Steady-state Security Region Research Articles

Steady-State Security Region of Integrated Energy System Considering Thermal Dynamics

Steady-State Security Region of Integrated Energy System Considering Thermal Dynamics

Accurate Identification of Critical Boundary Hyperplanes of Practical Steady-State Security Region in Distribution Grids

The practical steady-state security region (PSSR) in distribution grids describes the region where the power flow can be managed securely. The PSSR is irrelevant to operation states and its boundaries can be approximated by hyperplanes (HPs). Benefit from these, the PSSR can dramatically simplify complicated optimal scheduling problems, such as deliverable energy flexibility scheduling. However, calculating the PSSR boundaries corresponding to all the power flow security constraints indiscriminately will theoretically produce lots of HPs to bound the whole PSSR and thus make solving of the PSSRbased optimal scheduling challenging. In fact, the whole PSSR is the intersection of the regions bounded by all the HPs within practical power injection ranges, and only a few HPs, called the critical boundary hyperplanes (CHPs), can bound it. Therefore, it is necessary to identify the CHPs before applying them to the optimal scheduling as power flow security constraints, so as to accelerate the solution. In this paper, a fast and accurate method is first proposed to identify the CHPs. The identified results are irrelevant to the specific objective and can be applied to different optimal scheduling problems. The proposed method is applied to several case-study networks and the results demonstrate its effectiveness and speed.

A time-coupling consideration for evaluation of load carrying capacity in district multi-energy systems

This paper proposes a systematic approach to evaluate the load carrying capability of a district multi-energy system (MES) using the Energy Hub (EH) modeling approach. The EH approach is used to model the system, and the EH steady-state security region concept is introduced as a means of assessing the system's load carrying capacity. To calculate the security region, a multi-parametric programming (MPP) algorithm is proposed, while a standardized matrix modeling approach is utilized to formulate its mathematical representation. To handle the high-dimensional polytope resulting from time coupling, a strategy is employed to approximate the original polytope using a reduced number of lower-dimensional polytopes. These lower-dimensional polytopes are specifically associated with a limited number of time periods, thereby alleviating the computational complexity. The proposed method offers an improved balance between computational accuracy and efficiency compared to existing approaches, while retaining the inherent time coupling characteristics across different period combinations.

Credible capacity calculation method of distributed generation based on equal power supply reliability criterion

Increasing distributed generation (DG) enables distribution network (DN) carry more load. Therefore, DG includes both electricity and capacity values. The DG capacity value can be regarded as increased load capacity under equal power supply reliability, typically referred to as credible capacity (CC). A CC calculation method of DG based on equal power supply reliability criterion is proposed in the paper. The unserved electricity under fault state and insufficient electricity under normal state are both considered in reliability estimation for the first time. Firstly, an island partition optimization model is established to evaluate the unserved electricity under fault state. A heuristic prospective greedy algorithm is utilized to formulate the island schemes dynamically. Then, a minimizing load curtailment model is established to evaluate the insufficient power supply under normal state. DN steady-state security region method is introduced to avoid repeated power flow calculation. Finally, the DG CC calculation is conducted for the IEEE 33-bus system by the proposed method. It is found that the CC value will have a big deviation if the insufficient electricity under normal state is ignored. When the DG permeability increases from 10% to 50%, the CC value is about 30%–20% of the total capacity.

An Optimal Allocation Method of Distributed PV and Energy Storage Considering Moderate Curtailment Measure

