Stochastic Optimal Power Flow Research Articles

On polynomial real-time control policies in stochastic AC optimal power flow

In traditional power system operations real-time control policies are based on simple control policies such as automatic generation control and/or local voltage control. Although these simple policies have worked well in the past, the increased variability associated with higher penetrations of renewable energy strengthens the case for more general approaches. In this paper we analyze the design of real-time control policies through the lens of stochastic AC-OPF. Using a chance-constrained approach in combination with a reformulation based on polynomial chaos expansion, we show that the solution corresponds to a general polynomial control policy. By restricting this general policy, we are able to recover the traditional (affine) control policies as a special case. This allows to quantify the value of implementing non-affine policies, and to analyze their impact on the system behavior, as demonstrated in the numerical example.

Stochastic DC optimal power flow with reserve saturation

We propose an optimization framework for stochastic optimal power flow with uncertain loads and renewable generator capacity. Our model follows previous work in assuming that generator outputs respond to load imbalances according to an affine control policy, but introduces a model of saturation of generator reserves by assuming that when a generator’s target level hits its limit, it abandons the affine policy and produces at that limit. This is a particularly interesting feature in models where wind power plants, which have uncertain upper generation limits, are scheduled to provide reserves to balance load fluctuations. The resulting model is a nonsmooth nonconvex two-stage stochastic program, and we use a stochastic approximation method to find stationary solutions to a smooth approximation. Computational results on 6-bus and 118-bus test instances demonstrate that by considering the effects of saturation, our model can yield solutions with lower expected generation costs (at the same target line violation probability level) than those obtained from a model that enforces the affine policy to stay within generator limits with high probability.

Stochastic AC optimal power flow: A data-driven approach

There is an emerging need for efficient solutions to stochastic AC Optimal Power Flow (AC-OPF) to ensure optimal and reliable grid operations in the presence of increasing demand and generation uncertainty. This paper presents a highly scalable data-driven algorithm for stochastic AC-OPF that has extremely low sample requirement. The novelty behind the algorithm’s performance involves an iterative scenario design approach that merges information regarding constraint violations in the system with data-driven sparse regression. Compared to conventional methods with random scenario sampling, our approach is able to provide feasible operating points for realistic systems with much lower sample requirements. Furthermore, multiple sub-tasks in our approach can be easily paralleled and based on historical data to enhance its performance and application. We demonstrate the computational improvements of our approach through simulations on different test cases in the IEEE PES PGLib-OPF benchmark library.

Hybrid power systems with emission minimization: Multi-objective optimal operation

The demand of electrical power and energy is exponentially increased with the advancement of science and technology in past decades. To fulfil this increasing demand of energy, the burden on conventional fossil fuel based units has continuously been raised, which in turn has severe consequences on the environment. A clean pollution free and healthy environment necessitates the reduction in the use of conventional fossil fuel based units. In this context, integration of non-conventional and renewable power generation facilities with conventional power generators, for instance, hybrid power system is gaining attention. However, the intermittent posed by renewable power generation facilities may make the scheduling of generators and power system operation extremely challenging. These issues and its possible solution have been addressed in this proposed study. An attempt has been made in the evaluation of an optimum generation scheduling and coordination among different hybrid power system configurations in the form of wind-thermal, hydro-thermal-wind and hydro-thermal-wind-solar systems. This stochastic optimal power flow problem of the proposed system has been formulated in a multi-objective optimization framework while incorporating real-time operational constraints. A mathematical model, operational analysis and comparative evaluation between the optimum operational paradigms obtained with a modified bacteria foraging algorithm for wind-thermal, hydro-thermal-wind and hydro-thermal-wind-solar systems have been implemented. The effectiveness and promising solutions of hydro-thermal-wind-solar in response to fulfill the operational objectives like cost effective operation, minimization of transmission loss, emission and voltage variation over other hybrid configurations in multi-objective stochastic optimal power flow environment as implemented in IEEE30 bus power system has been demonstrated.

