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

On parameterized stabilization of networked dynamical systems

The problem of stabilizing networked dynamical systems (NDS) in a scalable fashion is addressed. As a first contribution, an example is provided to demonstrate that the standard NDS stabilization methods can fail even for simple linear time-invariant systems. Then, a solution to this issue is proposed, in which the controller synthesis is decentralized via a set of parameterized local functions. The corresponding stability conditions allow for max-type construction of a Lyapunov function (LF) for the full closed-loop system, while neither of the local functions is required to be a local LF. It is shown that the provided approach is non-conservative in the sense that it is able to find a stabilizing control law for the motivating example network, whereas state-of-the-art non-centralized Lyapunov techniques fail. For input-affine NDS and quadratic parameterized local functions, the combined LF synthesis and control scheme can be formulated as a set of low-complexity semi-definite programs that are solved on-line, in a receding horizon manner

Distributed, price-based control approach to market-based operation of future power systems

In this paper we present, discuss and illustrate on examples the price-based control paradigm as a suitable approach to solve some of the challenging problems facing future, market-based power systems. It is illustrated how global objectives and constraints are optimally translated into time-varying prices. The real-time varying price signals are guaranteed to adequately reflect the state of the physical system and present the signals that optimally shape, coordinate and synchronize local, profit driven behaviors of producers/consumers to mutually reinforce and guarantee global objectives and constraints. As an illustrative example, the real-time price-based power balance control with congestion management is presented

Systematic design of market-based balancing arrangements for deregulated power systems: An asynchronous solution

In the deregulated electrical energy market, network operators have to provide market participants with appropriate incentives to guarantee stable operation of the power grid. We demonstrate that the current synchronous energy-based market and incentive system do not necessarily induce power exchange profiles that contribute to grid stability and security of supply. State-of-the-art solutions for tackling the inconsistency between energy-based market mechanisms and power-related balancing objectives can decrease freedom of trade or increase market complexity. This paper provides an alternative scheduling concept as a means to overcome this issue, which relies on asynchronous settlement of energy transactions. We show that in this way, grid operation can become more robust and the strain on balancing reserves can be reduced considerably

On-line identification of vehicle fuel consumption for energy and emission management : an LTP system analysis

An Energy Management (EM) system traditionally relies on (quasi) static maps offering efficiency parameters of the vehicle powertrain. During a vehicle's life span, these maps lose validity, so optimal performance for EM is not assured. This paper presents a proof-of-concept for a novel measurement system, estimating important engine and generator characteristics on-line during driving. The generator applies a small excitation signal to the combustion engine and by means of correlation techniques and feedback control, the incremental fuel cost for generating electric power is estimated. This information is very relevant for EM in Hybrid Electric Vehicles. No additional sensors (e.g. torque estimators) are needed. Under mild assumptions it is shown that the measurement system satisfies a Linear Time Periodic (LTP) System. Harmonic analysis as well as Floquet Theory are used to analyze performance and stability criteria. Simulation results support this analysis and demonstrate good noise rejection of the system

Congestion management in the deregulated electricity market: An assessment of locational pricing, redispatch and regulation

We analyze the fundamental differences between locational pricing and redispatch-based congestion management, followed by an assessment of their effects on grid operation and market efficiency. It is indicated that although optimal nodal pricing and congestion redispatch can provide equal results in terms of power injections, they are not equivalent in terms of short-run social welfare. Moreover, a modeling framework is presented to decouple and analyze the effects of transmission system operator/regulator and prosumer behavior on energy market efficiency in a transparent fashion. All results are illustrated on the basis of case studies for the IEEE 39-bus New England test network

Congestion management in the deregulated electricity market: an assessment of locational pricing, redispatch and regulation

We analyze the fundamental differences between locational pricing and redispatch-based congestion management, followed by an assessment of their effects on grid operation and market efficiency. It is indicated that although optimal nodal pricing and congestion redispatch can provide equal results in terms of power injections, they are not equivalent in terms of short-run social welfare. Moreover, a modeling framework is presented to decouple and analyze the effects of transmission system operator/regulator and prosumer behavior on energy market efficiency in a transparent fashion. All results are illustrated on the basis of case studies for the IEEE 39-bus New England test network

Short Fiber Reinforced Thermoplastics: Prediction of Stiffness in Injection Molded PS-PPO Blends

The prediction of stiffness in short fiber reinforced thermoplastics is stud ied as a function of fiber length using injection molded blends of PS and PPO. The theoret ical models for predicting composite stiffness are reviewed. The results are first compared with the theoretical models advanced for uniaxially aligned composites. These models predict higher than experimental values. However, agreement between the predictions and experimental values improves when the effect of fiber orientation distribution in the injec tion molded samples is taken into account and as the ductility (or the PPO content) of the matrix increases. Cox's model when used with the "laminate analogy" gives the closest prediction to the experimental stiffness. Reinforcement efficiency factor for stiffness is a strong function of retained fiber lengths. The dependence of composite stiffness on the matrix ductility and the effects of compatibility on the mechanical properties of PS-PPO blend system are also discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68613/2/10.1177_089270579100400205.pd