Welfare Maximization Problem Research Articles

Theoretical study on demand-side management to reduce imbalance between electricity supply and demand

The gap between electricity supply and demand, which is the electricity imbalance, can have negative economic impacts on retail electricity suppliers. This paper presents a methodology for designing demand response (DR) programs while mitigating the negative impacts. The DR programs require the retailers to set target electricity consumption and prices of economic incentives for customers who cooperate with the DR programs. First, the target electricity consumption is determined by solving a problem of social welfare maximization in which the objective function is the sum of economic surplus of the retailers and their customers and impacts of electricity imbalance. The optimal electricity prices or the optimal rebate levels are then calculated under the principle that rational customers act to maximize their economic surplus. Through numerical simulations, the authors confirmed that the proposed methodology mitigated the impacts of electricity imbalance. Meanwhile, results of the numerical simulations showed that in practical situations, there were cases where the retailers unable to reduce the electricity imbalance profitably. Therefore, the authors additionally discuss ways to assess the electricity imbalance, which motivates the retailers to reduce the imbalance, in such cases.

Integrated Sensing, Communication, and Computing for Cost-effective Multimodal Federated Perception

Federated learning (FL) is a prominent paradigm of 6G edge intelligence (EI), which mitigates privacy breaches and high communication pressure caused by conventional centralized model training in the artificial intelligence of things (AIoT). The execution of multimodal federated perception (MFP) services comprises three sub-processes, including sensing-based multimodal data generation, communication-based model transmission, and computing-based model training, ultimately competitive on available underlying multi-domain physical resources such as time, frequency, and computing power. How to reasonably coordinate the multi-domain resources scheduling among sensing, communication, and computing, therefore, is vital to the MFP networks. To address the above issues, this article explores service-oriented resource management with integrated sensing, communication, and computing (ISCC). Specifically, employing the incentive mechanism of the MFP service market, the resources management problem is defined as a social welfare maximization problem, where the concept of “expanding resources” and “reducing costs” is used to enhance learning performance gain and reduce resource costs. Experimental results demonstrate the effectiveness and robustness of the proposed resource scheduling mechanisms.

Multi-market P2P trading of cooling–heating-power-hydrogen integrated energy systems: An equilibrium-heuristic online prediction optimization approach

In this paper, an equilibrium-heuristic online prediction optimization approach is proposed for multi-market peer-to-peer (P2P) electricity–hydrogen trading of integrated energy systems (IESs) with uncertainties. First, the IES, consisting of a hydrogen energy storage subsystem and a combined cooling, heating, and power subsystem, is constructed in the distribution network to improve energy utilization and market efficiency. Then, a bi-level optimization model for IESs, participating in the P2P electricity–hydrogen energy trading, the real-time electricity, and the ancillary service markets, is proposed, in which the top-level model can be formulated as a P2P electricity–hydrogen trading pricing model through the social welfare maximization problem, and the lower-level model is used to maximize the IES operating profit. To effectively solve the bi-level model, the game equilibrium-based ADMM distributed algorithm is used to obtain the P2P trading volume and prices of the top-level model, and a new hybrid heuristic algorithm, called hybrid sand cat swarm optimization and improved honey badger algorithm (SCIHB), is proposed to solve the lower level model. SCIHB utilizes a hybrid mechanism and an adaptive learning rate parameter to balance local exploitation and global exploration. Furthermore, a new online learning probabilistic prediction method based on the hidden Markov model and wavelet transform is introduced to describe the uncertainties of wind power, electricity prices, and frequency regulation prices. Finally, case studies are conducted on an IEEE 33-bus test system, and the numerical results verify the effectiveness of the proposed P2P trading model and solution approach.