Increasing distributed generations (DGs) are integrated into the distribution network. The risk of not satisfying operation constraints caused by the uncertainty of renewable energy output is increasing. The energy storage (ES) could stabilize the fluctuation of renewable energy generation output. Therefore, it can promote the consumption of renewable energy. A distributed photovoltaic (PV) and ES optimal allocation method based on the security region is proposed. Firstly, a bi-level optimal allocation model of PV and ES is established. The outer layer is a nonlinear optimization model, taking the maximum power supply benefit as the objective function. The inner layer is a day-ahead economic dispatching model. Then, a quick model solving method based on the steady-state security region is proposed. An initial allocation scheme of PV and ES is determined with the redundancy capacity. In addition, the linear hyperplane coefficient of the security region is used to convert the nonlinear day-ahead economic dispatching model into a linear one. Finally, the proposed method is used to analyze the improved IEEE 33-node system. It is found that a moderate curtailment measure of distributed PV peak output and the allocation of energy storage have a significant effect on the power supply benefit of the distribution system. The optimal quota capacity of DG exceeds the sum of the maximum load and the branch capacity. In addition, the optimal allocation scheme is closely related to the cost and technical parameters of distributed PV and ES. Dynamic allocation schemes should be formulated for distribution network.

Optimization planning method of distributed generation based on steady-state security region of distribution network

Distributed wind and photovoltaic (PV) power generation are boosting in China. The wide integration of these generators into the distribution network leads to the risk of branch overload and bus voltage violation. To cope with the above risk, some peak output of wind turbines and PV equipment may be curtailed. Although curtailment measure leads to the increase of wind and PV power generation cost, more wind and PV electricity can be integrated into distribution network. In order to balance the power supply cost and the penetration rate of wind and PV electricity, the principle of economic consumption is introduced. Then an optimization planning method considering wind and PV electricity curtailment measure is proposed, and a fast model solving method based on distribution network steady-state security region is proposed. The main work is as follows. Firstly, a maximum and minimum optimization planning model is established. The maximum optimization refers to the maximum consumption of renewable energy electricity during the operation scheme formulating. The minimum optimization refers to choosing the planning scheme with the lowest power supply cost. Secondly, steady-state security region of distribution network is used to solve the optimization model quickly. To the maximum optimization, the model is transformed into a linear programming model with the help of the security region linear expression in power injection space. To the minimum optimization, an initial solution formulation method based on the redundancy information of the system operation state is given, by which the initial solution is close to the final solution. Finally, a case study of the IEEE 33-bus system is carried out and proves the effectiveness of the method. It is found that under the principle of economic consumption, the penetration rate of renewable energy electricity can be effectively improved when suitable renewable electricity curtailment measure is taken.

Robust optimal transmission switching for wind farm‐integrated power systems from a perspective of steady‐state security region

Optimal transmission switching (OTS) is a new method in improving operational security and economy of power systems. However, with continuous improvement in wind power penetration level, how to rationally describe the uncertainty of wind power play an important role in determining robustness of the OTS model. Against this issue, a system robust domain (SRD) developed by steady-state security region is proposed to model the uncertainties of wind power outputs in OTS. This modelling method focuses on the robust domain of system rather than the robust intervals of variables in conventional robust optimisation, thus overcomes the high dependence of conventional robust optimisation on accurate estimation of each uncertainty intervals. SRD-OTS is formulated and a decomposition algorithm is employed to obtain the optimal solution. The obtained optimal solution can maintain the operational security in the worst case of wind power outputs and minimize operational cost with the forecasted wind power outputs. In addition, robustness of the proposed SRD-OTS can be adjusted by an uncertain budget. The numerical results on the IEEE test system verify effectiveness of the proposed SRD-OTS and show that the optimal solution is still robust with a relative lower accuracy of wind power prediction.

Two-Time-Scale Approach to Characterize the Steady-State Security Region for the Electricity-Gas Integrated Energy System

The knowledge of the steady-state security region is essential for secure operation of the integrated energy system (IES). The two-time-scale feature of the IES is explored to facilitate construction of its exact steady-state security region. Conditions allowing decomposition of the IES into fast and slow subsystems are established. A complete characterization of the IES steady-state security region via the stable equilibrium manifold of the fast subsystem and the slow subsystem is derived and theoretically proven. This characterization can significantly facilitate construction of the IES steady-state security region (SSR) and is derived under the AC power flow model and gas flow model without any model approximation and simplification. Numerical studies are conducted to validate the derived characterization of the SSR and to illustrate the advantages of the proposed characterization in terms of robustness and reduced computational burden. Numerical studies show that exploring the fast and slow subsystems can lead to fast computation of feasible solutions with a 20-fold speed up in calculation time, as compared with the direct integration of the original IES system. Hence, the proposed two-time-scale method appears to be fast and yet accurate.

