Power,Embedded Games,and Coalition Formation

Applications of game theory frequently presume but do not show that social structures contain games. This study shows that multiple games are embedded in strong power structures and that power is exercised because 1) the game of those low in power contains a dilemma whereas 2) the game of those high in power does not. As in previous analyses, we find those low in power play the Prisoner's Dilemma game. New to this analysis is the discovery that those high in power play the Privileged game, a game with no dilemma. Also new is the extension of the analysis to the design of coalitions. That extension shows that, when coalition formation succeeds, it eliminates the dilemma of those low in power by transforming their game from Prisoner's Dilemma to Privileged. By contrast, exactly the same coalition structure does not alter the game played by those high in power. Applying well-known game theoretic solution concepts, we predict that low power coalitions will countervail power, but that coalitions of those high in power will not affect power exercise. Experiments testing this theory investigate 1) coalitions of those high in power, 2) low power coalitions organized against multiple high power positions, and 3) opposed coalitions struggling for power against each other. Results strongly support the theory.     

功率型变分原理和功能型拟变分原理及其应用

自从钱伟长建立了功率型变分原理以来,功率型变分原理和功能型变分原理在理论方面和应用方面有什么区别和联系,成为学术界关注的课题.应用变积方法,根据Jourdain原理和d’Alembert原理,建立了不可压缩黏性流体力学的功率型变分原理和功能型拟变分原理,推导了不可压缩黏性流体力学的功率型变分原理的驻值条件和功能型拟变分原理的拟驻值条件.研究了不可压缩黏性流体力学的功率型变分原理在有限元素法中的应用.研究表明,功率型变分原理与Jourdain原理相吻合,功能型变分原理与d’Alembert原理相吻合.功率型变分原理直接在状态空间中研究问题,不仅在建立变分原理的过程中可以省略在时域空间中的一些变换,而且给动力学问题有限元素法的数值建模带来方便.     

工业化、城镇化进程中电力需求分析及预测

随着工业化、城镇化进程的不断加快,我国电力需求量将持续上升。电力的充足供应是我国经济稳步发展的重要保证,故合理准确的对电力需求进行分析及预测具有重要的现实意义。基于此,分析我国电力需求现状,利用通径分析筛选电力消费需求的核心驱动因素。在模型选择的基础上,基于单变量(ETS、ARIMA模型)和多变量(情景分析)两个维度进行电力需求量分析及预测。结果表明:GDP每提高1%使得电力需求量提高0.5249%;工业化水平每提高1%使得电力需求量提高2.2146%,城镇化水平每提高1%使电力需求量相应提高1.0076%。“十二五”末中国电力消费需求量将近61425.96KW/h,2020年中国电力消费需求将近81410.10KW/h。     

The non-Markovian approach to the valuation and hedging of European contingent claims on power with scaling spikes

We present and further develop a new approach to modeling power prices with spikes proposed earlier by the author. In contrast to other approaches, we model power prices with spikes as a non-Markovian stochastic process that allows for modeling spikes directly as self-reversing jumps. We show how this approach can be used to value European contingent claims on power with spikes as well as to value and dynamically hedge European contingent claims on forwards on power for power with spikes in a practically important special case of the scaling probability distribution for the magnitude of spikes.     

Modeling of uplink power control for cognitive radio networks: Cooperative and noncooperative

In this paper, the uplink power control problem is modeled by considering both cooperative and noncooperative methods respectively to protect licensed users in cognitive radio networks. The cooperative power control optimization problem is modeled as a concave minimization problem. According to the properties of the power control optimization problem, an improved branch and bound algorithm is proposed. On the other hand, for the noncooperative power control case, a game theoretic model with the exponential pricing function is adopted to restrict the interference to the licensed users. Further, Nash equilibrium for the power control game is discussed. Finally, the performance of the proposed models is evaluated by computer simulation.     

