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In this paper, we propose a parallel dual dynamic programming (PDDP)-based decentralized algorithm for the multi-area optimal power flow (MAOPF), which can preserve the information privacy and operational independence of each area. The MAOPF problem is decomposed into a series of subproblems for individual areas by the dual dynamic programming (DDP) algorithm, and the Benders cut-based value functions are used to reflect the impacts of one area’s decisions to the subsequent areas. The optimal solution of MAOPF can be obtained in a decentralized fashion, requiring only a limited amount of information exchange among neighbor areas. Moreover, a parallel processing technique is designed to avoid the waiting process of the basic DDP algorithm, thus accelerating the computing speed of the proposed decentralized algorithm. Compared with the existing decentralized algorithms, the proposed algorithm has better performance in terms of convergence and computational efficiency. In addition, there is no need for parameter tuning. Case studies on several IEEE test systems and a real 2298-bus system demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The energy management (EM) of active distribution network (ADN) under uncertainties is a stochastic, nonconvex and nonlinear problem, which cannot be solved by traditional algorithms in acceptable time. In this paper, we decouple this computationally intractable problem into a series of subproblems which are easier to handle, and then solve them successively according to an improved approximate dynamic programming (IADP) algorithm. Different from the existing approximate dynamic programming (ADP) algorithms, which need to update value functions iteratively, IADP obtains approximate value functions directly using Galerkin method. Such that the time of updating approximate value functions can be omitted. Furthermore, the influence of each basis function on the approximate value function is evaluated according to the absolute value inequality principle. Then the unimportant basis functions are removed from the basis function set to speed up the algorithm. The historical data can also be embedded into IADP to facilitate the online decision-making and reduce the dependency of real-time forecast information. Numerical simulations on two modified IEEE test systems and a real 682-bus ADN are given to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The stochastic economic dispatch problem of power system with multiple wind farms and pumped‐storage hydro stations is formulated as a specific stochastic dynamic programming (DP) model, i.e. stochastic storage model, it is impossible to obtain an accurate solution due to the curse of dimensionality. Based on the approximate DP (ADP) method, the stochastic storage model can be transformed into a series of mixed‐integer linear programming (MILP) models by describing the approximate value functions (AVFs) as convex piecewise linear functions in post‐decision states. The AVFs are first initialised using the results of the deterministic model under a forecast scenario of wind farm output and then trained by scanning stochastic sampling scenarios consecutively with the successive projective approximation routine algorithm. To obtain a near‐optimal day‐ahead dispatch scheme, the forecast scenario is substituted into the MILP models expressed by the trained AVFs and is solved forward through each time interval. The network constraints are incorporated by the while‐loop detection of critical lines. Test results on an actual provincial power system and the modified IEEE 39‐bus system, including the comparison among the ADP, DP, scenario‐based and chance‐constrained programming methods, demonstrate the feasibility and efficiency of the proposed model and algorithm. [ABSTRACT FROM AUTHOR]

This study proposes a decentralised methodology to deal with the optimal energy flow (OEF) problem of the electricity–natural gas system (EGS). The OEF problem of EGS is formulated as a multi‐stage dynamic programming (DP) process, and the approximate DP algorithm is used to decompose it into subproblems. The independent decision of each subproblem can be made by solving Bellman's equation, requiring just a moderate interchange of information among different subproblems. Such that the information privacy and dispatch independency of subsystems (including electricity and natural gas (NG) subsystems) can be ensured. Different from most existing decentralised algorithms, the impact of one subproblem's decision on other subproblems can be estimated in the proposed algorithm, and the parameters of the proposed algorithm are not required for tuning, which makes more sense in real applications. Furthermore, an improved linear cut technique is proposed to handle the non‐convexity of the NG network model, so that the tightness of all gas flow constraints can be ensured. Case studies containing small, large and complicated EGSs validate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This study focuses on the real‐time operation of a microgrid (MG). A novel approximate dynamic programming based spatiotemporal decomposition approach is developed to incorporate efficient management of distributed energy storage systems into MG real‐time operation while considering uncertainties in renewable generation. The original dynamic energy management problem is decomposed into single‐period and single‐unit sub‐problems, and the value functions are used to describe the interaction among the sub‐problems. A two‐stage procedure is further designed for the real‐time decisions of those sub‐problems. In the first stage, empirical data is utilised offline to approximate the value functions. Then in the second stage, each sub‐problem can make immediate and independent decision in both temporal and spatial dimensions to mitigate adverse effects of intermittent renewable generation in a MG. No central operator intervention is required, and the near optimal decisions can be obtained at a very fast speed. Case studies based on a six‐bus MG and an actual island MG are conducted to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

For large power systems with huge proportions of industrial loads, dynamic var sources (DVSs) such as STATCOMs and generators provide significant protection against short-term voltage instability. Simultaneously optimizing the locations and capacities of STATCOMs and the settings for adjustment coefficients of generator excitation systems is a goal of this paper; thus, we formulate a multi-objective, mixed-integer dynamic optimization (MOMIDO) model subject to short-term voltage security and rotor-angle stability under multiple contingencies. We also present a reduced convex relaxation (RCR) method to handle STATCOM locations (which are integer variables) and to avoid their combinatorial explosion, and convert the MOMIDO model into a multi-objective nonlinear programming problem via Radau collocation. To obtain complete Pareto optimal solutions for the MOMIDO model, we propose a reduced wide normalized normal constraint (RWNNC) method by enlarging the Utopia plane so that the Pareto optimal solutions are covered completely by its vertical projection, while pruning redundant sections on the Utopia plane to reduce the amount of calculations. Moreover, the simulation results on an IEEE standard 39-bus system and a real provincial power system demonstrate that the proposed method can handle integer variables effectively and obtain complete Pareto optimal solutions. [ABSTRACT FROM PUBLISHER]

