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DOE OSTI2018

Optimizing DER Participation in Inertial and Primary-Frequency Response

This paper develops an approach to enable the optimal participation of distributed energy resources (DERs) in inertial and primary-frequency response alongside conventional synchronous generators. Leveraging a reduced-order model description of frequency dynamics, DERs' synthetic inertias and droop coefficients are designed to meet time-domain performance objectives of frequency overshoot and steady-state regulation. Furthermore, an optimization-based method centered around classical economic dispatch is developed to ensure that DERs share the power injections for inertial- and primary-frequency response in proportion to their power ratings. Simulations for a modified New England test-case system composed of ten synchronous generators and six instances of the IEEE 37-node test feeder with frequency-responsive DERs validate the design strategy.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Load-Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity, and Linear Models

This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the Z-bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for the non-singularity of the load-flow Jacobian is proposed. Lastly, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.

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DOE OSTI2018

Locating the Source of Events in Power Distribution Systems Using Micro-PMU Data

A novel method is proposed to locate the source of events in power distribution systems by using distribution-level phasor measurement units, a.k.a., micro-PMUs. An event in this paper is defined rather broadly to include any major change in any component across the distribution feeder. The goal is to enhance situational awareness in distribution grid by keeping track of the operation (or misoperation) of various grid equipment, assets, distribution energy resources, loads, etc. The proposed method is built upon the compensation theorem in circuit theory to generate an equivalent circuit to represent the event by using voltage and current synchrophasors that are captured by micro-PMUs. Importantly, this method makes critical use of not only magnitude but also synchronized phase angle measurements, thus, it justifies the need to use micro-PMUs, as opposed to ordinary RMS-based voltage and current sensors. The proposed method can work with data from as a few as only two micro-PMUs. The effectiveness of the developed method is demonstrated through computer simulations on the IEEE 123-bus test system, and also on micro-PMUs measurements from a real-life 12.47 kV test feeder in Riverside, CA. In conclusion, the results verify that the proposed method is accurate and robust in locating the source of different types of events on power distribution systems.

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DOE OSTI2018

The Role of Concentrating Solar Power Toward High Renewable Energy Penetrated Power Systems

Achieving high renewable energy penetrated power systems requires considerable operational flexibility to hedge the variability and uncertainty of variable renewable energy (VRE) generation. Compared with VRE sources, concentrating solar power (CSP) is an emerging controllable renewable generation technique that utilizes solar thermal power to generate electricity. The operational dispatchability of CSP would contribute to the power system transition toward high renewable penetration. In this paper, we explore how the generation portfolio will change toward high renewable energy penetrations, how much cost is involved, and what role CSP will play in realizing a high renewable energy penetrated power system. This study relies on a stochastic two-stage generation and transmission expansion planning model with CSP plants. The model captures the uncertainty and variability of renewable generation and the flexibility limits of thermal plants. With the target of achieving a renewable-dominated minimum-cost system with an expected renewable energy penetration level, the investments of both generation and transmission facilities are optimized. A case study on IEEE test systems with renewable technology cost data in 2050 is performed to analyze the value of CSP toward high renewable energy penetrated power systems.

14 SOLAR ENERGY↗
DOE OSTI2018

Risk-Based Distributionally Robust Optimal Power Flow With Dynamic Line Rating

In this paper, we propose a risk-based data-driven distributionally robust approach to investigating the optimal power flow with dynamic line rating. The risk terms, including penalties for load shedding, wind generation curtailment and line overload, are embedded into the objective function. To robustify the solution, we consider a distributional uncertainty set based on the second-order moment, that captures the correlation between wind generation outputs and line ratings, and also the Wasserstein distance, that hedges against data perturbations. We show that the proposed model can be reformulated as a convex conic program. Approximations of the proposed model are suggested, which leads to a significant reduction of the number of the constraints. For practical large-scale test systems, a distributionally robust optimal power flow model with Wasserstein-distance-based distributional uncertainty set and its convex reformulation are also provided. Simulation results on the 5-bus, the IEEE 118-bus and the Polish 2736-bus test systems validate the effectiveness of the proposed models.

distributionally robust optimization↗
DOE OSTI2018

A Model Predictive Control Based Generator Start-Up Optimization Strategy for Restoration With Microgrids as Black-Start Resources

Microgrids (MGs) can operate in an islanded mode and serve as black-start resources for power system restoration (PSR). Here, a model predictive control (MPC) based generator start-up optimization strategy for PSR is proposed utilizing MGs as black-start resources. First, the generator start-up sequence (GSUS) optimization is formulated as a mixed integer linear programming. Then, the uncertainties of MG black-start resources (MBSRs) are modeled by discretizing the probability distribution of the forecast errors, and representative scenarios for MBSRs extracted by formulating the probability mass transportation problem. Third, the generator start-up optimization strategy considering MBSRs is proposed utilizing the MPC technique, in which the optimization objective is to maximize the energy capability of the power systems and minimize the load curtailment of the MGs in each looking-ahead interval. Simulations on the IEEE 118 bus system with MGs and Zhejiang provincial power system in China verify that the introduced strategy for PSR can successfully restore the power system and effectively determine the optimal GSUS.

