Robust Optimal Planning and Operation of Electrical Energy Systems

Nowadays, variable nature of electrical demand and uncertain behavior of renewable energy resources cause large power systems to operate at their stability boundaries. Hence, occurrence of a contingency may cause an interconnected electricity grid to be faced with cascaded outages, loss of dynamic stability, and a widespread blackout. In recent years, various methods have been presented by scholars to model uncertainties associated with energy market prices, electricity demand, and renewable energy resources. Information gap decision theory (IGDT) is a practical strategy with no need to probability distribution function of uncertain parameter (which is used in probabilistic approaches such as chance-constrained and stochastic programming methods) and membership functions employed in fuzzy algorithms. Hence, this chapter presents a comprehensive review on application of IGDT in power system studies. Moreover, a mathematical framework is provided to model the uncertain parameter using IGDT.

Solving optimization problems with multiple uncertainties has always been a challenging task in different scopes of science. While different approaches have been developed to take advantage of the stochastic space of the problem, these methods are intensively dependent of the probabilistic information of various variables which are not always available. Relying on the severity of the failure, information-gap decision theory (IGDT) is a robust optimization approach which is entirely autonomous from probabilistic information. In this model, a forecasted amount is presumed for each uncertain variable, and the sensitivity of objective functions is analyzed according to the deviation of each of these uncertain parameters from their forecasted value. In this method, two main types of uncertainty set models including energy-bound model and envelope-bound model are handled. In this chapter, these principles and fundamentals of IGDT are described.

Uncertainty has been always one of the challenging issues in power systems. To handle uncertainty, different solutions have been presented such as forecasting technologies. Although forecasting methods have been used to predict parameters with uncertain behavior, forecasts may not be always true; therefore uncertainty modeling is necessary. Uncertainty and its relevant impacts can be analyzed within various energy systems like hub energy systems or so-called multi-energy systems. Hub energy systems containing renewable energy resources should be scheduled to have safe operation under uncertainties of different parameters. In this chapter, by using information gap decision theory (IGDT), a risk-based optimization framework is proposed for optimal operation of hub energy system with considering net price uncertainty. IGDT benefits from two immunity functions determine appropriate operational strategies for robust and optimistic operation of hub energy system against uncertain behavior of net price: robustness and opportunity functions. A mixed-integer nonlinear programming is employed to model robustness and opportunity functions of IGDT. Also, a sample grid-connected hub system is analyzed, and the results are presented to validate the effectiveness of proposed approach. According to the results in the robustness function, hub energy system has become robust against 24.6% more price, while total operation cost of system has been increased 2.8%. Also, hub system has gained 75 $ economic benefit due to the reduction of price in the opportunity function.

In summer, air conditioning systems with high electricity requirement are large consumers, which may lead to load-generation mismatch, cascaded outages, and wide-area blackouts. To avoid them, on-peak electrical demand of air conditioning units can be supplied via renewable energy resources such as solar. By increasing rate of solar radiations and ambient temperature, total cooling demand of residential buildings increases causing a rise in electricity consumption. Hence, use of solar energy for making ice and building space cooling not only reduces CO₂ footprints of fossil fuel-based power generation facilities and electricity usage in residential sector but also increases the coefficient of performance of the ice harvesting cycle. Meanwhile, hourly fluctuations of solar irradiance lead to uncertainty of cooling demand. Therefore, this chapter presents an information gap decision theory (IGDT)-based framework for robust scheduling of an ice storage system, which consists of air source heat pump (ASHP). In ASHP’s cooling cycle, R134a absorbs heat from inside air at evaporator coil and extracts it to ambience, while producing a cooled air with temperature of −8 °C entering a water tank for making ice crystals. Uncertain nature of building cooling load affects optimum operating point of this refrigeration process. Hence, IGDT is implemented on cooling demand to minimize total energy cost of ice storage system and assess both robustness and opportunistic aspects of optimal operating strategies for making two risk-averse and risk-seeker decisions under uncertain operating conditions, respectively.

Recently, electricity utilization is increasing as a result of population growth. Hence, total fuel consumption of thermal units increases with their inefficient and uneconomical load dispatch. Moreover, uncertainty associated with electricity market prices changes daily profit of market operator. For this purpose, information gap decision theory (IGDT) is implemented on a multi-period unit commitment (UC) problem aiming to maximize total profit obtained from selling electricity to consumers. In this chapter, total revenue achieved from selling energy to customers minus total operational cost of thermal power plants is maximized considering ramp-up and ramp-down rates, minimum up- and downtimes, and production capacity of thermal generation stations in UC problem. Moreover, uncertainty of electricity prices is modeled using IGDT to assess how market operator can make a risk-averse decision at low market prices and obtain higher profit in comparison with base problem, which is solved with same prices. In other words, robustness mode of IGDT enables operator to find a good solution for hour-ahead scheduling of thermal units for underestimated energy rates in a way that total profit will not only be larger than a predefined critical profit but also is more than profit of UC problem, which is solved with same market prices and without application of IGDT strategy. Similarly, opportunistic mode of IGDT makes it possible to maximize profit for overestimated electricity prices so that it will not only be more than a target profit but also is larger than profit of UC problem, which is solved with same prices and without implementation of IGDT. To prove IGDT’s robustness and capability in modeling uncertainties, a ten-unit standard system is discussed in two case studies: case 1, without application of IGDT method, and case 2, with implementation of robustness and opportunistic modes of IGDT. It is found that risk-averse and risk-seeker decisions affect total cost, revenue, and expected profit. Both robust and opportunistic strategies cause more profit than that of obtained from solving UC problem, which is solved with underestimated or overestimated prices and without application of IGDT approach.