Random-Fuzzy Chance-Constrained Programming Optimal Power Flow of Wind Integrated Power Considering Voltage Stability

Considering the random and fuzzy nature of wind speed, this paper proposes a multi-objective random-fuzzy chance-constrained programming optimal power flow (OPF) for wind integrated power systems. The proposed method is based on random-fuzzy chance-constrained programming. The optimization model aims at minimizing generation cost, carbon dioxide (CO2) emission, and system functional power loss, and P-Q-V steady-state voltage stability is included in the constraints. Based on random-fuzzy chance-constrained programming, the corresponding solution process of the proposed multi-objective OPF is proposed, which is a hybrid of random-fuzzy simulation, non-dominated sorting genetic algorithm-II (NSGA-II), and fuzzy satisfaction-maximizing decision-making method. The proposed approach is simulated on the IEEE 30-bus system to provide an example of its application. The simulation results demonstrate that the proposed random-fuzzy chance-constrained programming OPF has higher security and more economy than dynamic stochastic optimal power flow (DSOPF) and dynamic fuzzy optimal power flow (DFOPF).

Stochastic Optimal Power Flow Under Forecast Errors and Failures in Communication

Communication networks play an important role in the operation and control of power grids. The integration of intermittent and stochastic renewable energy sources into the electricity system increases the criticality of these communications systems to maintain the reliability of the overall power network. Communication networks are employed to continually update system operators about the status of generators and loads in the system, as well as other key information. We present a stochastic optimal power flow formulation where we account for errors in forecasting future load and renewable generation while also considering random failures in the communication network employed to communicate the realized values of the quantities for which we have forecasts. The communication network is also assumed to be employed for the control of loads and generators in the power system. Thus, a failure to communicate between the grid operator and entities in the power grid can also result in the loss of controllability for any such entity. We illustrate the utility of our model by presenting results that identify the optimal topology for a communication network supporting the operation of an IEEE standard 9-bus system. We also discuss several properties regarding the identified optimal topologies.

Second‐order cone robust AC–DC DOPF considering correlation of wind power

Due to the increasing penetration, intermittent renewable energy sources (RESs), such as wind power, have added additional uncertainties to AC–DC power system operation. The strong correlation between wind power will bring larger computational errors. It makes generation dispatching incompatible with the current single-period optimal power flow practice. This study presents an AC–DC affinely adjustable robust dynamic optimal power flow (AARDOPF) model. Ellipsoidal uncertainty set is adopted to well fit the spatial-temporal correlated wind power. Affine policies are utilised in the re-dispatch process. To apply AC–DC AARDOPF, the base-point generation is calculated and determined to match the power with forecasted RES output. And once the uncertainty is revealed, generators reschedule its output through participation factors responding to the uncertain fluctuation of RES output to ensure a feasible solution for all realisations of RES output. Then original non-linear models are transformed into SOCP models. Finally, GUROBI is used to solve this model. Numerical results are obtained on modified AC–DC IEEE 30-bus and 118-bus system to minimise the expected operational cost. Comparing with stochastic dynamic optimal power flow (DOPF), this model is proved to be more practical and effective.

Scalable preconditioning of block-structured linear algebra systems using ADMM

We study the solution of block-structured linear algebra systems arising in optimization by using iterative solution techniques. These systems are the core computational bottleneck of many problems of interest such as parameter estimation, optimal control, network optimization, and stochastic programming. Our approach uses a Krylov solver (GMRES) that is preconditioned with an alternating method of multipliers (ADMM). We show that this ADMM-GMRES approach overcomes well-known scalability issues of Schur complement decomposition in problems that exhibit a high degree of coupling. The effectiveness of the approach is demonstrated using linear systems that arise in stochastic optimal power flow problems and that contain up to 2 million total variables and 4000 coupling variables. We find that ADMM-GMRES is nearly an order of magnitude faster than Schur complement decomposition. Moreover, we demonstrate that the approach is robust to the selection of the augmented Lagrangian penalty parameter, which is a key advantage over the direct use of ADMM.

