Network-constrained Economic Dispatch Research Articles

Fast Tuning-Free Distributed Algorithm for Solving the Network-Constrained Economic Dispatch

With the increasing penetration of distributed energy resources (DERs) and their participation in the electricity market, it becomes more desirable to apply distributed algorithms for resource allocation in order to address the resulting computational and communicational challenges. Most of the existing distributed algorithms for solving the network-constrained economic dispatch (NCED) problem require the tuning of certain auxiliary parameters. As a result, the robustness of these algorithms against the varieties in DERs is greatly undermined. In this paper, a new distributed algorithm, optimality condition consensus (OCC), is proposed to solve the NCED problem by using distributed power flow (DPF) and ratio consensus as fundamental tools. It inherits the advantages of existing distributed algorithms for the NCED problem but removes the need for parameter tuning to improve performance in practice. The effectiveness of the proposed distributed algorithm in terms of efficiency, scalability, and robustness is demonstrated through detailed case studies.

Financial arbitrage in electricity markets via virtual bidding

The concept of virtual bidding serves as a pure financial tool in electricity markets, aiming at enhancing their performance. Although virtual bidding helps reduce price gaps between different trading floors, there is evidence suggesting that this does not necessarily lead to improved welfare for market consumers. To gain a deeper understanding of virtual bidding and its impact on electricity market prices, this work delves into the strategic behavior of a financial player engaged in an electricity pool-based market. To this end, a bi-level model is formulated. The upper level optimizes the expected revenues of the virtual bidder while the lower-level represents the clearing of the market under network-constrained economic dispatch through a two-stage stochastic programming. The proposed model derives optimal arbitrage strategies in both scenarios of explicit and implicit virtual bidding. It also assesses the performance of virtual bidding under stochastic generation and transmission contingencies, including considerations of up-to-congestion virtual bidding.

An Auction-Based Local Market Clearing for Energy Management in a Virtual Power Plant

Virtual power plant (VPP) concept creates additional benefits for different stakeholders, such as system operators, distributed energy resources’ owners, and aggregators. This article presents an auction-based energy management solution from VPP aggregator point of view. To this end, a network-constrained economic dispatch has been developed taking into account a comprehensive resource portfolio, including the conventional and renewable distributed generations, energy storage units, and flexible loads. The VPP aggregator aims at minimizing its expected costs through optimal dispatch of its own resources as well as purchasing and selling electricity from/to upstream network. To this end, a stochastic programming approach has been employed to consider the generation uncertainty of renewable energy resources as well as day-ahead energy market prices using a set of plausible scenarios. The payments to the prosumers are according to an auction-based pricing method that could be an efficient strategy for the VPP aggregator in order to guarantee fairness among consumers and producers within the VPP. In the auction-based pricing scheme, the electricity price at each local node can be calculated according to the demand and generation in each time slot. The proposed framework is a mixed-integer linear programming problem and solved by the CPLEX solver in the GAMS software. It is noteworthy that the effectiveness of the model has been verified, considering several numerical studies.

Power economic dispatch against extreme weather conditions: The price of resilience

With climate change, we have been witnessing more frequent extreme weather events causing increasingly common large-scale power outages. It is essential and urgent to improve power system resilience, which also substantially impacts the resilience of dependent infrastructures, such as water and health systems. This work investigates the enhancement of power grid resilience using proactive network-constrained economic dispatch (NCED) strategies. An extreme weather event is modeled as an attacker interdicting a selected set of transmission lines to cause overloading of remaining lines, which potentially leads to cascading failures. We define a set of resilience metrics, with the first one being a weighted number of overloaded lines immediately after the attack to capture the potential cascading chain effect, the second one predicting the worst-case value of the first metric to provide a forward-looking evaluation, and the last one assessing whether each line can be overloaded in the worst case to supply more granular awareness. We also propose a defender–attacker–defender NCED model solved by a column-and-constraint generation algorithm to optimize the defined metrics. The model can generate strategies that (1) enhances resilience without additional NCED cost; (2) further enhances resilience with a budgeted extra NCED cost; and (3) achieves a moving target defense scheme shifting the grid’s vulnerable part(s). The associated price of resilience is specifically evaluated. Results on standard test systems demonstrate the proposed methods’ effectiveness. Overall, our methods and results provide insights on the establishment of social, economic and environmental resilience by contributing to the resolution of resilience-related power and energy issues.