• A mixed-integer linear model for coordinated scheduling of integrated T&D systems is proposed. • An improved Lipschitz dynamic programming-based decentralized algorithm is proposed for the decentralized model. • Two strategies for introducing reverse norm cuts are proposed to improve convergence. • A curve-fitting approach is proposed to obtain pre-defined lower bounds of the value functions for acceleration. • Performance of the proposed algorithms are verified using a constructed and a practical T&D system. In this study, we propose an improved Lipschitz dynamic programming-based decentralized algorithm for the coordinated scheduling of integrated transmission and distribution (T&D) systems, considering unit commitments in a transmission system and the AC power flow and discrete control devices in distribution systems. In this algorithm, reverse norm cuts are introduced iteratively to approximate the value functions of subproblems of distribution systems, which are formulated as mixed-integer linear programming models. Based on the characteristics of subproblems of distribution systems, two strategies for introducing the reverse norm cuts in the subproblem of the transmission system are developed to improve the convergence. Furthermore, to further accelerate the proposed decentralized algorithm, a curve-fitting approach is designed to obtain the pre-defined approximate lower bounds of the value functions of distribution systems at each scheduling time period, which are formulated as a linear constraint set with integer variables. Finally, case studies are conducted on a constructed integrated T&D system and a practical integrated T&D system to verify the accuracy and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• A SMES model of RIES considering the pipeline dynamics is proposed. • The method of characteristics and data-driven parameter correction method are proposed to solve the PDEs. • An improved ADP method is proposed to recursively solve the SMES model. • Test results show the accuracy and efficiency of the proposed method. In the regional integrated energy system (RIES), the pipeline dynamics in cooling, heating, and gas networks make their source outputs and load demands difficult to balance in real-time. Hence the economic dispatch problem of RIES requires considering the pipeline dynamics to make the results in line with the actual situation. In this paper, the method of characteristics is proposed to solve the approximate analytical solution (AAS) of partial differential equations describing the gas pipeline dynamics, and the corrected parameters in the AAS are identified by the data-driven method. The high computational accuracy of the obtained AAS is verified by an example. Considering the stochastic fluctuation of renewable energy output and the energy storage ability of cooling, heating, and gas pipelines in a RIES, a stochastic multiple energy storage model for the stochastic economic dispatch problem of RIES considering the pipeline dynamics is established. An improved approximate dynamic programming algorithm considering the coupling of power balance among several adjacent time intervals due to the pipeline dynamics is proposed to efficiently solve the stochastic multiple energy storage model. Test results on an actual RIES, including comparison with the scenario-based method, demonstrate the correctness and efficiency of the proposed model and algorithm. [ABSTRACT FROM AUTHOR]

• A stochastic optimal dispatch model of offshore-onshore regional integrated energy system is proposed. • An improved state-space approximate dynamic programming algorithm is proposed and expression of approximate value function can be obtained. • The near optimal dispatch scheme under the stochastic fluctuations can be obtained. • Results show the high efficiency, accuracy and robustness of the proposed method. The offshore-onshore regional integrated energy system (OORIES), which includes offshore gas production platforms and wind farms, along with the onshore gas-fired combined cooling, heating, and power supply campus, can effectively improve economic and environmental benefits by the complementary and coupling operation of multiple energies. In this paper, multi-energy coupling elements and multiple energy networks in the OORIES are modeled in detail. Considering the stochastic fluctuation of the offshore gas source and wind power output, a stochastic optimal dispatch (SOD) model of OORIES with multiple energy storages, including associated gas storage, hydrogen and heat storage tanks is proposed. Furthermore, a carbon trading mechanism is introduced to ensure the environmental benefits. An improved state-space approximate dynamic programming (SSADP) algorithm is proposed to solve the SOD model. By using the approximate value functions, the multi-period SOD model is decoupled into a series of single-period optimization models which are recursively solved period by period. The approximate analytical expression of the value function concerning states of each period is obtained based on the polynomial approximation, and combined with the transition probability matrices of stochastic quantities, an accurate and efficient solution for each single-period optimization model is obtained. A case study on an OORIES, and compared with the scenario-based algorithm, chance-constrained programming algorithm and traditional SSADP algorithm, demonstrates the effectiveness and high efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

• A dynamic energy management model for maximizing the expected-cost realization-probability. • A novel approximate dynamic programming algorithm designed to solve the proposed model. • Transformation of the DEM model into the Markov decision process. • Decomposition of the mixed-integer nonlinear programming problem into small nonlinear programming problems. Dynamic energy management (DEM) is being recognized as an important tool for the economical and efficient operation of microgrid. This paper proposes an expected-cost realization-probability (ECRP) optimization approach for the DEM of microgrid. In the model, the expected cost is taken as an economic goal to find the schedule with the maximum ECRP (i.e., the maximum probability of obtaining an actual operation cost which is lower than this economic goal). It is a stochastic mixed-integer nonlinear programming (MINLP) problem composed of the AC power flow, battery operation characters and logical variables. To solve this NP-hard problem, an ECRP-based approximate dynamic programming is proposed. The original MINLP problem is decomposed into small nonlinear programming subproblems to facilitate the solution. And the ECRP-based value function is formed to describe the relationship among the decisions of subproblems, which helps to obtain the near-optimal decision in a decomposed manner. Simulation examples presented on a real microgrid indicate that the ECRP of the proposed method is higher than those of the other two comparison algorithms. [ABSTRACT FROM AUTHOR]