Distributed control of deregulated electrical power networks

A prerequisite for reliable operation of electrical power networks is that supply and demand are balanced at all time, as efficient ways for storing large amounts of electrical energy are scarce. Balancing is challenging, however, due to the power system's dimensions and complexity, the low controllability and predictability of demand, and due to strict physical and security limitations, such as finitely fast generator dynamics and finite transmission-line capacities. The need for efficient and secure balancing arrangements is growing stronger with the increasing integration of distributed generation (DG), the ongoing deregulation of production and consumption of electrical energy, and thus, also the provision of many of the ancillary services that are essential for network stability. DG is mostly based on renewable, intermittent sources such as wind and sun, and consequently, it is associated with a much larger uncertainty in supply than conventional, centralized generation. Moreover, with the emergence of deregulated energy markets as core operational mechanism, the prime goal of power system operation is shifted from centralized minimization of costs to the maximization of individual profit by a large number of competing, autonomous market agents. The main objective of this thesis is to investigate the control-technical possibilities for ensuring efficient, reliable and stable operation of deregulated and badly predictable electrical power networks. Its contributions cover aspects of power system operation on a time scale ranging from day-ahead trading of electrical energy to second-based load-frequency control. As a first contribution, we identify the maximization of security of supply and market efficiency as the two main, yet conflicting objectives of power system operation. Special attention is paid to congestion management, which is an aspect of power system operation where the tension between reliability and efficiency is particularly apparent. More specifically, the differences between locational pricing and cost-based congestion redispatch are analyzed, followed by an assessment of their effects on grid operation. Next, we demonstrate that the current synchronous, energy-based market and incentive system does not necessarily motivate producers to exchange power profiles with the electricity grid that contribute to network stability and security of supply. The thesis provides an alternative production scheduling concept as a means to overcome this issue, which relies on standard market arrangements, but settles energy transactions in an asynchronous way. Theoretical analysis and simulation results illustrate that by adopting this method, scheduling efficiency is improved and the strain on balancing reserves can be reduced considerably. A major part of this thesis is dedicated to real-time, i.e., closed-loop, balancing or load-frequency control. With the increasing share of badly predictable DG, there is a growing need for efficient balancing mechanisms that can account for generator and transmission constraints during the operational day. A promising candidate solution is model predictive control (MPC). Because the large dimensions and complexity of electrical power networks hamper a standard, centralized implementation of MPC, we evaluate a number of scalable alternatives, in which the overall control action is computed by a set of local predictive control laws, instead. The extent of inter-controller communication is shown to be positively correlated with prediction accuracy and, thus, attainable closed-loop performance. Iterative, system-wide communication/coordination is usually not feasible for large networks, however, and consequently, Pareto-optimal performance and coupled-constraint handling are currently out of reach. This also hampers the application of standard cost-based stabilization schemes, in which closed-loop stability is attained via monotonic convergence of a single, optimal system-wide performance cost. Motivated by the observations regarding non-centralized MPC, the focus is then shifted to distributed control methods for networks of interconnected dynamical systems, with power systems as particular field of application, that can ensure stability based on local model and state information only. First, we propose a non-centralized, constraint-based stabilization scheme, in which the set of stabilizing control actions is specified via separable convergence conditions for a collection of a-priori synthesized structured max-control Lyapunov functions (max-CLFs). The method is shown to be non-conservative, in the sense that non-monotonic convergence of the structured functions along closed-loop trajectories is allowed, whereas their construction establishes the existence of a control Lyapunov function, and thus, stability, for the full, interconnected dynamics. Then, an alternative method is provided in which also the demand for a monotonically converging full-system CLF is relaxed while retaining the stability certificate. The conditions are embedded in an almost-decentralized Lyapunov-based MPC scheme, in which the local control laws rely on neighbor-to-neighbor communication only. Secondly, a generalized theorem and example system are provided to show that stabilization methods that rely on the off-line synthesis of fixed quadratic storage functions (SFs) fail for even the simplest of linear, time-invariant networks, if they contain one or more subsystems that are not stable under decoupled operation. This may also impede the application of max-CLF control. As key contribution of this thesis, to solve this issue, we endow the storage functions with a finite set of state-dependent parameters. Max-type convergence conditions are employed to construct a Lyapunov function for the full network, whereas monotonic convergence of the individual SFs is not required. The merit of the provided approach is that the storage functions can be constructed during operation, i.e., along a closed-loop trajectory, thus removing the impediment of centralized, off-line LF synthesis associated with fixed-parameter SFs. It is shown that parameterized-SF synthesis conditions can be efficiently exploited to obtain a scalable, trajectory-dependent control scheme that relies on non-iterative neighbor-to-neighbor communication only. For input-affine network dynamics and quadratic storage functions, the procedure can be implemented by solving a single semi-definite program per node and sampling instant, in a receding horizon fashion. Moreover, by interpolating a collection of so-obtained input trajectories, a low-complexity explicit control law for linear, time-invariant systems is obtained that extends the trajectory-specific convergence property to a much stronger guarantee of closed-loop asymptotic stability for a particular set of initial conditions. Finally, we consider the application of max-CLF and parameterized SFs for real-time balancing in multimachine electrical power networks. Given that generators are operated by competitive, profit-driven market agents, the stabilization scheme is extended with the competitive optimization of a set of arbitrarily chosen, local performance cost functions over a finite, receding prediction horizon. The suitability of the distributed Lyapunov-based predictive control and parameterized storage function algorithms is evaluated by simulating them in closed-loop with the 7-machine CIGRÉ benchmark system. The thesis concludes by summarizing the main contributions, followed by ideas for future research