Steady-state security assessment in distribution systems with high penetration of distributed energy resources

Modern Electric Power Systems are evolving from a centralized generation model toward a complex infrastructure with the presence of Distributed Energy Resources (DER). The transformative changes are especially pronounced at the level of the distribution system. The emergence of new generation technologies as solar, for example, affects the customer profile, expansion planning, and operation procedures of distribution utilities. Therefore, this paper describes a new methodology based on steady-state security regions concept for the security assessment of distribution systems with the presence of DER. The main objective of the proposed methodology is to allow an effective evaluation of the operating conditions of distribution systems with high penetration of DER, focusing on the intermittence of the new generation resources. The proposed methodology has been tested using two distribution systems. The first one is a tutorial 13-bus system, which is a small tutorial feeder, and the second one is a real large-scale model of a distribution network. The results presented indicate the effectiveness of the proposed technique in the distribution system security analysis. The proposed methodology is implemented using the Python language and uses the OpenDSS software as a power flow solver.

Sequential steady-state security region-based transmission power system resilience enhancement

The increased high-impact and low-probability extreme weather events have posed unprecedented impacts on power system operation, and it is necessary to have appropriate methods to analyze the impacts. In this paper, a sequential steady-state security region (SSSR) is proposed to better describe the operational region impacted by sequential weather events, and SSSR is a polytope describing a region, where the operational constraints are satisfied. Based on SSSR with uncertain topology changes because of extreme weather events, a bi-level programming model is proposed. By means of Karush–Kuhn–Tucker conditions, the lower-level optimization model is equivalently transformed into a set of linear constraints, which are included in the upper-level optimization model. System topology scenarios are generated with the Monte Carlo method to avoid the curse of dimensionality caused by numerous uncertain topology scenarios. The generated system topology scenarios are mapped into the binary variables, representing line states, by means of the recursive McCormick (RMC) envelopes. Two test systems validate the proposed model. The results show that the proposed SSSR can well describe the feasible sequential region with regard to extreme weather events.

Toward Complete Characterization of the Steady-State Security Region for the Electricity-Gas Integrated Energy System

The steady-state security region of the integrated energy system (IES) is a useful tool for rapid security assessment and security evaluation of the integrated energy system. A complete characterization of the IES steady-state security region is derived. The derivation is under the nonlinear and non-convex AC power flow model, the gas flow model, and the uncertainty of renewable energy without any linear simplification. Then a novel and robust computation scheme to compute the IES steady-state security region is proposed and shown to eliminate the estimation errors of the existing methods. It is shown that the IES steady-state security region is non-convex and composed of several disjoint components. Numerical studies are conducted to show that the IES steady-state security regions obtained from the existing methods can be inaccurate, while the proposed characterization gives an exact estimation of the IES steady-state security region that significantly improves the previously proposed methods.

Coordinated Control Between Prevention and Correction of AC/DC Hybrid Power System Based on Steady-State Security Region

Taking the Steady-state Security Region (SSR) of AC/DC hybrid power system as a link, the mathematical model of coordinated control optimization problem is established by using the complementarity between preventive control and corrective control. Firstly, taking into account the probability and severity of anticipated accidents, a two-layer optimization model of coordinated control with dynamic constraints is established with the lowest total cost of coordinated control as the objective function. Secondly, invalid anticipated accidents are eliminated based on the theory of dominant event, which reduces the scale of the model and the complexity of optimization space. Finally, based on the constraint relaxation outer-layer optimization method, the anticipated accident with the minimum Steady-state Security Distance(SSD) is eliminated from the preventive control subset and incorporated into the corrective control subset, providing fixed anticipated accident subsets for the inner-layer optimization. In the inner-layer optimization, the SSDs are used to replace the power flow equations as the constraint condition, then the nonlinear constraints are transformed into linear constraints, which can reduce the difficulty of solving the mathematical model. The transformed IEEE 39 node AC/DC hybrid system is analyzed and calculated, and the calculation results verify that the proposed method can effectively improve the efficiency of solving optimal control scheme, and provide the possibility for online application.

