Transmission Line Constraints Research Articles

Computationally Efficient Data-Driven Joint Chance Constraints for Power Systems Scheduling

Although data-driven nonparametric Joint Chance Constraints (JCCs) may lead to more reliable decision-making than individual chance constraints, their computational complexity is a major bottleneck. This paper presents computationally efficient data-driven nonparametric joint chance-constrained programming for multi-interval power systems management. Reserve and transmission line constraints are modeled as data-driven JCCs. Piecewise uniform kernel functions incorporate historical data of uncertain parameters into optimization. Data-driven nonparametric JCCs are modeled as a product of integrated kernel functions. Two approaches are proposed to linearize data-driven nonparametric JCCs. i) The noncontinuous kernel function is linearized with Special Ordered Sets of type 1 (SOS1) variables. ii) A tight convex envelope of multilinear monomial terms, which appear due to the product of kernel functions, is approximated by an optimization subproblem making the scheduling problem bi-level optimization. The continuity and linearity of the lower-level convex envelope approximation subproblem allow replacing it with optimality conditions to form a single-level scheduling problem. Simulation results show the tightness of the proposed linearization approaches and the computational efficiency of data-driven JCC programming.

Multi interval Zero Carbon Flexible Ramp Product

Traditional Fossil Fuel Generators (FFGs) are incapable of providing Flexible Ramp Product (FRP) due to lower FRP market time frame, while modern FFGs are characterized by high ramping costs. Also, ramping support providence from FFGs enhance carbon emissions. Wind and solar FRP can reduce system imbalances, however, their ramping capabilities are highly uncertain and may not reliably fulfill System Ramping Requirement (SRR). This paper proposes a reliable and deliverable Zero Carbon Flexible Ramp Product (ZCFRP) using wind, solar and Variable Speed Pumped Hydro Power Plants (VSPHPPs). The reliability of the proposed ZCFRP depends on the estimation of accurate SRR, Renewable FRP (RFRP) availability, and generation/pumping capacity of VSPHPP. SRR and RFRP availability are estimated using copula theory. VSPHPP’s generation/pumping capacities are optimally modeled considering historical SRR and maximum possible RFRP variation. Delivery of the proposed ZCFRP is ensured by considering transmission line constraints. Dynamic ramping constraints are considered to reflect the practical characteristics of thermal generators. A case study shows that the proposed ZCFRP is beneficial to both system and ZCFRP providers (ZCFRPPs) by reducing dispatch costs and increasing revenue, respectively.

Tractable Reformulation of Two-Side Chance-Constrained Economic Dispatch

Chance constrained economic dispatch (CCED) is widely used to handle uncertainties in power systems with high-proportion renewable energy sources (RESs). However, in such system, the upper and lower limits of reserve or transmission line constraints may be violated simultaneously, which makes single-side CCED (SS-CCED) inapplicable. This letter develops a two-side CCED (TS-CCED) model, in which the Gaussian mixture model (GMM) is used to characterize the correlated non-Gaussian distribution of RESs. We propose a hyperbolic tangent function based approximation method to approach GMM and make the TS-CCED tractable. Numerical studies show the proposed method is more applicable than SS-CCED with high efficiency.

Day-ahead stochastic scheduling of integrated electricity and heat system considering reserve provision by large-scale heat pumps

Integrating power and heat sectors can increase the flexibility of wind power integration. Power-to-heat devices powered by renewables can promote the electrification and decarbonization of the heat sector. This paper explores the feasibility and benefits of using large-scale heat pumps for reserve provision. A two-stage stochastic optimization model is proposed for the day-ahead centralized scheduling of the integrated electricity and heat system considering wind power uncertainties, with reserve provision of large-scale heat pumps, combined heat and power units, and thermal power units. The model co-optimizes energy, following reserve, regulating reserve, and heat regulation to handle wind power uncertainties. To reduce the computational complexity of the scenario-based stochastic optimization problem, inactive transmission line constraints are identified and removed based on an analytical calculation method, which considers the influence of power consumption of large-scale heat pumps on the power flow of transmission lines. The benefits of using reserves from large-scale heat pumps are tested on the modified IEEE-118 bus integrated electricity and heat system. The simulation results show that using large-scale heat pumps to provide the following reserve and regulating reserve show similar impacts on saving cost and reducing wind energy curtailment, and the acceleration algorithm can save computation time by approximately 64%.

