• Energy Research

Unit Commitment and Economic Dispatch (UCED) with combined cycle (CC) units and AC power flow is an important problem to be solved by ISOs. The problem is difficult because of complicated transitions in CC units and highly non-linear AC power flows. Currently, to solve the problem, transitions among CC states are simplified and AC power flow is approximated with DC power flow. However, the resulting solution may not be consistent with actual operations of power systems. In this paper, a more operational approach of modeling UCED with CC units and AC power flow is developed. Under the frequently used assumption of low network resistance, AC power flow is represented as a monotonic function. Then, the original problem is solved by exploiting the monotonicity through the novel dynamic linearization technique and separability after relaxing coupling system-wide demand constraints. The complexity of resulting subproblems is drastically reduced and linearity is efficiently exploited by using branch-and-cut. Subproblem solutions are efficiently coordinated by our recently developed surrogate Lagrangian relaxation and convergence is guaranteed. Based on a 30-bus system, numerical results demonstrate the new approach is more computationally efficient as compared to Benders decomposition.

Micro-grids’ operations offer local reliability; in the event of faults or low voltage/frequency events on the utility side, micro-grids can disconnect from the main grid and operate autonomously while providing the continued supply of power to local customers. With the ever-increasing penetration of renewable generation, however, the operations of micro-grids become increasingly complicated because of the associated fluctuations of voltages. As a result, transformer taps are adjusted frequently, thereby leading to the fast degradation of expensive tap-changer transformers. In the islanding mode, the difficulties also come from the drop of voltage and frequency upon disconnecting from the main grid. To appropriately model the above, the nonlinear AC power flow constraints are necessary. Computationally, the discrete nature of tap-changer operations and the stochasticity caused by renewables add two layers of difficulty on top of a complicated AC-OPF problem. To resolve the above computational difficulties, the main principles of the recently-developed "l1-proximal" Surrogate Lagrangian Relaxation are extended. Testing results based on 9-bus system demonstrate the efficiency of the method to obtain the exact feasible solutions for micro-grid operations thereby avoiding approximations inherent to existing methods, while demonstrating that through the optimization, 1. the number of tap changes is drastically reduced, and 2. the method is capable of handling networks with meshed topologies.

Unit Commitment is an important problem faced by independent system operators and vertically integrated utilities. The problem is to minimize the total commitment and dispatch cost by committing appropriate units while satisfying demand and other constraints. It is usually formulated as a Mixed Integer Linear Programming (MILP) problem, and is NP hard. To obtain high quality solutions within specified amounts of time, most research focuses on solution methodology, and very limited results have been reported on problem formulation. However, it is critically important since if constraints directly delineate the convex hull of an MILP problem, then the problem can be directly solved by linear programming. Tightening formulation, however, is difficult with no systematic approach to be found in the literature. In this paper, a systematic approach based on a novel integration of "constraint-and-vertex conversion" and "vertex projection" processes is developed. The focus is on single units assuming system-wide constraints have been relaxed. Innovative aspects also include the elimination of dependence on initial conditions, and the handling of units with different sets of parameters. Numerical simulation demonstrates great potential for tightening complicated MILP problems.

Proliferation of smart grid technologies has enhanced observability and controllability of distribution systems. If coordinated with the transmission system, resources of both systems can be used more efficiently. This paper proposes a model to operate transmission and distribution systems in a coordinated manner. The proposed model is solved using a Surrogate Lagrangian Relaxation (SLR) approach. The computational performance of this approach is compared against existing methods (e.g. subgradient method). Finally, the usefulness of the proposed model and solution approach is demonstrated via numerical experiments on the illustrative example and IEEE benchmarks.

Most ISOs in the US minimize the total bid cost and then settle the market based on locational marginal prices. Minimizing the total bid cost, however, may not lead to maximizing the social welfare. Studies indicate that for energy only, payment cost minimization (PCM) leads to reduced payments for a given set of bids, and the “hockey-stick” bidding a less likely to occur. Since co-optimization of energy with ancillary services leads to a more efficient allocation, it is important to solve PCM co-optimization while considering transmission capacity constraints for a comparison with other auction mechanisms. In this paper, PCM is formulated using price definition system-wide constraints. This problem formulation introduces difficulties such as nonlinearity, non-separability and complexity of convex hull. To overcome these difficulties, the nonlinear terms are linearized thereby allowing to be solved by using branch-and-cut. At the same time, the linearization is performed in a way that the “surrogate optimality condition” is satisfied thereby allowing the problem to be solved efficiently.

Energy prices are usually determined by the marginal costs obtained by solving economic dispatch problems without considering commitment costs. Hence, generating units are compensated through uplift payments. However, uplift payments may undermine market transparency as they are not publicly disclosed. Alternatively, energy prices can be obtained from the unit commitment problem which considers commitment costs. But, due to non-convexity, prices may not monotonically increase with demand. To resolve this issue, convex hull pricing has been introduced. It is defined as the slope of the convex envelope of the total cost function over the convex hull of a unit commitment (UC) problem. Although several approaches have been developed, a relevant survey has not been found to aid the understanding of convex hull pricing from the current limited literature. This paper provides a systematic survey of convex hull pricing. It reviews, compares, and links various existing approaches, focusing on the modeling and computation of convex hull prices. Furthermore, this paper explores potential areas of improvement and future challenges due to the ongoing efforts for power system decarbonization.

A distributed and asynchronous active fault management (DA-AFM) method is developed to manage networked microgrids’ (NMs) performance under balanced or unbalanced grid faults. The DA-AFM aims to (1) enable NMs’ fast fault ride-through capabilities, (2) limit the total fault contributions by coordinating heterogeneous microgrids in the NM system, and (3) deploy software-defined networks (SDN) to ensure highly resilient AFM. The problem is formulated in an optimization form that can incorporate various fault management objectives and constraints in a programmable and flexible fashion. The scalability and resiliency of the DA-AFM system are guaranteed by adopting an SDN-enabled distributed and asynchronous surrogate Lagrangian relaxation (DA-SLR) algorithm, which avoids single point of failure, preserves privacy, and eliminates the idle waiting of other subproblems. Case studies are performed on a six-microgrid NM system to validate the effectiveness and efficacy of DA-AFM. Testing results show that DA-AFM has excellent convergence performance, supports plug-and-play, is resilient to communication delay and failures, meets real-time requirements and is scalable.