An Endogenous Approach to Quantifying the Wind Power Reserve

Due to inherent uncertainty and volatility, large-scale wind power integration requires additional reserves for power balancing. However, it remains an open question as to how to quantify the required reserves corresponding to different uncertainties and penetration scales of wind power. This paper addresses this problem with an improved endogenous reserve determination method. Multiple uncertainties, including wind power outputs, load fluctuations, and generator failures, especially power flow uncertainties caused by wind power fluctuations and generator faults, are comprehensively integrated into a security and network-constrained economic dispatch (S&NCED) model to jointly schedule the generation and reserve. Affinely adjustable robust optimization (AARO) is adopted to address wind power and load uncertainties. Then the model is transformed into a two-stage (normal state optimization and fault verification) S&NCED model for iterative solving with the aid of Benders decomposition, and auxiliary constraints are designed to accelerate the convergence. Results of 6-bus and IEEE118-bus systems show that the proposed method can effectively provide a more economical and robust generation-reserve dispatch scheme and can clearly specify the reserve capacity required by wind power.

Non-Ideal Linear Operation Model for Li-Ion Batteries

Currently, the characterization of electric energy storage units used for power system operation and planning models relies on two major assumptions: charge and discharge efficiencies, and power limits are constant and independent of the electric energy storage state of charge. This approach can misestimate the available storage flexibility. This work proposes a detailed model for the characterization of steady-state operation of Li-ion batteries in optimization problems. The model characterizes the battery performance, including non-linear charge and discharge power limits and efficiencies, as a function of the state of charge and requested power. We then derive a linear reformulation of the model without introducing binary variables, which achieves high computational efficiency, while providing high approximation accuracy. The proposed model characterizes more accurately the performance and technical operational limits associated with Li-ion batteries than those present in classical ideal models. The developed battery model has been compared with three modelling approaches: the complete non-convex formulation; an ideal model typically used in the power system community; and a mixed integer linear reformulation approach. The models have been tested on a network-constrained economic dispatch for a 24-bus system. Based on the simulations, we observed approximately 12% of energy mismatches between schedules that use an ideal model and those that use the model proposed in this study.

Online Energy Price Matrix Factorization for Power Grid Topology Tracking

Grid security and open markets are two major smart grid goals. Transparency of market data facilitates a competitive and efficient energy environment, yet it may also reveal critical physical system information. Recovering the grid topology based solely on publicly available market data is explored here. Real-time energy prices are calculated as the Lagrange multipliers of network-constrained economic dispatch; that is, via a linear program (LP) typically solved every 5 minutes. Granted the grid Laplacian is a parameter of this LP, one could infer such a topology-revealing matrix upon observing successive LP dual outcomes. The matrix of spatio-temporal prices is first shown to factor as the product of the inverse Laplacian times a sparse matrix. Leveraging results from sparse matrix decompositions, topology recovery schemes with complementary strengths are subsequently formulated. Solvers scalable to high-dimensional and streaming market data are devised. Numerical validation using real load data on the IEEE 30-bus grid provide useful input for current and future market designs.

Using learning automata for multi-objective generation dispatch considering cost, voltage stability and power losses

The economical and secure operation of power systems has significant importance. Due to technical limitations, the best economical operation point is not always the desired operating point for system stability or power losses. In this study, first, the most economical operating point is obtained by solving the non-linear, network-constrained economic dispatch problem using a genetic algorithm. Then, the system voltage stability is analyzed to compare the different possible operating points using V-Q sensitivity analysis. The power losses, obtained for various operating points, are considered the third objective function. Finally, these 3 aspects of cost, voltage stability, and power losses are combined, using the learning automata technique, to achieve a multi-objective optimization solution. The methodology was implemented in MATLAB 7.8 and applied to the IEEE 30-bus test system. The same technique of learning automata may be applied in the future to similar problems that need multi-objective consideration.

Network-constrained economic dispatch using real-coded genetic algorithm

A genetic algorithm (GA) solution to the network-constrained economic dispatch problem is presented. A real-coded GA has been implemented to minimize the dispatch cost while satisfying generating unit and branch power flow limits. A binary-coded GA was also developed to provide a means of comparison. GA solutions do not impose any convexity restrictions on the dispatch problem. The proposed method was applied on the electrical grid of Crete Island with satisfactory results. Various tests with both convex and nonconvex unit cost functions demonstrate that the proposed GA locates the optimum solution, while it is more efficient than the binary-coded GA.

Network-Constrained Economic Dispatch Using Real-Coded Genetic Algorithm

A genetic algorithm (GA) solution to the network-constrained economic dispatch problem is presented. A real-coded GA has been implemented to minimize the dispatch cost while satisfying generating unit and branch power flow limits. A binary-coded GA was also developed to provide a means of comparison. GA solutions do not impose any convexity restrictions on the dispatch problem. The proposed method was applied on the electrical grid of Crete Island with satisfactory results. Various tests with both convex and nonconvex unit cost functions demonstrate that the proposed GA locates the optimum solution, while it is more efficient than the binary-coded GA.