Distributed Online Optimization Algorithm For The Operation Of Electrical Power Systems

Driven by the requirement of energy conservation and emission reduction,the structure of power systems composed of the generation,transmission,distribution have been changing substantially.Renewable energy sources(RESs),such as wind and solar energy,will gradually replace the fossil fuel generation and become the nonnegligible power sources;meanwhile,distributed energy resources(DERs),including distributed RESs and battery energy storage facilities and controllable loads,are connected to the distribution network in a distributed way with forming the active distribution networks.With the rapid increase of RESs,the operation and control of power systems will inevitably face the dilemma of insufficient regulation resources to track intermittent power generation.It is mainly reflected in the following aspects:the remaining fossil fuel power generation can not keep the real-time energy balance;the active distribution network will have serious voltage problems due to the bidirectional flow and uncertainty factors.To solve these operation regulation problems,it needs to optimize the set-points of the inverters to fully exploit the fast adjustable ability of DERs.In this regard,the researchers have proposed a class of online optimization methods supported by advanced measurement and communication technologies.These methods adjust the inputs according to the feedback states of physical systems with continuously optimizing the operation of the physical systems in a closed-loop manner.Thus the online methods are suitable to optimize the operation of DERs at fast time-scales.However,the current online optimization algorithms need to use centralized information acquisition and calculation while coping with the complex power flow constraints.Therefore,the current researches about the online methods only focus on the operation control of fossil fuel generations or the optimization of DERs in a small range of active distribution networks.These works do not achieve the overall unified coordinated control of the power system containing large numbers of DERs.To this end,this paper research the distributed online optimization methods of power system operation under the premise of wide-area measurement and communication technology.Taking the operation base points of automatic generation control(AGC)units and DERs as the decision variables,this paper attempts to solve the problem of rapid decision-making of operation base points by establishing distributed optimization mathematical models and deriving the corresponding algorithms.Based on the proposed methods,the base points of DERs can be quickly determined according to the measurement feedback only with the local information and boundary information for each area in power grids.The operation of power systems can be optimized in a closed-loop manner in coordination,which is mainly reflected in the realization of the cooperation of DERs and AGC units operation with the implementation of the voltage control of active distribution networks.The research provides a solution and theoretical basis for the distributed implementation of the closed-loop optimization of power systems in real time,and is of great significance for the realization of the high-level integration of DERs in the future.The contributions of this paper are as follows:(1)An online algorithm for coordinating DERs and AGC is proposed.From the perspective of synchronous operation of power systems and according to the control characteristics of AGC,the controllable range of AGC units is analyzed in real-time to distribute the load fluctuations beyond the controllable range of AGC units to DERs;meanwhile,the operating constraints of voltage and current of distribution networks are considered to construct the transmission-distribution optimization model For solving the optimization model,the power flow model is linearized and reformed to derive the optimization sensitivities into a formulation only relating to the inner and boundary information of each distribution network;besides,according to the integral control laws of AGC,the power imbalance is equivalently expressed as the ACE integral to integrate the optimization of DERs into the frequency regulation based on the original AGC.Numerical analysis shows that based on the proposed algorithm,DERs can organically participate in the frequency regulation to effectively absorb the load fluctuations that AGC units cannot cope with while meeting the operational constraints of the distribution networks.This work establishes the framework of the online optimization of power systems with the coordinated operation of DERs and AGC units,and gives the coordination mechanism and the implementation of distributed computing between transmission and distribution networks.With this framework remaining unchanged,the key problem is how to optimize the operation of DERs in active distribution networks in a distributed way.(2)To achieve the real-time power allocation in the active distribution networks,a distributed online optimal power flow(OPF)algorithm for single-phase distribution networks is proposed.Under the assumption that the distribution network is single-phase or operates in multi-phase balanced conditions,we construct an OPF model of the distribution network based on the Distflow model.Furthermore,we propose a back/forward sweep method to calculate power flow sensitivities.Based on this and further derivation,we give the interaction law of power flow between the various regions of distribution networks.That is,the effect of any region on the upper region is to affect the boundary injections to change the inner power flows;the effect of any region on the regions not on the upper position is to affect the inner power flows by changing its boundary voltage amplitudes.As a result,the optimization sensitivities are decoupled among different regions,and a distributed method for calculating the optimization sensitivities is designed to realize the online optimization in a distributed way.Numerical analysis shows that the algorithm can achieve almost the same convergence results as the online optimization in a centralized manner;it can steer the outputs of DERs towards the OPF solutions during the time-varying process while meeting the operational constraints in real time.(3)For the distribution networks operating under the multi-phase unbalanced conditions,a distributed online optimization algorithm for multi-phase unbalanced distribution networks is proposed.The optimization model is established based on the extended three-phase Distflow model.Furthermore,the extended Distflow model is linearized under the assumption that the voltage of each phase meets certain conditions.According to this,it is deduced that the power flow of different regions of distribution networks still satisfies the interaction laws similar to the results deduced under the single-phase conditions.Only the difference is that the voltage and current amplitudes are replaced by their square terms.Based on this,we decouple the optimization sensitivities and design the method to calculate the sensitivities in a distributed way to realize online optimization.Numerical analysis verifies the effectiveness of the proposed algorithm:the consideration of multi-phase imbalance can effectively reduce the regulation costs of DERs compared with the single-phase consideration;the online optimization algorithm can still drive the DER outputs to a range of the OPF solutions while meeting the voltage constraints with measurement errors and the input-output response delay of DERs.(4)The above distributed online optimization algorithms are all derived under the(extended)Distflow model,and assumed that the distribution networks are radial.But in fact,distribution networks may operate in mesh apologies especially for the future development trend of active distribution networks with high-reliability requirements and flexible power supply.In this regard,a novel distributed online OPF algorithm is derived under the general power flow model suitable to the networks with arbitrary apologies.We reveal that the interaction laws of power flow between different regions of distribution networks are similar to the results for radial networks.Only the difference is that the state quantities are increased by the addition of voltage phases.According to this,the optimization sensitivities can be decoupled between different regions of distribution networks.Further,under the general power flow model,a distributed calculation method for power flow sensitivity is designed,which can decompose the inversion of the Jacobian matrix into several parts starting from the root node to the bottom.Numerical analysis shows that the algorithm not only has high accuracy but also can greatly reduce the calculation time of inverting the Jacobian matrix to effectively meet the fast calculation needs of the online optimization.(5)The above methods are realized by decomposing the sensitivities only considering the gradient information,and gradients can only reflect the first-order information of the optimization problem,which may lead to a slower convergence rate.But it is generally required that the intermediate iterations can quickly track the time-varying optimal solutions for online optimization.Thus the online algorithms only considering the first-order information may not be sufficient to deal with the strong fluctuations such as the photovoltaic output changes in cloudy weather.In this regard,a distributed online optimization algorithm based on second-order Taylor expansion is further proposed.It uses a distributed model predictive control method to solve the second-order Taylor expansion problem of OPF in real time,and decompose the second-order Taylor expansion information(including the Jacobian matrix and the Hessian matrix).According to this,each region of distribution networks can form parts of the Jacobian matrix and the Hessian matrix,and then exchange and further combinate the obtained parts to form the complete second-order Taylor expansion information.Numerical analysis shows that compared with only considering the gradient information,the online optimization considering the second-order information can track the OPF solutions faster and meet the distribution network operation constraints more effectively.