Optimization Planning Method of Distributed Generation Based on Steady-State Security Region of Distribution Network

Optimization Planning Method of Distributed Generation Based on Steady-State Security Region of Distribution Network

Steady-state security region of energy hub: Modeling, calculation, and applications

Multi-energy systems (MES) provide various types of energy services by coupling different energy sectors. Such coupling increases the efficiency and flexibility of the entire energy system, and at the same time, however, increases the dependencies of the load carrying capability among different types of load demand. In the MES planning stage, we always want to assess and compare the load carrying capability among different planning schemes, considering the N-1 or N-M contingencies and the mutual effect of different energy sectors. While in the MES operation stage, we always want to know if the load of MES can be securely supplied considering potential contingencies and how far the current operation status is from the security boundary. This paper proposes a new concept named the energy hub (EH) security region and applying the concept to depict the load carrying capability of the district MES. The concept defines a region in a hyperspace where the MES can be safely operated under steady-state operational and security constraints. We first model the district MES using the EH approach and propose the mathematical form of the EH steady-state security region systematically. Then, a vertex-based algorithm is proposed to precisely calculate the security region using a space projection technique. We further propose indices to evaluate the load carrying capability of a district MES and identify critical components. Numerical case studies are conducted on two test systems to verify the validity of the proposed method. The results show the proposed EH security region concept and calculation method provide quantitive indicators on how to compare MES planning schemes and improve the load carrying capability.

Security region-based laminar flow coordinated optimization of grids

With the increasing penetration of renewable distributed generations in smart distribution grids, the coupling relationship between transmission and distribution grids has become increasingly complex. If power flow optimization for transmission and distribution grids is performed separately, the overall generation resources will not be fully utilized. In this paper, the power flow coordinated optimization based on layered decomposition is studied for the entire transmission and distribution grids, and the proposed method can be used on any scale grids. The core objective of this paper is the minimization of the overall supply cost. To this end, based on the steady-state security region (SSSR) in power injection spaces, the distributed local selfish optimization models of the transmission grid and each of the distribution grids is established, respectively. The coordination between transmission and distribution levels is achieved by using the Karush-Kuhn-Tucker (KKT) conditions. Due to the approximate hyperplane expressions of SSSR boundaries in power injection spaces, the operational constraints are transformed into a union of linear combinatorial inequalities of decision variables, and the variables in objective function and constraints are identical. Thus the optimization process and the determination of the KKT conditions become extremely simple, and the required number of iterations is very small. Several simulation results are presented, which show that the proposed method can accelerate the speed of solving problems by orders of magnitude.

Two-Stage Coordinated Control Strategy of AC/DC Hybrid Power System Based on Steady-State Security Region

The large-scale shift of power flow after DC blocking will seriously affect the secure operation of the system. Furthermore, after DC blocking, the system uses different control objectives in different operation stages. Therefore, a two-stage coordinated control of AC/DC hybrid power system based on steady-state security region (SSR) is proposed. Firstly, after DC blocking, the system needs to quickly restore secure operation with minimum cost. Therefore, the security correction guidance vector and the security distance sensitivity of the different control variables to it are obtained based on the linear fitting of the boundary surfaces of the SSR. The control cost of different control variables is characterized by the expansion and contraction of the SSR. According to the sensitivity of each control variable to the guidance vector and their actual adjustment ability, they are sorted and substituted into the security correction model to minimize the total adjustment cost during the process. Secondly, system will frequently be in a critical security state and not able to meet the needs of long-term secure and economic operation after security correction. Therefore, the security and economics of the system after security correction are comprehensively evaluated with the system generation cost, voltage deviation, and security margin under normal operating conditions and N-1 contingency conditions of heavy load lines. By calculating the security distance sensitivity of each control variable to the transmission limit of the crucial section, the sensitive generators and DCs that have significant effects on the transmission power of the crucial section are determined. Then the projections of security sub-region of high-sensibility control variables to optimization dispatch target, generation cost, voltage deviation, and the crucial section are depicted under different security margin, providing richer and more accurate operation information and strategic guidance for optimization dispatch. The calculation and analysis of the transformed IEEE 39-node system and the simplified actual power grid verify the correctness and effectiveness of the proposed coordinated control strategy.

