Economic Scheduling Research Articles

Optimal Power Flow of Hybrid Wind/Solar/Thermal Energy Integrated Power Systems Considering Costs and Emissions via a Novel and Efficient Search Optimization Algorithm

The OPF problem has significant importance in a power system’s operation, planning, economic scheduling, and security. Today’s electricity grid is rapidly evolving, with increased penetration of renewable power sources (RPSs). Conventional optimal power flow (OPF) has non-linear constraints that make it a highly non-linear, non-convex optimization problem. This complex problem escalates further with the integration of renewable energy resource (RES), which are generally intermittent in nature. This study suggests a new and effective improved optimizer via a TFWO algorithm (turbulent flow of water-based optimization), namely the ITFWO algorithm, to solve non-linear and non-convex OPF problems in energy networks with integrated solar photovoltaic (PV) and wind turbine (WT) units (being environmentally friendly and clean in nature). OPF in the energy networks is an optimization problem proposed to discover the optimal settings of an energy network. The OPF modeling contains the forecasted electric energy of WT and PV by considering the voltage value at PV and WT buses as decision parameters. Forecasting the active energy of PV and WT units has been founded on the real-time measurements of solar irradiance and wind speed. Eight scenarios are analyzed on the IEEE 30-bus test system in order to determine a cost-effective schedule for thermal power plants with different objectives that reflect fuel cost minimization, voltage profile improvement, emission gases, power loss reduction, and fuel cost minimization with consideration of the valve point effect of generation units. In addition, a carbon tax is considered in the goal function in the examined cases in order to investigate its effect on generator scheduling. A comparison of the simulation results with other recently published algorithms for solving OPF problems is made to illustrate the effectiveness and validity of the proposed ITFWO algorithm. Simulation results show that the improved turbulent flow of water-based optimization algorithm provides an effective and robust high-quality solution of the various optimal power-flow problems. Moreover, results obtained using the proposed ITFWO algorithm are either better than, or comparable to, those obtained using other techniques reported in the literature. The utility of solar and wind energy in scheduling problems has been proposed in this work.

An operationally induced approach to reliability-oriented ACOPF-constrained planning of interconnected multicarrier energy hubs: An MILP formulation

Energy hubs (EHs) are considered as prospective frameworks for future high-reliability energy systems, as interfaces for generation, conversion, storage, and consumption of different energy carriers. Interoperability and interconnection of the EHs may improve the reliability of the system, therefore, the system planning and operation should be constrained by AC optimal power flow (ACOPF), to ensure connectivity of the EHs and optimality of the operation. The main contribution of this paper lies in introducing an innovative operationally induced approach to reliability-oriented ACOPF-constrained planning of interconnected EHs. This manuscript presents an efficient mixed integer linear programming (MILP) formulation, aiming to result in optimal reliable and economic planning and scheduling of the microgrids including interconnected EHs, while reducing the computational effort. Further, this research investigates the effect of EHs interconnection and demand response (DR) on optimal planning and scheduling of microgrids. This is implemented on the IEEE 33-bus distribution test system by operating EHs in interconnected mode, revealing a significant improvement in reliability (CIC: customerinterruption cost, ENS: energy not supplied, and EIR: energy index of reliability), economic (DSOBenefit, EnergyRevenue, INVC &OPC: investment and operation costs), renewable energy share (REC: renewable energy curtailment, REUF: renewable energy utilization factor, and WPPCC: Wind-photovoltaic generation Pearson correlation coefficient), and microgrid-maingrid energy exchange.

Optimal Scheduling of Multi-energy System Considering Economy and Energy Conservation

In recent years, the optimal scheduling of multienergy has become the focus of the research. Against this background, this paper builds a model of a multienergy flow system of cooling, heating, and power, and advanced adiabatic compressed air energy storage (AA-CAES) is introduced to smooth wind power generation (WPG) and supply heating/cooling energy. Simulated annealing algorithm (SAA) is employed to energy-saving scheduling of the system with “exergy assessment” method. The energy-saving index and the exergy efficiency are compared in different cases. SAA is compared with the particle swarm optimization (PSO) algorithm in solving the optimal scheduling strategy. The cooling, heating, and power demands of an industrial park and WPG in typical days are employed to the simulation. The scheduling results of exergy input of SAA are far less than those of PSO in typical days of different seasons. The multienergy system without AA-CAES is also modeled, and energy-saving economic scheduling is carried out. The exergy efficiency of the system with AA-CAES is between 38% and 58% while the exergy efficiency of the system without AA-CAES is merely between 27% and 48%.

