Analytical Target Cascading Algorithm Research Articles

Coordinated restoration method of transmission and distribution network considering distribution network fault repair scenario

With the development of active distribution network (ADN) technology, coordinated restoration of transmission network (TN) and ADNs has received widespread attention. As an important part of power system resilience, power system restoration should consider the influence of low-probability high-risk events. Such extreme events are often accompanied by component damage, so the coordination of restoration process and repair scheduling needs to be considered. First, the handling of fault repair scenario on TN and ADNs side during black-start restoration (BSR) is discussed. The interaction between the coordinated restoration of TN/ADNs and the fault repair schemes of ADNs is analyzed. Next, the coordinated restoration of TN/ADNs considering the ADN fault repair scenario is modelled in this paper. For the restoration model of TN, the restoration logic relationship of plants/lines, the subsystem division, frequency constraints of the restored system and the power scheduling constraints of source/load are considered. For the restoration model of ADNs, the restoration logic relationship of DGs/lines/buses, the scheduling logic of repair crews and emergency power sources, frequency constraints and the power scheduling constraints of source/load are considered. Then, an analytical target cascading algorithm is used to solve the optimization model. Finally, a TN/ADNs system is constructed by an IEEE_30 bus transmission system and two IEEE_33 bus distribution system, the numerical case study on the TN/ADNs system verifies that the distributed collaborative optimization of the TN/ADNs restoration plan and the fault repair plan of ADNs can improve the overall restoration efficiency during BSR.

A tri-level framework for distribution-level market clearing considering strategic participation of electrical vehicles and interactions with wholesale market

With the increasing penetration of distributed renewable energy sources in distribution networks, a large number of independent market entities such as load serving entities will participate in the distribution-level market, which provides a platform for transparent energy transactions among them. This paper proposes a novel tri-level optimization model for distribution system operator market clearing, fully considering the strategic participation of electrical vehicles and the interactions with the transmission system operator in the market environment. The upper-level model addresses the bidding strategy problem of charging stations and the randomness of renewable energy sources, the middle-level model performs the distribution-level market clearing, and the lower-level model focuses on the joint optimization of power and reserve for transmission network. Furthermore, the Stackelberg game model between distribution system operator and each charging station is converted into a mathematical program with equilibrium constraints formulation, and a decentralized approach based on analytical target cascading algorithm is developed to realize the decoupling of distribution and transmission network. The simulation results show that the proposed distribution-level market clearing method can alleviate the congestion in transmission network and enhance the economic benefits of load serving entities in distribution network.

Low-carbon distribution system planning considering flexible support of zero-carbon energy station

Zero-carbon energy stations (ZCESs) have a promising prospect in reducing carbon emission, which also results in great impacts on the planning scheme of low-carbon distribution system (DS). In this context, this paper carries out the low-carbon DS planning considering the flexible support of ZCES. Firstly, a low-carbon DS planning model is established, where the material carbon emission and operational carbon emission are both considered. Then, for achieving the low-carbon goal of DS, the flexible support of ZCES is considered during the low-carbon DS planning process. Especially, ZCES is supplied by zero-carbon renewable energy (e.g., photovoltaics and wind power). Meanwhile, DS and ZCES are regarded as different stakeholders, which is addressed by the analytical target cascading (ATC) algorithm. In addition, a distributionally robust optimization method is proposed to cope with the probability distribution (PD) uncertainty of renewable energy and loads. Moreover, a tractable low-carbon planning model for DS considering the flexible support of ZCES is reformulated based on the duality method. Finally, the proposed planning model is tested on a modified IEEE 33-node and a practical 99-node distribution system with ZCES. Numerical results show that the proposed low-carbon planning model is effective in managing PD uncertainties, and improving the low-carbon and economic performance of DS while the ATC algorithm also exhibits good convergence performance.

