Uncertainties Of Load Demand Research Articles

Optimal Location Planning of Renewable Distributed Generation Units in Distribution Networks: An Analytical Approach

We study the optimal location planning of renewable distributed generation (RDG) units by taking into account the random uncertainties of renewable generation and load demand. In presence of the random uncertainties, location planning problem is naturally a two-stage stochastic mixed integer nonlinear programming problem, which is hard to solve efficiently. Instead of using traditional sampling methods or robust optimization methods, we propose a novel analytical approach in this paper to solve the problem efficiently and optimally. In particular, analytical expressions are derived for efficiently evaluating the performance of a candidate RDG placement decision. In this way, the stochastic mixed integer nonlinear programming problem is equivalently transformed into a deterministic integer problem, which can be solved efficiently using off-the-shelf tools. Numerical results show that the optimal RDG placement can save up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$4.2\%$</tex-math></inline-formula> of the long-term average cost and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$80.59\%$</tex-math></inline-formula> of the line losses on the IEEE 13-bus test feeder. In addition, our proposed approach effectively reduces the computational time by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$99.51\%$</tex-math></inline-formula> on the IEEE 123 node test feeder compared with other traditional sampling-based metaheuristic approaches.

Contingency-constrained robust transmission expansion planning under uncertainty

This paper studies the problem of robust transmission expansion planning (TEP) considering the N-k contingency and the uncertainty of load demand and renewable energy source (RES) generation. The expansion plan needs to meet constraints under the normal state and N-k contingency. Under the normal state, the problem to determine the worst-case loss-of-load and RES spillage is reformulated as a mixed integer linear programming (MILP) problem by application of dual theory. Under the N-k contingency, the problem to determine the worst-case loss-of-load is also reformulated as a MILP problem. The whole TEP problem is solved by the technique of Benders decomposition (BD). The expansion plan obtained by the proposed approach in this paper can accommodate all possible realizations of uncertain parameters defined by the uncertainty budget under both normal state and contingencies. Case studies are carried out on the revised IEEE 24-bus test system and revised IEEE RTS-96. Results show the optimal expansion plan is greatly affected by the uncertainty budget and N-k contingency.

Robust Capacity Assessment of Distributed Generation in Unbalanced Distribution Networks Incorporating ANM Techniques

To settle a large-scale integration of renewable distributed generations (DGs), it requires to assess the maximal DG hosting capacity of active distribution networks (ADNs). For fully exploiting the ability of ADNs to accommodate DG, this paper proposes a robust comprehensive DG capacity assessment method considering three-phase power flow modelling and active network management (ANM) techniques. The two-stage adjustable robust optimization is employed to tackle the uncertainties of load demands and DG outputs. With our method, system planners can obtain the maximum penetration level of DGs with their optimal sizing and sitting decisions. Meanwhile, the robust optimal ANM schemes can be generated for each operation time period, including network reconfiguration, on-load-tap-changers regulation, and reactive power compensation. In addition, a three-step optimization algorithm is proposed to enhance the accuracy of DG capacity assessment results. The optimality and robustness of our method are validated via numerical tests on an unbalanced IEEE 33-bus distribution system.

Improved harmony search algorithm for electrical distribution network expansion planning in the presence of distributed generators

Distribution network expansion planning problem is carried out to supply the forecasted demand of distribution network in a certain time in which optimal size and location of distribution substations and feeders should be determined. In this paper, this problem in the presence of different types of distributed generators is addressed. For this purpose, a new approach is applied to model several practical aspects such as pollution, investment and operation costs of distributed generators, purchased power form the main grid, dynamic planning, and uncertainties of load demand and electricity prices. The uncertainties are modeled using the probability distribution function and Monte-Carlo simulation is applied to insert them into the planning problem. Because the problem involves many variables and constraints and is a non-convex and large-scale one, improved harmony search algorithm is used to solve it. To show the effectiveness of the proposed model and solving approach, it is applied to the 9-node and 69-node standard radial distribution networks and a real system of western part of Iranian national 20 kV distribution grid. The results show that the harmony search algorithm can solve the problem in a better manner in comparison with other methods such as genetic algorithm and particle swarm optimization.

