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In an electricity market cleared by a merit-order economic dispatch we first identify the necessary conditions for the market outcomes supported by pure strategy Nash equilibria (NE) to exist when generating companies (Gencos) game through their incremental cost offers or supply functions. A Genco may own any number of units, each offering to generate power through an incremental cost curve or supply function consisting of multiple blocks. Then, we develop a mixed-integer linear programming (MILP) scheme to find the NE without approximations or iterations. In Part II of this paper, we show how to use these NE to derive a dominant offer strategy in terms of gaming or not gaming that best meet the risk/benefit expectations of the participating Gencos. The MILP scheme is tested on several systems of up to 30 generating units, each with four incremental cost blocks. Finally, based on these results, we carry out a number of numerical analyses of how market power is influenced by the number and size of the competing Gencos. Index Terms--Electricity markets, gaming, market outcomes, market power, merit order, mixed-integer linear programming, pure strategy Nash equilibria, strategic offers, supply function equilibrium.

In an electricity market cleared by a merit-order economic dispatch we make use of the mixed-integer linear programming (MILP) scheme derived in Part I to find the market outcomes supported by a pure strategy Nash equilibria (NE). From these NE, we identify offer strategies in terms of gaming or not gaming that best meet the risk/benefit expectations of the participating Gencos. To do this, a number of measures of potential profit gain and loss are developed that quantify the notion of risk/benefit under the possible multiple NE. The NE identification scheme is tested on several systems of up to 30 generating units, each with four incremental cost blocks, also showing how market power is influenced by the number and size of the competing Gencos as well as by the imposed price cap. Index Terms--Dominant strategy, electricity market, gaming, market power, merit order, mixed-integer linear programming, multiple pure strategy Nash equilibra, strategic offers, supply function equilibrium.

In their attempt to cut down on greenhouse gas emissions from electricity generation, several countries are committed to install wind power generation up to and beyond the 10%-20% penetration mark. However, the large-scale integration of wind power represents a challenge for power system operations planning because wind power 1) cannot be dispatched in the classical sense; and 2) its output varies as weather conditions change. This warrants the investigation of alternative short-term power system operations planning methods capable of better coping with the nature of wind generation while maintaining or even improving the current reliability and economic performance of power systems. To this end, this paper formulates a short-term forward electricity market-clearing problem with stochastic security capable of accounting for nondispatchable and variable wind power generation sources. The principal benefit of this stochastic operation planning approach is that, when compared to a deterministic worst-case scenario planning philosophy, it allows greater wind power penetration without sacrificing security. Index Terms--Electricity markets, expected load not served, level of penetration, reserve, stochastic security, uncertainty, unit commitment, wind power generation.

In mixed pool/bilateral electricity markets, participants can sign forward bilateral contracts several months in advance of its delivery. In addition, generators may sell to and loads may buy from the pool at the spot price through the dayahead or balancing markets. Forward bilateral contracts have the advantage of price predictability in comparison with the uncertain spot price. However, the risk is that such a contract commits the partners to a price that may be disadvantageous compared to the spot price. Here, we propose a systematic negotiation scheme through which a generator and load can reach a mutually beneficial and risk tolerable forward bilateral contract, either physical or financial. Under this approach, the generator and load respond rationally to a stream of bilateral bids/counter-bids and offers/counter-offers considering their respective benefits while accounting for the risks incurred by the prediction uncertainty in the pool spot price and other market parameters over the length of the contract. Each negotiating party can choose its own definition of risk which can be influenced by regret, value-at-risk or dispersion from the mean. Numerical tests show that this flexible negotiating approach can be readily put into practice. Index Terms--Contract negotiation, forward bilateral contracts, market uncertainty, pool/bilateral electricity markets, regret, risk/ benefit analysis, value-at-risk.

This paper presents an approach for the allocation of transmission network costs by controlling the nodal electricity prices. The proposed approach introduces generation and nodal injection penalties into the traditional economic dispatch so as to create nodal price differences that recover the required transmission revenue from the resulting congestion rent. As a consequence, the new electricity prices reflect not only the marginal costs of production subject to transmission constraints but also the capital costs of the network. This is the approach commonly adopted with most commodities whose price includes the unit cost of the good itself as well as the transportation cost from the production centers to the final consumer. Index Terms--Bilevel programming, congestion rent, economic dispatch (ED), nodal prices, transmission cost allocation (TCA).