Probabilistic Available Transfer Capability Evaluation Considering Dynamic Line Rating Based on a Sequential Game-Theoretic Approach

Available transfer capability (ATC) plays an essential role in deregulated power network scheduling. This value determines the power that can be transferred between deregulated regions. The ATC value is limited by transmission line constraints and reliability marginal terms. In this article, the impact of dynamic line rating (DLR) instruments, which are generally used to enhance the capacity of transmission lines, on the ATC is investigated. In addition, a robust ATC evaluation model is proposed to find worst cases for determining the reliability marginal terms and considering them in the ATC evaluation. The robust ATC evaluation model includes a master problem, formulated to determine ATC and total transfer capability, as well as two bilevel subproblems, formulated to find the reliability marginal terms. The Benders decomposition algorithm is derived to solve the proposed robust ATC evaluation. An uncertain environment, including wind farm powers, dynamic line capacities, and load demand values, is also considered to cover the stochastic nature of such uncertainty sources. A probabilistic approach is proposed to calculate the expected value of ATC and depict the cumulative distribution function of each variable. The proposed probabilistic model is based on dividing the stochastic set into smaller groups, similar to clustering techniques. However, the significant differences between the proposed probabilistic and cluster-based models are due to detecting the optimal value of a reduced number of stochastic sets and finding the members of each cluster set. In other words, a sequential game-theoretic approach is applied to divide the data into smaller sets. The impact of DLR on the proposed robust ATC evaluation problem and the efficiency of the proposed probabilistic model are evaluated by comprehensive studies based on the IEEE 118-bus test system.

Generation Capacity Expansion Planning Considering Hourly Dynamics of Renewable Resources

As more generation capacity using renewable sources is accommodated in the power system, methods to represent the uncertainty of renewable sources become more important, and stochastic models with different methods for uncertainty representation are introduced. This paper investigates the impacts of hourly variability representation of random variables on a stochastic generation capacity expansion planning model. In order to represent the hourly variability as well as uncertainty of the random parameters such as wind power availability, solar irradiance, and load, AutoRegressive-To-Anything (ARTA) stochastic process is applied. By using autocorrelations and marginal distributions of the random parameters, a stochastic process with hourly intervals is generated, where generated random sample paths are used for scenarios. A mathematical formulation using stochastic programming is presented, and a modified IEEE 300-bus system with transmission line constraints is employed to the mathematical model as a test system. Optimal generation capacity solutions obtained using GAMS/CPLEX are compared to the ones from the model only capturing the uncertainty and seasonal variability of the random parameters. The comparison results indicate that the economic value of solar photovoltaic (PV) generation may be overestimated in the case where the hourly variability is not reflected; thus, ignoring the hourly variability may lead to higher building costs and higher capacity of solar PV systems.

Introduction to Laguerre‐based stochastic economic predictive functional control for optimal real‐time power dispatch under uncertainty

This study presents a Laguerre-based stochastic economic predictive functional control (L-SEPFC) method for real-time power dispatch of balance responsible parties (BRPs). In this regard, at the control layer, an L-SEPFC method operates on the energy time scale and optimises the expected economic performance of the BRP. Calculated set points in this layer are average power injection of controllable generators, as well as known disturbance of prediction wind generation. The novel L-SEPFC scheme is able to cope with the wind uncertainty occurring in the real-time operation of BRPs. Furthermore, the proposed algorithm is able to take into account the technical constraints of generators and transmission line constraints of the power network. Due to the parameterisation of the future control signal based on the Laguerre function, the proposed method is faster than the nominal predictive algorithms. Simulations on an IEEE 118-bus test system with proposed method shows improvements inability to track reference production, economic performance, imbalance energy and computational burden with respect to nominal predictive controllers.