A Solution Compatible with Cost-Reliability for Multi-Stage Feeder Routing Problem with Considering Uncertainties

ABSTRACTThis paper proposes a stochastic multistage expansion planning method in order to solve the mid-term and long-term optimal feeder routing problem. Pseudo dynamic behaviour of the network parameters and geographical constraints besides the associated uncertainties of future load demand and market price are incorporated into the method. The proposed method is solved from the DisCo viewpoints using particle swarm optimization algorithm which finally converges to a solution with minimum costs. The proposed cost function is the sum of feeder's installation costs, power losses cost, cost of active purchased power from power market, and reliability costs. Meanwhile, the final solution must satisfy all the operation aspects of power system in acceptable levels. On the other hand, the implementation of the final strategy obtained from the proposed method of this paper, can increase the responsibility of the power system in lower costs. In this regard, distribution system can power its customers with higher power quality in acceptable reliability level and also in lower costs. The proposed method is applied on a large-scale distribution network and its practicability and also its effectiveness are analysed due to the simulation results.

Sliding mode voltage control of boost converters in DC microgrids

This paper deals with the design of a robust decentralized control scheme for voltage regulation in boost-based DC microgrids. The proposed solution consists of the design of a suitable manifold on which voltage regulation is achieved even in presence of unknown load demand and modeling uncertainties. A second order sliding mode control is used to constrain the state of the microgrid to this manifold by generating continuous control inputs that can be used as duty cycles of the power converters. The proposed control scheme has been theoretically analyzed and validated through experiments on a real DC microgrid.

Co-Planning of Demand Response and Distributed Generators in an Active Distribution Network

The integration of renewables is fast-growing, in light of smart grid technology development. As a result, the uncertain nature of renewables and load demand poses significant technical challenges to distribution network (DN) daily operation. To alleviate such issues, price-sensitive demand response and distributed generators can be coordinated to accommodate the renewable energy. However, the investment cost for demand response facilities, i.e., load control switch and advanced metering infrastructure, cannot be ignored, especially when the responsive demand is large. In this paper, an optimal coordinated investment for distributed generator and demand response facilities is proposed, based on a linearized, price-elastic demand response model. To hedge against the uncertainties of renewables and load demand, a two-stage robust investment scheme is proposed, where the investment decisions are optimized in the first stage, and the demand response participation with the coordination of distributed generators is adjusted in the second stage. Simulations on the modified IEEE 33-node and 123-node DN demonstrate the effectiveness of the proposed model.

Probabilistic operation cost minimization of Micro-Grid

In recent years due to the increasing integration of Renewable Energy Sources (RES) into the Micro-Grid (MG), necessity of Battery Energy Storage (BES) has increased quickly and size of BES plays vital role in this regard. Present paper aims to minimize total operation cost of MG in presence of BES of optimal size, by considering uncertainties present in the MG. Here, 2 m point estimate method (PEM) has been applied to model the uncertainties in load demand, market prices and available power from RES in the MG, as it is computationally efficient and reliable probabilistic method. Moreover, Gram-Charlier expansion is used to provide more accurate probability distribution of MG operation cost. Classical techniques may be applied here to solve the problem, but these techniques may increase complexity of the problem and hence may affect the accuracy. As evolvement of soft computing techniques are not restricted by the complexity of system model, therefore Swine Influenza Model Based Optimization with Quarantine (SIMBO-Q) and Whale Optimization Algorithm (WOA) have been applied here to minimize operation cost of MG. Simulation results obtained by SIMBO-Q and WOA prove the effectiveness of the algorithms. Here incorporation of BES of optimum size reduces operation cost of MG effectively.

