Line Capacity Limits Research Articles

Model of integrated pool/conventional/alternative electricity market operation using pay-as-bid pricing

A pricing model considering the simultaneous interaction of pool, conventional and alternative markets in a power system is presented. This work inserts a competition for alternative power plants separating the pricing for these three markets. The model use the ‘Pay-as-Bid’ (PAB) pricing approach in opposite of classical marginal pricing (MP) approach because the inelastic demand characteristic and the necessity of reduce total operation cost. In the model pricing approach, an integration process involves an AC Optimal Power Flow (OPF) for obtaining awarded bids in the pool and market with the presence of conventional or alternative energy bilateral contracts. As a result, the obtained prices of pool, conventional and alternative energy incorporate the influences of the topology, voltage levels, losses and capacity limits of generators and transmission lines. Results show that agents can plan their portfolios based on reasonable stable prices that reflect the impact of supplying several electricity types and associated costs of resources in several operation scenarios and bid strategies. From the perspective of the system regulator, the minimization of payments by PAB ensures the supply of energy, transmission losses and alternative energy requirements as well as enforcing financial adequacy. Numerical cases are presented for evaluating the model

A distributed approach for solving AC–DC multi-objective OPF problem

This paper first proposes an optimization model for Multi-Objective Optimal Power Flow (MO-OPF) problem in AC–DC networks. The considered objective functions are the fuel cost, active power losses, and environmental emission. The AC and DC power flow equations, the converter operating limits, the voltage magnitude limits, and line capacity limits are considered in the proposed AC–DC MO-OPF model. Then an equivalent Gradient Dynamical System (GDS) for the AC–DC MO-OPF model is derived. Each equilibrium point of this GDS is a Karush–Kuhn–Tucker (KKT) point of the original AC–DC MO-OPF model. In Theorem 1, we derive condition under which this KKT point is a saddle point of the original AC–DC MO-OPF problem. The equivalent GDS has the property that it can be solved using a distributed solution algorithm. Every bus in the AC–DC power grid is considered as a local agent in the proposed distributed GDS algorithm, which only obtains information only from its neighbors. In Theorem 2, we prove that proposed distributed approach is locally convergent to the saddle point of the original AC–DC MO-OPF problem. To show the performance of our distributed approach to solve our developed AC–DC MO-OPF model, the simulation results based on several test systems are provided.

Data-Driven Coordination of Distributed Energy Resources for Active Power Provision

In this paper, we propose a framework for coordinating distributed energy resources (DERs) connected to a power distribution system, the model of which is not completely known, so that they collectively provide a specified amount of active power to the bulk power system as quantified by the power exchange between both systems at the bus interconnecting them, while respecting distribution line capacity limits. The proposed framework consists of (i) a linear time-varying input-output (IO) system model that represents the relation between the DER active power injections (inputs), and the total active power exchanged between the distribution and bulk power systems (output); (ii) an estimator that aims to estimate the IO model parameters, and (iii) a controller that determines the optimal DER active power injections so the power exchanged between both systems equals to the specified amount at a minimum generating cost. We formulate the estimation problem as a quadratic program with box constraints and solve it using the projected gradient descent algorithm. To resolve the potential issue of collinearity in the measurements used by the estimator, we introduce random perturbations in the DER active power injections during the estimation process. Using the estimated IO model, the optimal DER coordination problem to be solved by the controller can be formulated as a convex optimization problem, which can be solved easily. The effectiveness of the framework is validated via numerical simulations using the IEEE 123-bus distribution test feeder.

On the Use of Matroid Theory for Distributed Cyber–Physical-Constrained Generator Scheduling in Smart Grid

Power systems are on the cusp of a rapid tech- nological, economic, and environmental evolution. Classi- cal problems considered by the power community must naturally adapt to new requirements. Physical and compu- tational constraints within a new landscape must be revis- ited. In this paper, we focus on the generator scheduling problem, which is also known as the unit commitment problem, in which we incorporate the new constraints of transmission line capacity limits and policy to give a more comprehensive view for planning in a smart grid. Moreover, we consider implications of our formulation to solution complexity. We introduce the concept of matroid theory to model unit commitment as a combinatorial problem and propose distributed solutions to facilitate optimal and correct generator scheduling. We account for communi- cations and computational complexity and demonstrate how although the constrained generator scheduling prob- lem is NP-hard, simpler versions of the problem lead to polynomial-time solutions.

Multiperiod optimal planning of thermal generation using cross decomposition

This work addresses the Multiperiod Optimal Planning of Thermal Generation (MOPTG). The model considered is based on a Unit Commitment Problem that has multiperiod character and determines the start up and shut down schedules of thermal plants considering the line capacity limits of transmission and line losses. The mathematical model is stated in the form of a Mixed Integer Non Linear Problem (MINLP) with binary variables. To reduce the computational time caused by the large number of time periods and electric generation nodes we apply the Generalized Cross Decomposition [1, 2]. The later exploits the structure of the problem to reduce solution time by decomposing the MOPTG into a primal subproblem, which is a Non Linear Problem (NLP), a dual subproblem, which is a MINLP, and a Mixed Integer Problem (MIP) called master problem. The approach is compared with Lagrangean Relaxation [3] and Generalized Benders Decomposition [4], To demonstrate the efficiency of the proposed decomposition strategy we present numerical results obtained for three test systems. The computational experiments show the superiority of the Cross Decomposition approach.

