We present explicit sufficient conditions that guarantee the existence and uniqueness of the load-flow solution for distribution networks with a generic topology (radial or meshed) modeled with positive sequence equivalents. In the problem, we also account for the presence of shunt elements. The conditions have low computational complexity and thus can be efficiently verified in a real system. Once the conditions are satisfied, the unique load-flow solution can be reached by a given fixed point iteration method of approximately linear complexity. Therefore, the proposed approach is of particular interest for modern active distribution network setup in the context of real-time control. The theory has been confirmed through numerical experiments.

Explicit Conditions on Existence and Uniqueness of Load-Flow Solutions in Distribution Networks

This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the $Z$ -bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring i) wye connections; ii) ungrounded delta connections; iii) a combination of wye-connected and delta-connected sources/loads; and iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for the nonsingularity of the load-flow Jacobian is proposed. Finally, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.

Load Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity and Linear Models

We propose a framework to study the impact of stochastic active/reactive power injections on power system dynamics with a focus on time scales involving electromechanical phenomena. In this framework, the active/reactive power injections evolve according to a continuous-time Markov chain (CTMC), while the power system dynamics are described by the standard differential algebraic equation (DAE) model. The DAE model is linearized around a nominal set of active/reactive power injections, and the combination of the linearized DAE model and the CTMC forms a stochastic process known as a stochastic hybrid system (SHS). The extended generator of the SHS yields a system of ordinary differential equations that governs the evolution of the power system dynamic and algebraic state moments. We illustrate the application of the framework to the computation of long-term power system state statistics, and to short-term probabilistic dynamic performance/reliability assessment.

/pdf/analysis-of-power-system-dynamics-subject-to-stochastic-1dhcj71gaw.pdf

Analysis of Power System Dynamics Subject to Stochastic Power Injections

Multiobjective clearing of reactive power market in deregulated power systems

Coupled energy and reactive power market clearing considering power system security

Reactive power is an important system support service in the current power market. Power producers or generators have the opportunity to offer this service to make a profit. Given the fact that a generator needs reactive power to transmit its own active power, however, it is possible that certain generators cannot support a system even if they are generating reactive power. This paper investigates such a phenomenon and proposes a method to determine the minimum amount of reactive power (Q/sub min/) required for a given generator. If a generator cannot supply this minimum amount, it actually draws reactive power support from the system to facilitate its own active power selling activity. Compensation to a generator's reactive power output should be made only to the amount that is above the Q/sub min/ amount. The proposed ideas are illustrated with simple systems in this paper and tested on a real-life power system. The test results verified the validity of the proposed concept and method.

An investigation on the reactive power support service needs of power producers

Ill-conditioned power-flow problems have been widely investigated and reported in the literatun:. A typical approach develops enhanced solution algorithms when a power-flow case is found divergent with the conventional Newton method. It is known that a genuine ill-conditioned problem is caused by the presence of a large condition number in the power-flow Jacobian matrix. Since a large condition number is associated with small singular values or eigenvalues of a matrix and the voltage collapse is also related to small eigenvalues, it is therefore postulated that an ill- conditioned power-flow problem is actually a voltage collapse problem. The objective of ths paper is to investigate the relationship between power-flow ill-conditioning and voltage instability. The findings confirm that power-flow ill-conditioning only occurs at the voltage collapse point. As a result, developing improved algorithms to solve the problem is an unprofitable strategy. The well- known voltage stability assessment techniques such as the PV curve method are sufficient for the problem. This conclusion is supported with case studies on five widely known ill-conditioned power- flow problems and rigorous mathematical analysis.

http://www.ece.ualberta.ca/~wxu/papers/VS-ILLConditionedPowerFlow.pdf

Analysis of ill-conditioned power-flow problems using voltage stability methodology

This paper presents a new phenomenon found for unbalanced power flow solutions: the existence of two voltage solutions at the neutral points of unbalanced three-phase circuits. The phenomenon is different from that found in traditional single-phase balanced power flow solutions. It is dependent on the degree of system or load unbalance. If the unbalance is reduced to zero, the two solutions will merge into one. This paper presents our observations and analysis on the problem. A test system is used to illustrate the practical significance of the phenomenon. We hope this work will stimulate further research on this challenging and interesting problem.

http://www.ece.ualberta.ca/~wxu/papers/PQ-MultiSolutionofUnbalancedLoadFlow.pdf

The existence of multiple power flow solutions in unbalanced three-phase circuits

Ill-conditioned power flow problems have been widely investigated and discussed in the literature. Typical approaches are to develop enhanced solution algorithms when a power flow case is found to diverge using the conventional Newton method. It is known that a genuine ill-conditioned problem is caused by the presence of a large condition number in the power flow Jacobian matrix. Since a large condition number is associated with small singular values and the voltage collapse is related to small eigenvalues, we therefore speculate that an ill-conditioned power flow problem is actually a voltage collapse problem. The objective of this letter is to demonstrate the relationship between power flow ill conditioning and voltage instability. Case studies of five classical ill-conditioned cases have confirmed that the ill conditioning of power flow indeed occurs-and only occurs-at the voltage collapse point.

Investigation of the relationship between ill-conditioned power flow and voltage collapse

Open access permits all players to inject real power into a system with few restrictions. As generators also provide reactive power to the system, there is a general conception that their Q-outputs are supportive to system security and should be financially compensated. Our research results show, however, that a generator's Q-output has double-applications. One is to support the shipment of its own active power, and the other is to support system security. Therefore, compensation should be made to the second component only. The main purpose of this paper is to introduce the problem and demonstrate the phenomena of the dual functions of generators Q-output. Simple systems are used to illustrate the phenomena. Analytical separation of the components is presented for these simple systems. Case-specific separation methods are also developed to demonstrate the problem. The paper contributes to introducing the phenomenon, as well as demonstrating its importance for defining fair compensation schemes for reactive power support services. It also shows that methods need to be developed to solve the problem for large-scale real-life power systems, Preliminary, but potential, ideas are discussed.

http://ieeexplore.ieee.org/iel5/7659/20924/00970318.pdf

Y. Wang

Papers

An investigation on the reactive power support service needs of power producers

Analysis of ill-conditioned power-flow problems using voltage stability methodology

The existence of multiple power flow solutions in unbalanced three-phase circuits

Investigation of the relationship between ill-conditioned power flow and voltage collapse

Investigation on the dual functions of generator reactive power support