We show that the system loss function in a power network is bounded below by any number of supporting hyper-planes in the space of generalized injections. A supporting hyper-plane is defined by the linear Taylor series expansion of the system loss function around a given operating point. The supporting hyper-plane property is valid provided that the expansion point is sufficiently near the flat-voltage profile. We have assessed experimentally the range of validity of this assumption, called the range of hyper-plane support (RHS), showing that for typical networks, the RHS is broad, particularly when the bus voltages are controlled near 1 per unit. The supporting hyper-plane model was also tested as part of an economic dispatch with transmission losses to demonstrate that this linear model provides the same results as when the losses are treated as a nonlinear function. Index Terms--Convexity, linear loss approximation, load flow, loss formulae, supporting hyper-planes, system loss.

This paper analyzes the market-clearing formulation with stochastic security developed in its companion paper through two case studies solved using mixed-integer linear programming techniques. The generation and reserve schedules as well as the nodal prices of energy and security are assessed under various conditions such as a) line flow limits, b) when nonspinning reserve is excluded from the formulation, c) demand-side valuation of energy not served, d) generator ramping limits, and e) the set of pre-selected contingencies. Index Terms--Computational complexity, electricity markets, expected load not served, marginal pricing, mixed-integer linear programming, reserve, security, stochastic unit commitment, value of lost load.

The unit commitment problem with tertiary reserve requirements has been broadly studied. Such reserves, when needed, are centrally deployed with relatively slow time constants of the order of minutes. In contrast, the scheduling of units offering primary frequency regulation reserve deployable in a decentralized manner within seconds of a contingency has received relatively little attention. In this paper, we formulate and solve a multiperiod unit commitment that simultaneously accounts for both primary and tertiary reserve constraints. What makes this scheduling problem particularly challenging is the characteristic that primary frequency regulation reserves have a common single degree of freedom, namely, the system frequency deviation. Index Terms--Mixed-integer linear programming, primary frequency regulation, primary reserve, security, tertiary reserve, unit commitment.

The first of this two-paper series formulates a stochastic security-constrained multi-period electricity market-clearing problem with unit commitment. The stochastic security criterion accounts for a pre-selected set of random generator and line outages with known historical failure rates and involuntary load shedding as optimization variables. Unlike the classical deterministic reserve-constrained unit commitment, here the reserve services are determined by economically penalizing the operation of the market by the expected load not served. The proposed formulation is a stochastic programming problem that optimizes, concurrently with the pre-contingency social welfare, the expected operating costs associated with the deployment of the reserves following the contingencies. This stochastic programming formulation is solved in the second companion paper using mixed-integer linear programming methods. Two cases are presented: a small transmission-constrained three-bus network scheduled over a horizon of four hours and the IEEE Reliability Test System scheduled over 24 h. The impact on the resulting generation and reserve schedules of transmission constraints and generation ramp limits, of demand-side reserve, of the value of load not served, and of the constitution of the pre-selected set of contingencies are assessed. Index Terms--Deterministic/probabilistic security criteria, electricity markets, expected load not served, failure rate, reserve, stochastic programming, transmission limits, unit commitment, value of lost load.

The concept of electrothermal coordination (ETC) in power system operation introduced in Part I proposes to exploit thermal inertia to coordinate line temperature dynamics with existing power system controls, thus increasing power transfer capability and enhancing system security and economic performance. In this Part II, the characteristics of ETC and its benefits in operational functions such as augmenting power transfer capability, emergency control, congestion management, and system loadability are numerically analyzed through a number of case studies. This paper also examines some practical issues concerning the deployment of ETC. Index Terms--Congestion management, emergency control, heat balance equation, line thermal rating, load shedding, power transfer capability, temperature dynamics.

This paper presents a solution procedure for the mixed-integer bilevel programming model of the electric grid security under disruptive threat problem, here concisely denoted by (ST-MIBLP), that was recently reported. Using results from linear programming theory and some basic linearization of products of binary-binary or binary-continuous variables, we recast (ST-MIBLP) into a standard (one-level) mixed-integer linear program (ST-MILP) with no more binary variables than in the original (ST-MIBLP). This transformation provides a framework for globally solving (ST-MIBLP) using available mixed-integer linear programming solvers. Some numerical results obtained by the new method are compared with those recently published, based on IEEE Reliability Test Systems. Index Terms--Bilevel programming, linear duality, mathematical program with optimization in the constraints, mixed-integer linear programming, network security.

