| Security operation and control with discrete controls are the basic elements and key problems of power system optimizations.This paper started with short-term voltage security problems,which were described as general optimization models with typical mathematical characteristics(e.g.,multi-objective,mixed-integers,dynamic optimization,et al).According to corresponding characteristics,this paper adopted several existing solution methods and proposed lots of useful improvements for their efficient solutions,which included advanced artificial intelligence and classical mathematical/numerical optimization algorithms.Moreover,dynamic modeling and mixed-integer optimization(MIO)methods were further generalized to optimal operation problems of active distributions networks with discrete controls.These methods efficiently handled discrete control problems and provided continuous-trajectory schemes,which were more accurate than classical precise-constant ones.Additionally,stochastic optimization algorithm was also extended to the solution of optimal operation problems,to adapt security operation of power girds with high penetrations of renewable.Specifically,this paper has achieved breakthroughs in the following four areas:(1)A coordinated generation-compensation Var control strategy with discrete controls has been proposed to mitigate short-term voltage instabilities.The short-term voltage security problem was described as multi-objective dynamic optimization(MODO)model with constraints of dynamics,load flows,and securities.Mitigating computational burdens efficiently,an innovative multi-objective reinforcement learning(MORL)method obtained Pareto solutions by means of filtering dominated ones.Different from those conventional ones,the innovative MORL method carved up an entire feasible region and obtained certain little individual regions.The MORL method finished dominated filter within each individual region.This helps eliminate the searching range for Pareto frontier(PF).Additionally,both state functions and their sensitivities were refined,which provided the judgement for learning and applying.To expand the distribution of PF,certain suspected solutions were introduced for dominated filter.At last,we obtained the tradeoff solution for saving short-term voltage security,by means of Fuzzy decision-making.Case studies for a 748-node grid confirmed its efficiency.(2)To mitigate short-term voltage instabilities,we proposed a multi-objective programming for dynamic var sources planning,where we provided unique insights for their modeling and solutions.For the modeling,this paper optimized three objectives including investment of STATCOMs,cost of compensation constant,and short-term voltage index.Particularly,the allocation of STATCOMs involved both their locations(integer variables)and capacities(continuous variables).The above planning problem could be described as a multi-objective mixed-integer dynamic optimization model,with short-term voltage security and angle stability constraints under multiple faults.For the solutions,the reduced convex relaxation(RCR)method was employed,to deal with MIO problem and to avoid combinatorial explosions.For complete PF of three-objective optimization,a reduced wide normalized normal constraint method expanded the Utopia surface until its vertical projection completely covered the entire PF.The redundant portion of the Utopia surface was trimmed to reduce the burden of computation.Simulation results of the IEEE 39-node and a real 1009-node power systems illustrated that,MIO problems were solved effectively and complete PFs were obtained in three-dimensional space.(3)We modelled the optimal operation problems with dynamic optimization(DO),and adopted MIO for their solutions.This paper innovatively combined MIO and DO organically,where we employed mixed-integer dynamic optimization(MIDO)model for dayahead optimal operation problems.It specifically described loads and generations by trajectories and offered operation trajectory for active distribution networks(ADNs).Nevertheless,absolute value constraints were adopted to restrict switching operations of discrete devices.This paper employed the RCR method to implement convexification and relaxation,after which the optimization model was transformed into a continuous one.It was then transformed into a non-linear programming problem,by means of Radau collocation method.At the same time,the constraints with absolute values that restricted switching operations,were replaced by certain linear ones.Efficiency of the proposed modeling and solution methods was illustrated by cases of IEEE 33-node,PG&E 69-node,and actual 110-node ADNs.(4)This paper adopted the stochastic collocation method with dimension-reduced sparse grid(SCM-W-DRSG)to manage the optimal scheduling of ADNs with stochastic optimizations,and highlighted the advantages of SCM-W-DRSG in stochastic optimizations.SCM-W-DRSG did not care about the internal firework of the stochastic optimization model,but regarded it as a black box and only focused on its inputs and outputs.By means of the tensor product between polynomials and inputs,SCM-W-DRSG approximated the internal firework and outputs of the black box.Moreover,SCM-W-DRSG combined the ideas of sparse grids and dimension reductions,and upgraded the overall scheme to approximate the black box.These mitigated combinatorial explosions corresponding to collocation points.Regarding the classical Monte Carlo method as a benchmark,SCM-W-DRSG performed excellently in approximating optimization models,and obtained extremely accurate costs and schemes.Moreover,SCM-W-DRSG was extremely efficient and took much shorter CPU time compared with Monte Carlo method.Even in the cases with massive scenarios,SCM-W-DRSG succeeded in managing the optimization,while Monte Carlo method could not manage the optimization.Additionally,increasing the order of SCM-W-DRSG did improve the accuracy and waste extra CPU time of approximating the black box.However,this extra CPU time was acceptable,compared to that in the case of increasing sampling scenarios. |
PDF Full Text Request