A new version of membrane search algorithm for hybrid renewable energy systems dynamic scheduling

It is a consensus that hydropower should be clean and renewable. The economic emission dynamic scheduling of hydro hybrid combined heat and power (Hydro-CHP) systems allows for further reduction of greenhouse gas emissions from the power sector. A new version of our Membrane Search Algorithm, denoted as IMSA, is proposed to solve the complex dynamic scheduling problems of CHP and hydro-thermal systems with spatio-temporal coupling, which can obtain competitive solutions. Furthermore, based on IMSA, we construct a multi-objective algorithm, called the Multi-objective Improved Membrane Search Algorithm (MOIMSA), which can solve the complex economic emission dynamic scheduling problem of CHP systems with ramp limits, and provide a solution set with relatively less emissions. Finally, a solution to the dynamic scheduling problem of the Hydro-CHP system is proposed. IMSA obtains the maximum power output of the hydro unit, and MOIMSA is used to search for the Pareto front of the economic emission of CHP. Compared with the unimproved MOMSA, the compromise solution provided by MOIMSA is better. Experiments show that this study contributes to the efficient use of renewable energy and the reduction of emissions.

A MILP-Based Battery Degradation Model for Economic Scheduling of Power System

Battery energy storage (BES) systems play an increasingly important part in power system operation because of their high efficiency and decreasing cost. This article proposes a mixed integer linear programming (MILP) model of battery degradation considering both depth of discharge (DoD) and state of charge (SoC), which can reflect the battery degradation mechanism. To improve computational efficiency for the economic scheduling of power system, a novel one-dimensional linearization is proposed to linearize this two-variable function, which significantly reduces computation burdens without loss of accuracy. Considering the battery degradation cost, a day-ahead economic scheduling model is built and a MILP algorithm is applied to solve it. The effectiveness of the MILP-based battery degradation model for economic scheduling is validated using the modified IEEE 30-bus system. For comparison, other existing battery degradation models are also implemented in the same system.

Development of a day-ahead solar power forecasting model chain for a 250 MW PV park in India

Due to the steep rise in grid-connected solar Photovoltaic (PV) capacity and the intermittent nature of solar generation, accurate forecasts are becoming ever more essential for the secure and economic day-ahead scheduling of PV systems. The inherent uncertainty in Numerical Weather Prediction (NWP) forecasts and the limited availability of measured datasets for PV system modeling impacts the achievable day-ahead solar PV power forecast accuracy in regions like India. In this study, an operational day-ahead PV power forecast model chain is developed for a 250 MWp solar PV park located in Southern India using NWP-predicted Global Horizontal Irradiance (GHI) from the European Centre of Medium Range Weather Forecasts (ECMWF) and National Centre for Medium Range Weather Forecasting (NCMRWF) models. The performance of the Lorenz polynomial and a Neural Network (NN)-based bias correction method are benchmarked on a sliding window basis against ground-measured GHI for ten months. The usefulness of GHI transposition, even with uncertain monthly tilt values, is analyzed by comparing the Global Tilted Irradiance (GTI) and GHI forecasts with measured GTI for four months. A simple technique for back-calculating the virtual DC power is developed using the available aggregated AC power measurements and the inverter efficiency curve from a nearby plant with a similar rated inverter capacity. The AC power forecasts are validated against aggregated AC power measurements for six months. The ECMWF derived forecast outperforms the reference convex combination of climatology and persistence. The linear combination of ECMWF and NCMRWF derived AC forecasts showed the best result.

