Chao Duan

FACTS Devices Allocation via Sparse Optimization

Although there are vast potential locations to install FACTS devices in a power system, the actual installation number is very limited due to economical consideration. Therefore the allocation strategy exhibits strong sparsity. This paper formulates FACTS device allocation problem as a general sparsity-constrained OPF problem and employs Lq(0 <; q ≤ 1) norms to enforce sparsity on FACTS devices setting values to achieve solutions with desirable device numbers and sites. An algorithm based on alternating direction method of multipliers is proposed to solve the sparsity-constrained OPF problem. The algorithm exploits the separability structure and decomposes the original problem into an NLP subproblem, an Lq regularization subproblem, and a simple dual variable update step. The NLP subproblem is solved by the interior point method. The Lq regularization subproblem has a closed-form solution expressed by shrinkage-threholding operators. The convergence of the proposed method is theoretically analyzed and discussed. The proposed method is successfully tested on allocation of SVC, TCSC, and TCPS on IEEE 30-, 118-, and 300-bus systems. Case studies are presented and discussed for both single-type and multiple-type FACTS devices allocation problems, which demonstrates the effectiveness and efficiency of the proposed formulation and algorithm.

Moment-SOS Approach to Interval Power Flow

Intermittent renewable sources and market-driven operation have brought many uncertainties into modern power systems. Power flow analysis tools are expected to be able to incorporate uncertainties into the solution process. Interval power flow (IPF) analysis which aims at obtaining the upper and lower bounds of power flow solutions under interval uncertainties, thereby emerges as a promising framework to meet such expectation. This paper describes a novel optimization-based method to obtain high-accuracy or even exact global solutions to IPF problems. At first, the IPF problems are formulated as polynomial optimization problems probably with rational objective functions. Then Lasserres hierarchy, or moment-SOS approach, is introduced to relax the non-convex problems to convex semidefinite programming (SDP) problems. Correlative sparsity in the polynomial optimization problems is exploited to improve numerical tractability and efficiency. Finally, case studies on IEEE 6-bus, 9-bus and 14-bus systems demonstrate the second-order moment relaxation is capable of obtaining exact global interval solutions on small-scale systems, and numerical results on IEEE 57-bus, 118-bus and 300-bus systems show the proposed method can significantly improve the interval solutions compared with recent Linear Programming (LP) relaxation method on larger systems.

Modified Quasi-Steady State Model of DC System for Transient Stability Simulation under Asymmetric Faults

As using the classical quasi-steady state (QSS) model could not be able to accurately simulate the dynamic characteristics of DC transmission and its controlling systems in electromechanical transient stability simulation, when asymmetric fault occurs in AC system, a modified quasi-steady state model (MQSS) is proposed. The model firstly analyzes the calculation error induced by classical QSS model under asymmetric commutation voltage, which is mainly caused by the commutation voltage zero offset thus making inaccurate calculation of the average DC voltage and the inverter extinction advance angle. The new MQSS model calculates the average DC voltage according to the actual half-cycle voltage waveform on the DC terminal after fault occurrence, and the extinction advance angle is also derived accordingly, so as to avoid the negative effect of the asymmetric commutation voltage. Simulation experiments show that the new MQSS model proposed in this paper has higher simulation precision than the classical QSS model when asymmetric fault occurs in the AC system, by comparing both of them with the results of detailed electromagnetic transient (EMT) model of the DC transmission and its controlling system.

Data-Driven Affinely Adjustable Distributionally Robust Unit Commitment

This paper proposes a data-driven affinely adjustable distributionally robust method for unit commitment considering uncertain load and renewable generation forecasting errors. The proposed formulation minimizes expected total operation costs, including the costs of generation, reserve, wind curtailment and load shedding, while guarantees the system security. Without any presumption about the probability distribution of the uncertainties, the proposed method constructs an ambiguity set of distributions using historical data and immunizes the operation strategies against the worst-case distribution in the ambiguity set. The more historical data is available, the smaller the ambiguity set is and the less conservative the solution is. The formulation is finally cast into a mixed integer linear programming whose scale remains unchanged as the amount of historical data increases. Numerical results and Monte Carlo simulations on the 118- and 1888-bus systems demonstrate the favorable features of the proposed method.

