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This paper proposes a mathematical model for transmission planning in an environment where there is imperfect competition in electricity supply industry. The model is developed based on the concept of the leader-followers game in applied mathematics. The leader of the game is the transmission planner and the followers are the strategic electricity producing firms. The reaction of the strategic electricity producing firms to the transmission planning decision is modeled using the introduced concept of the worst-Cournot-Nash equilibrium. The worst-Cournot-Nash equilibrium can handle the multiple Nash equilibria problem. The whole mathematical formulation is a bilevel mixed-integer linear programming problem. This formulation is achieved using the Karush-Kuhn-Tucker optimality conditions and a binary mapping approach. The application of the proposed approach to the three-node example system and the modified six-node Garver's example system are studied. The transmission planning with perfect competition is formulated and used as the benchmark. The numerical results show that the proposed approach in this paper can efficiently allocate the additional transmission capacity to the transmission grid such that it reduces the market power cost in the electricity supply industry. However, further studies should be carried out to scale up the proposed approach to the larger case studies. [ABSTRACT FROM PUBLISHER]

This paper proposes an investment cost recovery based efficient and reliable optimization approach to optimal allocation of thyristor controlled series compensator (TCSC) in double auction power market. The optimization technique has been used with an objective to maximizing the social welfare and minimizing the device investment cost by suitable location and rating of single TCSC in the system. The effectiveness of proposed approach for location of TCSC has been compared with some existing methods of single TCSC placement, in terms of its impact on social welfare, TCSC investment recovery and optimal generation as well as load patterns. The results have been obtained on 5-bus system, modified IEEE 14-bus system and 246-bus Indian practical Northern Regional Power Grid (NRPG) system. [ABSTRACT FROM PUBLISHER]

Isolated microgrid power systems are prone to large frequency and voltage deviations, since they have limited generation and finite inertia and may include pulse power loads and large proportion of dynamic loads. Thus, they require effective power management methods to operate optimally, while satisfying operating and security constraints. In this paper, a novel integrated security-constrained model-based power management approach is proposed for isolated microgrids in all-electric ships during the normal/alert operating state. The new power management method was formulated as a multi-objective optimal control problem. A method based on the Nondominated Sorting Genetic Algorithm II was developed to solve the problem. The developed integrated security-constrained power management approach was applied to a notional all-electric ship computer model. The simulation results, conducted in PSCAD, showed the effectiveness of the new power management method. [ABSTRACT FROM PUBLISHER]

In traditional power system, economic dispatch and generation control are separately applied. Online generation adjustment is necessary to regulate generation reference for real-time control to realize economic operation of power systems. Since most economic dispatch solutions are centralized, they are usually expensive to implement, susceptible to single-point-failures, and inflexible. To address the above-mentioned problems, this paper proposed a multi-agent system based distributed control solution that can realize optimal generation control. The solution is designed based upon an improved distributed gradient algorithm, which can address both equality and inequality constraints. To improve the reliability of multi-agent system, the N-1 rule is introduced to design the communication network topology. Compared with centralized solutions, the distributed control solution not only can achieve comparable solutions but also can respond timely when the system experiences change of operating conditions. MAS based real-time simulation results demonstrate the effectiveness of the proposed solution. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a distributed recharging rate control algorithm which combines the objectives of regulating frequency and improving the utilization of electric generators. An incentive policy \kappa is created that encourages electric vehicles (EVs) to demand energy when non-EV demand is low and electric generators are underutilized. EVs also act as frequency regulators which can control their participation role by modifying their respective payment rate wi. The proposed distributed recharging rate control algorithm can realize a Demand Management solution for EVs and does not require explicit real time communication from the electric generators or between the recharging sockets. A mechanism is presented that can trade off an ideal incentive policy with its approximation and enable the integration of the proposed controller with legacy protection system. Simulation is used to assess the algorithm and to highlight its embedded characteristics. [ABSTRACT FROM PUBLISHER]

This paper proposes a two-stage robust optimization approach to solve the N-k contingency-constrained unit commitment (CCUC) problem. In our approach, both generator and transmission line contingencies are considered. Compared to the traditional approach using a given set of components as candidates for possible failures, our approach considers all possible component failure scenarios. We consider the objectives of minimizing the total generation cost under the worst-case contingency scenario and/or the total pre-contingency cost. We formulate CCUC as a two-stage robust optimization problem and develop a decomposition framework to enable tractable computation. In our framework, the master problem makes unit commitment decisions and the subproblem discovers the worst-case contingency scenarios. By using linearization techniques and duality theory, we transform the subproblem into a mixed-integer linear program (MILP). The most violated inequalities generated from the subproblem are fed back into the master problem during each iteration. Our approach guarantees a globally optimal solution in a finite number of iterations. In reported computational experiments, we test both primal and dual decomposition approaches. Our computational results verify the effectiveness of our proposed approach. [ABSTRACT FROM PUBLISHER]

