Haiwang Zhong

Coupon Incentive-Based Demand Response: Theory and Case Study

This paper presents the formulation and critical assessment of a novel type of demand response (DR) program targeting retail customers (such as small/medium size commercial, industrial, and residential customers) who are equipped with smart meters yet still face a flat rate. Enabled by pervasive mobile communication capabilities and smart grid technologies, load serving entities (LSEs) could offer retail customers coupon incentives via near-real-time information networks to induce demand response for a future period of time in anticipation of intermittent generation ramping and/or price spikes. This scheme is referred to as coupon incentive-based demand response (CIDR). In contrast to the real-time pricing or peak load pricing DR programs, CIDR continues to offer a flat rate to retail customers and also provides them with voluntary incentives to induce demand response. Theoretical analysis shows the benefits of the proposed scheme in terms of social welfare, consumer surplus, LSE profit, the robustness of the retail electricity rate, and readiness for implementation. The pros and cons are discussed in comparison with existing DR programs. Numerical illustration is performed based on realistic supply and demand data obtained from the Electric Reliability Council of Texas (ERCOT).

Decentralized Multi-Area Economic Dispatch via Dynamic Multiplier-Based Lagrangian Relaxation

This paper introduces a dynamic multiplier-based Lagrangian relaxation approach for the solution to multi-area economic dispatch (MAED) in a fully decentralized manner. Dynamic multipliers refer to the multipliers associated with power balance equations at tie-line buses in each area. Dynamic multipliers can be approximated as linear functions of tie-line power exports via sensitivity analysis and can serve as the equivalent supply/demand functions to neighboring areas. In contrast to the conventional static point-wise multiplier, which is unable to reflect the marginal cost change that results from variations in the power exchange level, the proposed dynamic multiplier provides each area the look-ahead capability to foresee the range of the marginal cost for power export over a range of tie-line exchange variations. In turn, this allows for a significantly faster convergence to the global optimal solution. The algorithm is also shown to be early termination friendly, which is very desirable in practice for ultra-large systems such as the State Grid of China. Numerical examples in a 6-bus system, a 3-area 354-bus IEEE system, and large test systems illustrate the benefits of the proposed algorithm.

Optimal Reactive Power Dispatch With Accurately Modeled Discrete Control Devices: A Successive Linear Approximation Approach

In this paper, a novel solution to the optimal reactive power dispatch (ORPD) problem is proposed. The nonlinearity of the power flow equations is handled by a new successive linear approximation approach. For the voltage magnitude terms, a mathematical transformation that improves the accuracy and facilitates the linear modeling of shunt capacitors is used. Without loss of accuracy, the load tap changers and shunt capacitors are both modeled by linear constraints using discrete variables, which facilitates the linearly constrained mixed-integer formulation of the proposed ORPD model. An efficient iterative solving algorithm is introduced. The obtained solution strictly satisfies the power flow equations. Case studies on several IEEE benchmark systems show that the proposed algorithm can efficiently provide near-optimal solutions with the error of the objective functions of less than 0.1%. Compared with several commercial solvers, the proposed method shows distinct advantages in terms of both robustness and efficiency. Moreover, based on the round-off results, a heuristic method that reduces the optimization ranges of the discrete control variables is proposed. This method can further improve the computational efficiency with small losses in accuracy.

Optimal Transmission Switching With Short-Circuit Current Limitation Constraints

With the expansion and enhancement of the power transmission network, short-circuit current (SCC) has become a major concern in grid operations. While transmission switching is one effective solution to reduce the SCC without investing in additional equipment, switching lines could threaten system N-1 security. To find an efficient, and secure, yet economic switching solution, this paper proposes an optimal transmission switching model with SCC limitation and N-1 reliability. As the relationship between SCC and integer variables associated with the line states is coupled, nonlinear and difficult to explicitly express, an effective linearization method is proposed. Theoretical analysis of the linearization error is performed using an illustrative example. Case studies have shown that the linearization error is generally small and decreases rapidly with the increase of electrical distance. Based on the linearized expression for SCC, a transmission switching model with SCC limitation and N-1 reliability constraints is proposed. Furthermore, to assure the calculation accuracy for the SCC, an iterative algorithm is designed to compensate for the linearization error. Case studies on the modified IEEE 30-bus, 118-bus and practically-sized 300-bus systems validate the effectiveness of the proposed model and algorithm. The solving efficiency of the model is investigated and discussed as well.

