Kyri Baker

Optimal integration of intermittent energy sources using distributed multi-step optimization

The integration of renewable energy sources such as wind and solar into the electric power grid is a coveted yet challenging goal. The difficulties arise from the intermittency of the sources, the required increase in transmission capacity, and the lack of coordination between control entities. In this paper, a method is developed and implemented for the optimal coordination between storage and intermittent resources in multiple control areas. The problem is formulated as a decomposed multi-step optimization problem using the Optimality Condition Decomposition method. This allows reducing the computational effort by dividing the overall optimization problem into subproblems. Simulation results show convergence to the centralized solution and provide an indication of the benefits of coordinating control areas.

Energy Storage Sizing Taking Into Account Forecast Uncertainties and Receding Horizon Operation

Energy storage systems (ESS) have the potential to be very beneficial for applications such as reducing the ramping of generators, peak shaving, and balancing not only the variability introduced by renewable energy sources, but also the uncertainty introduced by errors in their forecasts. Optimal usage of storage may result in reduced generation costs and an increased use of renewable energy. However, optimally sizing these devices is a challenging problem. This paper aims to provide the tools to optimally size an ESS under the assumption that it will be operated under a model predictive control scheme and that the forecast of the renewable energy resources include prediction errors. A two-stage stochastic model predictive control is formulated and solved, where the optimal usage of the storage is simultaneously determined along with the optimal generation outputs and size of the storage. Wind forecast errors are taken into account in the optimization problem via probabilistic constraints for which an analytical form is derived. This allows for the stochastic optimization problem to be solved directly, without using sampling-based approaches, and sizing the storage to account not only for a wide range of potential scenarios, but also for a wide range of potential forecast errors. In the proposed formulation, we account for the fact that errors in the forecast affect how the device is operated later in the horizon and that a receding horizon scheme is used in operation to optimally use the available storage.

Chance-Constrained AC Optimal Power Flow for Distribution Systems With Renewables

This paper focuses on distribution systems featuring renewable energy sources (RESs) and energy storage systems, and presents an AC optimal power flow (OPF) approach to optimize system-level performance objectives while coping with uncertainty in both RES generation and loads. The proposed method hinges on a chance-constrained AC OPF formulation, where probabilistic constraints are utilized to enforce voltage regulation with prescribed probability. A computationally more affordable convex reformulation is developed by resorting to suitable linear approximations of the AC power-flow equations as well as convex approximations of the chance constraints. The approximate chance constraints provide conservative bounds that hold for arbitrary distributions of the forecasting errors. An adaptive strategy is then obtained by embedding the proposed AC OPF task into a model predictive control framework. Finally, a distributed solver is developed to strategically distribute the solution of the optimization problems across utility and customers.

Optimal Storage Sizing using Two-Stage Stochastic Optimization for Intra-Hourly Dispatch

With the increasing penetration of renewable energy sources into the electric power grid, a heightened amount of attention is being given to the topic of energy storage, a popular solution to account for the variability of these sources. Energy storage systems (ESS) can also be beneficial for load-levelling and peak-shaving, as well as reducing the ramping of generators. However, the optimal energy and power ratings for these devices is not immediately obvious. In this paper, the energy capacity and power rating of the ESS is optimized using two-stage stochastic optimization. In order to capture the wind and load variations in the different days throughout the year, it is advantageous to use a large number of scenarios. Optimizing generator outputs and storage decisions at the intra-hour level with a high number of scenarios will result in a very large optimization problem, and thus scenario reduction is employed. A relationship between the variance of the system price for each scenario and the optimal storage size determined for that scenario is shown. The correlation between these parameters allows for a natural clustering of similar scenarios. Scenario reduction is performed by exploiting this relationship in conjunction with centroid-linkage clustering, and stochastic optimization with the reduced number of scenarios is used to determine the optimal ESS size.