This paper deals with the problem of transmission cost allocation (TCA) in very large networks with multiple interconnected regions or countries. The basis of one scheme recently put forward is a single-area TCA algorithm from which inter-regional compensations are computed. One concern about this approach is that an international operator (IO) must have access to detailed information that autonomous regions or countries may not be willing or able to share. This led to the development of a new multiarea TCA scheme, called multiarea decoupled (MAD), in which each region carries out its own TCA, while the IO carries out a region-wise TCA on the network of tie lines. In MAD, the IO does not require detailed and possibly proprietary information about regional networks, relying only on the characteristics of the tie-line network and the extent to which each region uses such a network. This is a key issue, especially in North America, considering FERC's intention to provide Regional Transmission Organizations (RTOs) with exclusive autonomy to provide transmission service and to set and administer their own transmission-use tariffs. Numerical studies on the proposed scheme are described, including a four-area system based on the IEEE reliability test system (RTS) network. Index Terms--Equivalent bilateral exchange, flow based, multiarea networks, proportional sharing, tie lines, transmission cost allocation (TCA).

This paper analyzes some unresolved pricing issues in security-constrained electricity markets subject to transmission flow limits. Although the notion of separate reserve types as proposed by FERC can be precisely and unambiguously defined, when transmission constraints are active, the very existence of separate reserve prices and markets is open to question when the prices are based on marginal costs. Instead, we submit here that the only products whose marginal costs can be separately and uniquely defined and calculated are those of energy and security at each node. Thus, under marginal pricing, at any given network bus all scheduled reserve types should be priced not at separate rates but at a common rate equal to the marginal cost of security at that bus. Furthermore, we argue that nodal or area reserves cannot be prespecified but must be obtained as by-products of the market-clearing process. Simulations back up these conclusions. Index Terms--Contingency-constrained scheduling, demand-side reserve, electricity markets, security and energy pricing, transmission constraints, up and down-spinning reserve.

This paper generalizes the 'terrorist threat problem' first defined by Salmeron, Wood, and Baldick by formulating it as a bilevel programming problem. Specifically, the bilevel model allows one to define different objective functions for the terrorist and the system operator as well as permitting the imposition of constraints on the outer optimization that are functions of both the inner and outer variables. This degree of flexibility is not possible through existing max-min models. The bilevel formulation is investigated through a problem in which the goal of the destructive agent is to minimize the number of power system components that must be destroyed in order to cause a loss of load greater than or equal to a specified level. This goal is tempered by the logical assumption that, following a deliberate outage, the system operator will implement all feasible corrective actions to minimize the level of system load shed. The resulting nonlinear mixed-integer bilevel programming formulation is transformed into an equivalent single-level mixed-integer linear program by replacing the inner optimization by its Karush--Kuhn--Tucker optimality conditions and converting a number of nonlinearities to linear equivalents using some well-known integer algebra results. The equivalent formulation has been tested on two case studies, including the 24-bus IEEE Reliability Test System, through the use of commercially available software. Index Terms--Bilevel programming, deliberate outages, load shedding, mixed-integer linear programming (MILP), power system security and vulnerability, terrorist threat.

The concept of electrothermal coordination (ETC) in power system operation is proposed. ETC exploits thermal inertia to coordinate line temperature dynamics with existing system controls, thus increasing power transfer capability and enhancing system security and economic performance. This Part I begins with the theoretical basis of ETC and follows with an algorithm suitable for large-scale implementation in electricity markets, emphasizing that ETC can be readily integrated into existing software. The characteristics of ETC and its benefits in system operation are analyzed numerically in Part II through several case studies in power transfer capability, emergency load-shedding, congestion management, and system loadability. Index Terms--Day-ahead energy market clearing, electrothermal coordination, heat balance equation, line temperature dynamics, static and dynamic line thermal ratings.

