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At least 757 records · Page 42

Toward a MILP Modeling Framework for Distribution System Restoration

Large-scale blackouts and extreme weather events in recent decades raise the concern for improving the resilience of electric power infrastructures. Distribution service restoration (DSR), a fundamental application in outage management systems, allows restoration solutions for system operators when power outages happen. As distribution generators (DGs) and remotely controllable devices are increasingly installed in distribution systems, an advanced DSR framework is critical to perform optimally coordinated restoration that can achieve maximal restoration performance. This work introduces a DSR modeling framework, which can generate optimal switching sequences and estimated time of restoration in the presence of remotely controllable switches, manually operated switches, and dispatchable DGs. Two mathematical models, a variable time step model and a fixed time step model, are presented and compared. The proposed models are formulated as a mixed-integer linear programming model, and their effectiveness is evaluated via the IEEE 123 node test feeder.

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Multi-operator Production Cost Modeling

As contiguous power systems are often operated by several regional system operators, optimization models have traditionally been designed to generate optimal system-wide scheduling decisions. This report introduces an approach to reflect the existence of multiple system operators making scheduling decisions within an interconnected power system. The approach is explicitly designed to reflect each operator's limited knowledge about other regions when making scheduling decisions. Detailed analysis using a modified IEEE Reliability Test System reveals that the approach mimics real system operations by providing imperfect information to each operator about external operations and external constraints. The approach scales to a 78,000-bus model of the Eastern Interconnection, where a regression analysis provides quantitative insight into which constraints cause inefficiencies when improperly managed in a multi-operator simulation. Because the approach generates distinct regional scheduling problems, unit commitment and economic dispatch simulations can be applied to individual regions and solved in parallel, enabling production cost simulations at a previously intractable scale.

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Real-Time Optimized Load Recovery Considering Frequency Constraints

A self-healing power grid can mitigate the impact of power outages and recover the affected area swiftly. To properly size the optimal amount and location of de-energized loads in the presence of both conventional and renewable sources, a precise optimization-based load recovery tool is proposed herein. The steady-state and transient behaviors of loads have been taken into account. The proposed tool contains three separate problems that interact with each other during the restoration period. The first-level problem determines the dispatching of generation units. The second-level problem comprises the non-linear algebraic equations, whose task is to provide the initial conditions for the third-level problem. Finally, the third-level problem intends to determine the optimal location and amount of load pickup through modeling the governor of generators as well as loads' dynamic behaviors. To examine the effectiveness of the proposed tool, a modified IEEE 39-system under a partial blackout condition has been tested. The results are verified by a commercial time-domain simulation software (PSS/E) to demonstrate the accuracy of the proposed approach. Ultimately, the impact of wind turbine frequency control on the load recovery process has been studied under different penetration levels.

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Accelerated Voltage Regulation in Multi-Phase Distribution Networks Based on Hierarchical Distributed Algorithm

Here, we introduce a hierarchical distributed algorithm to solve optimal power flow (OPF) problems that aim at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm highlights unprecedented scalability to large multi-phase distribution networks by jointly exploring the tree/subtrees structure of a large radial distribution network and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves OPF. The proposed implementation significantly reduces the computation loads compared to the centrally coordinated implementation of the same primal-dual algorithm without compromising optimality. Numerical findings on a 4,521-node test feeder show that the designed algorithm achieves more than 10-fold acceleration in the speed of convergence compared to the centrally coordinated primal-dual algorithm through reducing and distributing computational loads.

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On Secured Spinning Reserve Deployment of Energy-Limited Resources Against Contingencies

Featured with fast response abilities and high ramp rates, energy storage systems (ESS), such as pumped-storage hydropower (PSH) plants and battery storage systems (BSS), are considered as key first-responders to provide spinning reserve in response to system contingencies. However, ESSs are energy-limited resources, and their sustained spinning reserve deployment is restricted by the stored energy and available capacity. Indeed, the spinning reserve deployment against contingencies may deviate actual state-of-charge (SOC) from the scheduled value, inducing potential SOC boundary violations and non-dispatchability in later hours. This paper proposes the post-contingency operation model and the spinning reserve secure constraints to address these issues. The post-contingency operation model describes that spinning reserve from ESSs is promptly deployed when contingency occurs, and then gradually substituted by quick-start units when they are switched online. By leveraging this operation strategy, spinning reserve secure constraints in terms of SOC headrooms are adopted to guarantee its deplorability. Furthermore, a modified IEEE 118-bus system with multiple PSHs and BSSs is used to verify the proposed approach.