Efficient algorithms for combined heat and power production planning under the deregulated electricity market

Combined heat and power (CHP) production is an important energy production technology that can yield much higher total energy efficiency than separate heat and power generation. In CHP production, the heat and power production follows a joint characteristic, which means that the production planning must be done in coordination. Cost-efficient operation of a CHP system can be planned by using an optimization model. A long-term planning model decomposes into thousands of hourly models. Earlier, in the regulated electric power market, the planning problem was symmetrically driven by heat and power demand. The liberalization of the power market has created an asymmetrical planning problem, where heat production responds to the demand and power production to the volatile market price. In this paper, we utilize this asymmetry to develop novel envelope-based dual algorithms for solving the hourly CHP models efficiently. The basic idea is to transform the three-dimensional characteristic operating region for heat and power production of each CHP plant into a two-dimensional envelope by taking the power price as a parameter. Then the envelopes of each plant are used for looking up the optimal solution rapidly. We propose two versions of the algorithm: the on-line envelope construction algorithm (ECON) where the envelopes are constructed for each hour based on the power price and the off-line envelope construction algorithm (ECOFF) where envelopes are pre-computed for all different power price ranges. We derive the theoretical time complexity of the two algorithms and compare their performance empirically with realistic test models against the ILOG CPLEX solver and the Power Simplex (PS) algorithm. PS is an extremely efficient specialized primal algorithm developed for the symmetrical CHP planning problem under the regulated market. On average, when reusing previous basic solutions, ECON is 603 times faster than CPLEX and 1.3 times faster than PS. ECOFF is 1860 times faster than CPLEX and four times faster than PS.     

Power contexts and their concept lattices

We introduce a framework for the study of formal contexts and their lattices induced by the additional structure of self-relations on top of the traditional incidence relation. The induced contexts use subsets as objects and attributes, hence the name power context and power concept. Six types of new incidence relations are introduced by taking into account all possible combinations of universal and existential quantifiers as well as the order of the quantifications in constructing the lifted power contexts. The structure of the power concept lattice is investigated through projection mappings from the baseline objects and attributes to those of the power context, respectively. We introduce the notions of extensional consistency and intensional consistency, corresponding to the topological notions of continuity in the analogous setting when concepts are viewed as closed sets. We establish Galois connections for these notions of consistency. We further introduce the notion of faithfulness for the first type of lifted incidence relation based on the fact that it can be equivalently characterized by a concept-faithful morphism. We also present conditions under which the power concept lattice serves as a factor lattice of the base concept lattice.     

农村小型风力发电机的控制与并网仿真

设计了双馈风力发电机组的定子磁链矢量控制系统,构造了容量为9MW的风力发电系统;通过MATLAB软件,分别在变风速和恒定风速两种情况时,对风力发电系统并网进行仿真.仿真结果表明,利用矢量变换技术的控制方法,风力发电系统可以实现有功功率和无功功率的快速解耦并且动态响应快,跟随性能好.     

政府激励下秸秆发电供应链的演化博弈模型与分析

农户供应链的序贯决策模型,得出了供应链三方的最优决策;对比了政府激励下供应链各主体决策及利润的变化,分析了政府激励的重要性;其次,建立了在政府激励作用下,发电厂、中间商之间的演化博弈模型,并得出了合理的激励策略。最后,以某地区秸秆发电供应为例,对电厂和中间商之间的合作关系进行分析,验证模型的正确性。揭示了秸秆发电供应链合作中的规律,对电厂、中间商制定合理的激励策略具有参考价值,同时为政府调控政策提供理论依据,从而建立持久的合作关系,推动秸秆发电行业的发展。     

Power Measures and Solutions for Games Under Precedence Constraints

Games under precedence constraints model situations, where players in a cooperative transferable utility game belong to some hierarchical structure, which is represented by an acyclic digraph (partial order). In this paper, we introduce the class of precedence power solutions for games under precedence constraints. These solutions are obtained by allocating the dividends in the game proportional to some power measure for acyclic digraphs. We show that all these solutions satisfy the desirable axiom of irrelevant player independence, which establishes that the payoffs assigned to relevant players are not affected by the presence of irrelevant players. We axiomatize these precedence power solutions using irrelevant player independence and an axiom that uses a digraph power measure. We give special attention to the hierarchical solution, which applies the hierarchical measure. We argue how this solution is related to the known precedence Shapley value, which does not satisfy irrelevant player independence, and thus is not a precedence power solution. We also axiomatize the hierarchical measure as a digraph power measure.     

模的r-比较与r-幂比较

本文研究模的r-比较性和r-幂比较性,给出了r-比较性的新刻划,得到了模的r-幂比较结构与其自同态环的r-幂比较性间的关系,证明了如果模M为r-幂比较的则它的任意直和项也是r-幂比较的．对于可分置换环,给出了r-幂比较性与r-比较性间的联系．     

Minimal-axiom characterizations of the Coleman and Banzhaf indices of voting power

Coleman [Coleman, J.S., 1971. Control of collectives and the power of a collectivity to act. In: Lieberman, B. (Ed.), Social Choice. Gordon and Breach, New York, pp. 269–298] suggested two indices of voting power, power to prevent an action and power to initiate an action. This paper develops two-axiom (and hence, minimal) characterizations of both the indices. We also show that similar characterizations can be done for other indices.     

