Distributed computing faces a persistent multi agent trust dilemma. In the computation process, participants may maliciously attack the system for personal gain by providing false data. Blockchain provides a possible solution for this problem with its immutability and multi-party consensus. However, existing blockchain data throughput has long been queried owing to its exorbitant time and energy costs by consensus mechanisms. This paper proposes a light blockchain structure in distributed computing scenarios. A No-Proof consensus (NPC) mechanism is designed for distributed computing problems with no extra proving process such as Proof-of-Work or Proof-of-Stake. This consensus mechanism notices that the distributed computing result has proven to be valid in the computation process automatically, which does not need to be verified again in the consensus mechanism. Further, the single-threaded data processing ability of the blockchain structure certainly leads to low efficiency when applied to distributed computation problems. An NPC-based blockchain is constructed in this paper to solve this problem. In this structure, the distributed computing is done off chain, and an oracle is designed to upload the computing results to the blockchain asynchronously. Upon the contribution in this paper, a distributed energy trading model is provided as a case study to verify the superiority of the designed blockchain in contrast with other similar structures.

Reactive power optimization (RPO) is a key task in the operation and control of active distribution networks (ADNs). The nonlinear power flow constraints and the integers introduced by voltage regulator (VR) constraints make the nonconvex RPO model difficult to solve. In this paper, a RPO model is proposed considering the nonuniform tap ratios of VRs. The three phases in VRs are independently controlled and the phase coupling effects are strictly considered. Moreover, to deal with the bilinear relationship among continuous complex voltage phasors and discrete tap ratios, the voltage phasor matrix is decoupled into real and imaginary parts, and a status variable method is proposed to exactly linearize the bilinear terms. Further, the nonlinear power flow constraints are relaxed to a set of second-order cone constraints without neglecting the coupling effect among the three phases and are proved to be equivalent to the semi-definite constraints, which does not require the rank-1 verification and is more efficient and scalable. Thus, the original nonconvex RPO for three-phase unbalanced ADNs is simplified to a mixed-integer second-order cone programming (MISOCP) model. Case studies validate the model’s effectiveness, and the computational efficiency meets practical requirements. Note to Practitioners—This paper simplifies the complex problem of reactive power optimization for active distribution networks with unbalanced three-phase power flows. We offer a novel RPO model improving the typically nonconvex and nonlinear optimal power flow problem, and addressing the particular challenges imposed by voltage regulators optimization with nonuniform tap ratios. Independent control of the VR phases and accurate incorporation of phase coupling effects have been realized, greatly simplifying the optimization process. The transformation of nonlinear power flow constraints into a computationally efficient set of second-order cone constraints eliminates the need for cumbersome rank-1 verification. Our mixed-integer second-order cone programming model integrates smoothly with standard optimization procedures, improving voltage regulation and network stability. The effectiveness and efficiency of the approach have been validated in case studies, offering a viable tool for industry application.

Solving large-scale stochastic dynamic economic dispatch problems involving energy storage over multiple time periods is inherently challenging. Decomposing the optimization problem across time scales to achieve parallel optimization is an effective strategy for enhancing computational efficiency. However, the introduction of energy storage complicates this task significantly due to its non-convex characteristics. To address this challenge, this paper presents a novel strategic two-stage Diagonal Quadratic Approximation Method (DQAM) that transforms the original problem into a two-stage structure amenable to parallel solving. In this structure, each sub-problem focuses on a single time period, effectively handling the mixed-integer and strong temporal coupling characteristics of energy storage. This extension broadens the applicability of the original DQAM to non-convex problems. Numerical results under various conditions demonstrate the effectiveness and performance of the proposed two-stage DQAM, achieving significantly improved solution efficiency while maintaining good solution accuracy. Leveraging computational processor and memory resources, the proposed method can achieve a maximum enhancement of 36.86 times in computational efficiency on large-scale systems with multiple time periods. Note to Practitioners—With the increasing scale of power systems and the growing penetration of renewable energy, the accuracy and real-time requirements for economic dispatch solutions have been continuously enhanced. Solving large-scale optimization problems over multiple time periods in power grids has become more challenging, especially with the additional computational burden introduced by the deployment of energy storage to mitigate renewable energy fluctuations. The configuration of energy storage generates a large number of binary decision variables, which results in the original problem becoming a large-scale mixed-integer programming model which is difficult to solve. This paper proposes a strategic two-stage DQAM to solve the stochastic dynamic economic dispatch problem with energy storage, utilizing a two-stage structure to determine an approximate energy storage optimization schedule through an optimization approximation function. Subsequently, the equivalent dynamic economic dispatch problem is transformed into a sizable form with smaller and more easily solvable sub-problems. By relaxing the temporal coupling constraint, the computational efficiency is significantly improved. Test results on systems of various scales and time periods demonstrate that the two-stage DQAM reduces computation time in all scenarios.

