Time-dependent Start-up Costs Research Articles

An extended formulation for two-stage stochastic unit commitment with reserves

We derive extended formulations for the two-stage stochastic unit commitment with reserves. Our approach can capture most physical characteristics of a complicated thermal generator including min-up/-down time limit, time-dependent start-up costs, start-up/shut-down ramping, general ramping in the stable region, and reserve amount commitments. The extended formulations include both the convex hull descriptions for the feasible region and convex envelopes for the convex piece-wise linear and convex quadratic objective functions, which provide the optimal objective value for the original problem.

A Bienstock–Zuckerberg-Based Algorithm for Solving a Network-Flow Formulation of the Convex Hull Pricing Problem

This paper studies the convex hull pricing problem in electricity markets using a network-flow-based formulation. The network represents the feasible operating region of a generating unit, and the associated flow constraints define a polyhedron with an integrality property. These facts provide modeling flexibility with respect to the inclusion of unit features and allow to obtain convex hull prices from a linear programming problem. The formulation is solved using a primal-dual approach based on the algorithm developed by Bienstock and Zuckerberg. The algorithm, together with the implemented pre-processing and initialization techniques, allows achieving lower solution times than those obtained by state-of-the-art algorithms available in commercial solvers, e.g., barrier and dual simplex. Furthermore, results suggest that the proposed formulation obtains the minimum uplift payments even when time-dependent start-up costs are included, making the approach more robust than the best documented compact formulation. The paper also discusses the effect of sub-optimal prices on uplift payments by relaxing the optimality criterion of the algorithm, observing a significant impact on lost opportunity costs.

Development and modelling of a novel electricity-hydrogen energy system based on reversible solid oxide cells and power to gas technology

Compared to the conventional thermal units and electrolytic devices, reversible fuel cells have very high efficiencies on both fuel cell mode of generating electricity and electrolysis mode of producing hydrogen or CHx. However, previous studies about fuel cells and its benefits of power to gas are not fully investigated in the electricity-gas energy system. Moreover, state-of-art studies indicate that hydrogen could be directly injected to the existing natural gas (NG) pipeline within an amount of 5%–20%, which are considered to make a slight influence on the natural gas technologies. This work proposes a novel electricity-hydrogen energy system based on reversible solid oxide cells (RSOCs) to demonstrate the future vision of multi-energy systems on integrating multiple energy carriers such as electricity, pure hydrogen, synthetic natural gas (SNG) and mixed gas of H2-natural gas. The P2G processes of RSOC are sub-divided modelled by power to H2 (P2H) and power to SNG (P2SNG). The co-electrolysis/generation processes and time-dependent start-up costs are considered within a unit commitment model of RSOC. The proposed electricity-hydrogen energy system optimization model is formulated as mixed-integer linear programming (MILP), where the H2-blended mixed gas flow is linearized by an incremental linearize relaxation technic. The aim of the optimization is to reduce the energy cost and enhance the system's ability to integrate sufficient renewables through NG networks. Besides quantified the benefits of renewable level and H2 injection limit on the P2G process, the numerical results show that RSOC combined with H2/SNG injection results in productive economic and environmental benefits through the energy system.

Closed-Loop Hierarchical Operation for Optimal Unit Commitment and Dispatch in Microgrids: A Hybrid System Approach

To contribute to a smart grid, the unit commitment and dispatch (UCD) is a very important problem to be revisited in the future microgrid environment. In this paper, the UCD problem is studied by taking account of both traditional thermal units and distributed generation units (DGs) while considering demand response (DR) and carbon emissions trading (CET). Then, the UCD problem is reformulated as the optimal switching problem of a hybrid system. The reformulation allows convenient handling of time-dependent start-up cost for dynamic programming (DP). Afterwards, a closed-loop hierarchical operation (CLHO) algorithm is developed which is capable of producing the optimal schedule in the closed-loop behavior. Theoretical analysis is also presented to show the equivalence of the reformulation and the effectiveness of the CLHO algorithm. Finally, the closed-loop behavior and the effectiveness of the algorithm are further verified by simulation studies. It is also shown that low emission quotas and high emission trading price help reduce the total carbon emissions.

The Ramping Polytope and Cut Generation for the Unit Commitment Problem

We present a perfect formulation for a single generator in the unit commitment problem, inspired by the dynamic programming approach taken by Frangioni and Gentile. This generator can have characteristics such as ramp-up/ramp-down constraints, time-dependent start-up costs, and start-up/shut-down limits. To develop this perfect formulation, we extend the result of Balas on unions of polyhedra to present a framework allowing for flexible combinations of polyhedra using indicator variables. We use this perfect formulation to create a cut-generating linear program, similar in spirit to lift-and-project cuts, and demonstrate computational efficacy of these cuts in a utility-scale unit commitment problem. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0802 .