This chapter aims to study energy management of a renewable energy-based smart home, which contains of photovoltaic (PV) system for supplying a ratio of electrical demand of the considered home. Moreover, the plug-in electric vehicles (PEVs) are considered in obtaining optimal robust scheduling of the studied smart home. The main objective is minimizing the consumer’s bill as a smart home energy management scheduling problem. The controllable appliances are considered including washing machine, water heater, fridge, and electric vehicle. The robust self-scheduling of PV panel installed in the smart home is formulated, and the best suited set point of all suppliers is obtained. Information-gap decision theory (IGDT) is implemented in order to handle the uncertain PV power generation. The optimal robust scheduling of different appliance categories is provided considering economic optimal dispatch of the energy sources.

The purpose of this chapter is investigating the unit commitment problem (UCP) in the presence of renewable energy sources (RESs), energy storage systems (ESSs), and modeling the uncertainties arising in this regard. To achieve this goal, the following subjects are presented in detail. The classic UC formulations, the uncertainties’ impacts on this problem, and the new research efforts in this regard are addressed. Also, the existing optimization methods applied to solve the UCP such as robust optimization (RO), information gap decision theory (IGDT), and Taguchi orthogonal array technique (TOAT) as well as their advantages and drawbacks are described in the next section. Also, the application techniques for modeling the renewable energy sources and energy storage systems are detailed. Various models of UC problem such as thermal power plants and thermal power plants combined with RESs and ESSs considering the most important uncertainties in the inactive networks are presented. The proposed models have been tested on standard case of IEEE, 10 units, and the results are presented.

This chapter introduces an information-gap decision theory (IGDT)-based robust security-constrained unit commitment (SCUC) modeling of coordinated electricity and natural gas networks for managing uncertainty of wind power production. A comprehensive transmission system of natural gas, which delivers natural gas fuel to natural gas-fired plants, is considered. Mixed-integer nonlinear programming (MINLP) has been used for modeling the proposed method in GAMS software. A six-bus system with a six-node gas transmission network is considered to perform numerical tests and evaluate the performance of the introduced model. The obtained results of the study indicate that the natural gas network constraints and the uncertainty of wind energy production have effect on the daily operation cost of natural gas-fired plants and their participation in energy market.

The short-term electrical distribution network (EDN) planning is a strategy that aims to enhance the efficiency of the system and to provide high-quality service to end users. This strategy uses some classical actions and devices to effectively control the system power factor, reactive power, and the voltage magnitude of the network. Over the past decades, trends in this decision-making process have changed due to the integration of modern technologies. Therefore, this chapter investigates a short-term EDN planning problem considering classical investment alternatives with sizing and placement of energy storage systems and distributed generation sources based on renewable energy. Since this optimization problem is inherently a non-convex mixed-integer nonlinear programming model, there is no guarantee in finding the global solution. Therefore, proper linearization techniques are used to find a mixed-integer linear programming (MILP) model. On the other hand, to address the uncertainty in electricity demand and renewable output power, this deterministic MILP model is transformed into a two-stage robust optimization model. To handle this complex trilevel optimization problem, the column-and-constraint generation algorithm (C&CG) is employed in a hierarchical environment. To assess the performance of the proposed approach, a 42-node distribution network is studied under different operational conditions. Numerical results of different case studies show the robustness and applicability of the proposed approach.

This chapter presents an approach for robust microgrid expansion planning (RMEP) considering intermittent power generations (IPGs) and responsive loads (RLs). A framework for RMEP is presented based on stochastic-robust optimization for the optimal presence of active microgrid in the electricity market taking into account the IPGs/RLs and contingency uncertainties. The microgrid topology and power flow constraints are considered. The formulated problem is modelled as a mixed-integer nonlinear programming (MINLP) problem, and a heuristic optimization method is utilized. This model is applied to the 9-bus and 33-bus test systems, and the numerical results assess the effectiveness of the introduced method.

The aim of transmission network expansion planning (TNEP) is providing enough capacity to transfer power from generation section to load centers in a reliable and economically efficient manner. The mission of this problem is identifying where, when, and what type of new transmission lines should be installed in transmission network. In this chapter, the robust TNEP (RTNEP) in the presence of two major uncertainties in power systems (loads and wind power generation) is studied. The robust methods of (a) information-gap decision theory (IGDT), (b) Taguchi’s orthogonal array testing (TOAT), and (c) scenario technique criteria (min-max regret criterion) are proposed and simulated here. Using each of these methods, the robust expansion plan for the modified 6-bus Garver transmission network test system is calculated. The obtained results verify the validity of the mentioned methods in RTNEP. These methods can easily be implemented on any large- and real-scale power system. Furthermore, different uncertainty types can be easily considered in this regard.