Optimization problems arise in various domains, ranging from power systems to resource allocation and large network management. An effective solution to these problems in a distributed manner has become a crucial research area due to the increasing scale and complexity of modern systems. In this article, we propose a novel local projection global tracking (LPGT) decentralized algorithm based on the Alternating Direction Method of Multipliers for general optimization problems. Unlike existing distributed methods that require problem-specific adaptations or centralized coordination, LPGT provides tailored solutions for handling generic local equality and inequality constraints, as well as global coupled equality and inequality constraints. Moreover, a projection-based analytical scheme is designed to handle generic local equality and inequality constraints without iterative subproblem solvers, and a fully decentralized deviation tracking mechanism is constructed to enforce both global coupled equalities and inequalities constraints via agent communications, eliminating the need for a central coordinator. Case studies for a local energy trading model are proposed to verify the feasibility and applicability of the algorithm.

Large-scale multi-scenario stochastic economic dispatch (SED) is hard to directly solve due to the huge number of variables and constraints. To reduce the computational burden, a nested dual-DQAM (Diagonal Quadratic Approximation Method) is proposed in this paper to decouple the SED problem in both scenarios and time periods, where each subproblem only contains one time period and one scenario. Moreover, these subproblems can be handled in parallel, such that the computational performance can be significantly improved. Besides, we have investigated the optimal policy to select the best parallel structure of the proposed dual-DQAM, and the theorical convergence performance is proved. Numerical results on several test systems show the effectiveness of the proposed dual-DQAM.Note to Practitioners—Nowadays, the safe operation and economic dispatch in power system are greatly challenged by the high penetration of renewable energy. Although the uncertainty of renewable energy can be well modeled by stochastic programming, the solution complexity will seriously increase due to the large number of typical scenarios. For this problem, the parallel solution using decomposition methods is the state-of-the-art strategy. In this paper, we propose an efficient solution to the multi-scenario SED problem by temporal and scenario decompositions. It realizes an important innovation in both reducing the computational burden and improving the solving efficiency, which greatly promotes the application of SED in large-scale systems. To better use this method, the following two properties should be highlighted: i) the proposed method has a convergence guarantee and works especially well on SED due to the sparsity property of linking constraint matrices. ii) the computational efficiency of the proposed method becomes more significant as the number of time periods and scenarios grows and can be further improved under a fast ramp rate.

