PDF(1146 KB)
连续时间调度方法在电力系统灵活运行中的应用综述
刘晶冠, 艾小猛, 周博, 薛熙臻, 王盛世, 崔世常, 方家琨, 文劲宇
电力建设 ›› 2026, Vol. 47 ›› Issue (1) : 112-124.
PDF(1146 KB)
PDF(1146 KB)
连续时间调度方法在电力系统灵活运行中的应用综述
A Review of the Application of Continuous-Time Scheduling Methods in the Flexible Operation of Power Systems
【目的】面向调度时段内功率波动刻画与灵活性资源配置,系统梳理连续时间调度方法在电力系统灵活运行中的应用现状与存在问题。【方法】首先对比离散时间与连续时间调度的数学描述与求解思路;然后按发电、输电、储能、用电四类典型物理对象分类综述代表性应用与问题;最后从数学角度提炼共性挑战并整理潜在理论发展方向。【结果】连续时间模型以连续曲线为决策变量,约束涵盖导数、积分及微分方程;求解思路主要包括类最优控制方法与伽辽金投影法。共性难点集中于连续时间随机性建模、启停/互斥等非凸约束求解,以及微分方程约束处理。【结论】文章据此归纳连续时间调度方法在多时间尺度调度协同、规划评估与市场机制中的未来应用趋势与后续研究课题。
[Objective] To enhance the representation of intra-interval power fluctuation and the allocation of flexibility resources,this paper provides a systematic review of the applications and existing challenges of continuous-time scheduling methods for flexible power system operation. [Methods] First,the mathematical formulations and solution paradigms of discrete-time and continuous-time scheduling are compared. Then,representative applications and problems are reviewed,organized according to four key domains:generation,transmission,storage,and demand. Finally,common challenges are synthesized from a mathematical point,and potential theoretical development directions are summarized. [Conclusions] In continuous-time scheduling,decision variables are modeled as continuous trajectories,and constraints involve derivatives,integrals,and differential equations. The main solution paradigms include optimal-control-inspired methods and Galerkin-projection-based approaches. Shared difficulties mainly arise from modeling uncertainty in continuous time,solving nonconvex constraints such as unit commitment and charge-discharge exclusivity,and handling differential-equation constraints. [Conclusions] Based on these findings,this paper outlines future application trends and follow-up research topics of continuous-time scheduling in multi-timescale scheduling coordination,planning assessment,and market mechanism design.
电力系统调度 / 可再生能源 / 连续时间调度 / 离散时间调度
power system scheduling / renewable energy / continuous-time scheduling / discrete-time scheduling
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Objectives Under the background of the “dual carbon” strategic goal, the demand for flexible regulation resources in the power system has significantly increased after the large-scale integration of new energy generation into the grid. At present, the coal-fired power is the main flexible resource on the power side with the ability to scale up peak shaving. Since 2016, the major domestic power generation companies have implemented a certain scale of flexibility transformation of coal-fired power units. Therefore, it is necessary to summarize and analyze the problems existing in the actual operation and maintenance of the unit after flexibility transformation. Methods The technical route, investment cost and actual operation of several coal-fired power units with flexible transformation in a company were statistically analyzed. Results After the flexibility improvement and transformation of the active coal-fired power generation unit, the minimum power generation output of the advanced unit can be reduced to 18% Pe (Pe is rated load) level, the load change rate with 20% Pe~30% Pe can reach 1.8% Pe/min, and an average unit capacity investment is 101 yuan/kW. In addition, under flexible operating conditions, the coal consumption of coal-fired power units after the transformation has significantly increased. Conclusions Suggestions are put forward for the operation, maintenance and further work of coal-fired power units under flexible operating conditions. The research results provide reference and inspiration for the flexibility improvement and transformation of existing coal-fired power units. |
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With high penetration renewable energy and a new type of accessed load, traditional distribution networks have been gradually transformed into multiconnected networks. AC/DC hybrid distribution networks with multi-voltage level interaction have become the development trend of distribution networks. Based on this trend, a two-layer optimization method for an AC/DC distribution network is proposed, considering multi-connected and different voltage level interactions. The objective function of the low-voltage network problem is to minimize the schedule cost and achieve dispatching of energy storage and EV. The objective function of the mid-voltage problem is to minimize the schedule cost and voltage deviation. Next, the exchange power of the voltage-source converter is obtained. Two issues are iterated and optimized until they reach convergence. Finally, a case study was conducted based on the IEEE33 system. The results show that the proposed method can minimize power loss and voltage fluctuation. |