Data-Based Distributionally Robust Stochastic Optimal Power Flow—Part I: Methodologies

We propose a data-based method to solve a multi-stage stochastic optimal power flow (OPF) problem based on limited information about forecast error distributions. The framework explicitly combines multi-stage feedback policies with any forecasting method and historical forecast error data. The objective is to determine power scheduling policies for controllable devices in a power network to balance operational cost and conditional value-at-risk of device and network constraint violations. These decisions include both nominal power schedules and reserve policies, which specify planned reactions to forecast errors in order to accommodate fluctuating renewable energy sources. Instead of assuming that the uncertainties across the networks follow prescribed probability distributions, we consider ambiguity sets of distributions centered around a finite training dataset. By utilizing the Wasserstein metric to quantify differences between the empirical data-based distribution and the real unknown data-generating distribution, we formulate a multi-stage distributionally robust OPF problem to compute control policies that are robust to both forecast errors and sampling errors inherent in the dataset. Two specific data-based distributionally robust stochastic OPF problems are proposed for distribution networks and transmission systems.

Data-Based Distributionally Robust Stochastic Optimal Power Flow—Part II: Case Studies

This is the second part of a two-part paper on data-based distributionally robust stochastic optimal power flow (OPF). The general problem formulation and methodology have been presented in Part I [1]. Here, we present extensive numerical experiments in both distribution and transmission networks to illustrate the effectiveness and flexibility of the proposed methodology for balancing efficiency, constraint violation risk, and out-of-sample performance. On the distribution side, the method mitigates overvoltages due to high photovoltaic penetration using local energy storage devices. On the transmission side, the method reduces N-1 security line flow constraint risks due to high wind penetration using reserve policies for controllable generators. In both cases, the data-based distributionally robust model predictive control (MPC) algorithm explicitly utilizes forecast error training datasets, which can be updated online. The numerical results illustrate inherent tradeoffs between the operational costs, risks of constraints violations, and out-of-sample performance, offering systematic techniques for system operators to balance these objectives.

An efficient Differential Evolution algorithm for stochastic OPF based active–reactive power dispatch problem considering renewable generators

Optimal active–reactive power dispatch problems (OARPD) are non-convex and highly nonlinear complex optimization problems. Typically, such problems are expensive in terms of computational time and cost due to the load variations over the scheduling period. The conventional constraint-based solvers that are generally used to tackle such problems require a considerable high budget and may not provide high quality solutions. In the last decade, complexity of OARPD has further increased due to the incorporation of renewable energy sources such as: wind, solar and small-hydro generators. More specifically, the incorporation of renewable sources introduces uncertainty in generation on top of the load variations in conventional OARPD, making the problem more complicated. Recently, Differential Evolution (DE) is viewed as an excellent algorithm to solve OARPD problems, due to its effectiveness to optimize the objective function which is subject to many operational constraints. A new efficient Differential Evolution algorithm, denoted as DEa-AR, is propounded to solve the contemporary stochastic optimal power flow OARPD problems considering the renewable generators. DEa-AR uses arithmetic recombination crossover and adapts the scaling factor based on Laplace distribution. In addition, an efficient archive strategy that acts as a corresponding image of the population and stores the inferior individuals for later use, is also incorporated. The target behind using this strategy is to consider the information of inferior individuals as a direction toward finding new good solutions. The IEEE 57-bus system is used to evaluate the OARPD problems with different stochastic scenarios based on different probability distributions employed to model parameters of renewable energy sources. The performance of the proposed work is compared with other state-of-the-art algorithms. Simulation results indicate that the proposed technique can solve the OARPD problems with renewable sources effectively and can provide high quality solutions. The proposed algorithm is ranked the first with a Friedman rank equals to 1.8333 with a clear statistical significant difference compared with the most recent studies on the used problems.

Interval optimal power flow applied to distribution networks under uncertainty of loads and renewable resources

Optimal power flow (OPF) has been used for energy dispatching in active distribution networks. To satisfy constraints fully and achieve strict operational bounds under the uncertainties from loads and sources, this paper derives an interval optimal power flow (I-OPF) method employing affine arithmetic and interval Taylor expansion. An enhanced I-OPF method based on successive linear approximation and second-order cone programming is developed to improve solution accuracy. The proposed methods are benchmarked against Monte Carlo simulation (MCS) and stochastic OPF. Tests on a modified IEEE 33-bus system and a real 113-bus distribution network validate the effectiveness and applicability of the proposed methods.

