1. Introduction
In the last few decades, electricity consumption and power load in most of China’s power grid has markedly increased due to rapid economic development [
1,
2,
3].
Figure 1 illustrates the changing process of electricity consumption and maximum load in Zhejiang power grid from 2010 to 2018. It can be seen clearly that within less than 10 years, the electricity consumption grows from 2824 TWh to 3963 TWh while the peak load grows from 42 GW to 73 GW. Meanwhile, renewable energy (like wind farms and photovoltaic power plants) has developed rapidly in recent years, while their randomness and fluctuation further increases the peak pressure of the power system [
4,
5,
6]. Obviously, it has become a giant challenge to guarantee the dynamic balance of energy production and electricity consumption during peak periods.
Figure 2 shows the installed capacity structure of Zhejiang power grid by the end of 2015, where the statistical data is taken from the 13th Five-Year Electric Power Development Plan of Zhejiang province. It can be observed that the thermal power plants occupy the dominant position in the energy structure of Zhejiang power grid, while gas energy has the largest share among all the peaking power sources. Under this background, the peak operation of the adjustable gas energy is attracting increasing popularity in China’s provincial grids [
7].
The gas-fired generating units emit less pollution in comparison with thermal plants. When the output of the gas-fired unit exceeds half of the total installed capacity, only a small amount of oxynitride and carbon monoxide is produced [
8]. In specific terms, the oxynitride and carbon monoxide of the widely-used F-level gas-fired generators are about 50 mg/m
3 and 25 mg/m
3, far less than 100 mg/m
3 and 35 mg/m
3 in China’s national standard. Moreover, the gas-fired generating units can modify the operation state in a short time of period as the working conditions change. For the single-cycle gas turbines, it only takes about 15~20 min to turn from the shutdown mode to the full-load operation mode, and about 20~30 min to reduce the output from full-load to zero; for the combined cycle generators, the start-stop time is relatively long but still far less than the thermal plants [
9]. Thus, with the merits of high efficiency and low pollution, the gas-fired generators have become one of the most important peaking power sources in the provincial electric system of China.
In practice, certain loads will lead to operational instabilities of the gas-fired generators. To avoid this problem, the idea of disjoint-prohibited operating zones is used to reduce the adverse effect of the potential instabilities [
10]. As shown in
Figure 3, the original continuous state space is divided into a sequence of discrete decision sub-spaces due to the disjoint-prohibited operating zones [
11]. In other words, the existence of a prohibited operating zone makes the studied problem become a typical combinatorial optimization problem, which has sharply increased the optimization difficulty of the peak operation of the gas-fired generating units. In order to reduce the complexity of the problem effectively, the relatively fixed mode based on historical experience is used to determine the generation process of gas-fired units [
12]: the gas-fired units often start before the morning-peak times, and then increase the output during peak periods based on the necessary security constraints, and gradually stop the service when the load demand is reached at a certain small level. Although the current method can reduce the operators’ workload, unreasonable scheduling results may be produced in some cases because the differences of load demand, power generation and other factors are not given full attention at the same time. Thus, it is necessary to further develop effective methods for the peak operation of gas-fired generating units in China’s provincial electric system.
