Zhijun Qin

Black-start strategy for power grids including fast cut thermal power units

The restoration of a power system after a black-out mainly includes following stages of black-start, network reconfiguration, and load restoration. The fast cut back (FCB) function of thermal power units assures the operation of auxiliary equipments after a power network black-out, which is helpful in black-start. This paper establishes a steady-state model of FCB units at the stage of black-start. Based on the established FCB unit model, an optimization mathematical model to maximize the total power generator output is constructed to get the optimal start-up sequence of units. A simplified algorithm is presented to solve this model. Considering the charging-time constraints of line branches, the obtained start-up sequence of units is corrected using the shortest path algorithm to get the start-up path of units. Case studies on the New England 10-unit 39-bus power system are given. The results indicate that FCB units make for power system restoration.

Dynamic Coordinated Condition-Based Maintenance for Multiple Components With External Conditions

This paper proposes a method to establish an optimal dynamic coordinated condition-based maintenance strategy that considers harsh external conditions, for example, harsh weather conditions. Component deterioration is modeled as a Markov process based on physical characteristics, with the effects of harsh external conditions represented as probabilistic models. The proposed model involves interactions between different maintenance strategies on various components, as well as influences on the operation of the entire system. The optimal maintenance strategies are obtained by optimizing the proposed model with the cost to go, including system reliability cost and maintenance cost. This proposed model is solved using a backward induction algorithm associated with a search space reduction approach developed to reduce the simulation time. Two IEEE systems and one actual system validate the proposed model. The results show that this optimal maintenance strategy model that considers harsh external conditions provides insight for scheduling appropriate maintenance activities.

A branch-and-cut method for computing load restoration plan considering transmission network and discrete load increment

This paper proposes an optimization model to compute optimal load restoration plan for the transmission network. The objective of this model is to maximize the load pickup subject to power flow constraints and discrete load increment constraints. This mix-integer optimal power flow model (MIOPF) is solved via a branch-and-cut (B&C) framework. The nodes in the B&C tree are solved by the interior point method. In particular, three cutting planes, namely, the Gomory rounding cut, the knapsack cover cut, and the fixing variable cut, are incorporated into each node of the B&C tree to reduce the scale of the sub-tree. This model can be used to aid the system operators to conduct load restoration actions or draw up a restoration plan. The load restoration plan is obtained by solving a number of co-related MIOPF models till all load increments are restored. The RTS 24-bus test case with 170 load increments (i.e., with 170 binary variables) is used to illustrate complexity of the proposed model and the computational efficiency improvement stemming from the cutting planes.

Generation dispatch with air pollutant dispersion consideration

This paper addresses a new generation dispatch method with constraints of geographical emission distribution of air pollutant dispersion. Traditionally, generation dispatch methodology considers the total cost and total amount of emission. However, even for the same amount of emission, the effect of emitted SO2, NOx and particles might be completed different due to the geographical distribution and meteorological condition. In this work, pollutants distribution associated with geographical distribution of power plants and meteorological condition will be integrated into the generation dispatch models. The generation dispatch pattern is thus established with acceptable air pollution level for a specified location. A highly efficient interior point method is employed to solve the proposed model. A standard IEEE test system is employed to demonstrate the proposed model and algorithms.

Convex envelopes of optimal power flow with branch flow model in rectangular form

Optimal power flow (OPF) is an important tool for economic dispatch and other power system applications. Due to the non-convex nature of OPF formulations, convex relaxation serves as a bridge linking OPF formulation variants with efficient polynomial-time algorithms to obtain a global optimum. This paper proposes: 1) an OPF model based on branch flow model in rectangular form, and 2) two convex envelopes for this OPF model. First, by introducing explicit redundant variables for bi-directional power flows, and the products of bus voltages for each branch, OPF is formulated into a non-convex quadratic programming (QP) model. For an n-bus, l-branch power system, the non-convex part of this QP model is collectively expressed by 2n quadratic terms and 4l bilinear terms. Second, primal and dual convex envelopes for these terms are derived to convert the non-convex QP model into a convex one. Third, the tightness of primal and dual convex envelopes is validated via a spatial branch-and-bound framework using IEEE 14-bus system. Numerical studies show that the proposed convex envelopes are tight to get an optimum with small optimality gap and slight bus power mismatches.