Stochastic economic model predictive control for real-time scheduling of balance responsible parties

This paper presents stochastic economic model predictive control (SEMPC) method for real-time economic dispatch of Balance Responsible Parties (BRPs) as load balance controller in power system structure. In this regard, SEMPC method operates on the energy time scale and optimizes the expected economic performance of the BRP. Calculated set-points are average power injection of controllable generators, as well as known disturbance of prediction wind generation. The novel SEMPC scheme is able to cope with the wind uncertainty occurring in the real-time operation of BRPs. Furthermore, the proposed algorithm can take into account the technical constraints of generators and transmission line constraints of the power network. Simulations on IEEE 9-bus and 57-bus test systems with proposed method shows improvements inability to track reference production, economic performance and imbalance energy with respect to nominal predictive controllers.

The State of Art in Particle Swarm Optimization Based Unit Commitment: A Review

Unit Commitment (UC) requires the optimization of the operation of generation units with varying loads, at every hour, under different technical and environmental constraints. Many solution techniques were developed for the UC problem, and the researchers are still working on improving the efficiency of these techniques. Particle swarm optimization (PSO) is an effective and efficient technique used for solving the UC problems, and it has gotten a considerable amount of attention in recent years. This study provides a state-of-the-art literature review on UC studies utilizing PSO or PSO-variant algorithms, by focusing on research articles published in the last decade. In this study, these algorithms/methods, objectives, constraints are reviewed, with focus on the UC problems that include at least one of the wind and solar technologies, along with thermal unit(s). Although, conventional PSO is one of the most effective techniques used in solving UC problem, other methods were also developed in literature to improve the convergence. In this study, these methods are grouped as extended PSO, modified PSO, and PSO with other techniques. This study shows that PSO with other techniques are utilized more than any other methods. In terms of constraints, it was observed that there are only few studies that considered Transmission Line (TL), Fuel (F), Emission (E), Storage (St) and Crew (Cr) constraints, while Power Balance (PB), Generation limit (GL), Unit minimum Up or Down Time (U/DT), Ramp Up or Ramp Down Time (R-U/DT) and system Spinning Reserve (SR) were the most utilized constraints in UC problems considering wind/solar as a renewable source. In addition, most of the studies are based on a single objective function (cost minimization) and, few of them are multi-objective (cost and emission minimization) based studies.

Wind farm power optimization through wake steering

Global power production increasingly relies on wind farms to supply low-carbon energy. The recent Intergovernmental Panel on Climate Change (IPCC) Special Report predicted that renewable energy production must leap from [Formula: see text] of the global energy mix in 2018 to [Formula: see text] by 2050 to keep global temperatures from rising 1.5°C above preindustrial levels. This increase requires reliable, low-cost energy production. However, wind turbines are often placed in close proximity within wind farms due to land and transmission line constraints, which results in wind farm efficiency degradation of up to [Formula: see text] for wind directions aligned with columns of turbines. To increase wind farm power production, we developed a wake steering control scheme. This approach maximizes the power of a wind farm through yaw misalignment that deflects wakes away from downstream turbines. Optimization was performed with site-specific analytic gradient ascent relying on historical operational data. The protocol was tested in an operational wind farm in Alberta, Canada, resulting in statistically significant ([Formula: see text]) power increases of 7-[Formula: see text] for wind speeds near the site average and wind directions which occur during less than [Formula: see text] of nocturnal operation and 28-[Formula: see text] for low wind speeds in the same wind directions. Wake steering also decreased the variability in the power production of the wind farm by up to [Formula: see text] Although the resulting gains in annual energy production were insignificant at this farm, these statistically significant wake steering results demonstrate the potential to increase the efficiency and predictability of power production through the reduction of wake losses.

Two‐stage stochastic programming for the joint dispatch of energy and reserve considering demand response

This paper formulates a two-stage stochastic programming model for energy and reserve joint dispatch considering wind power uncertainty and the participation of incentive-based demand response (IBDR). The model consists two stages, the first stage is to determine the day-ahead energy dispatch and the reserve capacity need, the second stage is to determine the deployment of reserves to accommodate the realisation of wind power uncertainty in real time. The IBDR program and the thermal power units provide reserve together to cope with the uncertainty of wind power. The IBDR model considers the maximum response times of a DR agent during a day to assure the reliability of using electricity for end users. To reduce the computation burden caused by wind power scenarios, the inactive constraints identification method is utilised to eliminate redundant transmission line constraints before solving the original model. Finally, the effectiveness of the proposed model and the solving method are tested on the modified IEEE 118-bus test system with 50 DR agents.