Evaluating Influence of Variable Renewable Energy Generation on Islanded Microgrid Power Flow

With the proliferation of renewable energy, the uncertainty has challenged the continuous operation of microgrids; thus, it is of importance to tackle uncertainties in power system operation. In this paper, a global sensitivity analysis (GSA) method is proposed to evaluate the influence of uncertainties on the power flow of islanded microgrids (IMGs). First, a probabilistic power flow model for IMGs is established considering the droop-controlled distributed generation units and the uncertainties of renewable energy generation output and load demands. Then, the global sensitivity analysis is introduced to identify important variables that affect IMG power flow. In addition to conventional GSA indices, the Shapley value-based GSA index is designed to evaluate the influence of correlated input variables. Moreover, the sparse polynomial chaos expansion is used to establish the surrogate models of IMG power flow, which improves the efficiency of GSA. Finally, the proposed method is tested on the 33-bus and 69-bus IMG systems, and the simulation results are compared with those considering other methods. The rankings of random input variables that affect IMG power flow are given, and the influence of correlation between different variables is discussed.

Multi-Stage Stochastic Programming With Nonanticipativity Constraints for Expansion of Combined Power and Natural Gas Systems

A novel multi-stage stochastic programming model is proposed for the expansion coplanning of gas and power networks considering the uncertainties in net load demand. Meanwhile, the nonanticipativity constraints are taken into account to guarantee the decisions should only depend on the information of realized uncertainties up to the present stage. Compared with the traditional two-stage stochastic programming model, the proposed multi-stage stochastic programming model yields sequential investment decisions with the uncertainties revealed gradually over time, such that the investment decisions are capable of keeping future options open and can shift from “never be changed” decisions to a flexible “wait and see” decisions. The test on three systems shows the effectiveness of the proposed multi-stage stochastic programming model.

Economic Power Capacity Design of Distributed Energy Resources for Reliable Community Microgrids

Community microgrids are developed within existing power systems by integrating local distributed energy resources (DERs). So power distribution systems can be seamlessly partitioned into community microgrids and end-users could be largely supported when an extreme event happens. However, because of the low inertia characteristics of DERs, their power capacity should be well designed to cover unexpected events and guarantee system reliability. This paper presents a quantitative and qualitative combined methodology for DERs selection, and an economic approach to meet the system reliability requirements. Discrete time Fourier transform (DTFT) and particle swarm optimization (PSO) are employed to obtain the optimal solution, with consideration of load demand and renewable generation uncertainties. In addition, a sensitivity analysis is conducted to show how DERs’ capacity design is impacted by counted portion of the forecasted renewable generation.

Adaptive Robust Transmission Expansion Planning Using Linear Decision Rules

This paper presents a novel model for two-stage adaptive robust transmission expansion planning (AR-TEP) problem considering the uncertainty of future load demand and future wind power production. Linear decision rules (LDRs) are utilized to reformulate the AR-TEP model as a tractable mixed-integer linear programming problem, which can be directly solved by off-the-shelf optimization packages. The proposed LDR-based AR-TEP model is illustrated using the Garver 6-bus test system, the IEEE 24-bus reliability test system, and a 236-bus test system under different conditions and compared with a decomposition-based AR-TEP model that uses primal cutting planes. Also, the robustness of the expansion plans obtained from these two AR-TEP models is evaluated by carrying out an ex-post out-of-sample analysis for different values of the budget of uncertainty. Simulation results demonstrate the effectiveness of the proposed LDR-based AR-TEP model.

Feasibility study, design and implementation of smart polygeneration microgrid at AMU