Decentralized strategy for real-time outages management and scheduling of networked microgrids

This paper presents a decentralized methodology in a parallel manner to provide an outage management strategy with the scheduling of networked microgrids (NMGs). Integrating MGs require a trustworthy strategy to determine the optimal amount of transaction power among them. Besides that, they are vulnerable versus unintentional tie-lines outages. The proposed approach addresses these challenges. The MGs' optimization problem is decomposed into the day-ahead normal operation scheduling as a master problem (MP) and real-time islanded examination as a sub-problem (SP) using Benders decomposition algorithm perspective. Decentralized scheduling with a parallel solution based on analytical target cascading algorithm is implemented on both MP and SP to coordinate the operation of NMGs. In the master problem, all NMGs are typically (grid-connected mode) and separately scheduled. The obtained results are also separately examined in the sub-problem to compute mismatches between generation and demand in the possible real-time islanding situations. Then the MP is revised in the next iteration according to existing mismatches in the previous iteration. This iterative procedure continues until all of the mismatches reach zero at the same iteration. The proposed methodology's performance and effectiveness are investigated and validated by four different case studies.

Multi-level interactive unit commitment of regional power system

Distributed energy resource (DER) including wind power, solar energy and energy storage system (ESS) are connected to the active distribution network (ADN) in various combination ways, which makes the distribution network have interaction. As a bridge connecting the transmission grid (TG) and micro grid (MG), ADN breaks the traditional operation pattern of TG + ADN + MG. Considering the physical connections and shared information among TG, ADN and MG, this paper proposes a decentralized and parallel analytical target cascading (ATC) algorithm for interactive unit commitment (UC) implementation in regional power systems. To explore the synergistic ability of the TG + ADN + MG coping with uncertainties of DER, i.e., wind power, the primary and secondary frequency regulation of TG are implemented to cope with uncertainties. Furthermore, the distributional uncertainty of wind power is well modeled by data driven, which is proposed in our previous work (Zhang et al., 2019) [1]. Both the startup/shutdown variables of the thermal units and the variables in TG + ADN + MG are integrated into the multi-level interactive UC model to optimize simultaneously, thus realizing the optimal goal of the whole network, resources complementary and optimal allocation of power system. An improved 6-bus system is used to test the proposed model, the numerical results show that the proposed decentralized algorithm is a fully parallelized procedure. And it also demonstrates the parallel implementation significantly enhances computations efficiency of the ATC algorithm.

Decentralized Coordinated Dispatch of Multi-microgrid Integrated Energy System Considering Source-Load Uncertainty

Multiple microgrids are connected to the regional electric power distribution system (EPS) and natural gas distribution system (NGS) to form a multi-microgrid integrated energy system (MMIES), where each stakeholder’s game behaviour and renewable energy uncertainty increase the complexity of dispatch decisions. In view of this, a decentralized coordinated dispatch model of MMIES considering source-load uncertainty is proposed in this paper. Firstly, based on fuzzy theory, the forecasts of wind/PV output and system load are described by fuzzy parameters, and consequently fuzzy chance constraints based on credibility theory are established. Secondly, for multi-stakeholders including EPS, NGS, and microgrid operator which consists of multiple microgrids, a decentralized dispatch model is established with the goal of maximizing each stakeholder’s interest considering network security constraints. Then, the fuzzy chance constraints are turned into their clear equivalent forms based on trapezoidal membership parameters, and the analytical target cascading algorithm is designed to decouple the coordination variables and solve the decentralized dispatch model collaboratively. Finally, an example of MMIES is carried out to verify the feasibility and effectiveness of the proposed method. Simulation results show that the method considers the source-load uncertainty and each stakeholder’s interest and realizes the reliable and economic optimal operation of MMIES.

