Shahab Bahrami

A Decentralized Electricity Market Scheme Enabling Demand Response Deployment

In smart grid, demand response (DR) programs can be deployed to encourage electricity consumers towards scheduling their controllable demands to off-peak periods. Motivating the consumers to participate in a DR program is a challenging task, as they experience a confidential discomfort cost by modifying their load demand from the desirable pattern to the scheduled pattern. Meanwhile, to balance the load and generation, the independent system operator (ISO) requires to motivate the suppliers towards modifying their generation profiles to follow the changes in the load demands. Additionally, to protect the entities’ privacy, the ISO needs to apply an effective well-designed pricing scheme. In this paper, we focus on proposing a decentralized DR framework considering the operating constraints of the grid. In our proposed framework, each individual entity responds to the control signals called conjectured prices from the ISO to modify its demand or generation profile with the locally-available information. We formulate the centralized problem of the ISO that jointly minimizes the suppliers’ generation cost and the consumers’ discomfort cost. We also discuss how the ISO determines the conjectured prices to motivate the entities toward an operating point that coincides with the solution to the centralized problem. The performance of the proposed algorithm is evaluated on a modified IEEE 14-bus in reducing the suppliers’ and consumers’ cost, as well as the transmission lines congestion.

An Online Learning Algorithm for Demand Response in Smart Grid

Demand response program with real-time pricing can encourage electricity users toward scheduling their energy usage to off-peak hours. A user needs to schedule the energy usage of his appliances in an online manner since he may not know the energy prices and the demand of his appliances ahead of time. In this paper, we study the users’ long-term load scheduling problem and model the changes of the price information and load demand as a Markov decision process, which enables us to capture the interactions among users as a partially observable stochastic game. To make the problem tractable, we approximate the users’ optimal scheduling policy by the Markov perfect equilibrium (MPE) of a fully observable stochastic game with incomplete information. We develop an online load scheduling learning (LSL) algorithm based on the actor-critic method to determine the users’ MPE policy. When compared with the benchmark of not performing demand response, simulation results show that the LSL algorithm can reduce the expected cost of users and the peak-to-average ratio in the aggregate load by 28% and 13%, respectively. When compared with the short-term scheduling policies, the users with the long-term policies can reduce their expected cost by 17%.

Optimal power flow for AC-DC networks

The presence of distributed generators with DC output power and the advancement in power electronics devices have motivated system planners and grid operators to move towards integration of DC microgrids into conventional AC grid. In this paper, we address the optimal power flow (OPF) problem in AC-DC networks. The goal of the AC-DC OPF problem is to jointly minimize the total electricity generation cost of the network and the cost of transferring active power from the AC grid to the DC microgrids. The optimization problem is subject to the power flow constraints, voltage magnitude limits, the limits of the network power lines, and the limits imposed by the power ratings of AC-DC power electronic converters. The formulated AC-DC OPF problem is shown to be nonlinear. We propose an approach to reformulate the AC-DC OPF problem as an equivalent traditional AC OPF problem. Due to the non-convexity of the AC OPF problem, we use convex relaxation techniques and transform the problem to a semidefinite program (SDP). We show that the relaxation gap is zero. That is the optimal solution of the non-convex and the transformed convex problems are equal. Simulation studies are performed on an IEEE 14-bus system connected to two 9-bus DC microgrids. We show that the sufficient condition for the zero relaxation gap is satisfied, and the proposed SDP approach enables us to find the global optimal solution efficiently.

A Decentralized Energy Management Framework for Energy Hubs in Dynamic Pricing Markets

With increasing the presence of co- and tri-generating units, energy hub operators are encouraged to optimally schedule the available energy resources in an economic way. This scheduling needs to be run in an online manner due to the uncertainties in energy prices and demands. In this paper, the real-time scheduling problem of energy hubs is formulated in a dynamic pricing market. The energy hubs interaction is modeled as an exact potential game to optimize each energy hub’s payments to the electricity and gas utilities, as well as the customers’ satisfaction from energy consumption. The potential game approach enables us to study the existence and uniqueness of the Nash equilibrium and to design an online distributed algorithm to achieve that equilibrium. Simulations results show that the proposed algorithm can increase the energy hubs’ average payoff by 18.8%. Furthermore, energy service companies can improve the technical performance of energy networks by reducing the peak-to-average ratio in the electricity and natural gas by 27% and 7%, respectively. When compared with a centralized approach with the objective of social welfare, the proposed algorithm has a significantly lower running time at the cost of lower social welfare.

