Research on Multi-objective Optimization Linear Programming Problem of Power Generation under Carbon Emission Trading

Carbon emissions trading is an important means to achieve the target of low carbon and energy saving, the construction and promotion of which has been widely concerned in recent years. As carbon emitters, electricity industry is shouldering more pressure to reduce emissions and will definitely participate in carbon emissions trading. Energy saving dispatching is one of the most important ways to realize energy saving and emission reduction for electricity power companies. One kind of multi-objective optimization linear programming model for generating units under carbon emissions trading is constructed in this paper. The model is verified by a practical case analysis, which ensures the optimal allocation of power resources with multi-objective of Energy saving, emission reduction and economy, and sustainable development of electricity power companies.


Introduction
As a means of market regulation, the introduction of carbon emissions trading will effectively promote the development of energy-saving and emission reduction technologies in power industry. However, with the introduction of carbon emissions trading system in power industry, carbon emissions trading has brought the great impact on the traditional trading and dispatching mode of power industry, which makes the mode of traditional power resource allocation and the mechanism of operation scheduling dispatching need to be further improved. In addition to considering the emission of sulfuric dioxide, nitrogen oxides and solid particles, it is critical to for power industry to optimize the allocation of power resources with carbon constraints. So far, there have been a lot of research results on the power generation scheduling under carbon emissions trading. For example, literature [1] has established three optimization models of interregional generation scheduling including clean energy generation, taking minimum regional generation cost and minimum comprehensive cost as objective functions respectively and the models considered the issues of economic efficiency, carbon emission and transmission constraints. Literature [2] has constructed a day-ahead dispatching scheduling model which takes minimum synthetically generation cost as optimization objective. Literature [3][4] has established the thermal power unit scheduling optimization models and multi-objective model according to the cost, energy consumption and emission quantity. And these models are compared with the traditional electricity distribution model. Literature [5][6]  a single-objective optimization model for power system energy consumption and carbon emissions as the goal of minimizing the total cost. Literature [7][8] has established optimization models based on equal utility efficiency, minimum coal consumption, minimum carbon emission, least generation cost and least total cost to analyse and evaluate the result of generation permit substitution with different allowance allocation. The optimal allocation of generation resources is a problem of generator unit commitment planning substantially. This paper studies the problem of priority scheduling strategy for generator units and established the multi-objective optimization linear programming model of power generation under carbon emissions trading, which is applied to a real case. Finally, electricity purchasing optimization strategy for electricity power companies is obtained in the mode of carbon emissions the transaction.

Priority strategy of generator units dispatching under carbon emission trading
The equal incremental principle refers to every generator unit in power system operating according to the same incremental rate of consumption. Therefore, the total energy loss in power system will at the lowest level. Similarly, if each generator unit in power system operates with the same consumption level, which includes total input among various type of resources such as primary energy consumption, the use of emission rights and capital investment, the total resources loss in power system would be at the lowest level while the system operation mode will be in most economical level accordingly. The process of constituting the priority strategy of generator units dispatching under carbon emission trading is mainly divided into four steps. First of all, it is necessary to collect the data of power supply, coal consumption, emissions of all pollutants and electricity purchase capital consumption in recent years. Through regression analysis based on the data obtained, the function mapping relation between unit power supply and coal consumption, emissions of all pollutants and electricity purchase capital consumption is put forward correspondingly. Secondly, according to the function mapping relation obtained, solve the derivative function of each function relation to power supply and get the relationship between the micro variations of power supply and the micro variations of coal consumption, emissions of all pollutants and electricity purchase capital consumption among each generator unit. Then, the weight of each unit coal consumption, emissions of all pollutants and electricity purchase capital consumption is calculated and multiplied by the micro-increment relationship obtained in the previous step. So that an integrated consumption of the micro-increment relationship can be received by the sum of the above results. Finally, making integrated consumption micro-increment rate of generator unit equal to each other, incremental value interval of each generator unit can be calculated combining with a series of constraint conditions under the equal incremental principle, and then the optimal generator unit dispatching program can be put forward according to the range of micro-increment rate.

Construction of linear programming model
Power trading center promotes energy saving and emission reduction in generator units through bilateral transactions. Therefore, the primary goal of the linear programming model is energy conservation, followed by emission reduction, the final consideration of electricity prices. Assuming that there are N generator units in the region, objective function can be obtained combining with energy-saving emission reduction targets.  Target of minimum coal consumption.
Combining with the constraint conditions, a set of constrained inequalities for multi-objective linear programming problems can be proposed.  Restriction of generator unit output power.
If electricity power companies promote energy saving and emission reduction in power generation companies through energy saving dispatching, the smaller the objective function values of formula (1) -(3) are, the better emission reduction effect is. Therefore, the model is to obtain the generating capacity of each generator unit when the objective function value is smallest based on the inequality constraint conditions (4) -(6), which is regarded as optimal program under linear programming. However, it is quite difficult to solve the problem of multi-objective linear programming directly. In this way, it is much easier to transform multi-objective linear programming problem into singleobjective linear programming problem.

Solution to linear programming model
First of all, under the constraints conditions of the inequalities, the optimal value of each objective function is obtained by solving the single-objective linear programming problem, which is written as M 0 , C 0 , S 0 , N 0 , G 0 and U 0 . At the same time, because the objective function is the minimum, and the direction of optimization is the same, we can introduce a super-objective function.
Among them, α, β, γ, βc, βs, βn and βg are all weight coefficient equal to or more than 0. In addition, compromise constraint condition is constructed.
After constructing the super-objective function and the compromise constraints, a new linear programming problem can be presented.
Among them, the constraint conditions are inequalities (4) to (6) and compromise constraints are inequalities (10) to (14). Finally, compromise solution set can be obtained by solving the linear programming problem above with the method of solving single-objective linear programming problem, which the non-inferior solution of the original multi-objective linear programming problem. At this point, the values of which is obtained are the optimal bilateral trading generator units and generating capacity under the multi-objective linear programming.

Model application
As a means of market regulation, carbon emissions trading will effectively promote the development of energy saving and emission reduction technologies in power industry and contribute to the realization of carbon emission reduction targets in China. However, with the introduction of carbon emissions trading system in power industry, carbon emissions trading has brought great impact on traditional trading and dispatching mode of power industry. So, the mode of power resource allocation and the mechanism of scheduling dispatching should be further improved. It is critical for power industry to optimize the allocation of power resources with carbon constraints.

Restriction of generator unit output power
Restrictions of 24 generator units' output are shown in Table 1. Compared to generator units dispatching with single objective including minimum coal consumption or minimum emissions of various pollutants, the difference among the operation modes of generator units with different targets is shown in Figure 1.

Conclusion
In this paper, and one kind of multi-objective optimization linear programming model for generating units under carbon emissions trading is constructed. Meanwhile, the model is solved by a practical case. The result obtained is considered as a compromise solution for all targets, which provides a solution for electricity power companies to the optimal allocation of power resources with multiobjective of energy saving, emission reduction and economy, and ensure scheduling operation of power system with multi objectives and sustainable development of electricity power companies. In order to solve the problems of energy shortage and environmental pollution, there will be a largescale renewable energy power. At this time, the constraints of power system dispatching are no longer limited to coal consumption and pollutant emissions, as well as more technical and environmental constraints. How to realize economic operation management of power system with a variety of constraints, will be the research direction of the new energy power system in the future.