With the increasing penetration of wind power into the power grid, maintaining system reliability has been a challenging issue for ISOs/RTOs, due to the intermittent nature of wind power. In addition to the traditional reserves provided by thermal, hydro, and gas generators, demand response (DR) programs have gained much attention recently as another reserve resource to mitigate wind power output uncertainty. However, the price-elastic demand curve is not exactly known in advance, which provides another dimension of uncertainty. To accommodate the combined uncertainties from wind power and DR, we allow the wind power output to vary within a given interval with the price-elastic demand curve also varying in this paper. We develop a robust optimization approach to derive an optimal unit commitment decision for the reliability unit commitment runs by ISOs/RTOs, with the objective of maximizing total social welfare under the joint worst-case wind power output and demand response scenario. The problem is formulated as a multi-stage robust mixed-integer programming problem. An exact solution approach leveraging Benders' decomposition is developed to obtain the optimal robust unit commitment schedule for the problem. Additional variables are introduced to parameterize the conservatism of our model and avoid over-protection. Finally, we test the performance of the proposed approach using a case study based on the IEEE 118-bus system. The results verify that our proposed approach can accommodate both wind power and demand response uncertainties, and demand response can help accommodate wind power output uncertainty by lowering the unit load cost. [ABSTRACT FROM PUBLISHER]

This paper examines the polytope of feasible power generation schedules in the unit commitment (UC) problem. We provide computational results comparing formulations for the UC problem commonly found in the literature. We introduce a new class of inequalities, giving a tighter description of feasible operating schedules for generators. Computational results show that these inequalities can significantly reduce overall solution times. [ABSTRACT FROM PUBLISHER]

This paper proposes an active-reactive power dispatch procedure that is expressed via a bilevel optimization problem whose upper and lower level criteria are, respectively, the minimum opportunity cost and minimum offered price of active power. It analyzes the impact of minimizing such criteria on system operation, and it investigates the behavior of marginal prices and opportunity costs and their use in mechanisms to compensate generators for power provision. The bilevel problem is solved using a version of interior point methods derived for mathematical programs with complementarity constraints. Results obtained with three test systems are analyzed. [ABSTRACT FROM PUBLISHER]

In this paper, a receding-horizon multi-step optimization is proposed to correct nonviable transmission voltages and prevent long-term voltage instability. The proposed control scheme is based on real-time control, inspired by model predictive control, and steady state power-flow-based equations. In order to anticipate load behavior and avoid using dynamic equations in the control scheme, explicit formulations are used to model evolution of load with time. The simulation results of the proposed technique are presented on the Nordic32 test system. [ABSTRACT FROM PUBLISHER]

In response to the challenges brought by uncertain bus load and volatile wind power to power system security, this paper presents a novel unit commitment formulation based on interval number optimization to improve the security as well as economy of power system operation. By using full-scenario analysis, the worst-case impact of volatile node injection on unit commitment is acquired, so that the proposed model can always provide a secure and economical unit commitment result to the operators. Scenarios generation and reduction method based on interval linear programming theory are used to accelerate the solution procedure without loss of optimality. Benders decomposition is also implemented to reduce the complexity of this large-scale interval mixed integer linear programming, and prove the rationality and rigor of our proposed method. The numerical results indicate better secure and economical features of the proposed method comparing with the traditional one. [ABSTRACT FROM PUBLISHER]

This paper presents a new approach for the contingency-constrained single-bus unit commitment problem. The proposed model explicitly incorporates an n - K security criterion by which power balance is guaranteed under any contingency state comprising the simultaneous loss of up to K generation units. Instead of considering all possible contingency states, which would render the problem intractable, a novel method based on robust optimization is proposed. Using the notion of umbrella contingency, the robust counterpart of the original problem is formulated. The resulting model is a particular instance of bilevel programming which is solved by its transformation to an equivalent single-level mixed-integer programming problem. Unlike previously reported contingency-dependent approaches, the robust model does not depend on the size of the set of credible contingencies, thus providing a computationally efficient framework. Simulation results back up these conclusions. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel approach to optimize a generator's profit in an offer-based electricity market cleared by an optimal power flow (OPF) program. A generator's offer is optimized based on its transmission-constrained residual demand derivative (TCRDD), which avoids representing the full network model in the optimization. The TCRDD can be easily calculated based on a solved OPF without changing existing OPF algorithms and programs. As demonstrated with an IEEE 118-bus example, the TCRDD approach is computationally efficient. The TCRDD approach can help market participants to bid into electricity markets, and help market monitors to diagnose bidding behaviors in the presence of transmission constraints. [ABSTRACT FROM PUBLISHER]

The extensive installation of gas-fired power plants in many parts of the world has led electric systems to depend heavily on reliable gas supplies. The use of gas-fired generators for peak load and reserve provision causes high intraday variability in withdrawals from high-pressure gas transmission systems. Such variability can lead to gas price fluctuations and supply disruptions that affect electric generator dispatch, electricity prices, and threaten the security of power systems and gas pipelines. These infrastructures function on vastly different spatio-temporal scales, which prevents current practices for separate operations and market clearing from being coordinated. In this paper, we apply new techniques for control of dynamic gas flows on pipeline networks to examine day-ahead scheduling of electric generator dispatch and gas compressor operation for different levels of integration, spanning from separate forecasting, and simulation to combined optimal control. We formulate multiple coordination scenarios and develop tractable physically accurate computational implementations. These scenarios are compared using an integrated model of test networks for power and gas systems with 24 nodes and 24 pipes, respectively, which are coupled through gas-fired generators. The analysis quantifies the economic efficiency and security benefits of gas–electric coordination and dynamic gas system operation. [ABSTRACT FROM AUTHOR]