A novel economic scheduling of multi-product deterministic demand for co-production air separation system with liquid air energy storage

Air separation units (ASUs) integrated with liquid air energy storage (LAES) have the potential to balance grid demand and improve production profits. This study aims to enhance the demand response of a novel co-production air separation system (NCASS) by maximizing the energy arbitrage of a LAES system. We developed a mixed-integer nonlinear programming model to minimize operating costs by using a proxy model to represent the ASU production space and a black box model to represent the material and energy flow balance of LAES. The model is based on rigorous mathematical programming and, considers material and energy flow balance, analyzes the production and delivery processes and constraints for each product, and matches equipment start-up and shutdown time constraints. The case study shows that the model achieves a high level of matter and energy matching between the distillation process and the LAES process, maximizing the LAES peak-shaving capacity and improving system economics. During the 24 h schedule period, the total electricity consumption of NCASS increases by 18.94% during the valley electricity period and decreases by 20.59% during the flat and peak electricity period. The economic benefits increase by 9.51 k$, accounting for 14.29% of the total costs. This study contributes to the wider application of NCAS with LAES technology for sustainable energy management.

Coordinated Economic Operation of Hydrothermal Units with HVDC Link Based on Lagrange Multipliers

Coordinated operation of hydrothermal scheduling with HVDC links considering network constraints becomes a vital issue due to their remote location and recent induction in the existing power system. The nonlinear and complex nature of the problem introduces many variables and constraints which results in a heavy computational burden. A widespread approach for handling these complexities is to reformulate the problem by several linearization methods. In this paper, a Lagrange multipliers-based method is proposed for the solution of hydrothermal economic scheduling including HVDC link. This method solves equality constraint optimization problems. The linear programming approach is embedded with the Lagrange method to consider both equality and inequality constraints. The proposed technique has been used on piecewise linear variables and constraints of the system considering generation, water volume, and line power flow limits. The formulated method efficiently minimizes the operational cost of thermal units and maximizes the utilization of hydro units while meeting all generation, water volume, and the HVDC link constraints. The method was successfully implemented in two scenarios of a case study. In the first scenario, hydrothermal scheduling was performed on the typical network without an HVDC line limit and equal nodal prices were found with minimal thermal generation cost of $278,822.3. In the second scenario, the proposed method optimally dispatches units to meet the HVDC line limit and minimizes thermal generation cost to $279,025.4 while satisfying hydro, thermal, and other operating constraints. Both scenarios are implemented for a 24 h period. The results have been presented to illustrate the performance of the proposed method.

Research on Data-Driven Optimal Scheduling of Power System

The uncertainty of output makes it difficult to effectively solve the economic security dispatching problem of the power grid when a high proportion of renewable energy generating units are integrated into the power grid. Based on the proximal policy optimization (PPO) algorithm, a safe and economical grid scheduling method is designed. First, constraints on the safe and economical operation of renewable energy power systems are defined. Then, the quintuple of Markov decision process is defined under the framework of deep reinforcement learning, and the dispatching optimization problem is transformed into Markov decision process. To solve the problem of low sample data utilization in online reinforcement learning strategies, a PPO optimization algorithm based on the Kullback–Leibler (KL) divergence penalty factor and importance sampling technique is proposed, which transforms on-policy into off-policy and improves sample utilization. Finally, the simulation analysis of the example shows that in a power system with a high proportion of renewable energy generating units connected to the grid, the proposed scheduling strategy can meet the load demand under different load trends. In the dispatch cycle with different renewable energy generation rates, renewable energy can be absorbed to the maximum extent to ensure the safe and economic operation of the grid.

Construction of an economic environment scheduling system based on the multi-objective fuzzy optimization model

Abstract To integrate the combination of electric vehicles and wind power of the transmission system, a wind farm environment multi-objective transmission model considering plug-in electric vehicles was established. The fuzzy optimal scheduling model for the environment and economy target of wind farm power system considering grid interconnection of electric vehicles designed by the author has the following characteristics: A fuzzy multi-objective dynamic scheduling model for the design of wind farm power system considering grid connection of plug-in electric vehicle is established, and the original 10 systems are taken as an example for power system design. The results show that the better model shows that the electric vehicle grid connection can greatly reduce the disadvantage of wind power stochastic uncertainties of system scheduling. The model can be used under different conditions further analyzing the rationality of the model determined by the author. An improved particle swarm optimization algorithm is used to solve this problem. The model takes the environmental and economic benefits into account, which improves the efficiency of the model.

