Integrating renewable energy sources into a power system imposes uncertainty in the power generation, rendering traditional power flow methods ineffective. By calculating uncertain power flow, we can obtain more realistic and reliable estimates of the system state. Interval methods have been recognized as a powerful tool for analyzing uncertain power systems and increasing their overall reliability. In this paper, an approach is proposed to formulate the uncertain power flow with interval uncertainties, called Interval Power Flow (IPF), as a convex feasibility problem. To attain this goal, the IPF problem is written in the form of Bilinear Matrix Inequalities. Then, the polytopic model of IPF is derived and it is proved that to guarantee the validity of IPF for the whole range of renewable energy changes, it is enough to solve the matrix inequalities in the corner points of the polytopic uncertain space. Then, the Inside-Ellipsoids Outside-Sphere model is applied to the IPF model resulting in a convex feasibility problem, plus a non-convex quadratic constraint which is later relaxed to achieve an LMI problem. The final problem is solved by one of the off-the-shelf solvers and a robust operating point for the IPF problem is obtained. The approach is tested for various case studies and the results prove its efficacy compared to the existing method.

This paper proposes a new approach for solving Quadratically Constrained Feasibility Problems (QCFPs). We introduce an isomorphic mapping (one-to-one and onto correspondence), which equivalently converts the QCFP to an optimization problem called the Inside-Ellipsoids Outside-Sphere Problem (IEOSP). This mapping preserves the convexity of convex constraints, but it converts all non-convex constraints to convex ones. The QCFP is a feasibility problem with non-convex constraints, while the IEOSP is an optimization problem with a convex feasible region and a non-convex objective function. It is shown that the global optimal solution of IEOSP is a feasible solution of the QCFP. Comparing the structures of QCFP and the proposed IEOSP, the second model only has one extra variable compared to the original QCFP because it employs one slack variable for the mapping. Thus, the problem dimension approximately remains unchanged. Due to the convexity of all constraints in IEOSP, it has a well-defined feasible region. Therefore, it can be solved much easier than the original QCFP. This paper proposes a solution algorithm for IEOSP that iteratively solves a convex optimization problem. The algorithm is mathematically shown to reach either a feasible solution of the QCFP or a local solution of the IEOSP. To illustrate our theoretical developments, a comprehensive numerical experiment is performed, and 500 different QCFPs are studied. All these numerical experiments confirm the promising performance and applicability of our theoretical developments in the current paper.

Investment in liberalized wholesale electricity markets is typically not driven by spot and forward wholesale energy price signals alone. Instead, in most wholesale electricity markets there is a separate mechanism to procure, fund or subsidize investment in generation or demand response capacity. These mechanisms are known as capacity markets and are often highly controversial. There remains substantial debate over whether these mechanisms are necessary and, if so, how they should be designed. This paper provides a theoretical analysis of the capacity market debate. We observe that an intuitive understanding of the effects of capacity mechanisms may be misleading. While a capacity mechanism may offset the effects of a price cap, if the price cap is funded through a levy on consumption the combined effect of the tax and subsidy is to nullify the price cap. We explore possible reasons for under-investment concerns in wholesale electricity markets, focusing on the potential for a lack of liquidity in the hedge market arising from the presence of uninsurable risks. We identify three groups of uninsurable risks and propose policies to address them.

This paper develops a new decomposition algorithm for solving Electricity Market Pricing (EMP) problem, taking into account both revenue-adequacy and Fast Frequency Reserve (FFR) constraints. Due to revenue-adequacy constraint, a bilevel model of the EMP problem is introduced (BL-EMP). The upper level of the BL-EMP model represents the non-convex unit commitment (UC) decisions as well as the revenue-adequacy constraints of the market participants (generators, loads, and battery-storage owner). The lower level is a convex economic dispatch model with FFR constraint. To tackle the computational complexity of the considered BL-EMP model, this paper develops, tests, and proposes a Strengthened Primal-Dual Decomposition (SPDD) algorithm, which takes benefits from both Benders-like and Lagrange Dual-like algorithms. The new SPDD algorithm has a series of interesting computational properties, which are theoretically discussed in the paper. The SPDD algorithm has better computational performance than standard Benders decomposition algorithm and it also does not need tuning of the Big-M (or disjunctive) parameters for solving the proposed BL-EMP problem. Results from the modified IEEE 24-bus, the IEEE 118-bus, and the IEEE 300-bus system show the superiority of proposed SPDD algorithm over the classic Benders algorithm.