Optimal Pricing of Electricity in Restructured Electricity Market

An effective pricing scheme that to provide the useful information to generation, transmission section and customers. These transmission pricing depends on generator, load levels and transmission line constraints. Transmission line constraints result is variations in energy prices throughout the network. The proposed approach is based on AC-DC optimal power flow model with considering of losses. Resulting optimization problem is solved by linear programming approach. Locational Marginal Pricing methodology is used to determine the energy price for transacted power and to manage the network congestion and marginal losses. Variation of LMP values with transmission constraint conditions also studied. Simulation is carried out on IEEE 57 bus system, 400/765kV MSETCL system of Maharashtra transmission line for real data bus system and the results are presented.

A systematic approach for the joint dispatch of energy and reserve incorporating demand response

The intermittent nature of wind power increases the need for flexibility of the power system. This paper proposes the systematic approach for the joint dispatch of energy and reserve incorporating demand response, including the formulation of the two-stage optimization, dynamic scenario generation, and inactive constraint identification. The incentive-based demand response model is adopted to improve flexibility by its cooperation with conventional units. The dynamic scenario generation method is developed to provide reasonable input for the two-stage optimization, considering the temporal correlations of the wind power. Three indicators are proposed to evaluate the quality of scenarios. To speed up the solution, the inactive constraint reduction has been applied to reduce the computational burden raised by the number of the scenarios and the system scale. Finally, the modified IEEE 118-bus test system with fifty incentive-based demand response aggregators is utilized to evaluate the effectiveness of the proposed method to improve operational economics and to promote wind power utilization. Simulation results show that 89.53% of the transmission line constraints can be removed, leading to a maximal reduction of 69.81% of the computational time. Compared to the conventional sampling method, the dynamic scenario set performs better in terms of three proposed indicators, and can reduce the total cost by 1.99%. Neglecting the constraint of response times, the economic efficiency would be overestimated by 0.98%.

Application of Firefly Optimization Technique for Solving Convex Economic Load Dispatch of Generation On Nigerian 330 kV, 24-Bus Grid System

Firefly optimization is a population based technique in which the attractiveness of a firefly is determined by its attractiveness which is then encoded as the objective function of the optimization problems. Firefly algorithm is one of the newest meta-heuristic algorithms based on the mating or flashing behavior of fireflies. Economic load dispatch of generation allocates power generation to match load demand at minimal possible cost without violating power units and system constraints. This paper presents application of firefly optimization technique (FFOT) for solving convex economic load dispatch of generation. The economic load dispatch problem was formulated to minimize the total fuel cost for the heat optimal combination of thermal generators without violating any of the system constraints using quadratic fuel cost model of Sapele, Delta, Afam and Egbin power stations as case studies. The equality and inequality constraints used on the system were the power balance equation and the transmission line constraints respectively. Firefly optimization technique was then developed using appropriate control parameters for a faster convergence of the technique. The optimization technique was tested and validated on the IEEE 30-bus system and Nigerian 24-bus system. The results obtained from the IEEE 30-bus system were compared to published results obtained via Differential Evolution (DE), Ant Colony Optimization (ACO) and Genetic Algorithm (GA). The comparison confirms the superiority, fast convergence and proficiency of the algorithm.

Application of Firefly Optimization Technique for Solving Convex Economic Load Dispatch of Generation On Nigerian 330 kV, 24-Bus Grid System

Firefly optimization is a population based technique in which the attractiveness of a firefly is determined by its attractiveness which is then encoded as the objective function of the optimization problems. Firefly algorithm is one of the newest meta-heuristic algorithms based on the mating or flashing behavior of fireflies. Economic load dispatch of generation allocates power generation to match load demand at minimal possible cost without violating power units and system constraints. This paper presents application of firefly optimization technique (FFOT) for solving convex economic load dispatch of generation. The economic load dispatch problem was formulated to minimize the total fuel cost for the heat optimal combination of thermal generators without violating any of the system constraints using quadratic fuel cost model of Sapele, Delta, Afam and Egbin power stations as case studies. The equality and inequality constraints used on the system were the power balance equation and the transmission line constraints respectively. Firefly optimization technique was then developed using appropriate control parameters for a faster convergence of the technique. The optimization technique was tested and validated on the IEEE 30-bus system and Nigerian 24-bus system. The results obtained from the IEEE 30-bus system were compared to published results obtained via Differential Evolution (DE), Ant Colony Optimization (ACO) and Genetic Algorithm (GA). The comparison confirms the superiority, fast convergence and proficiency of the algorithm.