As the arguments for and against the use of pay-as-bid (PAB) or marginal pricing (MP) in electricity pools tend to be qualitative, we compare the quantitative behavior of the two markets assuming that generators submit the best strategic offers that correspond to the specified pricing method. In Part I of this two-part study, assuming that the system marginal costs for PAB and MP are random with known probability density functions, we develop generator strategic offers by maximizing the corresponding expected values of the generator profits over the offer parameters. In Part II relations are established between the SMCs for each market type and a common random demand, thus allowing the two markets to be compared through the expected values and variances of the individual generation profits and of the consumer payments. This comparison demonstrates both theoretically and through simulation that: 1) the expected values of the individual generator profits as well as of the consumer payments are the same under MP and PAB and 2) the variances of the individual generator profits and of the consumer payments however are larger under MP than under PAB. The primary conclusion is then that although MP and PAB yield identical expected generator profits and consumer payments, the risk of not meeting these expected values is greater under MP than under PAB. Index Terms--Expected profit, marginal pricing, pay-as-bid, perfectly competitive markets, strategic offers, system marginal cost, uncertainty.

As the arguments for and against the use of pay-as-bid (PAB) or marginal pricing (MP) in electricity pools tend to be qualitative, we compare the quantitative behavior of the two markets assuming that generators submit the best strategic offers that correspond to the specified pricing method. In Part I of this two-part study, assuming that the system marginal costs for PAB and MP are random with known probability density functions, we develop generator strategic offers by maximizing the corresponding expected values of the generator profits over the offer parameters. In Part II, relations are established between the system marginal costs for each market type and a common random demand, thus allowing the two markets to be compared through the expected values and variances of the individual generation profits and of the consumer payments. This comparison demonstrates both theoretically and through simulation that: 1) he expected values of the individual generator profits as well as of the consumer payments are the same under MP and PAB and 2) the variances of the individual generator profits and of the consumer payments however are larger under MP than under PAB. The primary conclusion is then that although MP and PAB yield identical expected generator profits and consumer payments, the risk of not meeting these expected values is greater under MP than under PAB. Index Terms--Expected profit, marginal pricing, pay-as-bid, perfectly competitive markets, strategic offers, system marginal cost, uncertainty.

This paper is the second of a two-paper series. It is concerned with the numerical study of the solution procedure derived in [20] to solve the coordination problem that arises in a new equilibrium model [21], which for the purpose of this presentation applies to a static (no-time coupling costs or constraints) electricity pool market with price inelastic demand and no network. The new equilibrium model has the following main properties: i) every scheduled generator satisfies its minimum surplus (or bid profit) condition; ii) the energy price is a system marginal cost (a Lagrange multiplier associated with the power balance constraint to the related economic dispatch problem where all of the discrete variables are fixed to their optimal values); iii) the power balance and all of the generators' technical constraints are satisfied. We present some numerical results based on three test systems: a simple three-generating unit system that can be solved by hand, a 32-generating unit system that consists of piecewise linear offer curves, and a large system of 768 generating units with monotone and nonmonotone, piecewise linear offer curves, some of which are set as must-run units. The results demonstrate that the proposed procedure is more efficient than a heuristic approach, both in terms of solution quality and computational efficiency. Index Terms--Duality gap, integer programming, mathematical program with equilibrium constraints (MPEC), optimization methods, power generation economics, power generation scheduling.

This paper is concerned with developing an algorithm for solving the coordination problem that arises in a new equilibrium model [8], which for the purpose of this presentation applies to a static (no-time coupling costs or constraints) electricity pool market with price inelastic demand and no network. The new equilibrium model has the following main properties: i) every scheduled generator satisfies its minimum surplus (or bid profit) condition; ii) the energy price is a system marginal cost (Lagrange multiplier associated with the power balance constraint in the related economic dispatch problem where all of the discrete variables are fixed to their optimal values); iii) the power balance and all the generators' technical constraints are satisfied. To solve the coordination problem, which is a subproblem of the new equilibrium model, it is mathematically convenient to cast the former as a three-level nested optimization problem. We substitute the ensuing lower-level subproblems with an equivalent set of explicit algebraic equalities and inequalities. Hence, we obtain a one-level problem, which is a discrete-continuous mathematical program with complementarity or equilibrium constraints (MPEC). Finally, we transform the one-level mathematical program into mixed-integer linear form by substitution of the complementarity terms and the remaining nonlinear terms. Index Terms--Complementarity, coordination problem, integer programming, mathematical program with equilibrium constraints (MPEC), multilevel programming, operations research, optimization methods, power generation dispatch, power generation economics, power generation scheduling, power system economics.

