Search Results (10)

It is hardly realistic to assume that, under all decision circumstances, followers will always choose a solution that leads to the worst upper-level objective functional value. However, this generally accepted concept of the pessimistic solution to the ill-posed bilevel programming problems may lead to the leader’s attitude being more pessimistic vis à vis his anticipation of the follower’s decision being non-antagonistic. It will result in a wrong pessimistic solution and a greater potential of cooperation space between the leader and the followers. This paper presents a new concept of a non-antagonistic pessimistic solution with four numerical examples for bilevel programming problems from a non-antagonistic point of view. We prove that the objective function value of the non-antagonistic pessimistic solution generally dominates or is equal to the objective functional value of the pessimistic solution and the rewarding solution, and the maximum potential space for leader-follower cooperation can be overestimated in a generally applied pessimistic solution. Our research extends the concept of the pessimistic solution. It also sheds light on the insights that the non-antagonistic pessimistic solution can describe the practical potential of cooperation space between the leader and followers in non-antagonistic circumstances. Full article

After they reached the end of their useful EV life, lithium-ion batteries are still satisfactory for second life (SL) energy storage applications. However, the spread in their SL cell capacities may be much wider than in the EV, and this raises a question as to what type of cell voltage equalizer (EQU) should be used. Most users plan to retain the same passive EQU (PEQ) from the EV, but this means the battery capacity will be the same as the worst cell in the battery, just as it was in the EV. Unfortunately, the SL cell capacity spread may be much wider than it was in the EV, and if so, most of the cells will be under-utilized. This can be corrected by using an active EQU (AEQ) or a hybrid, such as the bilevel EQU (BEQ), to provide a capacity close to the cell average; but first, measured data is needed on the actual size of the cell capacity spread. To simplify and reduce the cost of these measurements, a new method is proposed that provides the capacities of the worst cell and the cell average. Full article

When adopted, wildlife protection policies in Canadian forests typically cover large areas and affect multiple economic agents working in these landscapes. Such measures are likely to increase the costs of timber for forestry companies operating in the area, which may hinder their acceptance of the policies unless harvesting remains profitable. We propose a bi-level wildlife protection problem that accounts for the profit-maximizing behavior of forestry companies operating in an area subject to protection. We consider the regulator with a wildlife protection mandate and forestry companies licensed to harvest public forest lands. We depict the relationship between the regulator and forestry companies as a leader-follower Stackelberg game. The leader sets the protected area target for each license area and the followers adjust their strategies to maximize payoffs while meeting the protection target set by the leader. The leader’s objective is to maximize the area-wide protection of spatially contiguous habitat while accounting for the followers’ profit-maximizing behavior. We apply the approach to investigate habitat protection policies for woodland caribou in the Churchill range, Ontario, Canada. We compare the game-theoretic solutions with solutions that do not consider the forest companies’ objectives and also with solutions equalizing the revenue losses among the companies. Full article

This paper investigates bilevel optimization models for demand response management, and highlights the often overlooked consequences of a common modeling assumption in the field. That is, the overwhelming majority of existing research deals with the so-called optimistic variant of the problem where, in case of multiple optimal consumption schedules for a consumer (follower), the consumer chooses an optimal schedule that is the most favorable for the electricity retailer (leader). However, this assumption is usually illegitimate in practice; as a result, consumers may easily deviate from their expected behavior during realization, and the retailer suffers significant losses. One way out is to solve the pessimistic variant instead, where the retailer prepares for the least favorable optimal responses from the consumers. The main contribution of the paper is an exact procedure for solving the pessimistic variant of the problem. First, key properties of optimal solutions are formally proven and efficiently solvable special cases are identified. Then, a detailed investigation of the optimistic and pessimistic variants of the problem is presented. It is demonstrated that the set of optimal consumption schedules typically contains various responses that are equal for the follower, but bring radically different profits for the leader. The main procedure for solving the pessimistic variant reduces the problem to solving the optimistic variant with slightly perturbed problem data. A numerical case study shows that the optimistic solution may perform poorly in practice, while the pessimistic solution gives very close to the highest profit that can be achieved theoretically. To the best of the authors’ knowledge, this paper is the first to propose an exact solution approach for the pessimistic variant of the problem. Full article

Once lithium-ion batteries degrade to below about 80% of their original capacity, they are no longer considered satisfactory for electric vehicles (EVs), but they are still adequate for second-life energy storage applications. However, once this level is reached, capacity fade increases at a much faster rate, and the spread between the cell capacities becomes much wider. If the passive equalizer (PEQ) from the EV is still used, battery capacity remains equal to that of the worst cell in the stack, just like it was in the EV. Unfortunately, the worst cell eventually becomes much weaker than the cell average, and the other cells are not fully utilized. If operated while the battery is in use, an active equalizer (AEQ) can increase the battery capacity to a much higher value close to the cell average, but AEQs are much more expensive and are not considered cost effective. However, it can be shown that the bilevel equalizer (BEQ), a PEQ/AEQ hybrid, also can provide a capacity very close to the cell average and at a much lower cost than an AEQ. Full article