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DOE OSTI2018

Optimizing Service Restoration in Distribution Systems With Uncertain Repair Time and Demand

This paper proposes a novel method to co-optimize the distribution system operation and repair crew routing for outage restoration after extreme weather events. A two-stage stochastic mixed integer linear program is developed. The first stage is to dispatch the repair crews to the damaged components. The second stage is distribution system restoration using distributed generators, and reconfiguration. We consider demand uncertainty in terms of a truncated normal forecast error distribution, and model the uncertainty of the repair time using a lognormal distribution. A new decomposition approach, combined with the progressive hedging algorithm, is developed for solving large-scale outage management problems in an effective and timely manner. Furthermore, the proposed method is validated on modified IEEE 34- and 8500-bus distribution test systems.

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DOE OSTI2019

Operation of a High Renewable Penetrated Power System With CSP Plants: A Look-Ahead Stochastic Unit Commitment Model

The integration of variable renewable energy (VRE) generation, i.e., wind power and solar photovoltaic, brings significant uncertainty for the power system operation. Different with VRE techniques, concentrating solar power (CSP) is an appealing renewable generation technology due to its dispatch ability through the use of thermal energy storage and is thus expected to play a significant role in high renewable energy penetrated power systems. In this paper, we propose a look-ahead stochastic unit commitment model to operate power systems with CSP under high renewable energy penetration. It has a three-stage structure. The first stage optimizes the operational decisions in a day-ahead framework based on forecasts; the second stage minimizes the expected generation cost for possible realizations in the real time; and the third stage accounts for look-ahead operation in future operating days. This paper has a dual purpose: first, exploring how CSP plants operate in high renewable penetrated power systems; and second, analyzing the benefits of CSP in accommodating VRE generation. A case study on a modified IEEE RTS-79 system with actual solar and wind power data is provided to validate the proposed method.

14 SOLAR ENERGY↗
DOE OSTI2018

Placement and Sizing of Inverter-Based Renewable Systems in Multi-Phase Distribution Networks

This study develops a tractable formulation for optimal placement and sizing of inverter-based renewable systems in multi-phase distribution networks. The goal of the formulation is to minimize the cost of inverter installation, average power import, and average distributed generation curtailment. Threephase and single-phase inverter models are presented that preserve the underlying mappings between renewable uncertainty to power injection. The uncertainty of distributed generators (DGs) and loads are characterized by a finite set of scenarios. Linear multi-phase power flow approximations are used in conjunction with scenario reduction techniques to arrive at a tractable twostage stochastic formulation for optimal DG placement and sizing. First-stage decisions are locations for DG deployment and capacity sizes, and second-stage decisions include DG real power curtailment, reactive power support, as well as feeder voltage profile. The resulting formulation is a mixed-integer second-order cone program and can be solved efficiently either by existing optimization solvers or by relaxing the binary variables to the [0,1] interval. Simulation studies on standard multi-phase IEEE test feeders promise that optimal stochastic planning of DGs reduces costs during validation, compared to a scheme where uncertainty is only represented by its average value.

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DOE OSTI2018

Voltage Stability Analysis of Power Systems With Induction Motors Based on Holomorphic Embedding

Load characteristics have substantial influence on the voltage stability of power systems. The self-restorative characteristic and stalling of induction motor loads can deteriorate the voltage stability, so it is necessary to develop accurate and efficient dynamic analysis methods for voltage stability analysis of systems with induction motor loads. In this paper, a set of methods based on holomorphic embedding is proposed, which is able to solve steady states and dynamics of a power system with induction motors. The paper is the first work that applies holomorphic embedding to dynamic problems of power systems. Here, the test cases on the IEEE 14-bus system, the NPCC 140-bus system, and the Polish 2383-bus system verify both accuracy and efficiency of the proposed methods.

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DOE OSTI2019

Introducing Uncertainty Components in Locational Marginal Prices for Pricing Wind Power and Load Uncertainties

With substantially increasing penetration levels of wind power, electric power system flexibility is needed to address the variability and uncertainty of wind power output. Thus, it has become an urgent issue to obtain an optimal trade-off between economics and reliability, and to price system uncertainties. This paper proposes a new electricity market-clearing mechanism based on locational marginal prices (LMPs) for pricing uncertain generation and load. The uncertainty contained locational marginal price (U-LMP) is derived from a distributionally robust chance-constrained optimal power flow (DRCC-OPF) model in which only the first-order and second-order moments of the uncertain sources' probability distribution are needed. Compared with traditional LMPs, the proposed U-LMP formulation includes two new uncertainty components: transmission line overload uncertainty price and generation violation uncertainty price. These LMP uncertainty components are the price signals reflecting the system costs as a result of wind generation and demand uncertainty at different locations. Finally, using parametric case studies, the relationship among uncertainty levels, system generation cost, and LMP uncertainty components are established. Case studies performed on the PJM 5-bus and IEEE 118-bus systems verify the proposed U-LMP method.

