Using Lagrangian Relaxation to Solve the Problem of Economical Load Distribution in SIS

Solving the problem of economical distribution of load can bring huge economic benefits to power generation companies, and it is one of the key issues to be solved in SIS. Before the bidding, power companies in the market must measure the cost of the power generation company by repeatedly solving the problem of load economic distribution. After bidding, the bidding power must be allocated to each unit by solving the problem of load economic distribution. There are many methods to solve the problem of economical distribution of loads, such as Lagrangian relaxation method and dynamic programming method, and artificial intelligence methods such as opacity optimization algorithm and genetic algorithm. Dynamic programming method can easily lead to "dimensional disasters". The opacity optimization methods and genetic algorithms are time-consuming to solve, and strongly depend on the selection of various parameters in a specific solution. The traditional Lagrangian relaxation method uses the Lagrangian multiplier to establish the augmented objective function, and determines the active power of each unit according to the equal-rate microincrease rate and the Kuhn-Tucker condition. However, this method requires the unit's power consumption characteristics. The curve increases monotonically. In this paper, Lagrangian relaxation method is used. After Lagrange multipliers are used to relax the load constraints of the system, the obtained augmented objective function is not directly solved. Instead, the obtained Lagrangian function is first decomposed into An upper and lower level optimization problem is then solved separately. This not only does not require monotonic increase of the consumption characteristic curve, but also guarantees the rapidity and effectiveness of the algorithm.

I. Mathematical model of economic distribution of the load When there are altogether one set of units requiring economic distribution, the mathematical model of the economic distribution of the load is described as follows: Since the real-time load economic allocation problem is to be solved in the SIS, in the specific solution process, there are For the i-th unit generating power for a period of time, Pmini is the minimum generating power of the i-th unit, Pmaxi is the maximum generating power of the i-th generating unit, and ΔPi is the climbing constraint of the i-th unit.

Second, the principle of Lagrangian relaxation algorithm and its implementation steps In the Lagrange relaxation method to solve the problem of economic distribution of the load, the Lagrange multiplier is first used to relax the load constraints of the system to obtain the Lagrangian function: The Lagrangian relaxation algorithm flow is shown in Figure 1. Third, the actual application of a power plant 4 units of the actual operating parameters are shown in Table 1, the total power generation constraint Pd = 820MW. In order to demonstrate the effectiveness of the algorithm, the same set of data was solved using Lagrangian relaxation method, mixed oil optimization algorithm and genetic algorithm. The simulation shows that the Lagrangian relaxation method has a significantly faster solution speed, and the result is superior to the chaos optimization algorithm and the genetic algorithm (Table 2). When using chaos optimization algorithm and genetic algorithm, in order to guarantee the fast convergence of the algorithm, this paper will convert the original problem into the following form.

Objective function: Power generation constraints: (2) The genetic algorithm uses a real-coded form. The initial population is 50, the crossover probability is 0.5, and the mutation probability is 0.4.

IV. CONCLUSION In this paper, Lagrange relaxation method is used to solve the problem of economical load distribution of SIS in power system. The simulation results show that the Lagrangian relaxation method has a simple search speed and provides an effective means for solving the problem of economic allocation of load in SIS. Lagrangian relaxation method not only can be used in power plant SIS, but also can be used in many issues such as load distribution in the electricity market, and has broad application prospects.

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