Improving security and economy of interconnected power network through explicit feasible region of tie-line power transfer

Highlights

• The transfer capability of tie-lines is explicitly captured.

• The PTDF matrix related to voltage magnitude and reactive power is derived.

• Transient constraints with tie-line power are derived.

• A linear model is proposed to improve power utilization via the tie-line scheduling.

Abstract

With the increasing power demand and renewables, the efficient utilization of power resources in each regional network relies on the tie-line power exchanges in interconnected power networks. Consequently, an accurate characterization of the feasible region of tie-line power transfer is crucial for scheduling tie-line power to achieve a secure and efficient utilization of power resources. This paper proposes a characterization method to explicitly capture a feasible region of tie-line power transfer considering steady-state constraints with reactive power and voltage limits and transient constraints. The steady-state and transient constraints are explicitly derived: 1) a power transfer distribution factor matrix with reactive power and voltage magnitude is derived to equivalently reflect the steady-state operational region with fewer variables and constraints; 2) the transient constraints of the tie-line power are derived based on the swing and current injection equations and a constraint transcription technology is adopted to convert transient constraints from continuous-time domain to a vector space, which makes it possible to identify the feasible region of tie-line power transfer. The steady-state and transient constraints are explicitly projected to the tie-line power space via a vertex search method. Finally, this paper utilizes the feasible region of tie-line power transfer to perform the tie-line scheduling via the proposed linear programming model. The proposed tie-line scheduling model can promote the optimal utilization of generation dispatches, which guarantees security and improve economics in the interconnected power network. The numerical results based on the IEEE 9-bus and IEEE 118-bus test systems verify the effectiveness of the proposed methods.

Introduction

Interconnections of regional networks promote the optimal utilization of power resources. The increased social welfares have been observed in many interconnected power systems [1], [2]. For example, HVDC tie lines across China deliver the rich renewable power in western China to satisfy the power demand centralized in eastern China [3]. European countries (e.g. Demark, Norway) accommodate high-penetration renewables via tie-line power exchanges in the European interconnection [4]. Some American independent system operators (e. g. PJM, MISO) coordinates power resources via tie lines under a joint operation framework [5].

For an interconnected power network, the regional networks are connected through tie-lines. For each regional power network, the tie-line power has a clear impact on the operation pattern of the inner power network. If the tie-line power is inappropriately determined, the operational constraints of the inner power network, including the steady-state constraints and transient constraints, will be violated. All combinations of P_B and Q_B within which the operation of each regional power network is feasible are described as a set of operational constraints in coordinates of tie-line power (i.e., P_B and Q_B). In this paper, such operational constraints are also referred as the feasible region of tie-line power transfer. For the interconnected power network, an intersection of all feasible regions of tie-line power transfer defines the transfer capability of tie-lines.

Currently, system operators firstly consider steady-state requirements associated with active power to calculate a feasible region of tie-line power transfer and then check its feasibility of transient requirements. For violated transient requirements, system operators will adjust the previous region in ad-hoc manners to eliminate violations. However, difficulties in finding a feasible solution rise because the security region of tie-line power transfer becomes smaller with increasing power demands and renewables. Consequently, a tie-line scheduling in existing practical industries is determined in ad-hoc manners, which could sacrifice the economy and security in the interconnected power networks.

In the existing studies and practical industries, a feasible region of tie-line power transfer is generally described by the available power transfer capability (ATC), which gives the maximum tie-line power at border nodes and interfaces. For example, considering state-steady requirements, Refs. [6], [7], [8] utilize a network flow method to capture the maximum tie-line power at border nodes and interfaces. Ref. [9] calculates the maximum tie-line power at border nodes and interfaces by solving several optimization problems. However, only certain assumed facets are used to describe the feasible region of tie-line power transfer, which leads to inaccuracy in the characterization. Also, these references describe the feasible region of tie-line power transfer by the line constraints in the equivalent model of a regional network. Line constraints are calculated by keeping the consistency of the power transfer capability among borer nodes before and after equivalence. However, the generator capacity constraints are neglected and the identified region is relevant to the current operating points, which can affect the accuracy in the identification.