Due to the spatially and temporally transferable workloads, data centers (DCs) become increasingly important in demand response (DR) implementations. By making full use of their owned DCs, data center operators (DCOs) are significant DR resource providers. To fully exploit the DR capability of the DCO on different time scales, we present a two-stage scheduling model for DCOs and the system operator (SO). In the DR scheduling, the SO formulates DR compensation prices first, and then each DCO decides its best-response power demands accordingly. Considering the profit-hunting property of the SO and DCOs, a two-stage DR Stackelberg game model is proposed. Furthermore, the existence and uniqueness of the Stackelberg equilibrium are proved. Finally, to protect the data privacy of DCOs, we design a Kriging-metamodel-based algorithm which avoids the DCO privacy exposure to the SO in the optimization process. Simulation results prove the accuracy and the calculation efficiency of the proposed Kriging-metamodel-based algorithm.Note to Practitioners—DCs play an increasingly important role in the power balance of grids in recent years. Existing studies focusing DCs’ DR participation generally consider the single-stage DR participation of DCs which ignores the role of DCOs in unified scheduling and management of their owned DCs. Considering the impacts of service request submitting time on the DR capabilities of DCs, this work proposes a novel two-stage DR scheduling model in the account of the unified scheduling role of DCs. Then, a Stackelberg game model is further proposed to characterize the profit-hunting property of the SO and DCOs. Finally, a privacy-protected algorithm is designed to address the optimization problem without explosions of DCO’s sensitive data. Simulation results show the effectiveness of the proposed model and algorithm in encouraging DCOs to adjust their energy consumption plans according to the SO’s request. Moreover, it is proven that the proposed algorithm can achieve global optimization with effective data privacy protection and low computation cost. Simulation results suggest that the proposed method can obtain a high-quality solution for a Stackelberg game model with privacy protection.

This paper proposed sufficient conditions of the zero duality gap for the second-order conic programming approach of the DC optimal power flow that quadratically embeds the transmission loss. The mechanism of the changes for locational marginal price with differently selecting the slack bus is revisited, based on which a load-weighted distributed slack bus method is introduced. Furthermore, a second-order conic programming-based convexification method is proposed by employing the duality analysis. A favorable property of the proposed method is that mild sufficient conditions of the zero duality gap can be derived by the analysis of Karush-Kuhn-Tucker conditions. Numerical results illustrate the effectiveness of the proposed method and physically prove the proposed sufficient conditions. Compared with traditional and similar market-clearing methods, the proposed method has better performance on convergence, robustness, and accuracy. Note to Practitioners—This paper was motivated by the problem of the pricing mechanism in the deregulated electricity market but it is also applicable to rapidly solving the power flow of power systems with sufficient reactive power. Existing approaches use the B-coefficient to estimate the transmission loss in the model non-linearly. In this paper, an improved approach considering transmission loss is proposed, which further introduces the distributed slack bus method and subsequently employs the second-order cone programming algorithm. The proposed method hedges the risk of appearing multiple solutions or lack of accuracy. Rigorous mathematical proofs are derived to support the method. For industrial practice, three sufficient conditions suitable for different kinds of power systems are given, indicating when the proposed approach can be efficiently applied. The proposed method can be integrated into the existing electricity market trading platform for independent system operators and facilitates real-time market clearing and electricity price calculation. Future research is expected to improve the accuracy of the model based on nodal power balance equations.

Security-constrained unit commitment (SCUC) is one of the most fundamental optimization problems in power systems. The objective of SCUC is to minimize the operating cost while respecting both system-wide and generator-specific constraints. It leads to a large-scale and mixed-integer programming (MIP) model with a large number of binary decision variables which is difficult to solve. This paper, based on the convex hull theory of single-unit, proposes a linearization method for the hydro-thermal SCUC problem with decoupled thermal units and variable-head hydro units. Then, the strategy of embedding two types of convex hulls in a multi-unit commitment and the heuristic method of constructing a feasible solution are designed, by which the multi-UC is approximated from large-scale mixed-integer programming to linear programming that can be solved in polynomial time. Finally, we theoretically prove that the optimal solution of the proposed LP model is always better than that of the Lagrangian Relaxation model. Numerical experiments on several large-scale test systems demonstrate the effectiveness and efficiency of the proposed method. Note to Practitioners— This paper proposes a linear programming model for the SCUC problem by lifting up to a higher-dimensional space. It realizes an important innovation in reducing the computational complexity of SCUC from the perspective of linearization. The proposed method can be well applied to large-scale long-term unit commitment problems. To better use this method, the following two properties should be highlighted: 1) the error of the proposed method is less than the Lagrangian relaxation method and decreases with the increasing system scales and 2) the computational efficiency of the proposed method is 10-100 times faster than that of the MIP model. We have tested many practical power systems and find that the error of the proposed LP model is usually very small compared with the precise MIP while the computational performance is significantly improved. In some practical cases, the decision makers usually do not want to find the precise optimal solution while only an approximation under a fast speed, because the boundary condition is imprecise. The proposed method is useful. Besides, for the cases that need the precise optimal solution, the proposed method can provide a high-quality initial solution for the MIP model to accelerate the convergence.