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DOE OSTI2018

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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DOE OSTI2019

Bi-Level Volt-VAR Optimization to Coordinate Smart Inverters with Voltage Control Devices

Conservation voltage reduction (CVR) uses voltage control to reduce customer power demand and help improve the operational efficiency of the electric power distribution system. With the advent of advanced distribution management systems (ADMS), the underlying data and control-rich platform can be utilized to enable a centralized Volt-VAR optimization (VVO) scheme that includes smart inverter controls along with legacy voltage control devices such as voltage regulators and capacitor banks to ensure a maximum CVR benefit. The objective of this paper to present a VVO approach that controls system’s legacy voltage control devices and coordinates their operation with smart inverter control. An optimal power flow (OPF) formulation is proposed by developing linear and nonlinear power flow approximations for a three-phase unbalanced electric power distribution system. A bi-level VVO approach is proposed where, Level-1 optimizes the control of legacy devices and smart inverters using a linear approximate three-phase power flow. In Level-2, the control parameters for smart inverters are adjusted to obtain an optimal and feasible solution by solving the approximate nonlinear OPF model. Level-1 is modeled as a Mixed Integer Linear Program (MILP) while Level-2 as a Quadratically Constrained Quadratic Program (QCQP). The proposed approach is validated using IEEE test cases and the results demonstrate the applicability of the framework in achieving the CVR objective.

Jha, Rahul Ranjan↗
DOE OSTI2019

Topology Estimation using Graphical Models in Multi-Phase Power Distribution Grids

Power distribution grids are structurally operated radially, such that energized lines form a collection of trees with a substation at the root of each tree. The operational topology may change from time to time, however tracking these changes, even though important for the distribution grid operation and control, is hindered by limited real-time monitoring. This work develops a learning framework to reconstruct the radial operational structure of the distribution grid from synchronized voltage measurements. To detect operational lines our learning algorithm uses conditional independence tests for continuous random variables that is applicable to a wide class of probability distributions and Gaussian injections in particular. Furthermore, our algorithm applies to the practical case of unbalanced three-phase power flow. The performance is validated on AC power flow simulations over three phase IEEE distribution grid test cases.

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DOE OSTI2019

On Information Transfer-Based Characterization of Power System Stability

In this study, we present a novel approach to identify the generators and states responsible for the small-signal stability of power networks. To this end, the newly developed notion of information transfer between the states of a dynamical system is used. In particular, using the concept of information transfer, which characterizes influence between the various states of a dynamical system, we identify the generators and states which are responsible for causing instability of the power network. While characterizing influence from state to state, information transfer can also describe influence from state to modes thereby generalizing the well-known notion of participation factor while at the same time overcoming some of the limitations of the participation factor. The developed framework is applied to reproduce known results for the three bus system, identifying the various causes of instabilities, and is extended to IEEE 39 bus system.

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DOE OSTI2019

PMU-Based Monitoring and Mitigation of Delayed Voltage Recovery Using Admittances

This project analyzes the delayed voltage recovery phenomenon by simplifying the Western Electricity Coordinating Council (WECC) composite load model using the load admittance and the thermal relay dynamics. From this analysis, a closed form expression approximating the recovery time is derived and the key load parameters impacting the behavior of voltage recovery are identified. A monitoring scheme based on the measured load admittance is then proposed to detect the onset of stalling, even in the presence of voltage oscillations, and estimate the duration of the delayed voltage recovery. A mitigation scheme utilizing smart thermostats and offline learning is also derived to ensure that the voltage recovers to the pre-contingency voltage within a specified time. Both the monitoring and mitigation schemes only need local measurements at a substation making them promising for online applications. Results for the monitoring and mitigation schemes are described in detail for the IEEE 162 bus system validating the various assumptions used for the analysis and establishing the connection between the delayed voltage recovery phenomenon and load admittance.

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DOE OSTI2019

The Dominant Influencer of Voltage Fluctuation (DIVF) for Power Distribution System

Variability in power generation at multiple consumer owned renewable energy sources can cause random voltage fluctuations, which may result in voltage violations at multiple nodes in a power distribution system. Traditional methods of voltage control are ineffective to address fast voltage variations. New dynamic methods of voltage control using end user devices can significantly benefit from the knowledge of the dominant influencer of voltage fluctuation (DIVF). This paper introduces information theoretic metrics to identify DIVF for every node in the power distribution system. A node can be DIVF due to its location in the distribution system and its capacity to generate and change its power. Use of traditional power flow algorithms to identify the DIVF is computationally complex which limits their use in real-time applications. In this work, information theoretic indicators of the DIVF are computed analytically in a computationally efficient manner, and their effectiveness to identify the DIVF is tested using the IEEE 69 node test system. From simulations, it is illustrated that differential entropy, Kullback-Leibler distance and Frechet distance are effective indicators of the DIVF and can successfully identify the most influential nodes providing the foundation for intelligent voltage control.

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DOE OSTI2019

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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