When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be op...When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming.展开更多
In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space w...In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.展开更多
Rolling dynamic compaction (RDC),which employs non-circular module towed behind a tractor,is an innovative soil compaction method that has proven to be successful in many ground improvement applications.RDC involves r...Rolling dynamic compaction (RDC),which employs non-circular module towed behind a tractor,is an innovative soil compaction method that has proven to be successful in many ground improvement applications.RDC involves repeatedly delivering high-energy impact blows onto the ground surface,which improves soil density and thus soil strength and stiffness.However,there exists a lack of methods to predict the effectiveness of RDC in different ground conditions,which has become a major obstacle to its adoption.For this,in this context,a prediction model is developed based on linear genetic programming (LGP),which is one of the common approaches in application of artificial intelligence for nonlinear forecasting.The model is based on in situ density-related data in terms of dynamic cone penetrometer (DCP) results obtained from several projects that have employed the 4-sided,8-t impact roller (BH-1300).It is shown that the model is accurate and reliable over a range of soil types.Furthermore,a series of parametric studies confirms its robustness in generalizing data.In addition,the results of the comparative study indicate that the optimal LGP model has a better predictive performance than the existing artificial neural network (ANN) model developed earlier by the authors.展开更多
In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that se...In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that separately design the proposed method takes all the desired designing modes into consideration when designing all the subfilters. First an initial solution is obtained by separately designing the subfilters and then the initial solution is updated by iteratively solving a SOCP problem. The proposed method is evaluated on a design example and simulation results demonstrate that jointly designing all the subfilters can obtain significantly lower minimax approximation errors compared to the conventional design method.展开更多
Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line （TDL） structure for nonuniform linear array （NLA） is designed according to the rule of...Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line （TDL） structure for nonuniform linear array （NLA） is designed according to the rule of minimizing the beamformer＇s output power while keeping the distortionless response （DR） in the direction of desired signal and keeping the constant beamwidth （CB） with the prescribed sidelobe level over the whole operating band. This kind of beamforming problem can be solved with the interior-point method after being converted to the form of standard second order cone programming （SOCP）. The computer simulations are presented which illustrate the effectiveness of our beamformer.展开更多
Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algor...Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton （AHO） directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O（rln（εo/ε）） is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.展开更多
By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algor...By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algorithm is globally convergent under suitable assumptions.展开更多
To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem,this paper reports a research about blind separation method against channel mismatch in multiple-input multiple...To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem,this paper reports a research about blind separation method against channel mismatch in multiple-input multiple-output(MIMO) systems.The channel mismatch problem can be described as a channel with bounded fluctuant errors due to channel distortion or channel estimation errors.The problem of blind signal separation/extraction with channel mismatch is formulated as a cost function of blind source separation(BSS) subject to the second-order cone constraint,which can be called as second-order cone programing optimization problem.Then the resulting cost function is solved by approximate negentropy maximization using quasi-Newton iterative methods for blind separation/extraction source signals.Theoretical analysis demonstrates that the proposed algorithm has low computational complexity and improved performance advantages.Simulation results verify that the capacity gain and bit error rate(BER) performance of the proposed blind separation method is superior to those of the existing methods in MIMO systems with channel mismatch problem.展开更多
We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the s...We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.展开更多
A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential correspondi...A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.展开更多
This paper investigates the optimal control problem of spacecraft reorientation subject to attitude forbidden constraints,angular velocity saturation and actuator saturation simultaneously.A second-order cone programm...This paper investigates the optimal control problem of spacecraft reorientation subject to attitude forbidden constraints,angular velocity saturation and actuator saturation simultaneously.A second-order cone programming(SOCP)technology is developed to solve the strong nonlinear and non-convex control problem in real time.Specifically,the nonlinear attitude kinematic and dynamic are transformed and relaxed to a standard affine system,and linearization and L1 penalty technique are adopted to convexify non-convex inequality constraints.With the proposed quadratic performance index of angular velocity,the optimal control solution is obtained with high accuracy using the successive SOCP algorithm.Finally,the effectiveness of the algorithm is validated by numerical simulation.展开更多
