This paper provides the convex hull description for the following basic operating con-straints of a single thermal generation unit in Unit Commitment (UC) problems: 1)generation limits, 2) startup and shutdown capabilities, and 3) minimum up and downtimes. Although the model does not consider some crucial constraints, such as ramping,the proposed constraints can be used as the core of any UC formulation, thus tighteningthe final UC model. We provide evidence that dramatic improvements in computationaltime are obtained by solving a self-UC problem for different case studies.
Modeling electricity storage to address challenges and opportunities of its applications for smart grids requires inter-temporal equalities to keep track of energy content over time. Prevalently, these constraints present crucial modeling elements as to what extent energy storage applications can enhance future electric power systems' sustainability, reliability, and efficiency. This paper presents a novel and improved mixed-integer linear problem (MILP) formulation for energy storage of plug-in (hybrid) electric vehicles (PEVs) for reserves in power system models. It is based on insights from the field of System Dynamics, in which complex interactions between different elements are studied by means of feedback loops as well as stocks, flows and co-flows. Generalized to a multi-bus system, this formulation includes improvements in the energy balance and surpasses shortcomings in the way existing literature deals with reserve constraints. Tested on the IEEE 14-bus system with realistic PEV mobility patterns, the deterministic results show changes in the scheduling of the units, often referred to as unit commitment (UC).
In recent years, high penetration of variable generating sources, such as wind power, has challenged independent system operators (ISO) in keeping a cheap and reliable power system operation. Any deviation between expected and real wind production must be absorbed by the power system resources (reserves), which must be available and ready to be deployed in real time. To guarantee this resource availability, the system resources must be committed in advance, usually the day-ahead, by solving the so-called unit commitment (UC) problem. If the quantity of committed resources is extremely low, there will be devastating and costly consequences in the system, such as significant load shedding. On the other hand, if this quantity is extremely high, the system operation will be excessively expensive, mainly because facilities will not be fully exploited.
This thesis proposes computationally efficient models for optimal day-ahead planning in (thermal) power systems to adequately face the stochastic nature of wind production in the real-time system operation. The models can support ISOs to face the new challenges in short-term planning as uncertainty increases dramatically due to the integration of variable generating resources. This thesis then tackles the UC problem in the following aspects:
This paper proposes a “robustified” network-constrained Unit Commitment (UC) formulation as an altern-ative to the robust and stochastic UC formulations under windgeneration uncertainty. The formulation draws a clear distinctionbetween power-capacity and ramp-capability reserves to deal withwind production uncertainty. These power and ramp require-ments can be obtained from wind forecast information. The modelis formulated under the ramp-based scheduling approach, whichschedules power-trajectories instead of the traditional energy-blocks and takes into account the inherent startup and shutdownpower trajectories of thermal units. These characteristics allowa correct representation of unit’s ramp schedule which definetheir ramp availability for reserves. The proposed formulationsignificantly decreases operation costs if compared to traditionaldeterministic and stochastic UC formulations while simultan-eously lowering the computational burden. The operation costcomparison is made through 5-min economic dispatch simulationunder hundreds of out-of-sample wind generation scenarios.
This paper provides the convex hull description for the basic operation of slow- and quick-startunits in power-based unit commitment (UC) problems. The basic operating constraints that are modeled forboth types of units are: 1) generation limits and 2) minimum up and down times. Apart from this, the startupand shutdown processes are also modeled, using 3) startup and shutdown power trajectories for slow-startunits, and 4) startup and shutdown capabilities for quick-start units. In the conventional UC problem, powerschedules are used to represent the staircase energy schedule; however, this simplification leads to infeasibleenergy delivery, as stated in the literature. To overcome this drawback, this paper provides a power-basedUC formulation drawing a clear distinction between power and energy. The proposed constraints can be usedas the core of any power-based UC formulation, thus tightening the final mixed-integer programming UCproblem. We provide evidence that dramatic improvements in computational time are obtained by solvingdifferent case studies, for self-UC and network-constrained UC problems.
This paper presents a mixed-integer linear programming (MILP) reformulation of the thermal unit commitment (UC) problem. The proposed formulation is simultaneously tight and compact. The tighter characteristic reduces the search space and the more compact characteristic increases the searching speed with which solvers explore that reduced space. Therefore, as a natural consequence, the proposed formulation significantly reduces the computational burden in comparison with analogous MILP-based UC formulations. We provide computational results comparing the proposed formulation with two others which have been recognized as computationally efficient in the literature. The experiments were carried out on 40 different power system mixes and sizes, running from 28 to 1870 generating units.