Real-time pricing based on convex hull method for smart grid with multiple generating units

With the growing demand and complex supply structure for electricity, higher requirements are proposed for generating units to regulate the peak load, resulting in significant increases in the startup cost. These issues bring urgent need to develop new pricing mechanisms. The real-time pricing (RTP) is an ideal pricing mechanism for clipping peak load and balancing supply and demand. This paper designs an RTP mechanism for the smart grid which integrates multiple generating units on the supply side and distributed renewable energy generation devices and energy storage systems on the demand side. Focusing on the interests of both supply and demand sides, a social welfare maximization model that incorporates startup costs of generating units is formulated. To tackle the discontinuity in the proposed model, the convex hull method is utilized to transform the primal model and derive the convex hull price which is widely regarded as an optimal price that can reflect the aggregate cost of generating units but has rarely extended to RTP. The related dual theory indicates that the convex hull price can be obtained by the Lagrange multiplier of the proposed social welfare maximization problem associated with the supply–demand balance constraint. Moreover, a distributed iterative algorithm based on the subgradient projection method is employed to solve the dual problem. Simulation results validate rationality and effectiveness of the proposed pricing mechanism.

Getting prices right on electricity spot markets: On the economic impact of advanced power flow models

As the share of variable renewable energy increases, adequate prices on electricity spot markets become increasingly important as they set signals for scarcity, investment, or demand response. Market prices are derived from the underlying welfare maximization problem. On electricity spot markets, this optimization problem is based on the non-convex and non-linear Alternating Current Optimal Power Flow (ACOPF) model. Since the ACOPF is intractable, electricity markets around the world use a linear approximation, the Direct Current Optimal Power Flow (DCOPF) model. Recent research has led to better non-linear relaxations of the ACOPF. We show that these non-linear relaxations increase welfare and imply significantly lower redispatch costs and side-payments. Most importantly, we show that the price signals obtained from non-linear relaxations are much improved. The DCOPF often yields high price differences between nodes when there is no line congestion in the AC-feasible solution or vice versa. Such biased price signals pose a significant problem in practice as they lead to inefficient demand response, distorted investment signals, and incorrect congestion incomes. The use of non-linear relaxations mitigates this problem and provides an important advantage of the resulting prices over prices based on the DCOPF.

Multi-microgrids distributed peer-to-peer energy trading in distribution system considering uncertainty risk

The cooperative energy trading model for multi-microgrids in the distribution network systems under uncertainty is investigated in this paper, which permits peer-to-peer (P2P) energy trading under the system network constraints. The model is formulated as a two-stage problem, i.e. cooperative welfare maximization problem based on the conditional value at risk (CVaR) (P1) and market clearing problem based on the Nash Bargaining theory (P2). In the first stage, the CVaR is used to quantify the risk of uncertainty of source and load, and a stochastic optimization model is formed to identify energy scheduling and reactive power control. The bi-level nested alternating direction method of multiplier based on consistent communication (Bi-CADMM) is offered as a privacy-preserving technique for solving P1. Then, the second stage determines the mutual payments of the microgrids (MGs) and network usage charges for the distribution systems operator (DSO) according to the negotiation coefficient in the form of centralized solving technology. Case studies on a modified IEEE-33 system with 4-MGs show that the Bi-CADMM has strong convergence performance and can guarantee the sub-optimal and feasible solution compared with the centralized technology first. The final results also show that the decision-makers with different preferences can determine the degree of conservatism of the scheduling through the risk factor to deal with the uncertainty, and the suggested energy trading model is beneficial in terms of lowering participants' costs and improving voltage security.

A Truthful Combinatorial Auction Mechanism Towards Mobile Edge Computing in Industrial Internet of Things

Mobile edge computing (MEC) shows prominent application prospects in the Industrial Internet of Things (IIoT) by allowing resource-restricted IIoT mobile devices (MDs) to offload their tasks to geographical proximity edge clouds. An efficient incentive mechanism should be designed jointly addressing resource allocation and pricing to incentivize MDs (i.e., buyers) and edge clouds (i.e., sellers) to participate in offloading service trading. This paper aims to solve the social welfare maximization problem of a personalized MEC computation offloading service market where each edge cloud can allocate different computing and wireless resources to each MD according to the MDs' delay and energy consumption constraints, and each MD submits bids to edge clouds differently based on the resource allocation of the edge clouds. We propose a truthful combinatorial auction (TCA) mechanism which involves three phases of resource allocation, buyer-seller matching, and payment determination. It should be highlighted that our proposed buyer-seller matching algorithm combines optimal matching and heuristic matching, so it greatly improves the auction effect while ensuring computational efficiency. Considerable theoretical analysis and experimental results prove that the performance of the proposed TCA mechanism is significantly superior to that of other auction mechanisms while holding the desirable properties.

