The Vector Optimization Method for Solving Integer Linear Programming Problems: Application for the Unit Commitment Problem in Electrical Power Production

  • Lenar Nizamov
Part of the Springer Optimization and Its Applications book series (SOIA, volume 149)


Nowadays information technology is continuously implemented in all fields of industry, including power generation. One of the most important tasks of modern energy systems is reliable, effective, and safe planning of their work. The task of planning is also vital for single power plants. The solution of this task must satisfy requirements of financial effectiveness and conditions of energy system. This chapter deals with the solution of the problem of integer linear programming. For this purpose the author consistently represents the statement of the problem, the objective function, and the system of constraints that must be considered. To solve considered problem, the vector optimization method (VOM) is proposed. To illustrate the performance of the proposed method, the author provided the example of how to solve the unit commitment problem for the power station, in order to reach a maximum total financial profit. As a result of planning, the desired optimal sequence of combinations of operating turbogenerators is determined. To assess effectiveness of the VOM, the chapter provides an estimate of its computational cost in comparison with the computational cost of the dynamic programming method. The comparison results demonstrate the advantages of the VOM.


  1. 1.
    Koller M, Hofmann R (2018) Mixed-Integer Linear Programming Formulation of Combined Heat and Power Units for the Unit Commitment Problem. Journal of Sustainable Development of Energy, Water and Environment Systems, 6(4): 755–769CrossRefGoogle Scholar
  2. 2.
    Castro P, Harjunkoski I, Grossmann I (2009) New continuous-time scheduling formulation for continuous plants under variable electricity cost. Industrial and Engineering Chemistry Research, 48, 14: 6701–6714CrossRefGoogle Scholar
  3. 3.
    Aminov R (1986) Determination of the gradient vector while in the distribution of loads in a mixed power system. News of higher educational institutions of the USSR. Power engineering Series, 2, 5: 59–63Google Scholar
  4. 4.
    Andryushenko A, Aminov R (1983) Optimization of modes and parameters of thermal power stations. Moscow: Higher school, MoscowGoogle Scholar
  5. 5.
    Silbernagl M, Huber M, Brandenberg R (2016) Improving accuracy and efficiency of Start-up Cost Formulations in MIP Unit commitment by modeling Power Plant Temperatures. IEEE Transactions on Power Systems, 31, 4: 2578–2586CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Lenar Nizamov
    • 1
  1. 1.Kazan State Power Engineering UniversityKazanRussian Federation

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