This paper addresses the problem of reliability-constrained market-clearing in pool-based electricity markets with unit commitment. In general, probabilistic reliability criteria that implicitly set the reserve requirement are defined by the loss-of-load probability and by the expected load not served. As the computation of such metrics is complicated by their nonlinear and combinatorial nature, we introduce the notion of hybrid metrics based on the probabilities of loss-of-load due to single and double generation outages only. The reliability-constrained market-clearing problem can then be formulated as a mixed-integer linear program and solved with large-scale commercial solvers. Numerical tests with data from the IEEE Reliability Test System indicate that the new method is computationally efficient and produces market-clearing results with the desired probabilistic characteristics. Index Terms--Expected load not served, loss-of-load probability, mixed-integer linear programming, pool-based electricity markets, reliability-constrained market-clearing, spinning reserve, unit commitment.

This paper presents a novel methodology for allocating the cost of a transmission network to its users based on the principle of equivalent bilateral exchanges, which states that after all physical laws governing the flow of power have been met, each demand is assigned a fraction of each generation and each generator is assigned a fraction of each demand in a uniform manner. Transmission cost allocation based on this principle presents several advantages, namely, independence from the choice of the slack bus, recognition of counter-flows, and transmission use charges that are stable and always positive. Index Terms--Equivalent bilateral exchanges, transmission cost allocation.

We propose a market model that includes demand-side reserve offers and where energy and reserve are jointly dispatched. Generators and consumers can submit offers and bids on five distinct products--energy, upspinning reserve, downspinning reserve, and two kinds of standby reserve. The resources are scheduled and dispatched in a joint auction through a mixed-integer optimization program. The extra scheduling flexibility introduced by demand-side reserve offers can lead to significant gains in economic efficiency. Thus, the results suggest that not only do the consumers increase their profits but, in addition, the market power of the generators is reduced. Index Terms--Ancillary services, demand side bids and offers, electricity pools, reserve markets, unit commitment.

This paper makes use of recent advances in mixed integer linear programming (MILP) to conduct a preliminary design study on the combinatorial optimal placement of thyristor controlled phase shifter transformers (TCPSTs) in large-scale power systems. The procedure finds the number, network location, and settings of phase shifters that maximize system loadability under the dc load flow model, subject to limits on the installation investment or total number of TCPSTs. It also accounts for active flow and generation limits, and phase shifter constraints. Simulation results are presented for the IEEE 24-, 118-, and 300-bus systems, as well as a 904-bus network. The principal characteristics of our approach are compared with those of other published flexible ac system transmission (FACTS) allocation methods. Index Terms--FACTS, large-scale systems, mixed integer linear programming, phase shifters, system loadability.

Under a common condition called profit suboptimality, market equilibrium cannot be reached in electricity pools; in other words, no system marginal price exists for which the profit-driven independent generators would self-schedule to levels that exactly meet the demand. On the other hand, although a centrally imposed generation schedule satisfies power balance, it may force some agents to operate at a profit below what they could achieve under self-scheduling. This paper examines these incompatible goals and proposes a conflict resolution scheme based on the notion of generalized uplift functions. These functions are defined such that they: i) change the offered generation cost characteristics so as to increase the system marginal price, thus forcing the consumers to compensate the generators for part of their combined loss of profit; ii) execute an equitable transfer of revenues among the generators so that these also participate in any loss of profit compensation; iii) ensure market equilibrium at the centralized minimum cost solution; iv) ensure that the net sum of the uplifts adds up to zero. Index Terms--Generalized uplifts, loss of profit, marginal pricing, market equilibrium, pool operation.

Some of the various services provided under mixed pool/bilateral electricity trading are i) power to satisfy bilateral contract demand; ii) power for transmission losses and congestion management due to bilateral contracts; iii) power for transmission losses and congestion management due to wheeling contracts; and iv) power for transmission losses and congestion management due to pool demand. A procedure is developed and tested to unbundle these MW services as well as their corresponding costs, thus allowing the calculation of the average cost of each service. Comparison of the average and marginal costs serves to evaluate the relative profitability of each service. The goal of these results is to help generator and load-serving entities choose appropriate relative levels of pool versus bilateral trades while considering risk, economic performance, and physical constraints. Index Terms--Average and marginal costs, congestion management, cost unbundling, losses, pool/bilateral/wheeling markets.