P2P Multigrade Energy Trading for Heterogeneous Distributed Energy Resources and Flexible Demand

This paper proposes a novel peer-to-peer (P2P) multi-grade energy trading design to encourage demand side flexibility to locally absorb the uncertainty of renewable distributed energy resources (DERs) in distribution networks. In particular, a reliability credit (RC) assignment method is developed for customers to differentiate the energy grades considering the heterogeneity in energy supplying reliability of DERs and the consumption preferences of customers. Later, an innovative P2P multi-grade energy trading model is introduced where different types of demand are matched up with the corresponding grades of energy. The market clearing is modeled as a social welfare maximization problem considering the net utilities of customers and the profits of DER producers. Furthermore, a fast decentralized pricing algorithm is developed that achieves the maximum of social welfare and also preserves the privacy of individual participants. To substantially improve the computational efficiency, a fast solution method is devised for customers to solve the optimal energy procurement combination problem, and closed-form solutions are derived for DER producers to allocate energy optimally. Numerical tests on a 69-node distribution feeder validate the superiority of the proposed P2P multi-grade energy trading scheme compared to the benchmark scheme. The high efficiency and scalability of the proposed fast pricing algorithm are corroborated by the simulation on the IEEE 8500-node distribution system.

Welfare Maximization Algorithm for Solving Budget-Constrained Multi-Component POMDPs

Partially Observable Markov Decision Processes (POMDPs) provide an efficient way to model real-world sequential decision making processes. Motivated by the problem of maintenance and inspection of a group of infrastructure components with independent dynamics, this letter presents an algorithm to find the optimal policy for a multi-component budget-constrained POMDP. We first introduce a budgeted-POMDP model (b-POMDP) which enables us to find the optimal policy for a POMDP while adhering to budget constraints. Next, we prove that the value function or maximal collected reward for a special class of b-POMDPs is a concave function of the budget for the finite horizon case. Our second contribution is an algorithm to calculate the optimal policy for a multi-component budget-constrained POMDP by finding the optimal budget split among the individual component POMDPs. The optimal budget split is posed as a welfare maximization problem and the solution is computed by exploiting the concavity of the value function. We illustrate the effectiveness of the proposed algorithm by proposing a maintenance and inspection policy for a group of real-world infrastructure components with different deterioration dynamics, inspection and maintenance costs. We show that the proposed algorithm vastly outperforms the policies currently used in practice.

A Decentralized Dynamic Pricing Model for Demand Management of Electric Vehicles

Transportation electrification is considered a green alternative to internal combustion vehicles. However, higher penetration of electric vehicles (EVs) can cause several technical challenges to the power systems, including local equipment overloading. This is especially challenging for distribution systems due to the direct connection of EVs with them. To mitigate equipment overloading, by managing EV loads locally, a dynamic pricing model is proposed in this study. First, a satisfaction function is devised for EVs considering the sensitivity of different EV owners to the battery state of charge and urgency of recharge. Then, a welfare function is developed for the EV fleet operator (EFO) considering the net load of EVs and the electricity price of the upstream grid. To this end, a welfare maximization problem is formulated considering the welfare of EVs and EFO. The problem is then decomposed into the EFO sub-problem and EV sub-problem to preserve privacy. Finally, a distributed mechanism is developed to solve the sub-problems iteratively without revealing private information. The performance of the proposed method is analyzed for a residential apartment complex in terms of load management and convergence for different day types (working days and holidays). Simulation results have shown the efficacy of the proposed method in mitigating the overloading of transformers during peak load hours.