The global enhancement in gas-fired units has increased the rate of interdependency between electricity and natural gas networks. Nowadays, electrical systems heavily depend on reliability of gas suppliers to ramp up/ramp down during the on-peak hours and intermittent renewable generation and contingencies. Because of interdependency between electricity and natural gas system, it is imperative to co-optimize such two systems in an integrated scheme for improving the overall efficiency of the whole system and minimizing total investment and operation costs. This work proposes a hybrid robust-stochastic approach, which focuses on coordinated optimal scheduling of natural gas and electricity co-generation by considering market price contingencies. It should be noted that in proposed work, the methodology only considers purchasing power from market. The proposed model minimizes total costs of these two systems simultaneously, where both electrical and natural gas demand uncertainties are considered. On the other hand, a real-time demand response (DR) program is also considered in order to make load profile smoother to avoid technical and operational issues during on-peak hours in the system. In addition, the proposed method is applied on IEEE 24-bus RTS combined with natural gas network, and the simulation results are reported to evaluate the performance of the proposed model. The obtained results show that the proposed hybrid model has more economic efficiency and takes benefits of gas-electricity coordinated scheduling.

The multi-agent system is emerging as an effecting tool for the realization of the smart power distribution system. The smart power distribution system comprises the different scattered entities such as grid supply, renewable generations, customers, etc. In this distributed system, with the use of information and communication technology (ICT) and control systems, multi-agent system can implement different control and management schemes. The renewable generations such as solar photovoltaic (PV), and wind, as well as electrical load are associated with uncertainties. In this chapter, different battery agents are designed to work for scattered distributed battery energy storage system (BESS). These battery agents decide the power exchange for charging and discharging of BESS in order to balance the power mismatch and cater uncertainties in the smart power distribution system. The LQR-based distributed robust optimal control schemes are designed for battery agents to achieve the objective of balancing the power mismatch in the presence of uncertainties. The proposed control schemes show that the effects of uncertainties in power distribution system, in terms of power and energy sharing, are distributed and catered by all energy storage devices as per their energy storing capacities.

The distribution system operator (DSO) needs an optimal day-ahead scheduling (ODAS) for the economic and sustainable supply of electrical energy considering input parameters such as the price of the upstream grid. Next-generation distribution networks or smart distribution networks are the future networks where responsive loads are available. Renewable sources include wind turbines and solar panels have expanded. The presence of electric vehicles and the purchase from the electricity upstream market is provided, and the network can be programmed and controlled through the devices which record and transmit information. In this chapter, a robust optimization (RO) method has been proposed to minimize the cost of ODAS of smart distribution system (SDS) considering load-responsive and renewable energy sources (RESs) such as wind turbine (WT) and nonrenewable sources such as diesel generators (DGs) and battery energy storage system (BESS). The proposed method considers all the technical constraints of the upstream grid and DGs and the utilized BESS. In order to model SDSs, a 33-base IEEE test system has been used in the evaluation of the proposed model. The proposed ODAS concept determines the optimal level of exchange with the upstream network, the production of each dispersed generation unit, and the participation of demand response (DR) programs. It also provides an optimal layout for charging and discharging the BESS. It can be observed that the proposed model has the optimal scheduling capabilities of the SDSs considering the uncertainties of power market price. Moreover, it is observed that the resilient optimization method reduces the cost of network operation and confronts the price of electricity with uncertainty.

Energy systems may be exposed to various uncertainties. In this chapter, in order to deal with severe uncertainty of upstream network price, robust optimization framework is presented to investigate uncertainty-based operation of multi-carrier energy system. Robust optimization technique determines the worst condition within the uncertainty and prepares appropriate strategies to handle such conditions in a way that safe operation of multi-carrier energy system is warrantied. So, a grid-connected multi-carrier energy system containing renewable and nonrenewable local generation units, combined heat and power (CHP), and boiler as well as electrical and thermal storage systems is studied under experiencing uncertainty of upstream network price, and the results declaring effectiveness of proposed technique are presented for comparison. It should be noted that simulations are carried out under general algebraic modeling system (GAMS) software.

Active network management (ANM) is responsible for real-time controlling of active distribution systems based on real-time measurements of the network parameters. The power systems problems with uncertainty parameters have been investigated using different uncertainty handling models. This chapter aims to study the effect of uncertain power market price on optimal scheduling of distribution systems. The robust optimization (RO) method is applied to deal with the uncertainty associated with power market price. The proposed robust optimal scheduling of active distribution systems is studied based on a multi-objective scheme to obtain maximum benefit of distribution company (DisCo) and maximum benefit of distributed generation owner (DGO). Accordingly, the obtained optimal solution by RO method for the scheduling of distribution network prevents the DisCo and DGO from being exposed to low benefit taking undesired deviation of market power prices into account. ε-constraint is implemented on the problem to deal with the multi-objectives, and the best compromise solution is selected using a fuzzy satisfying method. The proposed model has been implemented on a test system to evaluate the performance and verify the practicality of the model.