An Edge-Based Formulation for Combined-Cycle Units

As the number of combined-cycle units increases, efficient modeling approaches for these units play important roles for independent system operators (ISOs). Based on various combinations of combustion turbines (CTs) and steam turbines (STs), the combined-cycle unit could work at different configurations (modes) with different efficiencies. In this paper, we propose an edge-based formulation for the combined-cycle units in the unit commitment problem to improve the accuracy and effectiveness of current modeling approaches. Our formulation can 1) clearly describe the transition processes among different configurations so as to satisfy the ISO financial offer submission requirements and (2) capture physical constraints of each turbine, including the exact min-up/down time and time dependent startup cost, in the combined-cycle units so as to increase the operational flexibility while ensuring system feasibility. This model fits well with the current U.S. deregulated electricity market. The final numerical studies show that our approaches perform better than the current configuration-based modeling approach.

Optimal scheduling of combined heat and power plants using mixed-integer nonlinear programming

This paper presents the application of MINLP (mixed-integer nonlinear programming) approach for scheduling of a CHP (combined heat and power) plant in the day-ahead wholesale energy markets. This work employs first principles models to describe the nonlinear dynamics of a CHP plant and its individual components. The MINLP framework includes practical constraints such as minimum/maximum power output and steam flow restrictions, minimum up/down times, start-up and shut-down procedures, and fuel limits. Special care is given to the explicit modeling of the unit start-up types (hot, warm, and cold), which depend on the component's prior reservation time, resulting in the differences in the time-dependent start-up costs of generating units. The model also accounts for the different operating modes (synchronization, soak, dispatch, and desynchronization) during start-up and shut-down of each unit. We provide case studies involving the Hal C. Weaver power plant complex at the University of Texas at Austin to demonstrate the effectiveness of the proposed methodology. The results show that the optimized operating strategies can yield substantial net incomes from electricity sales.

Assessing Operating Regimes of CCS Power Plants in High Wind and Energy Storage Scenarios

Abstract This paper investigates the operating regimes of CCS power plants in future generation portfolios with large amounts of variable- output wind generation. An advanced electricity system dispatch model is developed and coupled with a Monte Carlo based energy storage optimization model to simulate the least-cost dispatch of an assumed thermal-energy storage generation portfolio with CCS. A historic high-resolution wind speed reanalysis dataset is employed and the proposed locations of future wind farms are used to produce plausible and internally consistent wind capacity deployment scenarios. The fundamental and structural changes that occur to CCS operating profiles and start-up/shut-down schedules are investigated for increasing levels of wind capacity, which creates seasonal and diurnal variations and potential flexibility implications. Non-linear interactions between flexible CCS power plants and other energy vectors are demonstrated for an illustrative case study example in Great Britain. This temporally explicit analysis of the short-term scheduling decisions of thermal plants with CCS highlights the asymmetric displacement of mid-merit thermal plants and the importance of using time-dependent start-up costs in wind-based unit commitment studies.

Genetic algorithm with binary representation of generating unit start-up and shut-down times for the unit commitment problem

An approach for solving the unit commitment problem based on genetic algorithm with binary representation of the unit start-up and shut-down times is presented. The proposed definition of the decision variables and their binary representation reduce the solution space and computational time in comparison to the classical genetic algorithm approach to unit commitment. The method incorporates time-dependent start-up costs, demand and reserve constraints, minimum up and down time constraints and units power generation limits. Penalty functions are applied to the infeasible solutions. Test results showed an improvement in effectiveness and computational time compared to results obtained from genetic algorithm with standard binary representation of the unit states and other methods.

Adaptive simulated annealing schedule to the unit commitment problem

This paper presents an approach for solving the unit commitment problem based on a simulated annealing algorithm with an adaptive schedule. The control parameter, temperature, is adapted to the cost levels on which the algorithm operates during the annealing process. This shortens the time taken to find a good solution meeting all constraints and improves the convergence of the algorithm. The operators specific to this problem, mutation and transposition, are used as the transition operators. The method incorporates time-dependent start-up costs, demand and reserve constraints, minimum up and down time constraints and unit power generation limits. There are different definitions of the objective function for the feasible and infeasible solutions. Test results showed an improvement in effectiveness compared to results obtained from simulated annealing with a static schedule, genetic algorithm and other techniques.

Solving unit commitment problems with general ramp constraints

Lagrangian relaxation (LR) algorithms are among the most successful approaches for solving large-scale hydro-thermal unit commitment (UC) problems; this is largely due to the fact that the single-unit commitment (1UC) problems resulting from the decomposition, incorporating many kinds of technical constraints such as minimum up- and down-time requirements and time-dependent startup costs, can be efficiently solved by dynamic programming (DP) techniques. Ramp constraints have historically eluded efficient exact DP approaches; however, this has recently changed [Frangioni A, Gentile C. Solving nonlinear single-unit commitment problems with ramping constraints. Oper Res 2006;54(4):767–75]. We show that the newly proposed DP algorithm for ramp-constrained (1UC) problems allows to extend existing LR approaches to ramp-constrained (UC); this is not obvious since the heuristic procedures typically used to recover a primal feasible solution are not easily extended to take ramp limits into account. However, dealing with ramp constraints in the subproblems turns out to be sufficient to provide the LR heuristic enough guidance to produce good feasible solutions even with no other modification of the approach; this is due to the fact that (sophisticated) LR algorithms to (UC) duly exploit the primal information computed by the Lagrangian Dual, which in the proposed approach is ramp feasible. We also show by computational experiments that the LR [approach] is competitive with those based on general-purpose mixed-integer program (MIP) solvers for large-scale instances, especially hydro-thermal ones.