The Adaptive Robust Multi-Period Alternating Current Optimal Power Flow Problem

This paper jointly addresses two major challenges in power system operations: 1) dealing with non-convexity in the power flow equations, and 2) systematically capturing uncertainty in renewable power availability and in active and reactive power consumption at load buses. To overcome these challenges, this paper proposes a two-stage adaptive robust optimization model for the multi-period AC optimal power flow problem (AC-OPF) with detailed modeling considerations, such as reactive capability curves of conventional and renewable generators and transmission constraints. This paper then applies strong second-order cone programming (SOCP)-based convex relaxations of AC-OPF combined with the use of an alternating direction method to identify worst-case uncertainty realizations, and also presents a speed-up technique based on screening transmission line constraints. Extensive computational experiments show that the solution method is efficient and that the robust AC OPF model has significant advantages both from the economic and reliability standpoints as compared to a deterministic AC-OPF model.

Decomposition-Coordinating Method for Parallel Solution of a Multi-area Combined Economic Emission Dispatch Problem

<p>Multi-area Combined Economic Emission Dispatch (MACEED) problem is an optimization task in power system operation for allocating the amount of generation to the committed units within the system areas. Its objective is to minimize the fuel cost and the quantity of emissions subject to the power balance, generator limits, transmission line and tie-line constraints. The solutions of the MACEED problem in the conditions of deregulation are difficult, due to the model size, nonlinearities, and the big number of interconnections, and require intensive computations in real-time. High-Performance Computing (HPC) gives possibilities for the reduction of the problem complexity and the time for calculation by the use of parallel processing techniques for running advanced application programs efficiently, reliably and quickly. These applications are considered as very new in the power system control centers because there are not available optimization methods and software based on them that can solve the MACEED problem in parallel, paying attention to the existence of the power system areas and the tie-lines between them. A decomposition-coordinating method based on Lagrange’s function is developed in this paper. Investigations of the performance of the method are done using IEEE benchmark power system models.</p>

Power Trading and Congestion Management Through Real Power Rescheduling Using Unified Power Flow Controller

Congestion is termed as the operating condition in which there is not enough transmission capacity to implement all the desired transactions. This paper deals with the power trading in electricity market to ensure regular supply at competitive rates. Bidding process of 75 Indian bus systems is analyzed. It is shown that how can congestion cost can be addressed through active power rescheduling with transmission line constraints using Unified power flow controller.

Modeling Transmission Line Constraints in Two-Stage Robust Unit Commitment Problem

Integration of renewable energy sources and demand response poses new challenges to system operators as they increase the uncertainty of the power supply and demand. Recently, robust optimization techniques are applied to the unit commitment problem with uncertainty as an alternative to the stochastic programming approaches. However, it remains challenging to solve the robust unit commitment model with full transmission line constraints. In this paper, we propose novel acceleration techniques for solving two-stage robust unit commitment problem with consideration of full transmission line constraints. We use 1) the cutting-plane algorithm for the master problem, which dynamically includes critical transmission line constraints, and 2) column-generation methods, including the branch-and-price-and-cut algorithm and heuristic approaches, for the subproblems, which add only necessary transmission line dual variables on the fly. Computational results for the modified IEEE 118-bus system show that the combination of the cutting-plane algorithm and the heuristic column-generation approach greatly reduces the total solution time of the two-stage robust unit commitment problem.

Energy Trading and Congestion Management Using Real and Reactive Power Rescheduling and Load Curtailment

Congestion is termed as the operating condition in which there is not enough transmission capacity to implement all the desired transactions. This paper deals with the power trading in electricity market to ensure regular supply at competitive rates with multi congestion case. Bidding process of 75 Indian bus systems is analyzed. It is shown that how can congestion cost can be addressed through active & reactive power rescheduling and load curtailment with transmission line constraints. With rescheduling of generation the congestion is removed with some congestion cost.