Experiences integrating transmission and distribution simulations for DERs with the Integrated Grid Modeling System (IGMS)

This paper discusses the development of, approaches for, experiences with, and some results from a large-scale, high-performance-computer-based (HPC-based) co-simulation of electric power transmission and distribution systems using the Integrated Grid Modeling System (IGMS). IGMS was developed at the National Renewable Energy Laboratory (NREL) as a novel Independent System Operator (ISO)-to-appliance scale electric power system modeling platform that combines off-the-shelf tools to simultaneously model 100s to 1000s of distribution systems in co-simulation with detailed ISO markets, transmission power flows, and AGC-level reserve deployment. Lessons learned from the co-simulation architecture development are shared, along with a case study that explores the reactive power impacts of PV inverter voltage support on the bulk power system.

Modeling stationary lithium-ion batteries for optimization and predictive control

Accurately modeling stationary battery storage behavior is crucial to pursuing cost-effective distributed energy resource opportunities. In this paper, a lithium-ion battery model was derived for building-integrated battery use cases. The proposed battery model aims to balance speed and accuracy when modeling battery behavior for real-time predictive control and optimization. To achieve these goals, a mixed modeling approach incorporates regression fits to experimental data and an equivalent circuit to model battery behavior. The proposed battery model is validated through comparison to manufacturer data. Additionally, a dynamic test case demonstrates the effects of using regression models to represent cycling losses and capacity fading. A proof-of-concept optimization test case with time-of-use pricing is performed to demonstrate how the battery model could be included in an optimization framework.

Final Technical Report: Integrated Distribution-Transmission Analysis for Very High Penetration Solar PV

Transmission and distribution simulations have historically been conducted separately, echoing their division in grid operations and planning while avoiding inherent computational challenges. Today, however, rapid growth in distributed energy resources (DERs)--including distributed generation from solar photovoltaics (DGPV)--requires understanding the unprecedented interactions between distribution and transmission. To capture these interactions, especially for high-penetration DGPV scenarios, this research project developed a first-of-its-kind, high performance computer (HPC) based, integrated transmission-distribution tool, the Integrated Grid Modeling System (IGMS). The tool was then used in initial explorations of system-wide operational interactions of high-penetration DGPV.

Inclusion of inter-temporal constraints into a distributed Newton-Raphson method

Newton-Raphson based methods are widely used for solving Optimal Power Flow (OPF) problems. Convergence can be sensitive to the starting point of the algorithm, the step size, and the condition number of the Jacobian. The inclusion of inter-temporal constraints, i.e., constraints that link successive time steps in the optimization, can in certain cases cause the Jacobian to become singular and Newton-Raphson to diverge. These cases occur when the binding inter-temporal constraints do not fulfill the Linear Independence Constraint Qualification (LICQ). In this paper, we discuss the conditions under which this happens, and analyze when singularities occur in a particular storage device model test case.

Incentive-based voltage regulation in distribution networks

This paper considers distribution networks featuring distributed energy resources, and designs an incentive-based algorithm that allows the network operator and the end-customers to pursue given operational and economic objectives, while concurrently ensuring that voltages are within prescribed limits. This social-welfare maximization problem is challenging due to the non-convexity. We first reformulate the problem as a convex task together with an incentive signal design strategy, and then propose a distributed algorithm for solving the reformulated problem. By doing so, we are able to achieve the solution of the original non-convex problem without exposure of any private information between end-customers and network operator. Stability of the proposed schemes is analytically established and numerically corroborated.

Distribution-agnostic stochastic optimal power flow for distribution grids

This paper outlines a data-driven, distributionally robust approach to solve chance-constrained AC optimal power flow problems in distribution networks. Uncertain forecasts for loads and power generated by photovoltaic (PV) systems are considered, with the goal of minimizing PV curtailment while meeting power flow and voltage regulation constraints. A data-driven approach is utilized to develop a distributionally robust conservative convex approximation of the chance-constraints; particularly, the mean and covariance matrix of the forecast errors are updated online, and leveraged to enforce voltage regulation with predetermined probability via Chebyshev-based bounds. By combining an accurate linear approximation of the AC power flow equations with the distributionally robust chance constraint reformulation, the resulting optimization problem becomes convex and computationally tractable.