13 HYDRO ENERGY↗

Switching Device-Cognizant Sequential Distribution System Restoration

This paper presents an optimization framework for sequential reconfiguration using an assortment of switching devices and repair process in distribution system restoration. Compared to existing studies, this paper considers types, capabilities and operational limits of different switching devices, making it applicable in practice. We develop a novel multi-phase method to find the optimal sequential operation of various switching devices and repair faulted areas. We consider circuit breakers, reclosers, sectionalizers, load breaker switches, and fuses. The switching operation problem is decomposed into two mixed-integer linear programming (MILP) subproblems. The first subproblem determines the optimal network topology and estimates the number of steps to reach that topology, while the second subproblem generates a sequence of switching operations to coordinate the switches. For repairing the faults, we design an MILP model that dispatches repair crews to clear faults and replace melted fuses. After clearing a fault, we update the topology of the network by generating a new sequence of switching operations, and the process continues until all faults are cleared. To improve the computational efficiency, a network reduction algorithm is developed to group line sections, such that only switchable sections are present in the reduced network. The proposed method is validated on the IEEE 123-bus and 8500-bus systems.

distribution system↗

Hierarchical Distributed Optimal Power Flow of HV and MV Distribution Networks With Continuous and Discrete Devices

With large-scale distributed photovoltaics (PVs) being integrated into distribution networks (DNs), coordinated optimal power flow (OPF) of high voltage (HV) and medium voltage (MV) DNs should be investigated to optimally dispatch the distributed PVs and other network devices. Here, this paper presents a hierarchical distributed OPF method for HV and MV DNs with on-load tap changers, reactive power compensators, feeder switches and distributed PVs. A hierarchical master-slave control architecture is applied to implement coordinated OPF of two-layer DNs. The HV master problem and MV subproblems are transformed into mixed-integer convex problems respectively with second order cone programming and LinDistFlow approximation. Since there is no efficient distributed algorithm to solve such OPF models with integer subproblems, a novel distributed algorithm is proposed in this paper to efficiently solve the hierarchical coordinated OPF model with integer subproblems in a distributed manner. In the proposed algorithm, the coordinated OPF model is solved in a branch-and-bound framework, where in each branch node generalized Benders decomposition (GBD) algorithm is applied to decompose the coordinated OPF model into a master problem and relaxed subproblems and solves them iteratively to get optimal solution. The GBD optimal and feasible cutting planes generated in a branch node are proved to be valid for its descendants. Moreover, three acceleration techniques are introduced into the proposed algorithm to improve computational efficiency. Finally, the effectiveness and accuracy of the proposed method are verified via simulation tests in Jinzhai DNs of China.

42 ENGINEERING↗

Data-Driven Probabilistic Voltage Risk Assessment of MiniWECC System with Uncertain PVs and Wind Generations using Realistic Data

Here, it is found from actual data that due to generation dispatch and uncertain renewable generations and loads with complicated correlations, inferring the probabilistic distributions for uncertain inputs is challenging. Many probabilistic power flow approaches have been developed in the literature but their validations using realistic systems and data are lacking. This paper proposes a data-driven probabilistic analysis approach for system risk assessment of the miniWECC system using actual data. The sparse Gaussian process (SGP) is advocated to quantify the impacts of uncertain inputs on voltage security. SGP does not need the probability distribution function of uncertain inputs, can handle correlations and is highly computationally efficient. Results on the miniWECC system using realistic data show that SGP outperforms existing approaches and is able to quantify the voltage violation risks.

17 WIND ENERGY↗

Analytical Models of Frequency and Voltage in Large-Scale All-Inverter Power Systems

Low-order frequency response models for power systems have a decades-long history in optimization and control problems such as unit commitment, economic dispatch, and wide-area control. With a few exceptions, these models are built upon the Newtonian mechanics of synchronous generators, assuming that the frequency dynamics across a system are approximately homogeneous, and assume the dynamics of nodal voltages for most operating conditions are negligible, and thus are not directly computed at all buses. As a result, the use of system frequency models results in the systematic underestimation of frequency minimum nadir and maximum RoCoF, and provides no insight into the reactive power-voltage dynamics. This paper proposes a low-order model of both frequency and voltage response in grid-forming inverter-dominated power systems. The proposed model accounts for spatial-temporal variations in frequency and voltage behavior across a system and as a result, demonstrates the heterogeneity of frequency response in future renewable power systems. Electromagnetic transient (EMT) simulations are used to validate the utility, accuracy, and computational efficiency of these models, setting the basis for them to serve as fast, scalable alternatives to EMT simulation, especially when dealing with very large-scale systems, for both planning and operational studies.

