Price-based optimal control of electrical power systems

During the past decade, electrical power systems have been going through some major restructuring processes. From monopolistic, highly regulated and one utility controlled operation, a system is being restructured to include many parties competing for energy production and consumption, and for provision of many of the ancillary services necessary for system operation. With the emergence of competitive markets as central operational mechanisms, the prime operational objective has shifted from a centralized, utility cost minimization objective to decentralized, profit maximization objectives of competing parties. The market-based (price-based) operation is shown to be practically the only approach that is capable to simultaneously provide incentives to hold the prices at marginal costs and to minimize the costs. As a result, such an operational structure inherently tends to maximize the social welfare of the system during its operation, and to accelerate developments and applications of new technologies. Another major change that is taking place in today’s power systems is an increasing integration of small-scale distributed generation (DG) units. Since in future power systems, a large amounts of DG will be based on renewable, intermittent energy sources, e.g. wind and sun, these systems will be characterized by significantly larger uncertainties than those of the present power systems. Power markets significantly deviate from standard economics since the demand side is largely disconnected from the market, i.e. it is not price responsive, and it exhibits uncertain, stochastic behavior. Furthermore, since electrical energy cannot be efficiently stored in large quantities, production has to meet these rapidly changing demands in real-time. In future power systems, efficient real-time power balancing schemes will become crucial and even more challenging due to the significant increase of uncertainties by large-scale integration of renewable sources. Physical and security limits on the maximal power flows in the lines of power transmission networks represent crucial system constraints, which must be satisfied to protect the integrity of the system. Creating an efficient congestion management scheme for dealing with these constraints is one of the toughest problems in the electricity market design, as the line power flows are characterized by complex dependencies on nodal power injections. Efficient congestion control has to account for those limits by adequately transforming them into market signals, i.e. into electricity prices. One of the main contributions of this thesis is the development of a novel dynamic, distributed feedback control scheme for optimal real-time update of electricity prices. The developed controller (which is called the KKT controller in the thesis) reacts on the network frequency deviation as a measure of power imbalance in the system and on measured violations of line flow limits in a transmission network. The output of the controller is a vector of nodal prices. Each producer/consumer in the system is allowed to autonomously react on the announced price by adjusting its production/consumption level to maximize its own benefit. Under the hypothesis of global asymptotic stability of the closed-loop system, the developed control scheme is proven to continuously balance the system by driving it towards the equilibrium where the transmission power flow constraints are satisfied, and where the total social welfare of the system is maximized. One of the advantageous features of the developed control scheme is that, to achieve this goal, it requires no knowledge of marginal cost/benefit functions of producers/consumers in the system (neither is it based on the estimates of those functions). The only system parameters that are explicitly included in the control law are the transmission network parameters, i.e. network topology and line impedances. Furthermore, the developed control law can be implemented in a distributed fashion. More precisely, it can be implemented through a set of nodal controllers, where one nodal controller (NC) is assigned to each node in the network. Each NC acts only on locally available information, i.e. on the measurements from the corresponding node and on the information obtained from NC’s of the adjacent nodes. The communication network graph among NC’s is therefore the same as the graph of the underlying physical network. Any change is the network topology requires only simple adjustments in NC’s that are local to the location of the change. To impose the hard constraints on the level to which the transmission network lines are overloaded during the transient periods following relatively large power imbalances in the system, a novel price-based hybrid model predictive control (MPC) scheme has been developed. The MPC control action adds corrective signals to the output of the KKT controller, i.e. to the nodal prices, and acts only when the predictions indicate that the imposed hard constraint will be violated. In any other case, output of the MPC controller is zero and only the KKT controller is active. Under certain hypothesis, recursive feasibility and asymptotic stability of the closed-loop system with the hybrid MPC controller are proven. Next contribution of this thesis is formulation of the autonomous power networks concept as a multilayered operational structure of future power systems, which allows for efficient large-scale integration of DG and smallscale consumers into power and ancillary service markets, i.e. markets for different classes of reserve capacities. An autonomous power network (AN) is an aggregation of networked producers and consumers, whose operation is coordinated/controlled with one central unit (AN market agent). By performing optimal dispatching and unit commitment services, the main goals of an AN market agent is to efficiently deploy the AN’s internal resources by its active involvement in power and ancillary service markets, and to optimally account for the local reliability needs. An autonomous power network is further defined as a major building block of power system operation, which is capable of keeping track of its contribution to the uncertainty in the overall system, and is capable of bearing the responsibility for it. With the introduction of such entities, the conditions are created that allow for the emergence of novel, competitive ancillary service market structures. More precisely, in ANs based power systems, each AN can be both producer and consumer of ancillary services, and ancillary service markets are characterized by double-sided competition, what is in contrast to today’s single-sided ancillary service markets. One of the main implications of this novel operational structure in that, by facilitating competition, it creates the strong incentive for ANs to reduce the uncertainties and to increase reliability of the system. On a more technical side, the AN concept is seen as decentralization and modularization approach for dealing with the future, large scale, complex power systems. As additional contribution of this thesis, motivated by the KKT controller for price-based real-time power balancing and congestion management, the general KKT control paradigm is presented in some detail. The developed control design procedure presents a solution to the problem of regulating a general linear time-invariant dynamical system to a time-varying economically optimal operating point. The system is characterized with a set of exogenous inputs as an abstraction of time-varying loads and disturbances. Economic optimality is defined through a constrained convex optimization problem with a set of system states as decision variables, and with the values of exogenous inputs as parameters in the optimization problem. A KKT controller belongs to a class of dynamic complementarity systems, which has been recently introduced and which has, due to its wide applicability and specific structural properties, gained a significant attention in systems and control community. The results of this thesis add to the list of applications of complementarity systems in control