To confront the challenges associated with the rising of carbon footprint and energy demand, the Renewable Energy Sources (RESs) based smart microgrids are becoming the viable paradigm. In this work, based on cost exploration, greenhouse gas (GHG) emission, and availability of RESs, the feasibility study, design, optimization, and implementation of institutional based smart Polygeneration microgrid is presented. To investigate the most optimal scenario, the detailed analysis of various microgrid topologies in grid connected as well as in off-grid mode with and without the storage system is carried out. The analysis outcome reveals that the solar PV system in grid connected (i.e. G+PV) mode is most preferable. But, the consideration of intermittency as well as the volatile behaviour of the solar PV system forces incorporation of a battery storage system to overcome the fluctuated voltage profile and interrupted power supply, which raises the Cost of Energy (COE), Net Present Cost (NPC), and operating cost to another extent. To obtain the more realistic results, the uncertainty of load demand, as well as RESs, is also taken into account. Further, the comparative analysis of the proposed microgrid topology with existing conventional system is also presented.The result shows that in grid-connected mode, the key cost parameter belongs to PV system (i.e. INR 20.68 million) followed by grid operating cost (i.e. INR7.28 million), battery (i.e. INR 3.11 million) and converter (i.e. INR 2.083 million). While in the off-grid mode the major part of the total system cost is covered by battery storage system (i.e. INR 74.76 million) followed by PV system (i.e. INR 27.96 million) and converter (i.e. 2.385 million). The comparative study shows total system cost associated with proposed microgrid G+PV+B (i.e. INR 33.163 million) is 31.57% of current scenario while the total system cost associated with PV+B (INR 105.036 million) is 95.41% higher than the current scenario. The recommended system mitigated 226.26-kilokg of CO2, 980.93kg of SO2, and 497.73kg of Nitrogen oxides per year.

Optimization of SMES and TCSC using particle swarm optimization for oscillation mitigation in a multi machines power system

Due to the uncertainty of load demand, the stability of power system becomes more insecure. Small signal stability or low-frequency oscillation is one of stability issues which correspond to power transmission between interconnected power systems. To enhance the small signal stability, an additional controller such as energy storage and flexible AC transmission system (FACTS) devices become inevitable. This paper investigates the application of superconducting magnetic energy storage (SMES) and thyristor controlled series compensator (TCSC) to mitigate oscillation in a power system. To get the best parameter values of SMES and TCSC, particle swarm optimization (PSO) is used. The performance of the power system equipped with SMES and TCSC was analyzed through time domain simulations. Three machines (whose power ratings are 71.641, 163, and 85 MW) nine buses power system was used for simulation. From the simulation results, it is concluded that SMES and TCSC can mitigate oscillatory condition on the power system especially in lowering the maximum overshoot up to 0.005 pu in this case. It was also approved that PSO can be used to obtain the optimal parameter of SMES and TCSC.

Generation expansion planning in electricity market considering uncertainty in load demand and presence of strategic GENCOs

This paper presents a new framework to study the generation capacity expansion in a multi-stage horizon in the presence of strategic generation companies (GENCOs). The proposed three-level model is a pool-based network-constrained electricity market that is presented under uncertainty in the predicted load demand modeled by the discrete Markov model. The first level includes decisions related to investment aimed to maximize the total profit of all GENCOs in the planning horizon, while the second level entails decisions related to investment aimed at maximizing the total profit of each GENCO. The third level consists of maximizing social welfare where the power market is cleared. The three-level optimization problem is converted to a one-level problem through an auxiliary mixed integer linear programming (MILP) using primal–dual transformation and Karush–Kuhn–Tucker (KKT) conditions. The efficiency of the proposed framework is examined on MAZANDARAN regional electric company (MREC) transmission network – a part of the Iranian interconnected power system. Simulation results confirm that the proposed framework could be a useful tool for analyzing the behaviour of investment in electricity markets in the presence of strategic GENCOs.

Robust Optimization based Energy Dispatch in Smart Grids Considering Simultaneously Multiple Uncertainties: Load Demands and Energy Prices

Solving the problem of energy dispatch in a heterogeneous complex system is not a trivial task. The problem becomes even more complex considering uncertainties in demands and energy prices. This paper discusses the development of several Economic Model Predictive Control (EMPC) based strategies for solving an energy dispatch problem in a smart micro-grid. The smart grid components are described using control-oriented model approach. Considering uncertainty of load demands and energy prices simultaneously, and using an economic objective function, leads to a non-linear non-convex problem. The technique of using an affine dependent controller is used to convexify the problem. The goal of this research is the development of a controller based on EMPC strategies that tackles both endogenous and exogenous uncertainties, in order to minimize economic costs and guarantee service reliability of the system. The developed strategies have been applied to a hybrid system comprising some photovoltaic (PV) panels, a wind generator, a hydroelectric generator, a diesel generator, and some storage devices interconnected via a DC Bus. Additionally, a comparison between the standard EMPC, and its combination with MPC tracking in single-layer and two-layer approaches was also carried out based on the daily cost of energy production.