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A Methodology for Quantifying Reliability Benefits From Improved Solar Power Forecasting in Multi-Timescale Power System Operations

Solar power forecasting improvements are mainly evaluated by statistical and economic metrics, and the practical reliability benefits of these forecasting enhancements have not yet been well quantified. This paper aims to quantify reliability benefits from solar power forecasting improvements. To systematically analyze the relationship between solar power forecasting improvements and reliability performance in power system operations, an expected synthetic reliability (ESR) metric is proposed to integrate state-of-the-art independent reliability metrics. The absolute value and standard deviation of area control errors (ACE), and the North American Electric Reliability Corporation Control Performance Standard 2 (CPS2) score are calculated through the multi-timescale scheduling simulation, including the day-ahead unit commitment (DU), real-time unit commitment (RU), real-time economic dispatch (RE), automatic generation control (AGC) sub-models. The absolute area control error in energy (AACEE), CPS2 violations, CPS2 score, and standard deviation of the raw ACE are all calculated and combined as the ESR metric. Numerical simulations show that the reliability benefits of multi-timescale power system operations are significantly increased due to the improved solar power forecasts.

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Optimal Load Ensemble Control in Chance-Constrained Optimal Power Flow

Distribution system operators (DSOs) world-wide foresee a rapid roll-out of distributed energy resources. From the system perspective, their reliable and cost effective integration requires accounting for their physical properties in operating tools used by the DSO. This work describes an decomposable approach to leverage the dispatch flexibility of thermostatically controlled loads (TCLs) for operating distribution systems with a high penetration level of photovoltaic resources. Each TCL ensemble is modeled using the Markov Decision Process (MDP). The MDP model is then integrated with a chance constrained optimal power flow that accounts for the uncertainty of PV resources. Since the integrated optimization model cannot be solved efficiently by existing dynamic programming methods or off-the-shelf solvers, this paper proposes an iterative Spatio-Temporal Dual Decomposition algorithm (ST-D2). Finally, we demonstrate the merits of the proposed integrated optimization and ST-D2 algorithm on the IEEE 33-bus test system.

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Repair and Resource Scheduling in Unbalanced Distribution Systems Using Neighborhood Search

—This paper proposes an optimization strategy to assist utility operators to recover power distribution systems after large outages. Specifically, a mixed-integer linear programming (MILP) model is developed for co-optimizing crews, resources, and network operations. The MILP model coordinates damage isolation, network reconfiguration, distributed generator re-dispatch, and crew/resource logistics. In addition, a framework for integrating different types of photovoltaic (PV) systems in the restoration process is developed. We consider two different types of crews, namely, line crews for damage repair and tree crews for obstacle removal. We also model the repair resource logistic constraints. Furthermore, a new algorithm is developed for solving the distribution system repair and restoration problem (DSRRP). The algorithm starts by solving DSRRP using an assignmentbased method, then a neighborhood search method is designed to iteratively improve the solution. The proposed method is validated on modified IEEE 123- and 8500-bus distribution test systems.

Outage management↗

A Learning-based Power Management Method for Networked Microgrids Under Incomplete Information

In this paper, we present a model-free reinforcement learning (RL)-based technique to solve the power management problem of networked microgrids (MGs), when the utility has only limited or no detailed knowledge of the MG asset models.The proposed method consists of two levels: at the first level, using an approximate RL strategy and aggregated data, a utility agent determines the locational price signals to maximize its profit under incomplete information on the MGs’ private data behind their points of common coupling (PCC). The proposed RL strategy enables the utility to adapt to changing system conditions and learn from previous experiences, while respecting the data ownership of the MGs. At the second level, the MGs receive the price signals to dispatch their generation/storage assets individually over look-ahead decision time window, while considering power flow constraints. The performance of the proposed RL technique has been verified under realistic operational scenarios.

Zhang, Qianzhi↗

Multi-Agent Safe Policy Learning for Power Management of Networked Microgrids

This paper presents a supervised multi-agent safe policy learning (SMAS-PL) method for optimal power management of networked microgrids (MGs) in distribution systems. While unconstrained reinforcement learning (RL) algorithms are black-box decision models that could fail to satisfy grid operational constraints, our proposed method considers AC power flow equations and other operational limits. Accordingly, the training process employs the gradient information of operational constraints to ensure that the optimal control policy functions generate safe and feasible decisions. Furthermore, we have developed a distributed consensus-based optimization approach to train the agents’ policy functions while maintaining MGs’ privacy and data ownership boundaries. After training, the learned optimal policy functions can be safely used by the MGs to dispatch their local resources, without the need to solve a complex optimization problem from scratch. Lastly, numerical experiments have been devised to verify the performance of the proposed method.