Optimal management of multi-stakeholder distributed energy systems in low-carbon communities considering demand response resources and carbon tax

As the climate is rapidly changing, the need for carbon emissions reduction in sustainable cities and communities has increased. To facilitate the development of low-carbon communities with the growing installation of distributed energy systems, this paper explores bidirectional interactive behaviors among multi-stakeholder energy systems and seek energy management strategies in neighboring communities. The distributed energy systems can share their surplus energy or request insufficient energy in one area, considering the demand-side resources. A collaborative hierarchical framework is developed to coordinate electricity and heat interaction. Multiple independent optimization problems for decentralized stakeholders are obtained and solved based on an analytical target cascading algorithm, in which Lagrangian penalty terms are considered to ensure consistency in energy bidirectional interaction. The influence of carbon tax, and electrical and thermal demand response on the results of the multi-stakeholders interaction problem has been analyzed. The results show that a win-win situation is achieved for all participators while considering the proposed coordination scheme. The total cost and carbon dioxide emissions are reduced obviously. Moreover, implementing carbon tax leads to a decrease in electricity and heat parallel interaction. If policymakers want to keep energy sharing among communities actively, the carbon tax should be set at a reasonable range.

Robust distributed optimization for energy dispatch of multi-stakeholder multiple microgrids under uncertainty

This paper addresses the energy dispatch problem for multi-stakeholder multiple microgrids (MMGs) under uncertainty while considering independent market operators (IMOs) based energy trading forms. Firstly, a collaborative hierarchical dispatch framework is proposed to adapt to decentralized multiple stakeholders and coordinate energy trading between IMOs and microgrids (MGs). And then this framework is further decomposed into different independent optimization problems for stakeholders based on an analytical target cascading (ATC) algorithm, in which Lagrangian penalty terms are introduced to ensure consistency in energy trading. In these optimization problems, energy trading and production of an individual MG is formulated as a two-stage adaptive robust optimization model to hedge against uncertainties from random renewable energy sources and loads. Moreover, in order to realize parallel computing for all independent optimization problems, a diagonal quadratic approximation method is applied to linearize quadratic terms. We integrate the ATC algorithm with a column-and-constraint generation algorithm to derive robust energy dispatch schemes in parallel. Finally, simulations on different cases are conducted to testify the rationality and validity of the proposed robust distributed energy dispatch approach. The results show that the hierarchical energy dispatch framework with IMOs has advantages over that without IMOs. Moreover, the proposed approach can reduce the impacts of uncertainties on distributed decision making of multiple stakeholder and enhance the computational efficiency.

Modelling on service capability maturity and resource configuration for public warehouse product service systems

The concept of service was quick to arise and has taken the world by storm in the past decade. It has gradually redefined the way warehouses are operated and has nurtured the emergence of a new kind of warehouse, namely the public warehouse (PW). Against this backdrop, a warehouse product service system (wPSS) based on the PW is established in this paper. Furthermore, in order to evaluate the service capability and optimise the resource configuration of a PW, a wPSS service capability maturity model (wPSS–SCMM) based on the analytical target cascading (ATC) algorithm is put forward. Firstly, the generation of wPSS service capability is clarified and the framework of wPSS–SCMM is proposed. After disassembling the wPSS service capability into a tree structure, its four main sub-capabilities, namely storage service capability, transportation service capability, cost control capability and time control capability, are modelled and quantised, respectively. Then the results of the four sub-capabilities are adopted in the ATC algorithm to search for the maximal service capability maturity and the optimal resource configuration solution. Finally, a numerical example of a PW with eight customers in an industrial park is analysed to demonstrate the feasibility and applicability of the proposed new approach. This research is expected to provide guidance for both investors who want to build a PW and managers who want to continuously improve an existing one.

A Note on the Convergence of Analytical Target Cascading With Infinite Norms

Analytical target cascading (ATC) is a multidisciplinary design optimization method for multilevel hierarchical systems. To improve computational efficiency, especially for problems under uncertainty or with strong monotonicity, a sequential linear programming (SLP) algorithm was previously employed as an alternate coordination strategy to solve ATC and probabilistic ATC problems. The SLP implementation utilizes L∞ norms to maintain the linearity of SLP subsequences. This note offers a proof that there exists a set of weights such that the ATC algorithm converges when L∞ norms are used. Examples are also provided to illustrate the effectiveness of using L∞ norms as a penalty function to maintain the formulation linear and differentiable. The examples show that the proposed method provides more robust results for linearized ATC problems due to the robustness of the linear programming solver.