Multi-period stochastic security-constrained OPF considering the uncertainty sources of wind power, load demand and equipment unavailability

The uncertainty sources of the intermittent generation and load demand as well as transmission line unavailability threaten the security of power systems. In this paper, to treat these uncertainties, a new stochastic optimal power flow considering the security constraints is proposed. A scenario generation method is also presented to model the uncertainties of wind generations and load demands considering their correlations. In the proposed model, the uncertainties are coped with through combination of optimal here-and-now and wait-and-see decisions. The effectiveness of the proposed model is shown on the well-known IEEE 24-bus test system. Higher effectiveness of the proposed model compared with four deterministic methods and one other stochastic method to determine procured reserve and ‘after-the-fact’ conditions is numerically illustrated. Additionally, the impact of the number of scenarios on the performance of the proposed model is evaluated by means of a sensitivity analysis. It has also been shown that the scenarios generated considering correlations have more smooth variations and can more effectively capture the uncertain behavior of load.

A multi-criteria decision analysis-based approach for dispatch of electric microgrids

This paper presents a decision support system (DSS) for multi-objective dispatch of an electric microgrid considering cost of operation, peak load reduction, and emissions. Discrete compromise programming (DCP) is used as the multi-criteria decision analysis (MCDA) technique for providing the decision support to the distribution system operator (DSO) by ranking various alternatives based on preference of the objectives. The focus of this paper is the application of DCP-based MCDA to select feasible dispatch solutions closest to the preference of the DSO when multiple objectives are considered in the microgrid dispatch. This technique obtains non-dominated solutions in case of conflicting objectives without generating a Pareto front, and hence avoiding prohibitive computational cost. DCP can be used for MCDA in both exact and metaheuristic dispatch algorithms. Uncertainty in renewable energy forecasting and load demand is included through a scenario-based approach by sampling empirical distributions. The dispatch algorithm considers a two hour look-ahead time horizon. Simulations are performed on a notional electric microgrid with diesel generator, solar photovoltaic, and energy storage. The microgrid is based on the IEEE 13-node test feeder and the results are presented.

Probabilistic load flow computation using saddle-point approximation

PurposeThe purpose of this paper is to present a new cumulant-based method, based on the properties of saddle-point approximation (SPA), to solve the probabilistic load flow (PLF) problem for distribution networks with wind generation.Design/methodology/approachThis technique combines cumulant properties with the SPA to improve the analytical approach of PLF calculation. The proposed approach takes into account the load demand and wind generation uncertainties in distribution networks, where a suitable probabilistic model of wind turbine (WT) is used.FindingsThe proposed procedure is applied to IEEE 33-bus distribution test system, and the results are discussed. The output variables, with and without WT connection, are presented for normal and gamma random variables (RVs). The case studies demonstrate that the proposed method gives accurate results with relatively low computational burden even for non-Gaussian probability density functions.Originality/valueThe main contribution of this paper is the use of SPA for the reconstruction of probability density function or cumulative distribution function in the PLF problem. To confirm the validity of the method, results are compared with Monte Carlo simulation and Gram–Charlier expansion results. From the viewpoint of accuracy and computational cost, SPA almost surpasses other approximations for obtaining the cumulative distribution function of the output RVs.

Risk-Limiting Scheduling of Optimal Non-Renewable Power Generation for Systems with Uncertain Power Generation and Load Demand

This study tackles a risk-limiting scheduling problem of non-renewable power generation for large power systems, and addresses potential violations of the security constraints owing to the volatility of renewable power generation and the uncertainty of load demand. To cope with the computational challenge that arises from the probabilistic constraints in the considered problem, a computationally efficient solution algorithm that involves a bisection method, an off-line constructed artificial neural network (ANN) and an on-line point estimation method is proposed and tested on the IEEE 118-bus system. The results of tests and comparisons reveal that the proposed solution algorithm is applicable to large power systems in real time, and the solution obtained herein is much better than the conventional optimal power flow (OPF) solution in obtaining a much higher probability of satisfying the security constraints.