Recently we have proposed anew method combininginterior and exterior approaches to solve linear programming problems. This method uses an interior point, and from there connected to the vertex of the so called station...Recently we have proposed anew method combininginterior and exterior approaches to solve linear programming problems. This method uses an interior point, and from there connected to the vertex of the so called station cone which is also a solution of the dual problem. This allows us to determine the entering vector and the new station cone. Here in this paper, we present a new modified algorithm for the case, when at each iteration we determine a new interior point. The new building interior point moves toward the optimal vertex. Thanks to the shortened from both inside and outside, the new version allows to find quicker the optimal solution. The computational experiments show that the number of iterations of the new modified algorithm is significantly smaller than that of the second phase of the dual simplex method.展开更多
An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary target.The problem with time-varying Proportional Navigation(PN)gain is first formulated as a...An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary target.The problem with time-varying Proportional Navigation(PN)gain is first formulated as a nonlinear optimal control problem,which is difficult to solve due to the existence of nonlinear kinematics and nonconvex constraints.After convexification treatments and discretization,the solution to the original problem can be approximately obtained by solving a sequence of Second-Order Cone Programming(SOCP)problems,which can be readily solved by state-of-the-art Interior-Point Methods(IPMs).To mitigate the sensibility of the algorithm on the user-provided initial profile,a Two-Stage Sequential Convex Programming(TSSCP)method is presented in detail.Furthermore,numerical simulations under different mission scenarios are conducted to show the superiority of the proposed method in solving the cooperative guidance problem.The research indicated that the TSSCP method is more tractable and reliable than the traditional methods and has great potential for real-time processing and on-board implementation.展开更多
A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorith...A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.展开更多
In this paper we present a new method combining interior and exterior approaches to solve linear programming problems. With the assumption that a feasible interior solution to the input system is known, this algorithm...In this paper we present a new method combining interior and exterior approaches to solve linear programming problems. With the assumption that a feasible interior solution to the input system is known, this algorithm uses it and appropriate constraints of the system to construct a sequence of the so called station cones whose vertices tend very fast to the solution to be found. The computational experiments show that the number of iterations of the new algorithm is significantly smaller than that of the second phase of the simplex method. Additionally, when the number of variables and constraints of the problem increase, the number of iterations of the new algorithm increase in a slower manner than that of the simplex method.展开更多
The variable and unpredictable nature of renewable energy generation(REG)presents challenges to its large-scale integration and the efficient and economic operation of the electricity network,particularly at the distr...The variable and unpredictable nature of renewable energy generation(REG)presents challenges to its large-scale integration and the efficient and economic operation of the electricity network,particularly at the distribution level.In this paper,an operational coordination optimization method is proposed for the electricity and natural gas networks,aiming to overcome the identified negative impacts.The method involves the implementation of bi-directional energy flows through power-to-gas units and gas-fired power plants.A detailed model of the three-phase power distribution system up to each phase is employed to improve the representation of multi-energy systems to consider real-world end-user consumption.This method allows for the full consideration of unbalanced operational scenarios.Meanwhile,the natural gas network is modelled and analyzed with steady-state gas flows and the dynamics of the line pack in pipelines.The sequential symmetrical second-order cone programming(SS-SOCP)method is employed to facilitate the simultaneous analysis of three-phase imbalance and line pack while accelerating the solution process.The efficacy of the operational coordination optimization method is demonstrated in case studies comprising a modified IEEE 123-node power distribution system with a 20-node natural gas network.The studies show that the operational coordination optimization method can simultaneously minimize the total operational cost,the curtailment of installed REG,the voltage imbalance of three-phase power system,and the overall carbon emissions.展开更多
基金Special Item of National Major Scientific Apparatus Development(No.2013YQ140431)
文摘When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming.
基金supported by the National Natural Science Foundation of China(11401126,71471140 and 11361018)Guangxi Natural Science Foundation(2016GXNSFBA380102 and 2014GXNSFFA118001)+2 种基金Guangxi Key Laboratory of Cryptography and Information Security(GCIS201618)Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ15112 and YQ16112)China
文摘In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP.