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随着可再生能源渗透率的提高,分布式可再生能源带来的波动性、间歇性会传递至主网中,对系统安全运行造成影响,研究不确定性优化方法对系统实际运行具有一定的指导作用。传统的随机优化以及鲁棒优化方法不满足系统实际运行的非预期性要求。文章以日运行期望成本最小为目标,考虑分布式可再生能源发电不确定性,建立多阶段随机规划模型,可以根据之前不确定信息的实现在每个阶段确定预调度决策,不会受到未来不确定信息的影响,符合系统实际运行规律,满足非预期性。为了避免多阶段随机规划问题求解的维数灾难,采用随机对偶动态规划(stochastic dual dynamic programming, SDDP)算法进行求解。仿真结果表明,相比于传统的确定性模型,多阶段随机优化得到的最优调度决策树较之确定性优化得到的单一决策方案具有更广泛的决策空间,可以基于上一阶段不确定信息的实现和决策来更新调度决策,降低系统的运行成本。
With the increase of renewable energy penetration, the volatility and intermittence brought by distributed renewable energy will be transferred to the main network, which will affect the safe operation of the system. The study of uncertainty optimization method plays a certain guiding role in the actual operation of the system. However, the traditional stochastic optimization and robust optimization methods do not meet the unpredictable requirements of the actual operation of the system. In this paper, a multi-stage stochastic programming model considering the uncertainty of distributed renewable power generation is established with the goal of minimizing the expected cost of daily operation. The pre-scheduling decision can be made at each stage according to the realization of the previous uncertain information, which will not be affected by the future uncertain information, and is in line with the actual operation law of the system, and meets the unexpected requirements. In order to avoid the disaster of dimensionality in solving multi-stage stochastic programming problems, the stochastic dual dynamic programming algorithm is used to solve the problem. The simulation results show that, compared with the traditional deterministic model, the optimal scheduling decision tree obtained by multi-stage stochastic optimization has wider decision space than the single decision scheme obtained by deterministic optimization. The scheduling decision can be updated according to the implementation and decision of the uncertain information in the previous stage, and the operating cost of the system can be reduced. |
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Modern electricity markets with large penetration of renewable energy resources require fair and accurate pricing methods to elicit generation flexibility and foster competition in electricity markets. This paper proposes the fundamental theory and closed-form formulas for continuous-time locational marginal price (LMP) of electricity, which more accurately integrates the spatio-temporal variations of load and operational constraints of power systems in the electricity price calculation. This paper first formulates the network-constrained generation scheduling and pricing problems as continuous-time optimal control problems using two methods for modeling transmission network, i.e., Theta and generation shift factor (GSF) methods. The continuous-time network-constrained scheduling and pricing problems minimize in their objective functional the total operation cost of power systems over the scheduling horizon subject to generation and transmission constraints. The closed-form continuous-time LMP formulas are derived for each transmission network model, which explicitly include terms that reflect the simultaneous spatio-temporal impacts of transmission flow limits and intertemporal generation ramping constraints in LMP formation. A scalable and computationally efficient function space solution method is proposed that converts the continuous-time problems into mixed integer linear programming problems with finite-dimensional decision space. The proposed solution method enables high-fidelity solution of transmission-constrained scheduling and pricing problems in higher dimensional spaces, while including as a special case the current discrete-time solutions. The proposed models are implemented on a three-bus system and the IEEE reliability test system, where the proposed models showcase more accuracy in reflecting the impacts of fast net-load variations over discrete-time counterparts.
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