Energy storage (ES), with its flexible characteristics, has been gaining attention in recent years. The ES planning problem is highly significant to establishing better utilization of ES in power systems, but different market regulations impact the ES planning strategy. Thus, this paper proposes a novel ES capacity planning model under the joint capacity and energy markets, which aims to minimize the total cost for power consumers. The great challenge is that the ES planning model has a large number of time periods, which significantly increases the problem dimensionality. In order to alleviate the computational burden, a fully parallel algorithm is proposed to temporally decompose the original problem into a series of small sub-problems, which can be solved in parallel. Moreover, we find that the corresponding analytical solutions to the sub-problems remarkably accelerate the calculation speed while ensuring accurate results. Finally, numerical results verify the effectiveness of the proposed model. Note to Practitioners—Energy storage (ES) has become more and more essential to guaranteeing power balance in power and energy systems by shifting peak loads to valley loads. However, investors may face challenges to ES capacity planning due to the lack of business models. To address this challenge, price tariffs should be carefully investigated. In the practical power system, the market price should consider both the energy price and capacity price for industries and big companies. In the energy market, investors can gain a profit by selling energy at the peak load (high price) and buying energy in the valley (low price). It should be noted that the energy market cannot recover the ES investment cost, but investors can, in fact, reduce their capacity cost since ES can reduce the peak load. Consequently, we have designed a new business model for ES planning under joint capacity and energy markets to analyze the profits via the two market regulations. The computational burden is another challenge for the proposed multi-period convex optimization model. The model must consider a long-term simulation, potentially containing thousands of time periods, which can be difficult to solve. In order to alleviate the computational burden resulting from the long-term market simulation, we further propose a fully parallel algorithm to solve the proposed business model for ES quickly. To sum up, the proposed model and method have been tested on a practical company with a practical price tariff in China to show their effectiveness.

Electric vehicles (EVs) have been gaining great popularity in recent years, but the lack of adequate infrastructure and the long battery charging time have hindered their further development. Therefore, a battery charging and swapping system (BCSS) can solve this problem by arranging battery charging and distributing the battery swapping system (BSS) to various locations while participating in the demand response of both power and transportation networks through time-of-use tariffs and congestion price. To optimally achieve the combined operation of BCSSs, this paper proposes a hybrid swapped battery charging and logistics dispatch model in the continuous-time domain. Specifically, the battery charging system will arrange the optimal battery charging strategy by a rectangle packing algorithm. Furthermore, the logistics system will set up a transportation dispatch model for the battery charging system to deliver the charged batteries from the battery charging system to the battery swapping system and then retrieve them. The combined model is involved in the demand side response considering the price. Simulation studies for different cases verify the effectiveness of the proposed model.

Data centers (DCs) have been playing a significant role in demand response (DR) programs in recent years due to their considerable DR capability. DCs are in the charge of the DC operator (DCO), who is responsible for making a reasonable allocation of computing tasks to provide DR resources. To relieve the transmission pressure of power systems, the system operator (SO) encourages DCOs to participate in the DR programs. To maximize the total welfare, a detailed DR scheduling model of DCOs and SO is proposed for the coordinative optimization. Considering the privacy issue of DCOs, a two-level distributed scheduling algorithm based on the alternating direction multiplier method (ADMM) is designed for privacy protection and distributed autonomy. Simulation results show that the proposed coordinative optimization algorithm can effectively realize the maximization of total social welfare with data privacy protection. For a power system with multiple DCOs, reasonable scheduling of DCO’s DR resources can reduce the peak-valley difference of system loads reliably and economically.