基金supported under Australian Research Council’s Discovery Projects funding scheme(project No. DP120101761)
文摘Rolling dynamic compaction (RDC),which employs non-circular module towed behind a tractor,is an innovative soil compaction method that has proven to be successful in many ground improvement applications.RDC involves repeatedly delivering high-energy impact blows onto the ground surface,which improves soil density and thus soil strength and stiffness.However,there exists a lack of methods to predict the effectiveness of RDC in different ground conditions,which has become a major obstacle to its adoption.For this,in this context,a prediction model is developed based on linear genetic programming (LGP),which is one of the common approaches in application of artificial intelligence for nonlinear forecasting.The model is based on in situ density-related data in terms of dynamic cone penetrometer (DCP) results obtained from several projects that have employed the 4-sided,8-t impact roller (BH-1300).It is shown that the model is accurate and reliable over a range of soil types.Furthermore,a series of parametric studies confirms its robustness in generalizing data.In addition,the results of the comparative study indicate that the optimal LGP model has a better predictive performance than the existing artificial neural network (ANN) model developed earlier by the authors.
基金The National Natural Science Foundation of China(No.61231002,61273266,61375028)the Ph.D.Programs Foundation of Ministry of Education of China(No.20110092130004)
文摘In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that separately design the proposed method takes all the desired designing modes into consideration when designing all the subfilters. First an initial solution is obtained by separately designing the subfilters and then the initial solution is updated by iteratively solving a SOCP problem. The proposed method is evaluated on a design example and simulation results demonstrate that jointly designing all the subfilters can obtain significantly lower minimax approximation errors compared to the conventional design method.
基金supported by the National Nature Science Foundation of China (60472101)President Award of ChineseAcademy of Sciences(O729031511).
文摘Adaptive broadband beamforraing is a key issue in array applications. The adaptive broadband beamformer with tapped delay line （TDL） structure for nonuniform linear array （NLA） is designed according to the rule of minimizing the beamformer＇s output power while keeping the distortionless response （DR） in the direction of desired signal and keeping the constant beamwidth （CB） with the prescribed sidelobe level over the whole operating band. This kind of beamforming problem can be solved with the interior-point method after being converted to the form of standard second order cone programming （SOCP）. The computer simulations are presented which illustrate the effectiveness of our beamformer.
基金supported by the National Natural Science Foundation of China (Nos. 71061002 and 11071158)the Natural Science Foundation of Guangxi Province of China (Nos. 0832052 and 2010GXNSFB013047)
文摘Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton （AHO） directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O（rln（εo/ε）） is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.
基金Supported by Liu Hui Centre for Applied Mathematics,Nankai University and Tianjin University
文摘By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algorithm is globally convergent under suitable assumptions.
基金supported by Sichuan Youth Science and Technology Innovation Research Team Project(No.2015TD0022)the Talents Project of Sichuan University of Science and Engineering(No.2017RCL11 and No.2017RCL10)the first batch of science and technology plan key R&D project of Sichuan province(No.2017GZ0068)
文摘To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem,this paper reports a research about blind separation method against channel mismatch in multiple-input multiple-output(MIMO) systems.The channel mismatch problem can be described as a channel with bounded fluctuant errors due to channel distortion or channel estimation errors.The problem of blind signal separation/extraction with channel mismatch is formulated as a cost function of blind source separation(BSS) subject to the second-order cone constraint,which can be called as second-order cone programing optimization problem.Then the resulting cost function is solved by approximate negentropy maximization using quasi-Newton iterative methods for blind separation/extraction source signals.Theoretical analysis demonstrates that the proposed algorithm has low computational complexity and improved performance advantages.Simulation results verify that the capacity gain and bit error rate(BER) performance of the proposed blind separation method is superior to those of the existing methods in MIMO systems with channel mismatch problem.
基金Supported by the National Natural Science Foundation of China(11471102,61301229)Supported by the Natural Science Foundation of Henan University of Science and Technology(2014QN039)
文摘We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples.
基金Project supported by the National Natural Science Foundation of China (No. 10771026)the Foundation of Dalian University of Technology (Nos. MXDUT73008 and MXDUT98009)
文摘A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.