Economic scheduling of virtual power plant in day-ahead and real-time markets considering uncertainties in electrical parameters

The virtual power plant (VPP) concept, which offers energy efficiency, benefits significantly from the tremendous potential of integrating distributed energy resources (DERs). This work proposes optimal economic dispatch of virtual power plant (VPP), and the problem is formulated in a novel way considering the potential of energy storage systems (ESS) of electric vehicles (EVs) and data center (DC) in a data center facility test model using optimized energy management system (EMS). The problem is evaluated for maximizing the revenue for VPP considering market prices and the uncertainties in the distributed energy resources. To this purpose, a techno-economic analysis of the proposed test system of VPP is evaluated using mixed-integer linear programming (MILP). Renewable generation, electricity price, load demand, and real-time EV behavior uncertainty analysis are forecasted using Long Short-Term Memory (LSTM) along with DC battery degradation analysis which constitutes the optimization model. The results showed that the VPP EMS can perform optimal power scheduling with the day ahead and real-time electricity price scenarios. Moreover, further analysis including battery degradation cost of DC UPS ESS proved the capability of the proposed framework by up to 2064.4 $/h revenue for day-ahead price and 562 $/h revenue for the real-time price compared to revenue without battery degradation cost. A simulation scenario is also carried out where the constant load demand and the battery storage powers are varied between 50% and 150%. It can be concluded that the 500 kW and 750 kW ESS (100% and 150%) are better choices as compared to 250 kW (50%) during increased load demand for investors due to their higher revenue. Hence it is concluded that this research highlights the importance of revenue benefits from deploying VPP with the collaborative operation of DERs.

Two-Stage Optimal Scheduling of Highway Self-Consistent Energy System in Western China

Under the background of “carbon peaking and carbon neutrality goals” in China, the Highway Self-Consistent Energy System (HSCES) with renewable energy as the main body has become a key research object. To study the operational status of the HSCES in a specific region and realize the economically optimal operation of the HSCES, an HSCES model in a low-load, abundant-renewable-energy and no-grid scenario is established, and a two-stage optimal scheduling method for the HSCES is proposed. Moreover, in the day-ahead stage, uncertainty optimization scenarios are generated by Latin hypercube sampling, and a definition of the self-consistent coefficient is proposed, which is used as one of the constraints to establish a day-ahead economic optimal scheduling model. Through the case comparison analysis, the validity of the day-ahead scheduling model is confirmed and the optimal day-ahead scheduling plan is attained. Furthermore, in the intra-day stage, an intra-day rolling optimization method is proposed, which can effectively track the day-ahead scheduling plan and reduce the impact of forecast errors and energy fluctuations by coordinating the unit output within the HSCES system. It is verified that the HSCES can operate economically and safely in Western China, and self-consistently, without grid support.

A Novel Loss Sensitivity Based Linearized OPF and LMP Calculations for Active Balanced Distribution Networks

The distribution system operator performs optimal power flow calculations for efficient and economical scheduling of the distributed energy resources (DERs) and congestion management of the active distribution network. A linearized version of the ac optimal power flow (ACOPF) model is more suitable for practical implementation due to its simplicity and fast convergence. Thus, this article proposes a linearized ACOPF framework and locational marginal price (LMP) calculations for a generalized (i.e., radial and meshed) active balanced distribution system. The proposed linearized ACOPF for the distribution level market is formulated based on novel active and reactive power loss sensitivities by considering the effects of high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{R/X}$</tex-math></inline-formula> ratio and network constraints. The distribution LMPs are mathematically derived for active and reactive power generations and loads. Different reactive power loads are represented as a function of active power loads using the concept of power-factors. Thus, the load portfolio consists of nominal active power demand and nominal power-factor. Different LMPs are calculated for loads with different power-factors. DERs submit a separate offer for active and reactive power generations. Thus, separate LMPs are derived for DERs. The efficacy and efficiency of the proposed ACOPF framework are illustrated and compared on different radial and meshed distribution systems.