An Approach for Integrated Generation and Transmission Maintenance Scheduling Considering N-1 Contingencies

This paper presents an approach for integrated generation and transmission maintenance scheduling model (IMS) that takes into consideration N-1 contingencies. The objective is to maximize the maintenance preference of facility owners while satisfying N-1 security and other constraints. To achieve this goal, Benders decomposition is employed to decompose the problem into a master problem and several sub-problems. A Relaxation Induced (RI) algorithm is proposed to efficiently solve the large mixed integer programming (MIP) master problem. This algorithm is based on the solution of the linear relaxed problem. It is demonstrated that the proposed algorithm can efficiently reach a near-optimal solution that is usually satisfactory. If this near-optimal solution is not acceptable, it is used as the initial solution to fast start the solution of the original IMS problem. The performance of the proposed method is demonstrated using a modified version of the IEEE 30-bus system and a model of the power system of a Chinese province. Case studies show that the proposed algorithm can improve the computational efficiency by more than an order of magnitude.

An Efficient Decomposition Method for the Integrated Dispatch of Generation and Load

In response to the computational challenges produced by the integrated dispatch of generation and load (IDGL), this paper proposes a novel and efficient decomposition method. The IDGL is formulated using the mixed-integer quadratic constrained programming (MIQCP) method. To efficiently solve this complex optimization problem, the nodal equivalent load shifting bidding curve (NELSBC) is proposed to represent the aggregated response characteristics of customers at a node. The IDGL is subsequently decomposed into a two-level optimization problem. At the upper level, grid operators optimize load shifting schedules based on the NELSBC of each node. Transmission losses are explicitly incorporated into the model to coordinate them with generating costs and load shifting costs. At the bottom level, customer load adjustments are optimized at individual nodes given the nodal load shifting requirement imposed by the grid operators. The key advantage of the proposed method is that the load shifting among different nodes can be coordinated via NELSBCs without iterations. The proposed decomposition method significantly improves the efficiency of the IDGL. Parallel computing techniques are utilized to accelerate the computations. Using numerical studies of IEEE 30-bus, 118-bus, and practically sized 300-bus systems, this study demonstrates that accurate and efficient IDGL scheduling results, which consider the nonlinear impact of transmission losses, can be achieved.

Optimal transmission switching based on auxiliary induce function

Optimal transmission switching (OTS) has become a research focus in recent years as a new operational method for power systems. OTS is modeled as a mixed-integer programming (MIP) problem and it is difficult to solve it within short time horizon. Current acceleration heuristics cannot guarantee both the computational accuracy and efficiency. In this paper, a new concept called auxiliary induce function (AIF) is proposed. Based on the result of the relaxation problem, the coefficients of integer variables are strategically decided in AIF. Then the AIF algorithm is proposed, which properly adds the AIF function into the objective function of the OTS model. AIF algorithm is able to speed up the solving process for OTS while achieving exactly the same optimal solution. Case study on the IEEE 118-bus system shows that the AIF algorithm can improve 5 times as much the computation speed while obtaining the same optimal solution. Another case study on the IEEE 662-bus system indicates that the AIF algorithm is also capable of further improving the computational efficiency of current acceleration heuristics.

A Two-Level Approach to AC Optimal Transmission Switching With an Accelerating Technique

DC-based optimal transmission switching (OTS) cannot consider AC feasibility, which hinders the exploitation of the benefits of OTS in power system operations. This paper proposes a new OTS approach that considers AC feasibility. The approach uses a two-level iterative framework in which a mixed integer second-order cone programming (MISOCP) OTS model provides candidate solutions at the upper level, while the AC feasibility check is conducted at the lower level. An accelerating technique is developed to significantly improve computational efficiency while maintaining accuracy. Case studies using the IEEE 57-bus system, the IEEE 118-bus system and a real-world large system demonstrate the efficacy of the proposed approach.

Coordination of Generation Maintenance Scheduling in Electricity Markets

Generation maintenance scheduling (GMS) plays an important role in power system operations. The restructuring of the power industry has forced changes to the traditional maintenance mechanism. On one hand, the generation companies seek to maximize their profit. On the other hand, the independent system operator (ISO) strives to maintain the operational reliability of the system while maximizing the social welfare. This paper proposes a coordination mechanism for generation maintenance scheduling in electricity markets. In order to solve the resulting large mixed integer programming (MIP) problem, a relaxation induced algorithm is utilized. This technique is based on the solution of the linear relaxed problem. The features of the coordination mechanism and the performance of the algorithm are demonstrated using the IEEE-118 bus system and a provincial power system in China. Case studies show that the proposed mechanism not only ensures the maintenance preference of the generating companies, but also maintains the operational reliability of the system. They also demonstrate that the algorithm is quite efficient at solving the optimization problem.

A conic programming approach to optimal transmission switching considering reactive power and voltage security

Optimal transmission switching (OTS) exploits the flexibility in grid topology to reduce the system dispatch cost. However, DC-power-flow-based OTS solution cannot guarantee a feasible AC dispatch, which is one of the challenges in practical implementation. To bridge the gap between the theoretical basis and practical implementation of OTS, this paper proposes a conic programming approach to the OTS problem. A mixed integer second order cone programming model is formulated to allow for incorporating reactive power and voltage security constraints, which significantly improves the AC feasibility of the OTS solution. The efficacy of the proposed model is illustrated in the IEEE 57-bus system.