A Computationally Efficient Mixed-Integer Linear Formulation for the Thermal Unit Commitment Problem

This paper presents a new mixed-integer linear formulation for the unit commitment problem of thermal units. The formulation proposed requires fewer binary variables and constraints than previously reported models, yielding a significant computational saving. Furthermore, the modeling framework provided by the new formulation allows including a precise description of time-dependent startup costs and intertemporal constraints such as ramping limits and minimum up and down times. A commercially available mixed-integer linear programming algorithm has been applied to efficiently solve the unit commitment problem for practical large-scale cases. Simulation results back these conclusions

Unit commitment by genetic algorithm with specialized search operators

An approach for solving the unit commitment problem based on genetic algorithm with new search operators is presented. These operators, specific to the problem, are mutation with a probability of bit change depending on load demand, production and start-up costs of the generating units and transposition. The method incorporates time-dependent start-up costs, demand and reserve constraints, minimum up and down time constraints and units power generation limits. Repair algorithms or penalty factors in the objective function are applied to the infeasible solutions. Numerical results showed an improvement in the solution cost compared to the results obtained from genetic algorithm with standard operators and other techniques.

Exhaust gas treatment by an atmospheric pressure microwave plasma : Destefani, C. A. and Siores, E. Int. J. Environmental Technology and Management, 2002, 2, (4), 402–408

This paper investigates the operating regimes of CCS power plants in future generation portfolios with large amounts of variable- output wind generation. An advanced electricity system dispatch model is developed and coupled with a Monte Carlo based energy storage optimization model to simulate the least-cost dispatch of an assumed thermal-energy storage generation portfolio with CCS. A historic high-resolution wind speed reanalysis dataset is employed and the proposed locations of future wind farms are used to produce plausible and internally consistent wind capacity deployment scenarios. The fundamental and structural changes that occur to CCS operating profiles and start-up/shut-down schedules are investigated for increasing levels of wind capacity, which creates seasonal and diurnal variations and potential flexibility implications. Non-linear interactions between flexible CCS power plants and other energy vectors are demonstrated for an illustrative case study example in Great Britain. This temporally explicit analysis of the short-term scheduling decisions of thermal plants with CCS highlights the asymmetric displacement of mid-merit thermal plants and the importance of using time-dependent start-up costs in wind-based unit commitment studies.

A computer model for power system control

A forward dynamic programming formulation of the optimal commitment of units for economic power generation is proposed, and it is shown how advantage is taken of the characteristics of the formulation as well as the structure of the problem itself to impose limiting conditions which reduce the size and complexity of the solution, while still ensuring that the generating schedules determined are costefficient. By employing a number of strategies which control the multiplicity of states, the proposed method eliminates the necessity for large computer storage—a drawback in the early dynamic programming methods. Operating constraints like non-linearities in the cost characteristics of units, deterministic spinning reserve, time-dependent start-up costs are incorporated in the model and operating schedules are produced over a 24-h horizon. Computational experience with the technique indicates its potentiality for on-line computer implementation.

A Method for Solving the Fuel Constrained Unit Commitment Problem

The unit commitment problem involves finding the hourly commitment schedule for the thermal units of an electrical system, and their associated generation, over a period of up to a week. For some utilities, contractual or other factors limit the amount of fuel available to certain of the units or plants. This paper describes a new method which solves the unit commitment problem in the presence of fuel constraints. The method uses a Lagrangian decomposition and successive approximation technique for solving the unit commitment problem where the generation, reserve and fuel constraints are adjoined onto the cost function using Lagrange multipliers. All important operating constraints have been incorporated including minimum up and down times, standby operation, ramping limits, time-dependent start-up cost, spinning and supplemental reserve. The method is being applied to a production-grade program suitable for Energy Management Systems applications.

A Branch-and-Bound Algorithm for Unit Commitment

A new approach is presented for solving the unit commitment problem based on branch-and-bound techniques. The method incorporates time-dependent start-up costs, demand and reserve constraints and minimum up and down time constraints. It does not require a priority ordering of the units. The method can be extended to allow for a probabilistic reserve constraint. Preliminary computational results are reported.

An Application of Mixed-Integer Programming Duality to Scheduling Thermal Generating Systems

A decomposable mixed-integer programming model for simultaneous economic consideration of unit commitment and short-term dispatch of thermal power generating equipment is presented. An optimum solution procedure is described which takes advantage of the structure of the model and promises computational efficiency in practical applications. Characterizing the demand forecast as a discretized function permits a probabilistic forecast to be incorporated in the scheduling model. The model minimizes the total expected costs of start-up, shutdown, and unit operating costs subject to the demand, reserve, and unit commitment constraints. Extensions to multiple periods and to include additional constraints such as time dependent start-up costs and geographic constraints are given.