基金This work was supported by the National Natural Science Foundation of China(Nos.61960206011,61633003)the Beijing Natural Science Foundation(No.JQ19017)。
文摘This paper investigates the optimal control problem of spacecraft reorientation subject to attitude forbidden constraints,angular velocity saturation and actuator saturation simultaneously.A second-order cone programming(SOCP)technology is developed to solve the strong nonlinear and non-convex control problem in real time.Specifically,the nonlinear attitude kinematic and dynamic are transformed and relaxed to a standard affine system,and linearization and L1 penalty technique are adopted to convexify non-convex inequality constraints.With the proposed quadratic performance index of angular velocity,the optimal control solution is obtained with high accuracy using the successive SOCP algorithm.Finally,the effectiveness of the algorithm is validated by numerical simulation.
文摘Recently we have proposed anew method combininginterior and exterior approaches to solve linear programming problems. This method uses an interior point, and from there connected to the vertex of the so called station cone which is also a solution of the dual problem. This allows us to determine the entering vector and the new station cone. Here in this paper, we present a new modified algorithm for the case, when at each iteration we determine a new interior point. The new building interior point moves toward the optimal vertex. Thanks to the shortened from both inside and outside, the new version allows to find quicker the optimal solution. The computational experiments show that the number of iterations of the new modified algorithm is significantly smaller than that of the second phase of the dual simplex method.
基金supported by the Joint Foundation of the Ministry of Education of China(No.6141A02022340).
文摘An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary target.The problem with time-varying Proportional Navigation(PN)gain is first formulated as a nonlinear optimal control problem,which is difficult to solve due to the existence of nonlinear kinematics and nonconvex constraints.After convexification treatments and discretization,the solution to the original problem can be approximately obtained by solving a sequence of Second-Order Cone Programming(SOCP)problems,which can be readily solved by state-of-the-art Interior-Point Methods(IPMs).To mitigate the sensibility of the algorithm on the user-provided initial profile,a Two-Stage Sequential Convex Programming(TSSCP)method is presented in detail.Furthermore,numerical simulations under different mission scenarios are conducted to show the superiority of the proposed method in solving the cooperative guidance problem.The research indicated that the TSSCP method is more tractable and reliable than the traditional methods and has great potential for real-time processing and on-board implementation.
基金the National Science Foundation(60574075, 60674108)
文摘A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.
文摘In this paper we present a new method combining interior and exterior approaches to solve linear programming problems. With the assumption that a feasible interior solution to the input system is known, this algorithm uses it and appropriate constraints of the system to construct a sequence of the so called station cones whose vertices tend very fast to the solution to be found. The computational experiments show that the number of iterations of the new algorithm is significantly smaller than that of the second phase of the simplex method. Additionally, when the number of variables and constraints of the problem increase, the number of iterations of the new algorithm increase in a slower manner than that of the simplex method.
基金supported by the Engineering and Physical Sciences Research Council(EPSRC,UK)in project“Street2Grid–an electricity blockchain platform for P2P energy trading”(No.EP/S001778/2).
文摘The variable and unpredictable nature of renewable energy generation(REG)presents challenges to its large-scale integration and the efficient and economic operation of the electricity network,particularly at the distribution level.In this paper,an operational coordination optimization method is proposed for the electricity and natural gas networks,aiming to overcome the identified negative impacts.The method involves the implementation of bi-directional energy flows through power-to-gas units and gas-fired power plants.A detailed model of the three-phase power distribution system up to each phase is employed to improve the representation of multi-energy systems to consider real-world end-user consumption.This method allows for the full consideration of unbalanced operational scenarios.Meanwhile,the natural gas network is modelled and analyzed with steady-state gas flows and the dynamics of the line pack in pipelines.The sequential symmetrical second-order cone programming(SS-SOCP)method is employed to facilitate the simultaneous analysis of three-phase imbalance and line pack while accelerating the solution process.The efficacy of the operational coordination optimization method is demonstrated in case studies comprising a modified IEEE 123-node power distribution system with a 20-node natural gas network.The studies show that the operational coordination optimization method can simultaneously minimize the total operational cost,the curtailment of installed REG,the voltage imbalance of three-phase power system,and the overall carbon emissions.