This paper deals with the dispatch of power net works under mixed pool/bilateral trading. The major questions that are examined are the following: 1) To what degree does the relative level of pool versus bilateral trading influence performance in terms of individual power levels, costs, prices, and revenues? 2) What is the comparative performance of mixed trading with firm and nonfirm bilateral contracts under various curtailment strategies? 3) Is the revenue derived from the pool and bilateral trading consistent with the corresponding unbundled costs? The above questions are sequentially addressed in separate parts of this three-part paper. The eventual goal of these results is to help generator and load-serving entities choose appropriate relative levels of pool versus bilateral trades while considering risk, economic performance, and physical constraints. In Part H, two types of bilateral contracts, firm and nonfirm, are introduced together with their respective curtailment and noncurtailment bids. The optimal power-flow problem from Part I is now modified to accommodate this new type of operation. Technical and economical performance measures defined in Part I, namely, generation revenues from bilateral and pool sales, pool demand payments, plus generation and load expenditures to cover transmission loss and congestion management attributed to bilateral exchanges are also used here together with revenues from contract curtailment and expenditures due to noncurtailment bidding. Simulation results illustrate the effects of firm and nonfirm contracts and their bidding strategies on the relative levels of pool/bilateral trading, as well as on economic performance of market participants. Index Terms--Bilateral contracts, costs, curtailment and noncurtailment bidding strategies, firm and nonfirm contracts, incremental costs, mixed trading strategies, pool operation, prices, revenues.

A transmission network plays a key role in allowing access to the most efficient generators to all consumers. In most cases, the new transmission projects are defined by a system operator, which focuses on improving the bulk system's reliability and reducing short-term operating problems. Because electricity market participants are prevented from investing in transmission facilities that may benefit them, transmission expansion may not have been sufficient to stimulate competition within the market. In this paper, we show formally through a mathematical formulation based on the Lagrangian relaxation technique that the investment on transmission capacity can be a profitable activity, and therefore, the introduction of competition in the transmission expansion could be possible. Such a competitive expansion of transmission capacity would allow the participants to improve the efficiency of the electricity market. Index Terms--Optimization methods, power transmission economics and planning, pricing.

In this paper, we discuss issues and methods for attaining equilibrium in electric power auction markets with unit commitment. We consider a generation-side competition whereby producers are profit maximizing agents subject to prices only. For expository purposes, we will consider the single-period unit commitment problem, which is still quite rich for this presentation. We show that it is possible to eliminate the duality gap or cycling that occurs in a decentralized decision-making environment that encompasses discontinuous nonconvex programs. This result extends previous work on coordination of locally constrained self-interested agents, and it has a broad scope of applications that may be of interest to power systems engineers, market designers, economists and mathematicians. Index Terms--Duality, integer programming, mathematical programming, operations research, optimization methods, power generation dispatch, power generation economics, power generation scheduling, power system economics, quadratic programming.

We present a single time period decentralized electricity market clearing model that includes reactive power and demand responsiveness in addition to the more common framework of generation-side competition for the real power commodity. The approach allows self-interested agents, namely producers and consumers, independently to maximize their individual surpluses subject to prices. This is consistent with the very notion of a competitive market as defined in equilibrium theory. An auctioneer computes equilibrium prices that achieve power balance at every network node as required by Kirchhoff's laws. The overall scheme is justified by duality theory for which there is a rich theoretical support, and convergence is achieved using a Newton price-updating algorithm. Index Terms--Auction, market coordination, market equilibrium, mathematical programming, optimization methods, power generation dispatch, power generation economics, power generation scheduling, power system economics.

This paper presents a multiperiod electricity auction market tool that explicitly takes into account transmission congestion and losses as well as intertemporal operating constraints such as start-up costs, ramp rates, and minimum up and down times that may be included in any generating unit's composite bid. This approach, which requires only existing mixed-integer linear solvers, provides the market operator with a valuable tool for scheduling participants in a competitive market where transparency, fairness, and confidentiality of participants' data are of paramount concern. Indeed, under this framework, only network data are of public domain; producers are not required to reveal corporate data, and they have more flexibility in specifying the structure of their composite bid. This paper demonstrates and illustrates, through numerical studies using test systems, that an efficient and fair competitive electricity market can be implemented, taking into account network constraints and losses. Index Terms--Congestion management, mixed-integer linear programming, nodal pricing, pool-based electricity market, social welfare maximization.