Near Optimal Learning-Driven Mechanisms for Stable NFV Markets in Multitier Cloud Networks

More and more 5G and AI applications demand flexible and low-cost processing of their traffic through diverse virtualized network functions (VNFs) to meet their security and privacy requirements. As such, the Network Function Virtualization (NFV) market has been emerged as a major service market that allows network service providers to trade their network services among customers. Since each service market usually involves complex interplays among players with different roles, efficient mechanisms that guarantee stable and efficient operations of the NFV market are urgently needed. One fundamental problem in the NFV market is how to maximize the social welfare of all players so that all players have incentives to participate in the activities of the market. In this paper, we first formulate a novel social welfare maximization problem in an NFV market of a multi-tier edge cloud network, with the aim to maximize the total revenue collected from all players, and we implement VNF services on Virtual Machines (VMs) leased by service providers to fulfill customers with service requests, where the edge cloud network consists of both cloudlets in edge networks and remote data centers in the core network. We then design an efficient incentive-compatible mechanism for the problem, and analyze the existence of a Nash equilibrium of the mechanism. Also, we consider an online social welfare maximization problem with uncertain values of customers and without the knowledge of future request arrivals, for which we devise an online learning algorithm by adopting the Multi-Armed Bandits (MAB) method with a bounded regret. We finally evaluate the performance of the proposed mechanisms through simulations and a testbed. Results show that the proposed mechanisms deliver up to 27% higher social welfare than those of existing studies

A bilevel game-theoretic decision-making framework for strategic retailers in both local and wholesale electricity markets

This paper proposes a bilevel game-theoretic model for multiple strategic retailers participating in both wholesale and local electricity markets while considering customers’ switching behaviors. At the upper level, each retailer maximizes its own profit by making optimal pricing decisions in the retail market and bidding decisions in the day-ahead wholesale (DAW) and local power exchange (LPE) markets. The interaction among multiple strategic retailers is formulated using the Bertrand competition model. For the lower level, there are three optimization problems. First, the welfare maximization problem is formulated for customers to model their switching behaviors among different retailers. Second, a market-clearing problem is formulated for the independent system operator (ISO) in the DAW market. Third, a novel LPE market is developed for retailers to facilitate their power balancing. In addition, the bilevel multi-leader multi-follower Stackelberg game forms an equilibrium problem with equilibrium constraints (EPEC) problem, which is solved by the diagonalization algorithm. Numerical results demonstrate the feasibility and effectiveness of the EPEC model and the importance of modeling customers’ switching behaviors. We corroborate that incentivizing customers’ switching behaviors and increasing the number of retailers facilitates retail competition, which results in reducing strategic retailers’ retail prices and profits. Moreover, the relationship between customers’ switching behaviors and welfare is reflected by a balance between the electricity purchasing cost (i.e., electricity price) and the electricity consumption level.

Edge-Weighted Online Bipartite Matching

Online bipartite matching is one of the most fundamental problems in the online algorithms literature. Karp, Vazirani, and Vazirani (STOC 1990) gave an elegant algorithm for unweighted bipartite matching that achieves an optimal competitive ratio of 1-1/e . Aggarwal et al. (SODA 2011) later generalized their algorithm and analysis to the vertex-weighted case. Little is known, however, about the most general edge-weighted problem aside from the trivial 1/2-competitive greedy algorithm. In this article, we present the first online algorithm that breaks the long-standing 1/2 barrier and achieves a competitive ratio of at least 0.5086. In light of the hardness result of Kapralov, Post, and Vondrák (SODA 2013), which restricts beating a 1/2 competitive ratio for the more general monotone submodular welfare maximization problem, our result can be seen as strong evidence that edge-weighted bipartite matching is strictly easier than submodular welfare maximization in an online setting. The main ingredient in our online matching algorithm is a novel subroutine called online correlated selection (OCS), which takes a sequence of pairs of vertices as input and selects one vertex from each pair. Instead of using a fresh random bit to choose a vertex from each pair, the OCS negatively correlates decisions across different pairs and provides a quantitative measure on the level of correlation. We believe our OCS technique is of independent interest and will find further applications in other online optimization problems.