A Novel Day Optimal Scheduling Strategy for Integrated Energy System including Electric Vehicle and Multisource Energy Storage

Aiming at problems such as high operating costs, the low utilization efficiency of renewable energy, and the increase in the peak-valley difference in user load caused by disordered charging of electric vehicles (EVs), the operation mode of “setting electricity by heat” or “setting heat by electricity” is adopted in the integrated energy system of intelligent residential areas on the distribution side. In this paper, a method is proposed to use multiple energy storage, demand response technology, and make EV orderly charge and discharge plan to consume renewable resources and realize optimal economic scheduling in the integrated energy system of combined heat and power (CHP). Firstly, the demand response model of electricity load adjusting according to renewable energy output and time-of-use electricity prices has been established. Secondly, considering the comfort of the space thermal load, the orderly charge and discharge plan of electric energy storage (ESS), thermal energy storage (HSS), and EV and aiming at the minimum operating cost of the integrated energy system, the optimal output operation of each equipment was scheduled. Finally, through simulation analysis and comparative experiments, it is verified that the proposed method can promote the local consumption of renewable energy, realize the decoupling of thermoelectric constraints, and reduce the operating cost of the integrated energy system.

Optimization of micro grid with distributed energy resources using physics based meta heuristic techniques

AbstractRecently, modern power systems depend heavily on MicroGrids (MGs), which can accommodate Distributed Energy Resources (DERs) economically and with high flexibility. MGs integrated with DERs can assist in enhancing energy security, significant cost savings, and reduction in emission of greenhouse gases. In this paper, the assessment of operating performance of proposed MG system with DERs is employed to investigate the multi‐objective problems of cost optimization and economic scheduling. A grid‐connected Micro‐grid (MG) combined with solar photovoltaic (PV), wind turbine (WT), fuel cell (FC), and Battery Energy Storage System (BESS) is implemented to model the problem. This proposed model is considered as a test system for cost optimization and battery charging/discharging optimization. The developed framework is presented as multi‐objective function with constraints that can be tackled using an effective optimization technique. The above stochastic multi‐objective problem is optimized using various commonly used Physics based Meta‐heuristic techniques such as Simulated Annealing (SA), Harmony Search (HS), Slime Mold Algorithm (SMA), Gravitational Search Algorithm (GSA), Black Hole Optimization (BHO), Sine Cosine Algorithm (SCA), Multiverse optimization (MVO) and Lightning Search Algorithm (LSA). The assessment of the aforementioned physics‐based optimization techniques used on the proposed MG test system is compared using the results. According to the analysis, Black Hole Optimization (BHO) and Lightning Search Algorithm (LSA) both provide greater cost savings overall and for battery charging, respectively. The suggested optimization methods will take the BESS charging/discharging pattern and total cost savings into account.

Multi-time-scale economic scheduling method for electro-hydrogen integrated energy system based on day-ahead long-time-scale and intra-day MPC hierarchical rolling optimization

To build a clean, secure, and efficient energy system, the hydrogen energy is an important developing trend for the energy revolution, and electro-hydrogen coupling system is expected to play an important role in the future. To obtain the optimal economic scheduling of the electro-hydrogen integrated energy system (E-H IES), this paper firstly establishes a refined model of the electrolyzer and hydrogen fuel cell and then proposes an optimal scheduling model based on day-ahead long-time-scale optimization and intra-day model predictive control (MPC) hierarchical rolling optimization. In the day-ahead stage, a long-time-scale optimization considering the impact of multi-day forecast information is proposed when performing the day-ahead optimization to achieve the effect of inter-day energy transfer of hydrogen energy and improve the overall economic efficiency. In addition, during the intra-day stage, the MPC is adopted to implement hierarchical rolling optimization to track and correct the day-ahead schedule and achieve coordinated operation between multi-energy systems while taking into account the different energy transfer characteristics. Finally, the simulation results demonstrate the feasibility of the proposed optimal scheduling model and the effectiveness of the proposed multi-time scale economic scheduling method.