This paper presents a mixed-integer linear programming (MILP) formulation of start-up (SU) and shut-down (SD) power trajectories of thermal units. Multiple SU power-trajectories and costs are modeled according to how long the unit has been offline. The proposed formulation significantly reduces the computational burden in comparison with others commonly found in the literature. This is because the formulation is 1) tighter, i.e., the relaxed solution is nearer to the optimal integer solution; and 2) more compact, i.e., it needs fewer constraints, variables and nonzero elements in the constraint matrix. For illustration, the self-unit commitment problem faced by a thermal unit is employed. We provide computational results comparing the proposed formulation with others found in the literature.
The day-ahead unit-commitment (UC)-based market-clearing (MC) is widely acknowledged to be the most economically efficient mechanism for scheduling resources in power systems. In conventional UC problems, power schedules are used to represent the staircase energy schedule. However, the realizability of this schedule cannot be guaranteed due to the violation of ramping limits, and hence conventional UC formulations do not manage the flexibility of generating units efficiently. This paper provides a UC-based MC formulation, drawing a clear distinction between power and energy. Demand and generation are modeled as hourly piecewise-linear functions representing their instantaneous power trajectories. The schedule of generating unit output is no longer a staircase function, but a smoother function that respects all ramp constraints. The formulation represents in detail the operating reserves (online and offline), their time deployment limits (e.g., 15 min), their potential substitution, and their limits according to the actual ramp schedule. Startup and shutdown power trajectories are also modeled, and thus a more efficient energy and reserves schedule is obtained. The model is formulated as a mixed-integer programming (MIP) problem, and was tested with a 10-unit and 100-unit system in which its computational performance was compared with a traditional UC formulation.
We propose a power-based unit commitment formulation with capacity and intra-hour ramp reserves for dealing with intra-hour wind power variability and uncertainty. Although the formulation has an hourly resolution, the intra-hour ramp requirements capture wind power ramp excursions with a time duration below one hour, and thus allows the formulation to consider intra-hourly wind variability and uncertainty. This increases the security of the formulation compared to using hourly ramp reserves and allows more efficient scheduling of units with high ramp rates. We test the formulation with different durations for the intra-hour reserves, and using both hourly and intra-hourly ramp reserves, to find the best reserve formulation. The formulations are evaluated using a 5-min economic dispatch, which simulates the real-time operation of the system, for hundreds of out-of-sample realizations of wind power production. The proposed formulations are then compared to two hourly stochastic formulations and a stochastic formulation with 5-min time resolution. The proposed formulations outperform the stochastic formulations in terms of security, showing that they provide a scheduling which is more robust against intra-hour wind power variations. The proposed formulations also outperform the hourly stochastic formulations in terms of total costs, giving a better trade-off between scheduling costs and security.
The planning of future power systems with high shares of renewable generation requires modelling large and complex systems over long time periods, resulting in models which are computationally heavy to solve. For this reason methods that can be used to decrease the size of power system dispatch models are needed. A common method in large scale planning models is to decrease the model size by increasing the size of the time steps. However, using larger time steps makes the representation of variability of renewable generation and load less accurate, which can affect the results from the model. In this paper, we investigate the possibility to use a power-based version of an economic dispatch model to decrease the model time resolution while getting results which are close to the original high-resolution model. We implement both power-based and the conventional, energy-based, versions of a dispatch model with different time resolutions, and show that the power-based model has better agreement with the high-resolution model, especially as the model time step increases. For example, using the power-based model gives more accurate results for wind power curtailment in a high-renewable scenario.
This paper presents power-based unit commitment (UC) formulations with N-1 security constraints. Two different formulations are proposed, one with constant reserves within the hour and one with time-varying reserves. The formulations are compared to a conventional energy-based UC formulation using different examples. We show that the energy-based formulation does not ensure N-1 security at all times within the hour, since it does not account for the power profile of units. In contrast, the proposed power-based formulations guarantee N-1 security within the whole hour for a piecewise linear demand profile. The formulations are also evaluated using a 5-min economic dispatch based on a real load profile, simulating the real-time operation of the power system, showing that the power-based formulations also provide increased security in this case. Compared to using a power-based formulation with constant reserves, using time-varying reserves decreases the reserve cost while ensuring a similar level of security.