Spatial dependencies of wind power and interrelations with spot price dynamics

Wind power has seen strong growth over the last decade and increasingly affects electricity spot prices. In particular, prices are more volatile due to the stochastic nature of wind, such that more generation of wind energy yields lower prices. Therefore, it is important to assess the value of wind power at different locations not only for an investor but for the electricity system as a whole. In this paper, we develop a stochastic simulation model that captures the full spatial dependence structure of wind power by using copulas, incorporated into a supply and demand based model for the electricity spot price. This model is calibrated with German data. We find that the specific location of a turbine – i.e., its spatial dependence with respect to the aggregated wind power in the system – is of high relevance for its value. Many of the locations analyzed show an upper tail dependence that adversely impacts the market value. Therefore, a model that assumes a linear dependence structure would systematically overestimate the market value of wind power in many cases. This effect becomes more important for increasing levels of wind power penetration and may render the large-scale integration into markets more difficult.     

Minimal-axiom characterizations of the Coleman and Banzhaf indices of voting power

Coleman [Coleman, J.S., 1971. Control of collectives and the power of a collectivity to act. In: Lieberman, B. (Ed.), Social Choice. Gordon and Breach, New York, pp. 269–298] suggested two indices of voting power, power to prevent an action and power to initiate an action. This paper develops two-axiom (and hence, minimal) characterizations of both the indices. We also show that similar characterizations can be done for other indices.     

A robust and informative method for solving large-scale power flow problems

Solving power flow problems is essential for the reliable and efficient operation of an electric power network. However, current software for solving these problems have questionable robustness due to the limitations of the solution methods used. These methods are typically based on the Newton–Raphson method combined with switching heuristics for handling generator reactive power limits and voltage regulation. Among the limitations are the requirement of a good initial solution estimate, the inability to handle near rank-deficient Jacobian matrices, and the convergence issues that may arise due to conflicts between the switching heuristics and the Newton–Raphson process. These limitations are addressed by reformulating the power flow problem and using robust optimization techniques. In particular, the problem is formulated as a constrained optimization problem in which the objective function incorporates prior knowledge about power flow solutions, and solved using an augmented Lagrangian algorithm. The prior information included in the objective adds convexity to the problem, guiding iterates towards physically meaningful solutions, and helps the algorithm handle near rank-deficient Jacobian matrices as well as poor initial solution estimates. To eliminate the negative effects of using switching heuristics, generator reactive power limits and voltage regulation are modeled with complementarity constraints, and these are handled using smooth approximations of the Fischer–Burmeister function. Furthermore, when no solution exists, the new method is able to provide sensitivity information that aids an operator on how best to alter the system. The proposed method has been extensively tested on real power flow networks of up to 58k buses.     

On some conjectures on generalized quadratic Gauss sums and related problems

The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic methods and algebraic geometric methods. We prove two conjectures which were proposed recently by the above authors in a previous article (2022). Here we obtain an asymptotic formula for arbitrary power means of generalized quadratic Gauss sums and one corresponding power moment of a character sum.     

Semisimple games,enactment power and generalized power indices

By allowing for individual abstention, the classC of simplen-person games is extended to the class ofsemisimple gamesS. Using this extension, any given index of individual power onC gives rise to a measure of individual power onS in the form of a vector function with 2 ⁿ ?1 components. After developing an axiomatic characterization of Coleman's notion of collective power, thisenactment power is combined with any index of individual power to provide a general nonnormalized meausre of individual power. Using these results, enactment and individual power in different games can be meaningfully compared. In the presence of abstention, various “paradoxes” associated with power indices lose some of the impact.     

On the minimum degree,edge-connectivity and connectivity of power graphs of finite groups

In this paper, the minimum degree of power graphs of certain cyclic groups, abelian p-groups, dihedral groups and dicyclic groups are obtained. It is ascertained that the edge-connectivity and minimum degree of power graphs are equal, and consequently, the minimum disconnecting sets of power graphs of the aforementioned groups are determined. In order to investigate the equality of connectivity and minimum degree of power graphs, certain necessary conditions for finite groups and a necessary and su?cient condition for finite cyclic groups are obtained. Moreover, the equality is discussed for the power graphs of abelian p-groups, dihedral groups and dicyclic groups.