Distribution locational pricing mechanisms for flexible interconnected distribution system with variable renewable energy generation

Nowadays, distribution locational pricing mechanism has been widely used in the radial distribution network to guide the energy consumption and promote the renewables utilization. Aiming to explore the reasonable pricing policy which is applicable to the merging flexible interconnected distribution system (FIDS), this paper develops two different distribution locational pricing mechanisms for distribution lines interconnected by soft open points (SOPs). First, based on the Wasserstein ambiguity sets for uncertainties from the main grid and distribution network, a carbon-oriented distributionally robust economic dispatch model is constructed for FIDS considering different price and carbon signals from the main grid. Then, by leveraging the optimal scheme from economic scheduling model, distribution locational marginal prices (DLMPs) and equivalent DLMPs (EDLMPs) are presented to measure the marginal cost and actual cost for energy consumption in the FIDS respectively. The calculation and decomposition methods of these price signals are also developed. In case studies, a practical 63-node FIDS is chosen to verify the effectiveness of the proposed methods. Numerical results illustrate the characteristics of DLMPs and EDLMPs in FIDS under multiple uncertainties. Comparing to DLMPs, EDLMPs are more appropriate to FIDS because this pricing mechanism can reflect the lower generation cost of renewables for each consumer.

Economic and resilient operation of hydrogen-based microgrids: An improved MPC-based optimal scheduling scheme considering security constraints of hydrogen facilities

Optimally scheduling alkaline electrolyzers (AELs) in a hydrogen-based microgrid (HBM) can greatly unleash the operational flexibility of the HBM. However, existing scheduling strategies of AELs mostly utilize a simplified AEL model, which ignores the nonlinear coupling of electric-hydrogen-thermal sectors, violating the AEL’s security constraints thereby making the scheduling scheme infeasible. This paper proposes an improved model predictive control (MPC) based optimal scheduling framework which incorporates a scheduling correction algorithm into the basic MPC structure. This framework is utilized for implementing economic and resilient scheduling of an HBM under normal and emergency conditions, respectively. With the scheduling correction algorithm, this framework can be formulated into a computationally efficient mixed-integer linear programming, meanwhile guaranteeing the solutions strictly satisfy the security constraints of hydrogen facilities (i.e. AEL and hydrogen tank). Case studies are conducted based on real operating data of a Danish energy island Bornholm. The results demonstrate that the proposed scheduling scheme under normal conditions can contribute to significant comprehensive benefits from the daily operation cost saving of 68%, computational time saving of 98%, and satisfying the security constraints of hydrogen facilities, compared to previous scheduling strategies. Besides, it sharply reduces load shedding under emergency conditions by proactively allocating distributed energy sources in the HBM.

Low-Carbon and economic flexibility scheduling of power system with multiple generation resources penetration

The operation flexibility of the power system suffers great challenges due to the vigorously developing of renewable energy resources under the promotion of the carbon neutralization goal. To this end, this paper proposes an economical and flexible energy scheduling method for power system integrated with multiple generation resources while considering the operation of low-carbon. Specifically, flexibility evaluation indexes are constructed to describe the characteristics of the flexible generation units. Then they are connected with the flexibility of the power system in an economic and low-carbon flexible energy scheduling model. To coordinate the operation economy, flexibility, and carbon emission reduction, the model incorporates demand response, operational characteristics, and flexibility requirements. Further, the model is fully validated through the simulation on the modified IEEE 30-bus system. Results demonstrate that: the proposed method can reduce the system’s carbon emission and total operating costs and promote photovoltaic consumption.

Curve and double-layer economic dispatching considering reasonable wind abandonment under different time granularities

In view of the large output of wind power during the load trough time, the peak regulation cost may increase sharply, and the traditional hourly dispatch may not be able to accurately track the load fluctuation due to the fluctuation of renewable energy. In this paper, based on different time granularities, an adaptive segmented double-layer economic scheduling model of the net load curve considering reasonable wind abandonment is constructed. The model can better cope with net load changes while reducing the load peak-to-valley difference. First, a reasonable wind abandonment model is established under different time granularities of 5 min, 15 min, 30 min, and 1 h; Then, based on the static thinking of the net load curve by time period, the load change in the hourly scale is fully considered without changing the total number of dispatching periods so that each dispatching period can adaptively select the duration according to the change of net load gradient, and a self-adaptive subsection model of the net load curve is established to minimize the total running cost. Finally, taking IEEE-30 nodes as the example system, the NSGA-II algorithm and CPLEX solver are used to solve the model. The results verify the economy and feasibility of the proposed model.