Non-Convex Economic Dispatch of a Virtual Power Plant via a Distributed Randomized Gradient-Free Algorithm

Xie, Jun; Cao, Chi

doi:10.3390/en10071051

Cited by 14 publications

(22 citation statements)

References 27 publications

(41 reference statements)

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“…When s = t, e st is called self-elasticity, and when s = t, e st is called cross-elasticity. The detailed mathematical description is provided in literature [6].…”

Section: Constraint Conditionsmentioning

confidence: 99%

“…The slope coefficients of the two parts were 105 ¥/MW and 355 ¥/MW, respectively, and the power generation loss of the unit was about 2.5%. The charging power of ESS did not exceed 0.04 MW, the discharge power did not exceed 0.05 MW [6], and the initial storage capacity of the ESS was 0. In addition, in order to ensure the safe and reliable operation of the energy storage, the ESS could not charge and discharge at the same time.…”

Section: Basic Datamentioning

confidence: 99%

“…From 2005 to 2009, the United Kingdom, Spain, and France established a flexible electricity network in order to integrate the expected energy solution (FENIX) project [5] for the sustainable development of the EU power supply. The Netherlands established a power matching device VPP project consisting of 10 CHP units [6]. Cassell University integrated wind turbine, solar photovoltaic system, biogas power station and hydro power plant into VPP [7].…”

Section: Introductionmentioning

confidence: 99%

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A CVaR-Robust Risk Aversion Scheduling Model for Virtual Power Plants Connected with Wind-Photovoltaic-Hydropower-Energy Storage Systems, Conventional Gas Turbines and Incentive-Based Demand Responses

Tan

et al. 2018

Energies

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To make full use of distributed energy resources to meet load demand, this study aggregated wind power plants (WPPs), photovoltaic power generation (PV), small hydropower stations (SHSs), energy storage systems (ESSs), conventional gas turbines (CGTs) and incentive-based demand responses (IBDRs) into a virtual power plant (VPP) with price-based demand response (PBDR). Firstly, a basic scheduling model for the VPP was proposed in this study with the objective of the maximum operation revenue. Secondly, a risk aversion model for the VPP was constructed based on the conditional value at risk (CVaR) method and robust optimization theory considering the operating risk from WPP and PV. Thirdly, a solution methodology was constructed and three cases were considered for comparative analyses. Finally, an independent micro-grid on an industrial park in East China was utilized for an example analysis. The results show the following: (1) the proposed risk aversion scheduling model could cope with the uncertainty risk via a reasonable confidence degree β and robust coefficient Γ. When Γ ≤ 0.85 or Γ ≥ 0.95, a small uncertainty brought great risk, indicating that the risk attitude of the decision maker will affect the scheduling scheme of the VPP, and the decision maker belongs to the risk extreme aversion type. When Γ ∈ (0.85, 0.95), the decision-making scheme was in a stable state, the growth of β lead to the increase of CVaR, but the magnitude was not large. When the prediction error e was higher, the value of CVaR increased more when Γ increased by the same magnitude, which indicates that a lower prediction accuracy will amplify the uncertainty risk. (2) when the capacity ratio of (WPP, PV): ESS was higher than 1.5:1 and the peak-to-valley price gap was higher than 3:1, the values of revenue, VaR, and CVaR changed slower, indicating that both ESS and PBDR can improve the operating revenue, but the capacity scale of ESS and the peak-valley price gap need to be set properly, considering both economic benefits and operating risks. Therefore, the proposed risk aversion model could maximize the utilization of clean energy to obtain higher economic benefits while rationally controlling risks and provide reliable decision support for developing optimal operation plans for the VPP.