Truthful auction mechanisms for VNF chain provisioning and allocation across geo-distributed datacenters

With the fast development of network function virtualization (NFV), NFV markets are emerging that allows network service providers (NSPs) to trade different virtual network function (VNF) chains among users. Therefore, efficient mechanisms for VNF chain provisioning and allocation are key to guarantee efficient operations of the NFV markets. One fundamental issue is how to maximize the social welfare of the market such that selfish users have incentives to acquire VNF chains from the markets. To overcome this issue, in this paper, we propose a truthful randomized combinatorial auction mechanism (TRCAM), which integrates the primal–dual approximation algorithm design technique and efficient pricing strategy. This mechanism considers dynamic VNF chain provisioning of the NSP and flexible VNF chain deployment of users. To be specific, we first formulate the social welfare maximization problem as an integer linear program, which is proven to be NP-hard. Then, we propose a primal–dual approximate algorithm which is near-optimal with polynomial-time complexity and employ it as a building block to design the TRCAM. Furthermore, we develop a novel binary-search-based algorithm to boost the average-case performance of the TRCAM. Both strict theoretical analysis and extensive experimental studies demonstrate the effectiveness of our proposed TRCAM, which achieves approximate truthfulness, near-optimal social welfare, individual rationality, and computational efficiency.

Tight social welfare approximation of probabilistic serial

We study the problem of approximate social welfare maximization (without money) in assignment problems for n agents who have cardinal preferences over a finite set of items. Probabilistic Serial (PS) mechanism is known to be ordinally efficient and envy-free. We prove that its social welfare approximation ratio is Θ(n−12) while no envy-free mechanism can achieve an approximation ratio better than O(n−12). In addition, our proof also implies a Θ(n−12) rank approximation of PS, answering an open question posted in [8].

Peer-to-Peer Energy Trading With Energy Path Conflict Management in Energy Local Area Network

The increasing penetration of distributed renewable generations has given rise to a novel energy management mechanism, peer-to-peer (P2P) energy trading. The concept of Energy Internet (EI) is proposed as a new energy system framework to facilitate P2P energy trading where all distributed electrical devices are interconnected via energy routers (ERs). A proper market clearing approach is required to coordinate decentralized decision making in P2P market for demand-supply balance and feasible end-to-end energy delivery. In this paper, a decentralized market clearing mechanism considering energy path conflict management is proposed for P2P energy trading in energy local area network (e-LAN). An adjusted conflict-based search (ACBS) algorithm is proposed to deal with the non-convexity of the social welfare maximization problem where the nonconvex problem is transformed into multiple independent convex problems. Considering the privacy protection of participants, a dual decomposition based approach is proposed to solve these convex problems in a decentralized manner where self rationality of each participant can be satisfied by maximizing its personal welfare. In addition, energy path conflicts caused by decentralized optimization is resolved by imposing penalty fee and observing the rule of energy sharing maximization. Numerical simulations are presented to verify the effectiveness of the proposed market clearing approach.

A consensus-based privacy-preserving energy management strategy for microgrids with event-triggered scheme

In terms of the distributed energy management (DEM) in microgrids, increasing distributed generators and users will bring tremendous data transmitted in the communication network. Considering the data security and the computation efficiency, protecting the participants’ privacy and saving the communication network resources are essential. This paper proposes a consensus-based distributed privacy-preserving energy management strategy with the event-triggered scheme to achieve privacy-preserving and network resource-saving simultaneously. Firstly, the DEM in microgrids is formulated as a social welfare maximization problem. Then the privacy disclosure of both generators and consumers under the consensus-based distributed control strategy is analyzed. Next, a consensus-based privacy-preserving algorithm using differential privacy is designed to protect private information. An event-triggered scheme is applied to the strategy to save network resources. Besides, theoretical analysis, including convergence, accuracy and differential privacy, is presented to guarantee the algorithm’s sufficiency. The trade-off between the accuracy and privacy level is also investigated. Finally, simulation results demonstrate the effectiveness of the proposed algorithm.

