Simulation and the monte carlo method

We present a two-stage stochastic programming model for committing reserves in systems with large amounts of wind power. We describe wind power generation in terms of a representative set of appropriately weighted scenarios, and we present a dual decomposition algorithm for solving the resulting stochastic program. We test our scenario generation methodology on a model of California consisting of 122 generators, and we show that the stochastic programming unit commitment policy outperforms common reserve rules.

Reserve Requirements for Wind Power Integration: A Scenario-Based Stochastic Programming Framework

Optimization models have been widely used in the power industry to aid the decision-making process of scheduling and dispatching electric power generation resources, a process known as unit commitment (UC). Since UC’s birth, there have been two major waves of revolution on UC research and real life practice. The first wave has made mixed integer programming stand out from the early solution and modeling approaches for deterministic UC, such as priority list, dynamic programming, and Lagrangian relaxation. With the high penetration of renewable energy, increasing deregulation of the electricity industry, and growing demands on system reliability, the next wave is focused on transitioning from traditional deterministic approaches to stochastic optimization for unit commitment. Since the literature has grown rapidly in the past several years, this paper is to review the works that have contributed to the modeling and computational aspects of stochastic optimization (SO) based UC. Relevant lines of future research are also discussed to help transform research advances into real-world applications.

Stochastic Optimization for Unit Commitment—A Review

As the penetration of variable renewable generation increases in power systems worldwide, planning for the effects of variability will become more important. Traditional capacity adequacy planning techniques have been supplemented with integration studies, which have been carried out in power systems with high targets for renewable generation. These have highlighted the increased variability that a system may experience in the future. As system generation planning techniques evolve with the challenge of integrating variable generation, the flexibility of a system to manage periods of high variability needs to be assessed. The insufficient ramping resource expectation (IRRE) metric is proposed to measure power system flexibility for use in long-term planning, and is derived from traditional generation adequacy metrics. Compared to existing generation adequacy metrics, flexibility assessment is more data intensive. A flexibility metric can identify the time intervals over which a system is most likely to face a shortage of flexible resources, and can measure the relative impact of changing operational policies and the addition of flexible resources. The flexibility of a test system with increasing penetrations of variable generation is assessed. The results highlight the time horizons of increased and decreased risk associated with the integration of VG.

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Evaluation of Power System Flexibility

Monte Carlo simulation method combined with simple random sampling (SRS) suffers from long computation time and heavy computer storage requirement when used in probabilistic load flow (PLF) evaluation and other power system probabilistic analyses. This paper proposes the use of an efficient sampling method, Latin hypercube sampling (LHS) combined with Cholesky decomposition method (LHS-CD), into Monte Carlo simulation for solving the PLF problems. The LHS-CD sampling method is investigated using IEEE 14-bus and 118-bus systems. The method is compared with SRS and LHS only with random permutation (LHS-RP). LHS-CD is found to be robust and flexible and has the potential to be applied in many power system probabilistic problems.

Probabilistic Load Flow Evaluation With Hybrid Latin Hypercube Sampling and Cholesky Decomposition

This paper analyzes the behavior of Hong's point estimate methods to account for uncertainties on the probabilistic power flow problem. This uncertainty may arise from different sources as load demand or generation unit outages. Point estimate methods constitute a remarkable tool to handle stochastic power system problems because good results can be achieved by using the same routines as those corresponding to deterministic problems, while keeping low the computational burden. In previous works related to power systems, only the two-point estimate method has been considered. In this paper, four different Hong's point estimate schemes are presented and tested on the probabilistic power flow problem. Binomial and normal distributions are used to model input random variables. Results for two different case studies, based on the IEEE 14-bus and IEEE 118-bus test systems, respectively, are presented and compared against those obtained from the Monte Carlo simulation. Particularly, this paper shows that the use of the scheme provides the best performance when a high number of random variables, both continuous and discrete, are considered.

Point Estimate Schemes to Solve the Probabilistic Power Flow

This paper proposes a methodology to determine the required level of spinning and nonspinning reserves in a power system with a high penetration of wind power. The computation of the required reserve levels and their costs is achieved through a stochastic programming market-clearing model spanning a daily time horizon. This model considers the network constraints and takes into account the cost of both the load shedding and the wind spillage. The methodology proposed is illustrated using an example and a realistic case study. Some conclusions are finally drawn.

Economic Valuation of Reserves in Power Systems With High Penetration of Wind Power

This paper presents a technique to derive the best offering strategy for a wind power producer in an electricity market that includes various trading floors. Uncertainty pertaining to wind availability, market prices at the different trading stages, and balancing energy needs are properly taken into account. Risk on profit variability is suitably controlled at the cost of a small reduction in expected profit. The proposed technique translates into a linear programming problem of moderate size, which is readily solvable using commercially available software. A variety of numerical case studies demonstrate the interest and effectiveness of the proposed technique. Appropriate conclusions are duly drawn.

Short-Term Trading for a Wind Power Producer

This paper proposes a methodology to determine the required level of spinning and non-spinning reserves in a power system with a high penetration of wind power. The computation of the required reserve levels and their costs is achieved through a stochastic programming market-clearing model spanning a daily time horizon. This model considers the network constraints and takes into account the cost of both the load shedding and the wind spillage. The methodology proposed is illustrated using an example and a realistic case study. Some conclusions are finally drawn.

Economic valuation of reserves in power systems with high penetration of wind power

This panel presentation is based on paper “J. M. Morales, A. J. Conejo, J. Perez-Ruiz, Short-Term Trading for a Wind Power Producer. IEEE Transactions on Power Systems, in press, 2010.” It presents a technique to derive the best offering strategy for a wind power producer in an electricity market that includes several trading floors. Uncertainty pertaining to wind availability, market prices at the different trading stages, and balancing energy needs are properly taken into account. Risk on profit variability is suitably controlled at the cost of a small reduction in expected profit. The proposed technique translates into a linear programming problem of moderate size, which is readily solvable using commercially available software.

Juan Perez-Ruiz

Papers

Point Estimate Schemes to Solve the Probabilistic Power Flow

Economic Valuation of Reserves in Power Systems With High Penetration of Wind Power

Short-Term Trading for a Wind Power Producer

Economic valuation of reserves in power systems with high penetration of wind power

Short-Term Trading for a Wind Power Producer