Incentives to encourage the uptake of renewable energy generation have fostered wind energy in many power systems. These incentives usually take the form of market instruments (e.g., feed-in tariff or premium) that are not directly amenable to optimization representations of the market. In this paper, we propose an equilibrium model of the short-term market to address the impact of wind operation under different structural assumptions. The model is formulated for several price taking, risk averse firms in competition. It accounts for wind generation uncertainty and embeds a representation of the day ahead and balancing mechanisms. The consumer is modeled by a linear inverse demand function. We focus on feed-in premium as the incentive to wind as this is the instrument most favored today in European discussions. The model is formulated as a stochastic equilibrium problem where the Karush-Kuhn-Tucker (KKT) conditions from the optimization problem of each firm are simultaneously solved together with market clearing conditions on energy, capacity for reserve and energy for reserve. The problem for each firm consists of a two-stage stochastic optimization problem with a recourse function based on the conditional value at risk (CVaR\theta ) as a risk measure. Due to price taking assumptions the model is a single stage complementarity problem; it is implemented and solved using the software GAMS. An example based on a stylized simplification of the Spanish power market and motivated by the impact of wind penetration on the revenue of conventional plants is used to illustrate the proposed approach. [ABSTRACT FROM PUBLISHER]

A linear and convex model has been recently presented for the operation of battery energy storage units that does not explicitly prevent their simultaneous charge and discharge in the problem formulation. This letter claims that the model in such a literature contribution is capable of ensuring the physical realizability of the battery dispatch only when nondiscrete decisions are considered in the optimization problem. This claim is demonstrated through the solution of two instances of a simple unit-commitment-based example comprising two generating units, one battery energy storage unit, and two time periods. [ABSTRACT FROM AUTHOR]

This letter develops a mathematical model to distribute the under-frequency load shedding amount across the power system load points. The objective is to preserve the system operating point at post-contingency and after the load shedding as close as possible to that of pre-contingency. To do so, the total absolute change in line flows is sought to be minimized. Hence, the system security constraints satisfied before contingency occurrence are less vulnerable to violation. It is proven that when the number of credible contingencies exceeds load shedding candidates, an even distribution across the load points is optimal. [ABSTRACT FROM AUTHOR]

The environmental-economic dispatch (EED) is a bi-objective optimization problem. The Nash bargaining theory provides one way to determine a compromising solution without a clear carbon tax or carbon cap, or any subjective attitudes on both objectives, which yields a non-convex program. This letter proposes a convex formulation for Nash bargaining based EED and a linear programming (LP) based algorithm. Case studies show its scalability on real-world large-scale power systems. [ABSTRACT FROM PUBLISHER]

The security-constrained unit commitment problem schedules power generators to minimize cost subject to operating constraints. Reserve requirements ensure that reserve is available to re-balance the system following a contingency but do not guarantee reliability in congested systems where reserve activation is limited by transmission constraints. Operators improve reserve deliverability by limiting power flows and controlling the location of reserves. Zones are used to address inter-zonal congestion but operators lack efficient ways to handle intra-zonal congestion. We propose dynamically relating minimum reserve levels to transmission stress in a computationally efficient approach that complements existing reserve models from the literature. Analysis on the IEEE RTS 96 test case demonstrates the approach can mitigate intra-zonal congestion more economically than traditional reserve policies. [ABSTRACT FROM PUBLISHER]

For the nonlinear power flow problem specified with standard PQ, PV, and slack bus equality constraints, we present a sufficient condition under which the specified set of nonlinear algebraic equations has no solution. This sufficient condition is constructed in a framework of an associated feasible, convex optimization problem. The objective employed in this optimization problem yields a measure of distance (in a parameter set) to the power flow solution boundary. In practical terms, this distance is closely related to quantities that previous authors have proposed as voltage stability margins. A typical margin is expressed in terms of the parameters of system loading (injected powers); here we additionally introduce a new margin in terms of the parameters of regulated bus voltages. [ABSTRACT FROM PUBLISHER]

The article focuses on the discussion of Hybrid Differential Evolution with Biogeography-Based Optimization for Solution of Economic Load Dispatch (ELD). The authors present a hybrid method that combines differential evolution with the biogeography-based optimization (DE/BBO) algorithm to solve convex and non-convex ELD in four test cases to prove feasibility. The author adds that only test case 1 was the only case wherein the ramp-rates and prohibited operating zones (POZ) was considered.

This letter proposes a methodology for finding the equilibrium point of a microgrid operating in a wide range of loading levels, which includes the possible exhaustion of the power reserve of some of the generating units. The search of the equilibrium would require the use of two different models when using Newton-Raphson-like methods. It is shown herein that the problem can be reformulated instead within the nonlinear constrained minimization framework by employing a complementarity condition. [ABSTRACT FROM PUBLISHER]