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“…When s = t, e st is called self-elasticity, and when s = t, e st is called cross-elasticity. The detailed mathematical description is provided in literature [6].…”

Section: Constraint Conditionsmentioning

confidence: 99%

Section: Basic Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A CVaR-Robust Risk Aversion Scheduling Model for Virtual Power Plants Connected with Wind-Photovoltaic-Hydropower-Energy Storage Systems, Conventional Gas Turbines and Incentive-Based Demand Responses

Tan

et al. 2018

Energies

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“…Besides, a hybrid evolutionary algorithm, the hybrid grey wolf optimizer-particle swarm optimization algorithm, has been proposed to solve the problem. Xie et al have made a great contribution for the case when a large number of DG resources are integrated into a VPP, and to the study of optimal VPP dispatching, however, the benefits of the VPP participating in the power grid dispatching and auxiliary services are not taken into account [11][12][13][14]. The economic dispatch model of VPP is established, and a distributed randomized gradient-free algorithm is used to solve the economic dispatch problem of a VPP, which was becoming non-convex for distributed generators' characteristics of valve-point loading effects, prohibited operating zones, and multiple fuel options [11].…”

Section: Introductionmentioning

confidence: 99%

Optimal Operation Modes of Virtual Power Plants Based on Typical Scenarios Considering Output Evaluation Criteria

Luo

Gao

Yang³

et al. 2018

Energies

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Stimulated by the severe energy crisis and the increasing awareness about the need for environmental protection, the efficient use of renewable energy has become a hot topic. The virtual power plant (VPP) is an effective way of integrating distributed energy systems (DES) by effectively deploying them in power grid dispatching or electricity trading. In this paper, the operating mode of the VPP with penetration of wind power, solar power and energy storage is investigated. Firstly, the grid-connection requirements of VPP according to the current wind and solar photovoltaic (PV) grid-connection requirements, and analyzed its profitability are examined. Secondly, under several typical scenarios grouped by a self-organization map (SOM) clustering algorithm using the VPP's output data, a profit optimization model is established as a guideline for the VPP's optimal operation. Based on this model, case studies are performed and the results indicate that this model is both feasible and effective.

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“…The economic dispatch (ED) problem [1][2][3][4][5] in a modern power system involves allocating the output power of each generator to minimize the total cost of the power generation satisfying load demand and transmission loss (TL) under the constraints of the generators' limits, line congestion, emission, renewable energy resources, and demand response. In a large interconnected power system, power is transmitted over long distances to distribution systems; consequently, TL is the dominating factor in power system ED.…”

Section: Introductionmentioning

confidence: 99%

Derivation and Application of a New Transmission Loss Formula for Power System Economic Dispatch

et al. 2018

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Abstract:The expression and calculation of transmission loss (TL) play key roles for solving the power system economic dispatch (ED) problem. ED including TL must compute the total TL and incremental transmission loss (ITL) by executing power flow equations. However, solving the power flow equations is time-consuming and may result in divergence by the iteration procedure. This approach is unsuitable for real-time ED in practical power systems. To avoid solving nonlinear power flow equations, most power companies continue to adopt the TL formula in ED. Traditional loss formulas are composed of network parameters and in terms of the generator's real power outputs. These formulas are derived by several assumptions, but these basic assumptions sacrifice accuracy. In this study, a new expression for the loss formula is proposed to improve the shortcomings of traditional loss formulas. The coefficients in the new loss formula can be obtained by recording the power losses according to varying real and reactive power outputs without any assumptions. The simultaneous equations of the second-order expansion of the Taylor series are then established. Finally, the corresponding coefficients can be calculated by solving the simultaneous equations. These new coefficients can be used in optimal real and reactive power dispatch problems. The proposed approach is tested by IEEE 14-bus and 30-bus systems, and the results are compared with those obtained from the traditional B coefficient method and the load flow method. The numerical results show that the proposed new loss formula for ED can hold high accuracy for different loading conditions and is very suitable for real-time applications.

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Non-Convex Economic Dispatch of a Virtual Power Plant via a Distributed Randomized Gradient-Free Algorithm

Cited by 14 publications

References 27 publications

A CVaR-Robust Risk Aversion Scheduling Model for Virtual Power Plants Connected with Wind-Photovoltaic-Hydropower-Energy Storage Systems, Conventional Gas Turbines and Incentive-Based Demand Responses

A CVaR-Robust Risk Aversion Scheduling Model for Virtual Power Plants Connected with Wind-Photovoltaic-Hydropower-Energy Storage Systems, Conventional Gas Turbines and Incentive-Based Demand Responses

Optimal Operation Modes of Virtual Power Plants Based on Typical Scenarios Considering Output Evaluation Criteria

Derivation and Application of a New Transmission Loss Formula for Power System Economic Dispatch

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