, policy gradient↗

Power System Resilience Enhancement in Typhoons Using a Three-Stage Day-Ahead Unit Commitment

In this work, we propose a three-stage resilient unit commitment model which considers uncertain typhoon paths and line outages to improve the power system resilience against typhoon events. The proposed solution coordinates resources in response to the worst-case scenario for each possible typhoon path. The optimal decision is based on the characterization of the power system schedule into three stages of preventive control, emergency control, and restoration. Preventive control is performed before the typhoon occurs by quickly adjusting the three-stage resilient unit commitment schedule; emergency control is conducted during the typhoon by shedding local loads to meet the power balance, while other control strategies are assumed to be unavailable due to possible interruptions in the communication system; restoration is realized after the typhoon, when resources are optimally dispatched to repair the outages of critical devices and recover the normal operation state of the power system quickly. Considering the typhoon path uncertainty, we have introduced a stochastic model for possible typhoon paths where all possible affected lines along each typhoon path are assumed to be on outage during the typhoon. Accordingly, we explore the strategy for co-optimizing the three stages in unit commitment. The proposed model is tested on the IEEE 118-bus system and the real-world provincial system to verify its effectiveness.

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Distribution Market-Clearing and Pricing Considering Coordination of DSOs and ISO: An EPEC Approach

Distribution-level electricity market provides a platform for trading energy and grid services from large-amount of small-scale distributed energy resources (DERs) located on distribution grids. The behavior of the DERs in the distribution electricity market may ultimately impact the market-clearing and locational marginal prices (LMPs) in the wholesale market. This paper proposes a bi-level optimization model for distribution market clearing and distribution locational marginal pricing (DLMP) considering the interactions between distribution and transmission wholesale markets. In the proposed model, the upper-level model represents the distribution system operator (DSO) market-clearing and the lower-level model represents the wholesale market-clearing by the independent system operator (ISO). The LMP at the substation will impact the DER dispatch and power demands of the DSO as well as the DLMP. In turn, the power demands of the DSO will further impact the ISO market and its LMPs. The equilibrium problem with equilibrium constraints (EPEC) approach is applied to find the equilibria of multiple DSOs and the ISO. The EPEC problem is transformed into a single-level mixed-integer convex problem in order to allow for efficient solving. Finally, the effectiveness of the proposed model and solution method are demonstrated through case studies.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Transmission-and-Distribution Dynamic Co-simulation Framework for Distributed Energy Resource Frequency Response

The rapid deployment of distributed energy resources (DERs) in distribution networks has made it challenging to balance the transmission system and stabilize frequency. DERs have the ability to provide frequency regulation services; however, existing frequency dynamic simulation tools - which were developed mainly for the transmission system - lack the capability to simulate distribution network dynamics with high penetrations of DERs. Although electromagnetic transient simulation tools can simulate distribution network dynamics, the computation efficiency limits their use for large-scale transmission-and-distribution (T&D) co-simulation. This paper presents an efficient open-source T&D dynamic co-simulation framework for DER frequency response based on the HELICS platform and off-the-shelf T&D simulators. The challenge of synchronizing the simulation time between the transmission network and the DERs in the distribution network is solved through the detailed modeling of DERs in frequency dynamic models while DER power flow models are also preserved in the distribution networks, thereby respecting local voltage constraints when dispatching DER power for frequency response. DER frequency response (primary and secondary) is simulated in case studies to validate the proposed framework. Last, the accuracy of the proposed co-simulation model is benchmarked, and a large T&D system simulation (2k transmission and 1M distribution nodes) is presented to demonstrate the efficiency and effectiveness of the overall framework.

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A Network-Aware Distributed Energy Resource Aggregation Framework for Flexible, Cost-Optimal, and Resilient Operation

To efficiently use the ubiquitous behind-the-meter distributed energy resources (DERs) in distribution systems for providing grid services, this paper presents a hierarchical control framework for DER optimal aggregation and control. We first develop a convex optimization model to evaluate the DER flexibility, and then use a convex model-predictive-control based approach to dispatch those DERs. The hierarchical control framework consists of a utility controller, community aggregators and multiple home energy management systems. The flexibility of the DERs is evaluated by each controller in the hierarchy such that the resultant flexibility is feasible given its operational domain. Based on the determined flexibility, the hierarchical controllers then compute optimal setpoints for the DERs to help the distribution system regulate node voltages and provide other distribution grid services. Numerical simulations performed on a model of a real distribution feeder in Colorado, using actual DER data in a residential community demonstrate that the proposed approach can effectively alleviate voltage issues and support resilient operation.

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