As mentioned above, the goal of this paper is to determine the optimal unit commitment of all the gas-fired generating units to smooth the residual load series of power system. Mathematically, the problem presented here is classified as a constrained optimization problem subjected to a variety of complicated equality or inequality constraints. Over the past decades, a variety of optimization algorithms has been developed by scholars throughout the world [
13,
14,
15,
16,
17,
18], like mixed integer linear programming (MILP) [
19], non-linear programming [
20], dynamic programming [
21,
22,
23], Lagrangian relaxation [
24] and evolutionary algorithms [
25,
26,
27]. For non-linear programming, it is difficult to guarantee the global optimal solution for the indefinite problem while the costs of execution time and memory usage may be too large [
28]. For dynamic programming, the dimensionality problem has limited its widespread application in high-dimensional optimization problems [
29]. For Lagrange relaxation, it is often difficult to select the appropriate Lagrange multiplier and conversion strategies between dual and original solutions [
30]. For evolutionary algorithms, it is not easy to produce stable solutions in different runs due to the premature convergence problem [
31,
32,
33]. By contrast with the aforementioned methods, MILP-based approaches can obtain the globally optimal solution within a finite number of iterations when the objective function and physical constraints become the linear functions of decision variables [
34,
35,
36]. Besides, numerous softwares have been developed to solve large-scale MILP problems and the users can gain access to the information on the proximity to the optimal solution in the search process. Due to the above merits, a great deal of attention has been paid to the popular MILP-based methods in practical problems [
34,
35,
36,
37]. For instance, the MILP models are developed to determine the generation of head-sensitive reservoir and distribution networks [
38,
39,
40]; the MILP model is used for the short-term operation of hydro-wind-solar hybrid system [
41]; the MILP procedure is developed for the analysis of electric grid security under a disruptive threat [
42]; a mixed-integer linear framework is developed for robust hydrothermal unit commitment [
43]; the MILP model is developed for day-ahead hydro-thermal self-scheduling considering price uncertainty and forced outage rate [
44].
However, in the traditional mathematical models, the goal is often set to minimize the variance of the residual load series, making it become a typical quadratic programming (QP) based problem. Obviously, all the variables in the scheduling horizon are tightly coupled and then the Hessian matrix involved in the objective function may become indefinite in practice [
45]. By this time, it will be NP-hard to resolve the peak operation problem of gas-fired generators. Thus, there is a visible gap between the existing research results and the problem presented here, and it is necessary to develop more effective optimization models for the peak operation of gas-fired units. Based on the depth analysis, it is found that the widely used inseparable non-linear objective can be replaced by a linear objective minimizing the peak-valley difference of the residual load curve, while all the considered physical constraints can be linearly expressed by the decision variables. On this basis, a novel MILP model is developed for the peak operation of gas-fired generating units with disjoint-prohibited operating zones. The practicability and feasibility of the MILP model is successfully proved in the real-world simulations.
Finally, to better understand our work, the novel contributions are given as below: one is that a practical mixed integer linear programming model is developed for the peak operation of gas-fired generators with disjoint prohibited operating zones, which may be the first research report by far; the other is that the developed model achieves satisfying performance in reducing the peak loads of the power system, demonstrating its practicability and reliability in different cases. Hence, an effective model is presented for the optimal operation of China’s provincial power system where the gas-fired generators play an important role in responding to the load change at peak periods.
The rest of this research is organized as below.
Section 2 develops the MILP model for the peak operation of the gas-fired generating units with disjoint-prohibited operating zones.
Section 3 tests the performances of the MILP model in different cases.
Section 4 gives the conclusions.
4. Conclusions
Due to booming economic development in recent decades, peak operation pressure has become a giant challenge for almost all the power grids in China. In practice, gas-fired units are asked to satisfy the rapid load change at peak periods in many provincial power systems where the installed capacity of adjustable flexible energy is not large enough. Hence, this paper proposes a practical mixed integer linear programming model to optimize the generation scheduling process of the gas-fired generating units with disjoint-prohibited operating zones and peak shaving operation aspects. The gas-fired generating units in the dispatching center of Zhejiang power grid of China are chosen to verify the feasibility of the developed model. The simulations show that with thousands of constraints and decision variables, the proposed model is able to generate satisfying results within reasonable execution time. For instance, the developed model can make about 6.14%, 19.71%, 12.93% and 5.02% improvements on the peak, peak-valley difference and standard deviation of the original loads in the long run, which will effectively alleviate the peak regulation pressure and guarantee the safe operation of the power grid. Thus, the presented model is an alternative method to reduce the peak operation pressure of China’s provincial electric system.
Besides, based on the empirical results, the following management implications can be obtained: a well-designed optimization model is helpful to reduce the solution difficulty and produce a better scheduling result for peak operation; the dynamic adjustment of the essential factors (like generated energy and operation limits) can increase the adaptive ability of gas-fired generators to the actual working conditions; and the share of peak power sources should be increased to improve the energy structure of China in the long run.