Stochastic Dynamic Economic Dispatch Research Articles

Data-driven stochastic dynamic economic dispatch for combined heat and power systems using particle swarm optimization

In modern power systems, the uncertain behavior of renewable energy sources (RESs) may result in deviations from the optimal operating dispatches for the various power sources. The electric power generation from Combined Heat and Power (CHP) units is characterized by high efficiency with less pollution. To use CHP units more efficiently, the dynamic economic dispatch problem is applied to obtain the optimal power and heat sources’ outputs to satisfy heat and power demands while meeting the different operational constraints. In this paper, data-driven stochastic optimization is used to model these uncertainties utilizing the Generative Adversarial Networks in scenario generation that are accurate and do not require fitting models or modeling probability distributions. Then, the Fast Forward Selection technique is used to decrease the number of scenarios to improve system tractability. The results obtained indicate that the variability in electrical load, photovoltaic (PV), and wind turbine (WT) output significantly impacts the overall operational costs of the power system. Therefore, it is essential to incorporate the uncertainties associated with electrical load, PV, and WT when aiming for accurate results in economic dispatch. the study found that the overall operation cost of the dynamic economic dispatch of the electrical system for 24 hours after integrating RES achieved a daily savings of 2.5 % in the first scenario. Furthermore, the findings demonstrate that RESs positively contribute to reducing the total operational costs of the power system. The economic dispatch of CHP systems is influenced by the integration of RESs and the uncertainties associated with electrical parameters.

Stochastic Economic Dispatch Incorporating Commercial Electric Vehicles and Fluctuating Energy Sources

Increase in utilization of electric vehicles and penetration of Renewable Energy Sources (RES) creates a greater impact on traditional power systems. Intermittent output from renewable energy resources and uneven usage pattern of electric vehicles creates a greater impact on the economic operation of power system. In this article, a stochastic Dynamic Economic Dispatch (DED) problem incorporating Commercial Electric Vehicles (CEVs) and intermittent renewable energy resources is addressed. The charging pattern of CEVs as well as intermittency of solar and wind resources creates a significant impact on power system peak demand. The behaviour of these CEVs and RES in various seasons is considered and the same is tested on a real time south Indian practical test system. An attempt is made to improve the swarm-based Moth Flame Optimization (MFO), named as IMFO is developed and utilized for solving the considered problem. The efficacy of the said method is tested and necessary validations are carried out in this article.

Stochastic dynamic economic dispatch of high wind-integrated electricity and natural gas systems considering security risk constraints

As the proportion of wind power generation increases in power systems, it is necessary to develop new ways for wind power accommodation and improve the existing power dispatch model. The power-to-gas technology, which offers a new approach to accommodate surplus wind power, is an excellent way to solve the former. Hence, this paper proposes to involve power-to-gas technology in the integrated electricity and natural gas systems (IEGSs). To solve the latter, on one hand, a new indicator, the scale factor of wind power integration, is introduced into the wind power stochastic model to better describe the uncertainty of grid-connected wind power; on the other hand, for quantizing and minimizing the impact of the uncertainties of wind power and system loads on system security, security risk constraints are established for the IEGS by the conditional value-at-risk method. By considering these two aspects, an MILP formulation of a security-risk based stochastic dynamic economic dispatch model for an IEGS is established, and GUROBI obtained from GAMS is used for the solution. Case studies are conducted on an IEGS consisting of a modified IEEE 39-bus system and the Belgium 20-node natural gas system to examine the effectiveness of the proposed dispatch model.