Optimizing the Preventive and Corrective Control Scheme in Integrated Variable Renewable Energy Generation

Variable renewable energy integration makes the revolution in modern power system operation and control which lead to perform the preventive and corrective control for maintaining the system continuity againts the voltage security and instability. On the other hand, the power system utility should maintain the economical aspect for its operation, which is hard to be obtained in the system prioring the preventive and corrective scheme. This paper proposes the optimal management between preventive and corrective scheme for achieving the most economical operating cost to solve a stochastic security-constrained optimal power flow for the upcoming time-slot considering voltage stability, line contingency occurence and renewable energy source fluctuation by controlling the generation power, compensator and load shedding scheme while maintaining the computation speed. The main contribution of the proposed method is the active control between preventive and corrective schemes simultaneously for achieving the most economical solution. Scenarios developed in modified IEEE 57-bus test system are used to demonstrate the effectiveness of the proposed method. The simulations show that the proposed method can make a significant contribution for achieving more economical solution while maintaining the computation speed.

Distributed Generation Planning Guidance Through Feasibility and Profit Analysis

This letter presents a feasibility and profit-based planning guidance for the regulatory of distributed generation (DG) integration. Different from the conventional planning frameworks, our approach yields a capacity interval enveloped by feasibility and profit bounds for DG installation, instead of a particular capacity scheme. On one hand, the feasibility bound is determined through multi-period stochastic optimal power flow to enforce the feasibility constraints of the distribution network operation subject to the uncertainties of DG output. On the other hand, the profit bound is derived using chance constrained program to guide profitable DG investment under controllable risk level. Numerical tests on IEEE 33-bus distribution system demonstrate the effectiveness of the proposed approach.

Non‐deterministic optimal power flow considering the uncertainties of wind power and load demand by multi‐objective information gap decision theory and directed search domain method

Optimal power flow (OPF) as an important operation function of wind power-integrated power systems encounters the uncertainties of load demand and wind power. To cope with these uncertainty sources, various OPF models including deterministic OPF, probabilistic OPF, scenario-based OPF, stochastic OPF, robust OPF and recently information gap decision theory (IGDT)-based OPF have been presented in the literature. A multi-objective IGDT-based AC OPF model is presented which can simultaneously optimise various uncertainty horizons pertaining to load demands and wind powers considering the specified robustness level. Another main contribution of this study is presenting an effective directed search domain (DSD)-based multi-objective solution method to solve the proposed multi-objective IGDT-based AC OPF problem. The proposed OPF model and solution approach are tested on the IEEE 118-bus test system and the obtained results are compared with the results of other OPF models and solution methods. These comparisons illustrate the effectiveness of the proposed multi-objective IGDT-based AC OPF model as well as the proposed DSD-based multi-objective solution method.

A stochastic optimal power flow for scheduling flexible resources in microgrids operation

Microgrid operations are challenging due to variability in loads and renewable energy generation. Advanced tools capable of taking uncertainty into account are essential to maximize microgrid benefits when operating microgrid owned DERs. This paper proposes a novel optimization model for day-ahead economic dispatch of flexible resources within a microgrid environment, considering uncertainty of PV and loads.This model is conceived to support the microgrid supervisory control layer, providing a security-constrained day-ahead strategy to operate three types of microgrid flexible resources: PV, electric storage and controllable loads. The work presented in this paper introduces a novelty in microgrid operations by presenting a stochastic version of the day ahead scheduling of microgrid DERs to deal with uncertainties associated with PV, load and temperature while considering microgrid network limits and end-user comfort as optimization constraints. An annual analysis quantifies the benefits of to the microgrid-owner of a stochastic formulation over a deterministic one both in terms of ensuring end-user comfort and decreasing operation costs.

