to damp inter-area modes of oscillation in the WI by using wide area synchrophasor feedback. A custom model is developed in General Electric's PSLF software for the wide area damping control scheme, and simulations are analyzed on a validated full 22,000 bus WI model. Results indicate that implementing the proposed control technique to the existing HVDC links in the WI can significantly improve the damping of the inter-area modes of the system.
A methodology for the design of control systems for wide-area power systems using solid-state transformers (SSTs) as actuators is presented. Due to their ability to isolate the primary side from the secondary side, an SST can limit the propagation of disturbances, such as frequency and voltage deviations, from one side to the other. This paper studies a control strategy based on SSTs deployed in the transmission grid to improve the resilience of power grids to disturbances. The control design is based on an empirical model of an SST that is appropriate for control design in grid level applications. A simulation example illustrating the improvement provided by an SST in a large-scale power system via a reduction in load shedding due to severe disturbances are presented.
A methodology for the design of control systems for wide-area power systems using solid-state transformers (SSTs) as actuators is presented. Due to their ability to isolate the primary side from the secondary side, an SST can limit the propagation of disturbances, such as frequency and voltage deviations, from one side to the other. This paper studies a control strategy based on SSTs deployed in the transmission grid to improve the resilience of power grids to disturbances. The control design is based on an empirical model of an SST that is appropriate for control design in grid level applications. A simulation example illustrating the improvement provided by an SST in a large-scale power system via a reduction in load shedding due to severe disturbances are presented.
This paper presents a novel dynamic programming (DP) technique for the determination of optimal investment decisions to improve power distribution system reliability metrics. This model is designed to select the optimal small-scale investments to protect an electrical distribution system from disruptions. The objective is to minimize distribution system reliability metrics: System Average Interruption Duration Index (SAIDI) and System Average Interruption Frequency Index (SAIFI). The primary input to this optimization model is years of recent utility historical outage data. The DP optimization technique is compared and validated against an equivalent mixed integer linear program (MILP). Through testing on synthetic and real datasets, both approaches are verified to yield equally optimal solutions. Efficiency profiles of each approach indicate that the DP algorithm is more efficient when considering wide budget ranges or a larger outage history, while the MILP model more efficiently handles larger distribution systems. The model is tested with utility data from a distribution system operator in the U.S. Results demonstrate a significant improvement in SAIDI and SAIFI metrics with the optimal small-scale investments.
This report presents a framework to evaluate the impact of a high-altitude electromagnetic pulse (HEMP) event on a bulk electric power grid. This report limits itself to modeling the impact of EMP E1 and E3 components. The co-simulation of E1 and E3 is presented in detail, and the focus of the paper is on the framework rather than actual results. This approach is highly conservative as E1 and E3 are not maximized with the same event characteristics and may only slightly overlap. The actual results shown in this report are based on a synthetic grid with synthetic data and a limited exemplary EMP model. The framework presented can be leveraged and used to analyze the impact of other threat scenarios, both manmade and natural disasters. This report d escribes a Monte-Carlo based methodology to probabilistically quantify the transient response of the power grid to a HEMP event. The approach uses multiple fundamental steps to characterize the system response to HEMP events, focused on the E1 and E3 components of the event. 1) Obtain component failure data related to HEMP events testing of components and creating component failure models. Use the component failure model to create component failure conditional probability density function (PDF) that is a function of the HEMP induced terminal voltage. 2) Model HEMP scenarios and calculate the E1 coupled voltage profiles seen by all system components. Model the same HEMP scenarios and calculate the transformer reactive power consumption profiles due to E3. 3) Sample each component failure PDF to determine which grid components will fail, due to the E1 voltage spike, for each scenario. 4) Perform dynamic simulations that incorporate the predicted component failures from E1 and reactive power consumption at each transformer affected by E3. These simulations allow for secondary transients to affect the relays/protection remaining in service which can lead to cascading outages. 5) Identify the locations and amount of load lost for each scenario through grid dynamic simulation. This can be an indication of the immediate grid impacts from a HEMP event. In addition, perform more detailed analysis to determine critical nodes and system trends. 6) To help realize the longer-term impacts, a security constrained alternating current optimal power flow (ACOPF) is run to maximize critical load served. This report describes a modeling framework to assess the systemic grid impacts due to a HEMP event. This stochastic simulation framework generates a large amount of data for each Monte Carlo replication, including HEMP location and characteristics, relay and component failures, E3 GIC profiles, cascading dynamics including voltage and frequency over time, and final system state. This data can then be analyzed to identify trends, e.g., unique system behavior modes or critical components whose failure is more likely to cause serious systemic effects. The proposed analysis process is demonstrated on a representative system. In order to draw realistic conclusions of the impact of a HEMP event on the grid, a significant amount of work remains with respect to modeling the impact on various grid components.
Sandia National Laboratories sponsored a three-year internally funded Laboratory Directed Research and Development (LDRD) effort to investigate the vulnerabilities and mitigations of a high-altitude electromagnetic pulse (HEMP) on the electric power grid. The research was focused on understanding the vulnerabilities and potential mitigations for components and systems at the high voltage transmission level. Results from the research included a broad array of subtopics, covered in twenty-three reports and papers, and which are highlighted in this executive summary report. These subtopics include high altitude electromagnetic pulse (HEMP) characterization, HEMP coupling analysis, system-wide effects, and mitigating technologies.
This paper presents a multi-Time period two-stage stochastic mixed-integer linear optimization model which determines the optimal hardening investments to improve power system resilience to natural disaster threat scenarios. The input to the optimization model is a set of scenarios for specific natural disaster events, that is based on historical data. The objective of the optimization model is to minimize the expected weighted load shed from the initial impact and the restoration process over all scenarios. The optimization model considers the initial impact of the severe event by using electromechanical transient dynamic simulations. The initial impact weighted load shed is determined by the transient simulation, which allows for secondary transients from protection devices and cascading failures. The rest of the event, after the initial shock, is modeled in the optimization with a multi-Time period dc optimal power flow (DCOPF) which is initialized with the solution from the dynamic simulation. The first stage of the optimization model determines the optimal investments. The second stage, given the investments, determines the optimal unit commitment, generator dispatch, and transmission line switching during the multi-Time period restoration process to minimize the weighted load shed over all scenarios. Note, an investment will change the transient simulation result, and therefore change the initialization to the DCOPF restoration model. The investment optimization model encompasses both the initial impact (dynamic transient simulation results) and the restoration period (DCOPF) of the event, as components come back online. The model is tested on the IEEE RTS-96 system.
Forced oscillations in power systems are of particular interest when they interact and reinforce inter-area oscillations. This paper determines how a previously proposed inter-area damping controller mitigates forced oscillations. The damping controller modulates active power on the Pacific DC Intertie (PDCI) based on phasor measurement units (PMU) frequency measurements. The primary goal of the controller is to improve the small signal stability of the north south B mode in the North American Western Interconnection (WI). The paper presents small signal stability analysis in a reduced order system, time-domain simulations of a detailed representation of the WI and actual system test results to demonstrate that the PDCI damping controller provides effective damping to forced oscillations in the frequency range below 1 Hz.