To overcome these defects, some methods have been proposed to improve the accuracy in the feasible region of tie-line power transfer. Refs. [10], [11] investigate the feasible region of tie-line power transfer via multi-parametric programming. When the tie-line power varies, the combination of active and inactive constraints of the optimization problem in one certain regional network will change. If combinations of active and inactive constraints can be enumerated, the feasible region of tie-line power transfer is obtained. To accelerate the calculation in Refs. [10], [11], Ref. [12] proposes fast multi-parametric programming by only exploring the combinations of active and inactive constraints related to boundaries of the feasible region of tie-line power transfer. Ref. [13] determines the feasible region of tie-line power transfer by enumerating the vertices of the feasible region of tie-line power transfer. Vertices are calculated based on repeatedly solving optimization problems. However, the above references only focus on the feasible region of tie-line power transfer considering constraints associated with active power. Once the voltage magnitude and reactive power are incorporated, a large number of introduced variables and constraints could affect the computational efficiency of the identification.

Few studies are reported for the feasible region of tie-line power transfer considering transient constraints, although some studies have focused on the feasible region in the pre-fault generator-demand space that satisfies transient constraints [14], [15]. Refs. [14], [15] point out that the feasible region in the pre-fault generator-demand space can be approximated by a convex hull. Refs. [14], [15] adopt the energy function as the transient requirement. Given the operating point with the critical energy function, Ref. [14] performs a linearization on the critical energy function to approximate a boundary of the feasible region. In Ref. [15], the boundary is approximated based on solving nonlinear equations associated with the critical energy function. However, it is tricky to find the operation point corresponding to the critical energy function because the operating point can be only explored by repeated trials, particularly in multimachine systems. Also, in the existing practical industries, one common transient requirement is measured by the rotor angles relevant to the center of inertia, which is adopted in this paper. However, the tie-line power has not been incorporated in transient requirements and thus few studies have been reported for the tie-line schedule considering transient constraints.

Consequently, three main problems in existing methods will be addressed in this paper:

Problem 1

): How to consider steady-state constraints with voltage magnitude and reactive power in a feasible region of tie-line power transfer?

Problem 2

): How to incorporate transient constraints in a feasible region of tie-line power transfer?

Problem 3

): How to explicitly perform a tie-line scheduling when both steady-state and transient constraints are considered?

Regarding the importance of the feasible region of tie-line power transfer and defects of the existing studies, this paper presents a method to capture an explicit feasible region of tie-line power transfer with steady-state and transient constraints, and then focuses on its application in the tie-line scheduling, which improves the security and economy of the interconnected power networks. The contributions of this paper are summarized as follows:

This paper proposes a determination method of the feasible region of tie-line power transfer considering steady-state and transient constraints. The feasible region of tie-line power transfer is explicitly identified based on a vertex search method. Steady-state and transient constraints that are appropriate to the vertex search method are derived for the first time: 1) a power transfer distribution factor (PTDF) matrix of a linear power flow model with reactive power and voltage magnitude is derived for the first time to equivalently reflects the used linear model with fewer variables and constraints; 2) the transient constraints of the tie-line power are derived based on the swing and current injection equations, and then converted from the continuous-time domain to a vector space using a constraint transcription technology. Also, the Jacobian matrices of converted constraints are provided to guarantee their compatibility in the existing determination method. Furthermore, a linear programming (LP) model is proposed on the basis of the feasible region of tie-line power transfer to efficiently and explicitly perform the tie-line scheduling that satisfies both state-steady constraints and transient constraints in interconnected networks. The proposed tie-line scheduling model can provide an accurate dispatch boundary for each regional network and then promotes the optimal utilization of generation dispatches in interconnected power networks.