Structure-Exploiting Delay-Dependent Stability Analysis Applied to Power System Load Frequency Control

Linear matrix inequality (LMI) based delay-dependent stability analysis/synthesis methods have been applied to power system load frequency control (LFC) which has communication networks in its loops. However, the computational burden of solving large-scale LMIs poses a great challenge to the application of those methods to real-world power systems. This paper investigates the computational aspect of delay-dependent stability analysis (DDSA) of LFC. The basic idea is to improve the numerical tractability of DDSA by exploiting the chordal sparsity and symmetry of the graph related to LFC loops. The graph-theoretic analysis yields the structure restrictions of weighting matrices needed for the LMIs to inherit the chordal sparsity of the control loops. By enforcing those structure restrictions on weighting matrices, the positive semidefinite constraints in the LMIs can be decomposed into smaller ones, and the number of decision variables can be greatly reduced. Symmetry in LFC control loops is also exploited to reduce the number of decision variables. Numerical studies show the proposed structure-exploiting techniques significantly improves the numerical tractability of DDSA at the cost of the introduction of acceptable minor conservatism.

Fault current limiting by phase shifting angle control of TCPST

Limiting the short-circuit fault current value has become more and more important for high voltage circuit breakers in modern large scale power systems. Conventional fault current limiters, such as Superconducting Fault Current Limiters (SFCLs) will cause large amount of additional investments. Fast thyristor controlled FACTS devices have opened a new way of limiting the fault current, while maintaining their normal functions of power flow regulation or stability control. The chief objective of this paper is to utilize Thyristor Controlled Phase Shifting Transformer (TCPST) as a new type of fault current suppression equipment under proper phase shifting angle (PSA) control. The relationship between the equivalent impedance of TCPST and multiple PSA switching modes is investigated through theoretical analysis firstly. And simulation results on IEEE 14-bus power system have demonstrated the excellent current limiting capability through the PSA control induced impedances with various fault location.

Energy Consumption Scheduling of HVAC Considering Weather Forecast Error Through the Distributionally Robust Approach

In this paper, the distributionally robust optimization approach (DROA) is proposed to schedule the energy consumption of the heating, ventilation and air conditioning (HVAC) system with consideration of the weather forecast error. The maximum interval of the outdoor temperature is partitioned into subintervals, and the proposed DROA constructs the ambiguity set of the probability distribution of the outdoor temperature based on the probabilistic information of these subintervals of historical weather data. The actual energy consumption will be adjusted according to the forecast error and the scheduled consumption in real time. The energy consumption scheduling of HVAC through the proposed DROA is formulated as a nonlinear problem with distributionally robust chance constraints. These constraints are reformulated to be linear and then the problem is solved via linear programming. Compared with the method that takes into account the weather forecast error based on the mean and the variance of historical data, simulation results demonstrate that the proposed DROA effectively reduces the electricity cost with less computation time, and the electricity cost is reduced compared with the traditional robust method.

Multi-period OPF with energy storages and renewable sources: A parallel moment approach

Multi-period optimal power flow (OPF) is a basic tool to achieve optimal operation of a power system with energy storages devices and renewable sources. A novel convex relaxation based decomposeition algorithm is proposed in this paper to solve the full AC multi-period OPF with energy storages and renewable sources. Based on alternating direction method of multipliers (ADMM), the original time-correlated non-convex optimization problem is decomposed into two subproblems. The first subproblem is non-convex and separable among different time slots. Moment relaxation can be constructed and solved for each time slot in parallel. The second subproblem is a convex quadratic program (QP) and separable among different buses, which can be solved in parallel by standard interior point (IPM) solver. Case study on a benchmark system demonstrates the effectiveness of the proposed algorithm.

FACTS devices allocation via sparse optimization

Although there are vast potential locations to install FACTS devices in a power system, the actual installation number is very limited due to economical consideration. Therefore the allocation strategy exhibits strong sparsity. This paper formulates FACTS device allocation problem as a general sparsity constrained OPF problem and employs Lq(0 <q < 1) norms to enforce sparsity on FACTS devices setting values to achieve solutions with desirable device numbers and sites. An algorithm based on alternating direction method of multipliers is proposed to solve the sparsity-constrained OPF problem. The algorithm exploits the separability structure and decomposes the original problem into an NLP subproblem, an Lq regularization subproblem, and a simple dual variable update step. The NLP subproblem is solved by the interior point method. The Lq regularization subproblem has a closed-form solution expressed by shrinkagethreholding operators. The convergence of the proposed method is theoretically analyzed and discussed. The proposed method is successfully tested on allocation of SVC, TCSC and TCPS on IEEE 30-, 118- and 300-bus systems. Case studies are presented and discussed for both single-type and multiple-type FACTS devices allocation problems, which demonstrates the effectiveness and efficiency of the proposed formulation and algorithm.