Virtual Synchroscope: a novel application of PMU for system restoration

Power system restoration is well recognized as one of the key technologies to improve the reliability of power systems. Generally, the restoration process is divided into several stages as preparation, system restoration, load restoration, synchronization and inter-connection. Currently, re-closure of breakers is done by field crews with synchroscope. A novel methodology, entitled as “virtual synchroscope”, is proposed in this paper. By utilizing Phasor Measurement Units (PMUs), the proposed methodology compares phasors of voltages at connection points from the two islands with the accurately time-stamped measurements. By adjusting voltage magnitude, frequency, and phase angle in the control center, all the requirements for synchronization are satisfied and the synchronization can be implemented. A case study on a power system is presented to validate the feasibility of the proposed method. It is proved that the proposed method can meet the requirements of all standards and resulting in smooth synchronization.

Considering geographical distribution of pollutants emission in production costing

With the haze weather happening more frequently especially in developing countries, the air quality problem is attracting increasing attention. As a major source of air pollutants emission, the electricity industry is expected to conduct environmental-friendly power system planning and operation. Traditionally, the total pollutants emission is considered. However, it is well identified that the geographical distribution of pollutants emission is a significant factor determining the influence of pollutants. In this work, geographical location of power plants and loads, and meteorological conditions are considered to obtain the geographical distribution information of pollutants emission. A prototype production costing model with air quality constraints is built, which can be employed to aid generation expansion planning, fuel budgeting and system operation. Case studies are conducted on a system with both traditional generations and renewable generations, to reveal the cost of geographical consideration of pollutants.

Constructing restoration strategies with availability risk constraints

System restoration strategies are established and implemented based on the availabilities of components of a system. However, due to lack of accurate information, availabilities of some components may not be known during establishment of restoration strategies after a blackout. In this paper, a novel risk-based methodology is proposed for constructing restoration strategies with stochastic availability constraints for both individual components and restoration paths. Based on a stochastic model of the availability, a multistage stochastic optimization model is constructed. A bi-level method is used to solve the proposed model. The established restoration strategy is to achieve a reasonable restoration duration subjects to operating constraints and acceptable risk levels. The proposed risk constraints are introduced into the EPRIs System Restoration Navigator (SRN) with a little modification. Case studies demonstrate the proposed model and methods.

Application of non-linear programming for large-scale AC-DC power flow analysis

This paper proposes a robust, non-divergent model for large-scale AC-DC power flow analysis. By introducing relaxation variables into power flow equations, the conventional power flow model is turned into a non-linear programming model to minimize the L2 norm of the relaxation variables subject to operation constraints and DC station control modes. The interior point method (IPM) is used to solve the model. Due to the special structure of the proposed model, the size of coefficient of correction equations in the IPM can be reduced to the same as Jacobian in the conventional Newton method. Further, the coefficient is symmetrical positive-definite with a diagonal perturbation, which leads to a better convergence than Newton direction. The model and algorithm proposed also have the following features: (1) no special initial value is needed; (2) strong robustness for power grids with plenty of small/negative impedance; (3) applicable for searching a desirable operation point by appropriate settings of inequality constraints; (4) striving for ultimate close to power flow solution avoiding to stop too early at a local minimizer. Numerical simulations on a 6527 buses power grid in China with 8 HVDC lines show that the proposed model has robust convergent property in the feasible region, around the boundary of the feasible region and even beyond the feasible region of power flow.

Multi-Area Dynamic State Estimation With PMU Measurements by an Equality Constrained Extended Kalman Filter

To achieve higher accuracy of estimated dynamic states, phasor measurement unit (PMU) measurements of buses in a network can be used for dynamic state estimation (DSE). However, it is difficult to coordinate the states of boundary buses in different areas when performing multiarea DSE. By using PMU measurements of buses in the network, this paper proposes an extended Kalman filter-based method with equality constraints to conduct multi-area DSE. First, a corrective strategy is proposed to estimate a corrective internal voltage (CIV) and a corrective rotor angle (CRA) of each generator with all PMUs’ measurements. The proposed corrective strategy can also ensure the consistency of the boundary buses in the multiareas. Then, the CIV and the CRA are used to establish equality constraints for updating the dynamic states with the PMU measurements. An IEEE 30-bus system and an IEEE 118-bus system are used to validate the proposed method, with the results showing the feasibility and accuracy of the proposed method.