In this paper, a bi-level microstrip differential directional coupler has been investigated. It has been shown that the equalization of coupling coefficients can be successfully made with the use of appropriate dielectric stack-up and conductor geometry. The application of additional top dielectric layer can ensure proper equalization of coupling coefficients by lowering the value of capacitive coupling coefficient to the value of the inductive one. The theoretically investigated coupled-line section has been used for the design of a 3-dB differential directional coupler. The measurement results are compared with the theoretical ones. Full article

Aiming at problems of power allocation and economic scheduling for independent multi-microgrid systems, a bi-level optimization method based on optimal power flow and consensus algorithm is proposed. The novelty of the method is that an independent multi-microgrid system is divided into two layers: in the upper layer, with the predicted output range of the microgrids as the input data, each microgrid is considered as a virtual power supply or virtual load, and taking the minimum network loss as the goal, the energy mutual aid and power allocation among the microgrids are transformed into solving the optimal power flow; in the lower layer, taking the upper layer power distribution scheme as the constraint condition, considering load fluctuation and wind/solar generation uncertainty, the optimal dispatch model of the controllable distributed generator is established based on the distributed theory and the consensus algorithm of equal cost increment, and the "plug and play" of the distributed generator is also realized. An islanded multi-microgrid cluster is taken as an example to verify the economy, security, and reliability of the proposed scheme. The advantages of the scheme have been shown by the simulation example. Simulation results show that the upper-layer method not only realizes the optimal power allocation of microgrids, but also reduces the power loss of the energy mutual aid among the microgrids; through the optimal scheduling of controllable power supply in the microgrid, the lower-level scheme not only improves the economic benefit of the microgrid, but also well suppresses the negative effects of the uncertainties, prediction errors and power fault removal on the multi-microgrid system, which improves the robustness of the system. Full article

There is a strong interest in second life applications for the growing number of used electric vehicle (EV) batteries, but capacity variations amongst these used cells present a problem. Even when these cells are matched for capacity, some imbalance is bound to remain, and a few lower capacity cells are also likely to develop after the pack begins its second life. Conventional cell voltage equalizers (EQU) do not address this problem, and they only provide a battery discharge capacity that is exactly equal to that of the weakest cell in the pack. This can easily result in a capacity loss of perhaps 20% to 25%, or more. This indicates the need for a new class of EQUs that can provide a discharge capacity that is close to the average of the cells, instead of the weakest cell. It is proposed to call these “capacity EQUs”, and the properties they must have are described. One such EQU is the bilevel equalizer (BEQ), described previously. This present paper provides an enhanced analysis of the BEQ and improved modelling methods. It also presents more details that are necessary to implement the microcontroller algorithm for the BEQ hardware. Full article

Water scarcity is an important issue in many countries, and it is therefore necessary to improve the efficiency and equality of water resource allocation for decision makers. Based on game theory (GT), a bi-level optimization model is developed from the perspective of a leader-follower relationship among agents (stakeholders) of a river basin in this study, which consists of a single-agent GT-based optimization model of common interest and a multi-agent cooperative GT-based model. The Hanjiang River Basin is chosen as a case study, where there are conflicts among different interest agents in this basin. The results show that the proposed bi-level model could attain the same improvement of common interest by 8%, with the conventional optimal model. However, different from the conventional optimal model, since the individual interests have been considered in the bi-level optimization model, the willingness of cooperation of individuals has risen from 20% to 80%. With a slight decrease by 3% of only one agent, the increases of interest of other agents are 14%, 18%, 7%, and 14%, respectively, when using the bi-level optimization model. The conclusion could be drawn that the proposed model is superior to the conventional optimal model. Moreover, this study provides scientific support for the large spatial scale water resource allocation model. Full article

Due to variations among the cells, large lithium ion batteries (LIB) such as those in battery energy storage stations (BESS) and electric vehicles (EVs) must have an equalizer (EQU) circuit to balance the cell voltages. In spite of their significant losses and other limitations, passive equalizers (PEQ) are used in most applications because they are relatively simple and low cost. Active equalizers (AEQ) reduce these PEQ problems, but are not as widely used due to their much higher cost and complexity. A new hybrid circuit called the Bilevel EQU (BEQ) combines the PEQ and AEQ to provide much higher performance than a pure PEQ but at a much lower cost than a pure AEQ. Full article