2017 IEEE competition on modern heuristic optimizers for smart grid operation: Testbeds and results

This paper summarizes the two testbeds, datasets, and results of the IEEE PES Working Group on Modern Heuristic Optimization (WGMHO) 2017 Competition on Smart Grid Operation Problems. The competition is organized with the aim of closing the gap between theory and real-world applications of evolutionary computation. Testbed 1 considers stochastic OPF (Optimal Power Flow) based Active-Reactive Power Dispatch (ARPD) under uncertainty and Testbed 2 large-scale optimal scheduling of distributed energy resources. Classical optimization methods are not able to deal with the proposed optimization problems within a reasonable time, often requiring more than one day to provide the optimal solution and a significant amount of memory to perform the computation. The proposed problems can be addressed using modern heuristic optimization approaches, enabling the achievement of good solutions in much lower execution times, adequate for the envisaged decision-making processes. Results from the competition show that metaheuristics can be successfully applied in search of efficient near-optimal solutions for the Stochastic Optimal Power Flow and large-scale energy resource management problems.

A stochastic mixed-integer conic programming model for distribution system expansion planning considering wind generation

This paper presents a stochastic scenario-based approach to finding an efficient plan for the electrical power distribution systems. In this paper the stochasticity for the distribution system expansion planning (DSEP) problem refers to the loads and wind speed behavior. The proposed DSEP model consist the expansion and/or construction of new substations, installation of new primary feeders and/or reinforcement the existing, installation of wind-distributed generation based, reconfiguration of existing network, and the proposed DSEP is solved considering uncertainty in electric demand and distributed generation. In this regard, a two-stage stochastic programming model is used, wherein the first stage the investment decision is made and the second stage calculates the expected operating value which depends on the stochastic scenarios. The mathematical approach is based on a mixed integer conic programming (MICP) model. By using this MICP model and a commercial optimization solver, finding the optimal global solution is guaranteed. Moreover, in this paper by using the Tabu Search algorithm and take the advantages of a stochastic conic optimal power flow model, an efficient hybrid algorithm is developed. With the aim of comparing the performance of the optimization techniques based on solution of MICP model directly and using a hybrid proposed methodology, they are tested in a 24-node distribution system and the results are compared in detail. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

Optimal day‐ahead demand response contract for congestion management in the deregulated power market considering wind power

In the liberalised electricity market, congestion management (CM) with a high penetration of wind energy is a challenging task for Independent System Operators (ISOs). Even though demand response (DR) provides an opportunity to alleviate transmission congestion, strategic selection of aggregated loads to contract with for DR in the day-ahead economic dispatch is still under-investigated. To solve this problem, this study proposes a bi-level optimisation model to determine the optimal DR buses for CM in the day-ahead market considering the uncertainty of wind power. The upper model serves to compute the available transfer capability (ATC), while the lower model is to calculate the stochastic dynamic optimal power flow. Through converting the stochastic ATC values to a summation of load supply capability of each load node, the loads which will deteriorate transmission congestion if the corresponding demand grows are determined. The corresponding loads with DR are selected as the optimal candidates. Furthermore, this study constructs a two-stage optimisation model for optimal load dispatch by incorporating both price-based DR and incentive-based DR. The result can be used to assist system operators in decision-making of electricity biddings from DRs for load curtailment and shift in the market clearing. As a result, the difference of peak and valley loads is reduced; ISOs as well as DR participators can both get economic benefits. Simulation results from the PJM 5-bus training system and the modified IEEE 30-bus system demonstrate the effectiveness of the proposed algorithm for DR contracting in CM.

Queuing Analysis Based PEV Load Modeling Considering Battery Charging Behavior and Their Impact on Distribution System Operation

This paper presents a queuing analysis-based method for modeling the 24-h charging load profile of a plug-in electric vehicle (PEV) charging station. The queuing model considers the arrival of PEVs as a non-homogeneous Poisson process with different arrival rates over the day. The first PEV charging load profile assumes customer convenience as the factor that influences the hourly arrival rate of vehicles at the station, while the second profile is developed assuming that customers would respond to PEV charging prices and arrival rates are accordingly affected. One of the main contributions of this paper is to model the PEV service time considering different factors such as the state-of-charge of the vehicle battery, as well as the effect of the battery charging behavior. The impact of PEV load models on distribution systems is studied for a deterministic case, and the impact of uncertainties is examined and compared using the stochastic optimal power flow and the model predictive control approaches.