This three-paper series deals with the dispatch of power networks under mixed pool/bilateral trading. The major questions examined are i) To what degree does the relative level of pool versus bilateral trading influence performance in terms of individual power levels, costs, prices, revenues and expenditures; ii) what is the comparative performance of mixed trading with firm and nonfirm bilateral contracts under various curtailment strategies; and iii) is the revenue derived from the pool and bilateral trading consistent with the corresponding unbundled costs? The above issues are sequentially addressed in each of the three parts. The eventual goal of these results is to help generator and load-serving entities choose appropriate relative levels of pool versus bilateral trades while considering risk, economic performance, as well as physical constraints. This paper proposes a one-step optimal power flow model that dispatches the pool in combination with the privately negotiated bilateral contracts while minimizing cost and accounting for both losses and congestion. In Part I, notions of pool/bilateral demand and generation as well as a number of technical and economic performance measures for each competing entity are defined. This dissection of total and individual financial measures according to pool or bilateral trading allows market participant to evaluate the profitability of each component of its chosen pool/bilateral mix. A number of simulation results illustrate the effect of varying the relative levels of pool/bilateral trading on the values of individual performance measures. Index Terms--Bilateral contracts, costs, economic and technical performance, expenditures, mixed trading strategies, nodal prices, pool operation, revenues.

Incremental transmission loss analysis has been used for decades, but recent interest in its application to loss allocation calls for new in-depth results. This paper demonstrates that, for incremental methods to be applied correctly in loss allocation, it is first necessary to specify the load distribution and loss supply strategies. Incremental loss allocation among bus power injections is shown to be arbitrary and, therefore, open to challenge as discriminatory. Loss allocation is possible among incremental loads and/or generators, but the proportion of the total losses assigned to either one is arbitrary. Unique, nonarbitrary incremental loss allocations are however possible among the 'equivalent' incremental bilateral exchanges between generators and loads. From these basic components it is possible then to calculate the allocation among generators or loads in any specified proportion. The main results, although developed initially for small increments, are extended to large variations. Finally, a general incremental loss allocation algorithm is developed and tested. Index Terms--Equivalent bilateral contracts, incremental transmission loss analysis, loss allocation, loss supply, numerical algorithm, pool dispatch.

This paper addresses one of the most critical questions in operation and planning in a deregulated environment, namely, how to evaluate an electricity transaction on the basis of system security, especially when numerous transactions have to be processed simultaneously. From a planning perspective, the question of how to identify the most suitable reinforcements needed to maintain system security so that all entities (e.g. producers, consumers and traders etc.) can have equal opportunity to buy or sell is also addressed. Monte Carlo simulations are used to construct a large population of random Bilateral Transaction Matrices (BTM) simulating the market activities. Quantitative measures, termed the Probabilities of Secure Transactions (POST), are derived from the simulation results to analyze the feasibility of transactions in terms of security. The impact of firm contracts on system security as measured by POST is also studied under different operating and planning scenarios. Keywords: Deregulation, bilateral transaction, probabilistic security analysis, Monte Carlo simulations

Several models are being considered by the power industry for competition under open access transmission Each alternative offers a radically different solution which must be evaluated, not only in terms of economic benefits, but also in terms of impact on power system security. This paper therefore presents a general mathematical framework for the analysis and management of power transactions under open access subject to system security constraints. The framework introduces the notions of a virtual network of transactions and the transactions matrix, both describing virtual power flows among financial entities. Finally, this paper shows how the transactions selected by the market forces are influenced by the security requirements of the physical network. Keywords: Open access, power networks, power transactions, system security, reservation and trading of transaction rights.

This paper presents a systematic analysis of the main reasons for the failure of solution algorithms in the general non-linear optimal power flow (OPF) problem. It defines the concept of critical and non-critical OPF problems and identifies and categorizes the main types of such cases. In essence, a non-critical case is one where a small variation in a parameter leads to a small change in the optimum solution. Alternatively, critical cases are such that a small variation in a problem parameter leads to either the loss of local optimality or feasibility. Both of these can result in a sharp discontinuity in the solution. Numerical and theoretical examples illustrate each of these cases. Keywords: Optimal Power Flow; Parameter Variation; Loss of Local Optimality; Loss of Local Feasibility.