A Combined Pool/Bilateral/Reserve Electricity Market Operating Under Pay-as-Bid Pricing

A pricing model considering the simultaneous interaction of pool, bilateral and reserve markets in a power system is presented. The model is able to work under the classical marginal pricing (MP) or under the ldquopay-as-bidrdquo (PAB) pricing. In the PAB pricing approach, an integration process involves an AC optimal power flow (OPF) for obtaining awarded bids in the pool and reserve market considering the presence of long-term firm bilateral contracts. As a result, prices of energy and reserve services incorporate the influences of topology, voltage levels, losses, capacity limits of generators and transmission lines. Results show that agents can plan their portfolios based on prices reflecting the impact of supplying several electricity services and associated costs of resources in several operation scenarios and bid strategies. From the perspective of the system regulator, the minimization of payments by PAB ensures the supply of energy, transmission losses and reserve requirements besides enforcing financial adequacy. Numerical cases are presented for evaluating the model.

Reconfiguration of MV Distribution Networks With Multicost and Multipoint Alternative Supply, Part I: Economic Dispatch Through Radialization

A new approach to improve the reconfiguration operations of distribution systems is presented in two papers. In this first part an economic dispatch (ED) through radialization method for medium voltage (MV) distribution networks with several alternative supply points and several energy prices is presented. The optimization criterion is based on energy purchase cost minimization to supply both the load and the loss. The ED through radialization (EDR) method assesses the economic impact of different energy prices for alternative supply points on the operative radial topology for a specific load level. Capacity limits of supply points and MV lines are considered, as well as the quality technical product using ac power flow calculations. The results obtained for a distribution network widely used in the literature show the effectiveness of the proposed methodology. The second part presents a methodology to determine the optimal reconfiguration plan for short and medium terms. This approach integrates purchase and switching costs associated to the reconfiguration plan.

Optimising location of unified power flow controllers by means of improved evolutionary programming

The unified power flow controller (UPFC) is one of the most promising Flexible AC Transmission Systems (FACTS) devices for the load flow control. Simultaneous optimisation of location and parameters for UPFCs is an important issue when the given number of UPFCs is applied to the power system with the purpose of increasing system loadability. This paper presents a mathematical model about optimal location and parameters of UPFCs to maximise the system loadability subject to the transmission line capacity limits and specified voltage level. An improved computational intelligence approach: self-adaptive evolutionary programming (SAEP) is used to solve the nonlinear programming problem presented above for better accuracy. Case studies of the IEEE 30- and 118-bus systems using the proposed model and technique demonstrate that the proposed mathematical model is corrective and efficient. Furthermore, steady-state performance of power system can be effectively enhanced due to the optimal location and parameters of UPFCs.

Multiperiod optimal power flow using Benders decomposition

This paper addresses a multiperiod optimal power flow, properly modeling the start-up and shut-down of thermal units, the transmission network in terms of line capacity limits and line losses, and the constraints of hydroelectric plants integrated in river systems. The generalized Benders decomposition is used to solve this large-scale multiperiod problem. Spot prices are obtained as a byproduct of the decomposition procedure. A realistic case study based on the electric energy system of mainland Spain is analyzed and the results obtained are reported.

Dynamic load dispatch with voltage security and environmental constraints

A Linear Programming (LP) based approach is applied to dynamic load dispatch of electric power systems considering security and environment constraints. In addition to the basic constraints (such as generator real power limits and real power demand), a comprehensive set of constraints are considered including transmission line capacity limits, generators dynamic ramp rate, voltage security margin and/or environmental issues. The voltage security margin, which is calculated using the modified N-R continuation method, is considered heuristically through the control of transmission line capacity limits during the solution process by the LP, and the environmental issue is considered as an operating constraint which has restrictions on hourly SO 2 emission allowances. Application results of the proposed algorithm to the New England test system are presented to numerically illustrate the effectiveness of the approach.

Short-term generation scheduling of thermal units with voltage security and environmental constraints

A dynamic and linear programming-based approach is investigated for the short-term scheduling of thermal power plant units considering the security and environmental constraints of electric power systems. In addition to the basic constraints (i.e. real power limits of the generators, real power demand, spinning reserve, minimum up and down lime of units) a comprehensive set of constraints is considered including: transmission line capacity limits; generators dynamic ramp rate; voltage security margin; and environmental issues. An optimal multiplier continuation method is adopted to effectively calculate the voltage security margin. The constraint relating to the voltage security margin is considered as a transition constraint in the dynamic programming process. The environmental issue is considered as a restriction on the hourly SO/sub 2/ emission allowances and other constraints are considered in the dynamic/linear programming procedures. Results of the application of the proposed algorithm to a test system are presented to illustrate the effectiveness of the approach.