Low-carbon power dispatch with wind power based on carbon trading mechanism

Low-carbon power dispatching with wind power has been attracting increasing attention recently, whereas it also encounters some difficulties under carbon trading mechanism, such as the resistance to carbon emission reduction, the fairness of carbon trading, and the disturbance of wind power uncertainty. For harmonizing these contradictions, this paper presents a stochastic dynamic economic dispatch model focusing on wind power uncertainty and carbon emission rights simultaneously, which tries to minimize total electrical energy costs under uncertainty, and to meet the specific requirement of carbon emission reductions. Moreover, several traditional allocation methods for initial carbon emission rights emphasizing the equality are introduced, and the uncertainty characterizations of wind power are discussed through the scenario-generation technique. The simulation results eventually demonstrate that the operating cost for non-cooperative mode cannot be optimized as the ratio of carbon emission reductions rises; carbon trading mechanism is beneficial for lower cost under the pressure of carbon emission reduction; carbon price ranges that suit both carbon trading parties could be deduced. Synthesizing wind power uncertainty and carbon emission rights, this study is helpful for allocating the load demand of wind power integrated system to each generating unit more scientifically and reasonably based on carbon trading mechanism.

Model predictive control to two-stage stochastic dynamic economic dispatch problem

A multi-stage model predictive control approach is proposed to compensate the forecast error in a scenario-based two-stage stochastic dynamic economic dispatch problem through a feedback mechanism. Reformulating the problem as a finite moving-horizon optimal control problem, the proposed approach decelerates the growth of the number of scenarios by updating the system as uncertainties are gradually realized. Consequently, the computation time is reduced, and the problem is solved without the need for using scenario reduction techniques that compromise the accuracy of the solution. To exhibit the computational efficiency of the proposed approach, numerical experiments are conducted on the IEEE 118-bus system.

Decentralised method for solving multi‐area stochastic dynamic economic dispatch problem

This study discusses the implementation of a decentralised optimisation method for the multi-area stochastic dynamic economic dispatch (MASDED) of power systems with wind power integrated. Firstly, the volatility of wind power is represented by sampling wind scenarios, and the consensus constraints of tie-line power flows among the forecast scenario and sampling scenarios are built. Secondly, the multi-area power system is decomposed into different areas by creating a coordination centre and duplicating boarder variables. Finally, analytical target cascading method is applied to solve the MASDED in a decentralised way. The master problem of the coordination centre, the forecast scenario subproblems, and the sampling scenario subproblems of each area are solved iteratively. In order to increase computation speed, the decentralised deterministic optimisation is implemented before the decentralised stochastic optimisation. The three-area IEEE reliability test system is tested to demonstrate the effectiveness of the proposed method.

A Two-Stage Stochastic Dynamic Economic Dispatch Model Considering Wind Uncertainty

This paper proposes a two-stage stochastic dynamic economic dispatch model aiming at better managing system variability and uncertainty influenced by wind generation. Stochastic decomposition algorithm is proposed to solve the model in order to facilitate real-time application. The proposed method is tested on PJM-5 and RTS-24 systems and the results verify that the model inherits advantages from conventional dynamic economic dispatch, which is able to make out of merit order dispatch instructions for future benefits. Furthermore, the proposed model can correct false generator pre-ramp instructions due to forecast error and evaluate potential nodal wise reserve requirement therefore improving reserve deliverability. For computational efficiency assessment, stochastic decomposition is compared with sample average approximation. A modified IEEE-118 bus case study is shown.

Stochastic Dynamic Economic Dispatch for Grids with Significant Wind Using Mixed Gaussian Distribution

Generation scheduling is becoming a challenge in power grids with high penetration of renewable energy sources due to their stochastic nature. In this paper, an efficient stochastic multi-period dynamic economic dispatch (DED) model is presented. It allocates optimally generation levels among the online thermal generators in a way that maximizes the utilization of wind resources. In order to accommodate wind uncertainty, the conditional probability distribution function of the wind power output given the forecast level is used. Mixed Gaussian (MG) distribution is utilized for wind uncertainty characterization as it greatly enhances computational speed and accuracy. The statistical analysis shows the advantages of MG function over other distributions presented in the literature. Simulation results of a system with thermal and wind power plants show the merits of the proposed MG-based stochastic DED methodology.