The relevance of exergetic analysis in the design of electric energy systems is demonstrated. This analysis provides a quantitative measure of the quality of energy in terms of its ability to perform work and leads to a more rational use of energy. A general and easy-to-use model, implemented in object oriented programming, is developed for the planning of electric energy systems including cxergetic considerations. The model presented is applied to a space-heating study and to a regional planning case. KEYWORDS: electric energy system planning, exergy, energy, object-oriented programming, simulation.

This paper shows how the use of new-generation tools such as a generalized shell for dynamic security analysis can help improve our understanding of fundamental power systems behaviour. Using the ELISA prototype shell as a laboratory tool, it is shown that the signal energy of the network impulse response acts as a barometer to define the relative severity of a contingency with respect to some parameter, for instance power generation or power transfer. In addition, for a given contingency, as the parameter is varied and a network approaches instability, signal energy increases smoothly and predictably towards an asymptote which defines the network's stability limit: this, in turn, permits us to compare the severity of different contingencies. Using a Fourier transform approach, it is shown that this behaviour can be explained in terms of the effect of increasing power on the damping component of a power system's dominant poles. A simple function is derived which estimates network stability limits with surprising accuracy from two or three simulations, provided that at least one of these is within 5% of the limit. These results hold notwithstanding the presence of many active, nonlinear voltage-support elements (i.e. generators, synchronous condensers, SVCs, static excitation systems, etc.) in the network.

This paper introduces the concept of a generalized shell for performing power-system dynamic security analysis. The generalized shell mechanizes routines traditionally carried out by human experts and that are essential to power-system dynamic security analysis, thereby greatly accelerating the realization of complex processes. The shell semantics express high-level goals and tasks using a friendly, highly compact syntax which closely matches the language of operations planners. Typically, the shell will execute appropriate load-flow and transient-stability simulations (i.e. using commercially available simulation software), perform result analysis, make input changes and repeat this process until a user-defined goal has been achieved. A working shell prototype for performing key algorithmic processes is described and results of a typical sensitivity study are presented using a 700-bus model of the Hydro-Quebec network. It is expected that the prototype will reduce study-cycle time, improve the accuracy of dynamic security limits and, indeed, transform the working environment of operations and system planners. Eventually, it can be foreseen that the approach will gravitate towards supporting on-line dynamic security analysis.

The solid-state, pulse width modulated (PWM) phase-shifter is based on gate-turn-off (GTO) thyristors or other valves with force commutation capabilities. Besides serving the phase-shifter function, it offers regulated control over 3 independent quantities: the real power passing through it and the VARs on both sides to which it is connected. The power transferred can be bidirectional and the VARs can be leading or lagging.

This paper presents a new procedure for allocating transmission losses to generators and loads in the context of pools operated under a single marginal price derived from a merit-order approach. The procedure is based on the network Z-bus matrix, although all required computations exploit the sparse Y-bus matrix. One innovative feature and advantage of this method is that, unlike other proposed approaches, it exploits the full set of network equations and does not require any simplifying assumptions. The method is based on a solved load flow and is easily understood and implemented. The loss allocation process emphasizes current rather than power injections, an approach that is intuitively reasonable and leads to a natural separation of system losses among the network buses. Results illustrate the consistency of the new allocation process with expected results and with the performance of other methods. Index Terms--Ancillary service, impedance and admittance matrix, transmission loss allocation.

The Switching Curve Law is an analytic procedure derived from the dual of the Lagrangian Relaxation approach to the static unit commitment (SUC) problem. It is argued here that this analytic result provides a new understanding of the general unit commitment problem not otherwise possible from numerical methods. Moreover, the SUC problem and the analytic results presented here have direct applications in the scheduling of hydro generation in power plants and in the interpretation of the pricing rules of the England and Wales Power Pool. Index Terms--Unit commitment, Lagrangian Relaxation, Switching Curve Law.

Under open access, market driven transactions have become the new independent decision variables defining the behavior of the power system. Understanding the impact of bilateral transactions on system losses is important to be able to allocate a corresponding loss component to each individual transaction and improve economic efficiency. The theory presented here is based on the argument that it is always possible to compute the exact loss allocation corresponding to an infinitesimal bilateral transaction. This leads to a set of governing differential equations whose solution yields the loss allocation for contracts of any size. Several examples illustrate the properties of both the proposed allocation equations and other methods, the dependence of the proposed solution on the path of integration, and a number of implementation issues. Index Terms--Bilateral transactions, open access, transmission loss allocation.