Towards Incentive for Electrical Vehicles Demand Response With Location Privacy Guaranteeing in Microgrids

The rapid and wide adoption of microgrids (MGs) and the increasing popularity of electric vehicles (EVs) have created a unique opportunity for the integration of these technologies. In this article, we address the issue of demand response of EVs during MG outages by leveraging Vehicle-to-Grid (V2G) technology. Particularly, we investigate an auction trading market that allows EVs with surplus energy to act as sellers, and EVs that want to be charged to act as buyers. A novel distributed double auction scheme is proposed to allow each buyer EV to submit multiple bids to seller EVs in different parking lots. Nonetheless, the locations of buyer EVs could be inferred by an adversary through analyzing the valuations, posing serious privacy and security risks. In this regard, a valuation-based attack scheme is investigated to validate the potential privacy risk. To defend against such an attack, we present a location privacy-preserving double auction scheme, in which the MicroGrid Central Controller (MGCC) acts as the auctioneer, solving the social welfare maximization problem of matching buyers to sellers, and the cloud is used to conduct calculations for the auctioneer, protecting the privacy of participants via homomorphic encryption. Theoretical analysis is conducted to validate our auction scheme in satisfying the designed economic and privacy properties (e.g., strategy-proofness and <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula> -anonymity). The experimental results show that our auction scheme can not only mitigate the demand response problem in MGs, but also provides good performance with respect to social welfare, satisfaction ratio, computational and communication overhead, and privacy leakage.

Where Am I Parking: Incentive Online Parking-Space Sharing Mechanism With Privacy Protection

Sharing private parking spaces during their idle time periods has shown great potential for addressing urban traffic congestion and illegitimate parking problems in smart cities. In this article, aiming to address the online parking-space sharing issue while ensuring the privacy of customer parking destination locations, we propose a novel destination privacy-preserving online parking sharing (DPOPS) incentive scheme. In particular, the online parking-space sharing problem is formalized as a social welfare maximization problem in a two-sided market, where parking-space providers (PSPs) and customers are regarded as sellers and buyers. Then, novel threshold value-based rules are designed to determine winners, payments, and reimbursement. Finally, winners are matched by solving a mixed-integer nonlinear programming problem, aiming to minimize the distance between customer’s destination and allocated parking space. In addition, the location privacy of the customers’ destinations is protected by the Laplace mechanism. We prove that DPOPS achieves several economically effective properties and approximate differential privacy. We analyze the upper bound of the efficiency loss of our scheme. Extensive evaluation results demonstrate that our scheme can not only achieve good performance regarding social welfare, PSP satisfaction ratio, privacy preservation, and computation overhead but also leads to shorter travel distances for customers comparing to the baseline scheme. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In this article, we address the online parking-space sharing issue with considering the parking-space providers (PSPs) and customers’ individual utility while preserving the location privacy of customers’ destinations. Most of the previous works focused on designing a centralized mechanism for allocating parking spaces without considering the protection of the customers’ location privacy. In particular, we propose an online parking-space sharing scheme called DPOPS, including a novel threshold value-based winner determination rule and a parking-space allocation rule. The proposed scheme DPOPS allows the PSPs and customers submit their bids and asks according to their own willingness and is able to improve the utilization of private parking spaces during their idle time periods. Moreover, the location privacy of customers’ destinations is protected by the Laplace mechanism. The experiments demonstrate that the proposed approach outperforms the exponential-based scheme in terms of PSP satisfaction ratio and the travel distance for parking-space customer. The proposed scheme is helpful in managing the vacant parking space in a competitive market and can be readily implemented in the real-world online parking-space sharing systems.

Economic Implications of Agricultural Land Conversion to Solar Power Production

Meeting greenhouse gas (GHG) reduction targets will require a significant increase in electricity production from sustainable and renewable sources such as solar energy. Farmers have recognized this need as a chance to increase the profitability of their farms by allocating farmland to solar power production. However, the shift from agriculture to power production has many tradeoffs, arising primarily from alternative land uses and other means of production. This paper models the farmers’ decision as a constrained profit maximization problem, subject to the amount of land owned by the farmers, who have to allocate it between agriculture and solar power fields, while considering factors affecting production costs. The farmers’ problem is nested in the social welfare maximization problem, which includes additional factors such as ecological and aesthetical values of the competing land uses. Empirical analysis using data from a solar field operating in Israel shows that landowners will choose to have solar power production on their land unless agricultural production generates an unusually high net income. Adding the values of non-market services provided by agricultural land does not change this result. The consideration of the reduction in GHG emissions further increases the social welfare from solar fields.