Semidefinite Relaxation of Optimal Power Flow for AC–DC Grids

The proliferation of technologies operating on dc power has motivated the system planners toward integration of dc and ac grids. The optimal power flow (OPF) analysis is widely used to determine the economically efficient operating points of the power grids. The OPF problem in ac-dc grids is a non-convex optimization problem due to the nonlinear power flow equations and the operating constraints imposed by the ac-dc converters. In this paper, we study the OPF problem in ac-dc grids to address the non-convexity of the problem. The objective of the ac-dc OPF problem is to jointly minimize the generation cost and the losses on the lines and converters. The optimization problem is subject to the ac and dc power flow constraints, the limits of the voltages and line flows, and the operating limits of the converters. We use convex relaxation techniques and transform the problem to a semidefinite program. We derive a sufficient condition for zero relaxation gap to obtain the global optimal solution. Simulations are performed on an IEEE 118-bus test system connected to sample dc grids. We show that the zero relaxation gap condition holds for the case study and the global optimal solution can be obtained.

An Input-to-State Stability Approach to Inertial Frequency Response Analysis of Doubly-Fed Induction Generator-Based Wind Turbines

Due to the proliferation of wind turbines in power networks, participation of doubly-fed induction generator (DFIG)-based wind turbines in the frequency regulation task is attracting more attention during recent decades. It is a challenge to design an effective DFIGs auxiliary frequency controller, since back-to-back converters used in DFIG make the possibility of large deviations in current and speed of rotor during frequency support period. Hence, it is necessary to use exact expression of DFIGs output power in the frequency-related studies. This paper addresses this challenge by developing a nonlinear dynamic model for the DFIGs output power integrated into the dynamic model of power grid. A state feedback controller is proposed by considering whether the DFIGs participate in the frequency regulation task or not. The stability of overall system is studied using a nonlinear control tool, namely, the input-to-state stability (ISS). We provide the sufficient conditions for the controllers parameters to guarantee the power grid with wind speed and load variations to be ISS. The controller is then embedded in the DFIGs detailed model and simulations are performed to evaluate its performance. Negligible recovery period, higher output power, and smoother frequency response are observed by using the proposed controller.

Modification of DFIG's Active Power Control Loop for Speed Control Enhancement and Inertial Frequency Response

This paper proposes a fuzzy-based speed controller for the doubly fed induction generator (DFIG)-based wind turbines with the rotor speed and wind speed inputs. The controller parameters are optimized using the particle swarm optimization algorithm. To accelerate tracking the maximum power point trajectory, the conventional controller is augmented with a feed-forward compensator, which uses the wind speed input and includes a high-pass filter. The proposed combined speed controller is robust against wind measurement errors and as the accuracy of anemometers increases the speed regulation tends toward the ideal controller. The cutoff frequency of the applied filter is determined considering a compromise between the sensitivity to measurement errors and speed of regulation process. We also design an auxiliary frequency controller to equip the DFIGs with an inertial frequency response. In the proposed controller, two important constraints are taken into account: the feasible rotor speed range during the injection period, and the minimum time to recover the DFIGs speed. The impacts of the proposed controllers are evaluated through extensive time-domain simulations on an IEEE 9-bus test system using the DIgSILENT/PowerFactory software. Results confirm the effectiveness of the proposed controllers in serious transients and load disturbances.

Power dispatch and load control with generation uncertainty

In this paper, we focus on the problem of joint load scheduling and generation management to better match supply and demand. We formulate an optimization problem to jointly minimize the generation cost and discomfort cost of the users subject to the voltage and power balance equations for the equivalent circuit of the power system. The optimal power flow (OPF) equations are solved using semidefinite programming (SDP) relaxation technique. In our system model, we assume that users can exploit renewable energy resources (RERs). RERs are random in nature and may cause voltage variations in different nodes of the system. To minimize the risk of having high voltage values, a barrier term is added to the objective function. This term is calculated based on the concept of conditional value-at-risk (CVaR). Simulation results show that compared to the case where there is no control over the load, our proposed algorithm reduces the generation cost by better matching the generation and demand. Moreover, the proposed algorithm reduces the voltage variations at different nodes of the system.

Decomposition Methods for Distributed Optimal Power Flow: Panorama and Case Studies of the DC Model

Abstract Efficient and well-designed optimization tools are necessary to determine an economically efficient operating point of the power systems in a timely fashion, while maintaining the generation-load balance in the system. In this regard, the optimal power flow (OPF) analysis is widely used by system operators to minimize the grid-wide generation cost and active power losses subject to the physical and operational constraints of the underlying network. The OPF problem can suffer from high computational complexity in large power networks. Hence, centralized optimization techniques are not the proper choice to deal with large-scale OPF problems with thousands of decision variables and constraints. Moreover, centralized approaches require real-time information on the decision-making parameters of the generators and load demands, which are not generally available to the system operators due to privacy concerns. In this chapter, we focus on distributed/decentralized approaches to solve the OPF problem in a power system. To this end, we take advantage of the widely used DC power flow formulation, which is a simplified power flow model with an acceptable approximation for transmission networks. We first review the state-of-the-art decomposition techniques to address the scalability of the OPF analysis in the general case. Then, we discuss the application of the Lagrangian relaxation (LR) decomposition and augmented LR in designing decentralized OPF algorithms for the DC model. We also introduce a consensus-based distributed optimization method to deal with the OPF problem.