Distributed predictive control of the 7-Machine CIGRÉ power system

Stable operation of the future electrical power system will require efficient techniques for supply-demand balancing, i.e., load-frequency control, due to liberalization of electrical energy production. Currently, there is a growing interest for asymptotically stabilizing the grid frequency via model predictive control (MPC). However, the centralized implementation of standard MPC is hampered by the scale and complexity of power networks. In this paper we therefore evaluate the suitability of a scalable, distributed Lyapunovbased MPC algorithm as an alternative to conventional balancing techniques. The approach is particularly suited for largescale power networks, as it employs only local information and limited communication between directly-coupled generator buses to provide a stabilizing control action. The effectiveness of the distributed control scheme is assessed by simulating it in closed-loop with the 7-machine CIGRE benchmark system

A Comprehensive Review on Constant Power Loads Compensation Techniques

Microgrid, because of its advantages over conventional utility grids, is a prudent approach to implement renewable resource-based electricity generation. Despite its advantages, microgrid has to operate with a significant proportion of constant power loads that exhibit negative incremental impedance and thus cause serious instability in the system. In this paper, a comprehensive review is presented on accomplished research work on stabilization of dc and ac microgrid. After reviewing these, microgrid system stabilization techniques are classified with required discussions. As found out in this paper, the stabilization techniques can basically be classified as compensation done: 1) at feeder side; 2) by adding intermediate circuitry; and 3) at load side. Finally, after analyzing the merits and drawbacks of each generalized technique, several infographics are presented to highlight the key findings of this paper

Decentralized Optimal Control With Application In Power System

An output-feedback decentralized optimal controller is proposed for power systems with renewable energy penetration. Renewable energy source is modeled similar to the classical generator model and is equipped with the unified power flow controller (UPFC). The transient performance of power system is considered and stability of the dynamical states are investigated. An offline decentralized optimal controller is designed that utilizes only the local states. The network comprises conventional synchronous generators as well as renewable sources with inverter equipped with UPFC. Subsequently, the optimal decentralized controller is compared to the initial stabilizing controller used to obtain the optimal controller. An online decentralized optimal controller is designed for discrete-time system. Two neuro networks are utilized to estimate value function and optimal control strategy. Furthermore, a novel observer-based decentralized optimal controller is developed on small scale discrete-time power system. The system is trained followed by least square rules and successive approximation. Simulation results on IEEE 14-, 30-, and 118-bus power system benchmarks shows satisfactory performance of the online decentralized controller. And also, simulation results demonstrate great performance of the observer and the optimal controller compare to the centralized optimal controller

Network Synchronization and Control Based on Inverse Optimality : A Study of Inverter-Based Power Generation

This thesis dwells upon the synthesis of system-theoretical tools to understand and control the behavior of nonlinear networked systems. This work is at the crossroads of three topics: synchronization in coupled high-order oscillators, inverse optimal control and the application of inverter-based power systems. The control and stability of power systems leverages the theoretical results obtained for synchronization in coupled high-order oscillators and inverse optimal control.First, we study the dynamics of coupled high-order nonlinear oscillators. These are characterized by their rotational invariance, meaning that their dynamics remain unchanged following a static shift of their angles. We provide sufficient conditions for local frequency synchronization based on both direct, indirect Lyapunov methods and center manifold theory. Second, we study inverse optimal control problems, embedded in networked settings. In this framework, we depart from a given stabilizing control law, with an associated control Lyapunov function and reverse engineer the cost functional to guarantee the optimality of the controller. In this way, inverse optimal control generates a whole family of optimal controllers corresponding to different cost functions. This provides analytically explicit and numerically feasible solutions in closed-form. This approach circumvents the complexity of solving partial differential equations descending from dynamic programming and Bellman's principle of optimality. We show this to be the case also in the presence of disturbances in the dynamics and the cost. In networks, the controller obtained from inverse optimal control has a topological structure (e.g., it is distributed) and thus feasible for implementation. The tuning is analogous to that of linear quadratic regulators.Third, motivated by the pressing changes witnessed by the electrical grid toward renewable energy generation, we consider power system stability and control as the main application of this thesis. In particular, we apply our theoretical findings to study a network of power electronic inverters. We first propose a controller we term the matching controller, a control strategy that, based on DC voltage measurements, endows the inverters with an oscillatory behavior at a common desired frequency. In closed-loop with the matching control, inverters can be considered as nonlinear oscillators. Our study of the dynamics of nonlinear oscillator network provides feasible physical conditions that ask for damping on DC- and AC-side of each converter, that are sufficient for system-wide frequency synchronization.Furthermore, we showcase the usefulness of inverse optimal control for inverter-based generation at two different settings to synthesize robust angle controllers with respect to common disturbances in the grid and provable stability guarantees. All the controllers proposed in this thesis, provide the electrical grid with important services, namely power support whenever needed, as well as power sharing among all inverters