The expansion of variable generation has driven a transition toward a 100% non-fossil power system. New system needs are challenging system stability and suggesting the need for a redesign of the ancillary service (AS) markets. This paper presents a comprehensive and broad review for industrial practitioners and academic researchers regarding the challenges and potential solutions to accommodate high shares of variable renewable energy (VRE) generation levels. We detail the main drivers enabling the energy transition and facilitating the provision of ASs. A systematic review of the United States and European AS markets is conducted. We clearly organize the main ASs in a standard taxonomy, identifying current practices and initiatives to support the increasing VRE share. Furthermore, we envision the future of modern AS markets, proposing potential solutions for some remaining fundamental technical and market design challenges.

The Australian National Electricity Market (NEM) and the Texas wholesale electricity market (ERCOT) are two of the most prominent examples of energy-only wholesale electricity markets in the world. In early 2021 and mid 2022 these markets suffered from unprecedented crises, prompting some commentators to question the energy-only market design. Both markets are now considering implementing a form of capacity mechanism. Are these crises evidence of a fundamental flaw in the energy-only market design, or something else? We argue that, although the crises were very different in form, both crises arose in part from the effect of price caps in the wholesale market. We set out a model of the optimal mix of generation technologies in a framework in which generators can invest to protect against extreme weather events. We show that a price cap (below VoLL) reduces incentives for investment in hardening generation. Rather than further lowering the price caps – as was done in Texas – we propose a range of reforms to strengthen and enhance the confidence in the wholesale market.

Virtual power plant planning (VPP) has received much attention in recent years. VPP refers to the integration of multiple power units, considered as a single power plant. In this paper, three VPPs are considered, each consisting of different power plant units and expected to supply the desired load. In addition to providing the desired load, they must maximize their profits. A decentralized optimization method was used to optimize these three VPPs. The reason for using a decentralized approach is to increase network security and eliminate the need for a central computer. However, using decentralized optimization increases the speed of problem-solving. Finally, the obtained results are compared with the centralized method. Simulations show that almost the same results are achieved using different optimization methods. These results increase the trend of using decentralized methods in VPP. Another feature of decentralized methods compared to the centralized method is the reduction in the speed of problem-solving, which in this article has greatly reduced the solution time. If the considered network becomes wider and the number of problem variables and their limitations increases, the use of decentralized methods will become more efficient, and in those problems, the difference in problem-solving time by centralized and decentralized methods will increase.

The carbon capture-transportation-utilization (C-CTU) chain strengthens the coupling between terminal energy consumption and renewable energy resources (RES), achieving carbon emission reduction in power generation sectors. However, the dynamic operation of the C-CTU chain and the uncertainties induced by RES output pose new challenges for the low-carbon operation. To address above challenges, the nonlinear dynamic operation model of C-CTU chain is first proposed in this study. It is further incorporated into the day-ahead operation scheme of the electricity-carbon integrated system considering the stochastic nature of wind power. This scheme is treated as a two-stage stochastic integer programming (TS-SIP) problem with a mixed-integer nonlinear recourse. By means of the polyhedral envelope-based linearization method, this recourse is reformulated into its linear counterpart. To further improve the computational performance of classical decomposition algorithms, a novel Benders decomposition framework with hybrid cutting plane strategies is proposed to obtain better feasible solutions within a limited time. Simulations are conducted on two power system test cases with the C-CTU chain. Numerical results indicate that the engagement of C-CTU chain promotes the low-carbon economic operation of the power system. Also, the proposed decomposition algorithm shows a superior solution capability to handle large-scale TS-SIP than state-of-the-art commercial solvers.

Many electricity economists have long hoped that it might be possible to establish competition, not just in providing generation and load assets, but also in the provision of the transmission network itself. Attempts in the 1990s to achieve so-called merchant transmission investment using conventional Financial Transmission Rights (FTRs) proved disappointing. We develop an extension of screening-curve models to include the optimal choice of both generation and transmission. Such models, although stylised, provide valuable insight into the long-run co-optimisation of generation and transmission. We propose new regulatory and merchant transmission investment mechanisms that achieve the socially optimal investment.

The investment decisions of energy-intensive consumers can alter the balance of supply and demand in an electricity market. In particular, they can increase the market power of incumbent generators such that prices may increase as a consequence of their investments. Whilst it is therefore intuitive that such investors will wish to consider their effects on the market, it is a challenging problem analytically and one that has been under-researched. In general, the problem can be manifest in any supply chain where demand-side investments influence endogenous price formation in the intermediate product markets. Theoretically, we show how the presence of producer market power decreases demand-side investments and then, computationally we formulate a quad-level program to model the operational implications for a demand-side investor in more detail. With an innovative reduction in complexity to a bilevel model, an efficient solution algorithm for the optimal investment by a demand-side investor is facilitated. We demonstrate computability on a small scale electricity system and the results confirm the theory.