Optimal spatial allocation of ancillary services for power systems

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Assessing soil N availability indices - is inorganic N enough?

Non-Peer ReviewedAssessing soil N availability is complicated enormously by the complexity of the N-cycle. Over the years, several methods of estimating potentially available N have been suggested. In an ongoing study, we have been assessing the suitability of a number of these methods for predicting potential crop response to fertilizer N. In particular, we correlated amino-sugar N levels to wheat yield across a variable landscape. This relatively new soil N test appears to be sensitive to changes in organic matter quality as related to landscape position and holds some promise for assessing potentially available N. The results presented here are preliminary

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

Price-based control of electrical power systems

In this chapter we present the price-based control as a suitable approach to solve some of the challenging problems facing future, market-based power sys tems. On the example of economically optimal power balance and transmission network congestion control, we present how global objectives and constraints can in real-time be translated into time-varying prices which adequately reflect the cur rent state of the physical system. Furthermore, we show how the price signals can be efficiently used for control purposes. Becoming the crucial control signals, the timevarying prices are employed to optimally shape, coordinate and synchronize local, profit-driven behaviors of producers/consumers to mutually reinforce and guarantee global objectives and constraints. The main focus in the chapter is on exploiting specific structural properties of the global system constraints in the synthesis of price-based controllers. The global constraints arise from sparse and highly struc tured power flow equations. Preserving this structure in the controller synthesis implies that the devised solutions can be implemented in a distributed fashion

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

Combined bidding at power and ancillary service markets

Power and ancillary service markets are strongly coupled. However, at the moment auctions are organized in such a manner that the coupling is not taken into account. Every market participant submits bids at power and/or AS markets without possibility to adjust with respect to the outcome of the other market. Inexact approximations of the actual market price induce deviations from the optimal social welfare value. In this paper, we firstly describe and analyze the consequences of power and ancillary service market coupling. Secondly, we present two different market design strategies, both of which are based on the idea of iterative auction and have the goal to optimally account for power and AS coupling, enabling the overall system to maximize its social welfare. An illustrative example is used to present potential benefits and downsides that might arise as a result of introducing proposed market arrangements

Price-based control of ancillary services for power balancing

A reliable and an efficient power system is a necessity for any industrialized society. Governments have to enforce regulations to guarantee that such a power system, in spite of many competing stakeholders, participants, companies, and regulating agencies can be operational. This paper analyzes the present arrangements and the future requirements to be posed on incentives and regulation for ancillary services (AS) for power balancing. The paper proposes companies to assess their own needs for AS. A two-sided market for AS is being described to replace the existing arrangements for secondary control. The proposed solution guarantees a reliable and efficient operation of power systems in a market environment with responsive, reliable, and accountable but also competing prosumers, a large penetration of less-predictable renewables and continent-spanning transmission networks