P. R. Bijwe

Real-Time Economic Dispatch Considering Renewable Power Generation Variability and Uncertainty Over Scheduling Period

Real-time economic dispatch (RTED) is performed every 5-15 min with the static snapshot forecast data. During the period between two consecutive schedules, generators participate in managing power imbalance, based on participation factors (PFs) from previous economic dispatch (ED). In modern power systems with considerable renewable energy sources that have high variability, this conventional approach may not adequately accommodate the economic implication of the said variability. This paper proposes the evaluation of “best-fit” PFs by taking into account the minute-to-minute variability of solar, wind, and load demand, for a scheduling period. Since “best-fit” PFs are evaluated only once, i.e., at the start of scheduling interval, the dimensionality of optimization problem remains the same as that of conventional approach. The proposed approach is suggested for sequential and dynamic variants. Results for two test systems have been obtained to verify the benefit of the proposed approach.

Joint Energy and Spinning Reserve Market Clearing Incorporating Wind Power and Load Forecast Uncertainties

This paper proposes an energy and spinning reserve market clearing (ESRMC) mechanism for wind-thermal power system, considering uncertainties in wind power and load forecasts. Two different market models for the ESRMC are proposed. One model includes reserve offers from the conventional thermal generators, and the other includes reserve offers from both thermal generators and demand/consumers. The stochastic behavior of wind speed and wind power is represented by the Weibull probability density function (pdf), and that of the load is represented by a normal pdf. This paper considers two objectives: total cost minimization and the system-risk-level minimization. The first objective includes the cost of energy provided by thermal and wind generators, and the cost of reserves provided by thermal generators and loads. It also includes costs due to overestimation and underestimation of available wind power and load demand. The system risk level is considered as another objective as wind power is highly uncertain. Multiobjective Strength Pareto Evolutionary Algorithm 2+ (SPEA 2+) has been used to solve the ESRMC problem. The results of the IEEE 30 bus system demonstrate the utility of the proposed approach.

Optimal Posturing in Day-Ahead Market Clearing for Uncertainties Considering Anticipated Real-Time Adjustment Costs

This paper proposes a market-clearing mechanism which explicitly takes into account the impact of uncertainties in wind power generation and load forecast. Since market clearing is a multisettlement process-day ahead and real time (RT), a strategy is proposed, which provides best-fit day-ahead (DA) schedule, which minimizes the twin (both DA and RT adjustment) costs/maximizes social welfare, under all possible scenarios in RT. This two-stage optimization strategy consists of a genetic algorithm (GA) based DA market clearing and a two-point estimate-based probabilistic RT optimal power flow (OPF). The former generates sample schedules, while the latter provides mean adjustment costs. Two commonly employed standard market practices to incorporate wind energy into wholesale electricity markets have been presented. The results for a sample system with GA and two-point estimate OPF, and GA and Monte Carlo simulation have been obtained to ascertain the effectiveness of the proposed method.

Transmission network expansion planning with adaptive particle swarm optimization

Transmission network expansion planning is a very important problem to power system. The problem is very complex due to its mixed integer, non linear, non convex nature. Meta heuristic techniques are known to provide good/ optimal solutions for such type of combinatorial problems. In light of above, this paper presents an adaptive particle swarm optimization algorithm for transmission network expansion planning Results for IEEE 24 bus system are taken to confirm the potential of the proposed algorithm.

Co-optimization of Energy and Demand-Side Reserves in Day-Ahead Electricity Markets

Abstract This paper presents a new multi-objective day-ahead market clearing (DAMC) mechanism with demand-side reserves/demand response (DR) offers, considering realistic voltage-dependent load modeling. The paper proposes objectives such as social welfare maximization (SWM) including demand-side reserves, and load served error (LSE) minimization. In this paper, energy and demand-side reserves are cleared simultaneously through co-optimization process. The paper clearly brings out the unsuitability of conventional SWM for DAMC in the presence of voltage-dependent loads, due to reduction of load served (LS). Under such circumstances multi-objective DAMC with DR offers is essential. Multi-objective Strength Pareto Evolutionary Algorithm 2+ (SPEA 2+) has been used to solve the optimization problem. The effectiveness of the proposed scheme is confirmed with results obtained from IEEE 30 bus system.

Multi-Objective Day-Ahead Real Power Market Clearing with Voltage Dependent Load Models

In this paper, we investigate the influence of voltage dependent load models on day ahead real power market clearing (DA-RPMC). The investigations clearly bring out the unsuitability of conventional single objectives such as production cost minimization (PCM) (or social welfare maximization (SWM)), due to reduction of load served. Hence, the multi-objective optimization is essential in this context. The paper proposes several objectives such as production cost minimization (PCM) (or social welfare maximization (SWM)), load served maximization (LSM), and Voltage Stability Enhancement Index (VSEI); which can be judiciously combined as per the needs of the operating condition. Multi-objective Strength Pareto Evolutionary Algorithm (SPEA) has been used to solve the DA-RPMC problem. The effectiveness of the proposed approach is tested on IEEE 30 bus system and the detailed simulation studies have been carried out by considering different operating conditions with voltage dependent load modeling.

A combination of heuristic and bacteria foraging-differential evolution algorithm for transmission network expansion planning with security constraints

Transmission network expansion planning (TNEP) is an important component of power system planning. Its task is to determine the optimal set of transmission lines to be constructed such that the cost of expansion plan is minimum and no network constraints are violated during the planning horizon. The problem is very complex due to large number of options to be analysed and the discrete nature of the optimization variables. Hence, more efficient and robust techniques are required to solve this complex problem. This paper presents a new hybrid approach for TNEP with security constraints, where first the solution is obtained very quickly with a new promising heuristic method, which is used as a starting point for the proposed metaheuristic approach known as bacteria foraging differential evolution algorithm (BF-DEA). The heuristic method used for generating the initial solution is based on a DC power flow based compensation approach to simulate single/double line modifications arising out of a candidate line addition and an outage of other line. This method can be used to quickly obtain a suboptimal/optimal transmission network expansion plan. One of the difficulties with metaheuristic methods is the possibility of premature convergence to a nonoptimal solution. The worst part is that in many situations we do not even know as to how close/far the optimal solution obtained is from the global optimum one. The plan obtained with the heuristic method provides an upper bound on the solution obtained with BF-DEA. The hybrid method thus ensures that BF-DEA will provide a solution which is much closer to the global optimum. Results for two sample systems demonstrate the potential of the proposed scheme.

Transmission Network Expansion Planning with Security Constraints and Uncertainty in Load Specifications

Transmission network expansion planning is a very critical problem due to not only the huge investment cost involved, but also the associated security issues. Any long range planning problem is confronted with the challenge of non-statistical uncertainty in the data. Although large number of papers have been published in this area, the efforts to tackle the above mentioned security and uncertainty issues have been relatively very few, due to the formidable complexity involved. This paper tries to bridge this gap by proposing a technique to tackle these problems. Boundary DC power flow is used to ascertain the worst power flows on the lines. A simple basic binary Genetic algorithm is used to solve the optimization problem as an illustration. Results for two sample test systems have been obtained to demonstrate the potential of the proposed method.

Differential evolution-based efficient multi-objective optimal power flow

This paper proposes a novel-efficient evolutionary-based multi-objective optimization (MOO) approaches for solving the optimal power flow (OPF) problem using the concept of incremental load flow model based on sensitivities and some heuristics. This paper is useful in robust decision-making for the system operator. The main disadvantage of meta-heuristic-based MOO approach is computationally burdensome. The motivation of this paper is to overcome this drawback. By using the proposed efficient MOO approach, the number of load flows to be performed is reduced substantially, resulting to the solution speed up. Here, three objective functions, i.e., generator fuel cost minimization, loss minimization, and L index minimization are considered. The proposed approach can effectively handle the complex non-linearities, discontinuities, discrete variables, and multiple objectives. The potential and suitability of the proposed efficient MOO approach is tested on the IEEE 30 bus system. The results obtained with the proposed efficient MOO approach are also compared with the meta-heuristic-based non-dominated sorting genetic algorithm-2 (NSGA-II) technique. In this paper, the proposed efficient MOO approach is implemented using the differential evolutionary (DE) algorithm. However, it is a generic one and can be implemented with any type of evolutionary algorithm.

Multi-Objective Optimal Power Flow Using Efficient Evolutionary Algorithm

Abstract A novel efficient multi-objective optimization (MOO) technique for solving the optimal power flow (OPF) problem has been proposed in this paper. In this efficient approach uses the concept of incremental power flow model based on sensitivities and some heuristics. The proposed approach is designed to overcome the main drawback of conventional MOO approach, i. e., the excess computational time. In the present paper, three objective functions i. e., generation cost, system losses and voltage stability index are considered. In the proposed efficient MOO approach, the first half of the specified number of Pareto optimal solutions are obtained by optimizing the fuel cost objective while considering other objective (i. e., system loss or voltage stability index) as constraint while the second half is obtained in a vice versa manner. After obtaining the total Pareto optimal solutions, they are sorted in the ascending order of fuel cost objective function value obtained for each solution leads to the Pareto optimal front. The proposed efficient approach is implemented using the differential evolution (DE) algorithm. The proposed efficient MOO approach can effectively handle the complex non-linearities, discrete variables, discontinuities and multiple objectives. The effectiveness of the proposed approach is tested on standard IEEE 30 bus test system. The simulation studies show that the Pareto optimal solutions obtained with proposed efficient MOO approach are diverse and well distributed over the entire Pareto optimal front. The simulation results indicate that the execution speed of proposed efficient MOO approach is approximately 10 times faster than the conventional evolutionary based MOO approaches.