Effective steady-state security regions of power systems considering voltage magnitude

With high-level variable renewable energy integrating into power systems, the uncertainty significant challenges to the real-time dispatch (RTD). Meanwhile, the influence of voltage magnitude and reactive power on RTD always were ignored. Based on effective steady-state security regions of power systems and linear power flow model, a real-time dispatching method considering voltage magnitude and reactive power is proposed in this paper. This model has two goals, one is the security goal, the other is the economic goal, and priority of security objectives is higher than economy. Unlike previous real-time dispatch methods, all of the operation base point, reactive power output and participation factors of automatic generation control (AGC) generators are chosen as decision variables in the model. In order to ensure computational efficiency, the model is finally transformed into a deterministic linear programming (LP) problem by robust optimization and other methods. The accuracy and computational efficiency of the method are illustrated by modified IEEE 9-bus system and IEEE 118-bus system.

Steady-State Security Region-Based Voltage/Var Optimization Considering Power Injection Uncertainties in Distribution Grids

Solving the power injection uncertainties of wind power generation, photovoltaic power generation, and demand response is a challenge for voltage/var optimization in distribution grids. An effective solution is to establish a chance-constrained optimization model. However, there is no fast and efficient method to determine the chance constraints, and the established models are difficult to solve. Therefore, this paper establishes a steady-state security region-based chance-constrained model. First, we find that the boundaries of the steady-state security region, which satisfy the voltage and current constraints, can be approximated by the union of a few hyperplanes in complex power injection spaces. Additionally, the expressions for hyperplanes are uniquely determined by the grid topology and are irrelevant to power injections. Then, we set the power injection adjustments as variables and propose a fast generation method for the linear expressions of the chance constraints. Because the variables of constraints and the objective function are identical, the computational burden for optimization is significantly reduced. Meanwhile, using the minimum power loss as the objective function, we present a quadratic optimization model that is easily solved by the quadratic programming method. Optimization results for IEEE 33-bus and PG&E 69-bus distribution grids are presented to verify the effectiveness of the proposed method.

Constructing Convex Inner Approximations of Steady-State Security Regions

We propose a scalable optimization framework for estimating convex inner approximations of the steady-state security sets. The framework is based on Brouwer fixed point theorem applied to a fixed-point form of the power flow equations. It establishes a certificate for the self-mapping of a polytope region constructed around a given feasible operating point. This certificate is based on the explicit bounds on the nonlinear terms that hold within the self-mapped polytope. The shape of the polytope is adapted to find the largest approximation of the steady-state security region. While the corresponding optimization problem is nonlinear and non-convex, every feasible solution found by local search defines a valid inner approximation. The number of variables scales linearly with the system size, and the general framework can naturally be applied to other nonlinear equations with affine dependence on inputs. Test cases, with the system sizes up to 1354 buses, are used to illustrate the scalability of the approach. The results show that the approximated regions are not unreasonably conservative and that they cover substantial fractions of the true steady-state security regions for most medium-sized test cases.

Novel Method for Rapidly Constructing Active Power Steady-State Security Regions Incorporating the Equivalent Reactances of TCSCs

Active power steady-state security regions (APSSRs), which can provide guidance for prevention and control through security checks, is of great importance for the safe operation of power systems in which more and more sustainable energy power generation is integrated. As a mature flexible AC transmission system (FACTS) device, thyristor-controlled series compensators (TCSCs) can carry out series compensation for the transmission line by controlling its equivalent reactance. With the change of the equivalent reactance parameter of a TCSC, the nodal admittance matrix and power flow distribution of the power system also changes. Inevitably, the APSSR will be different. Therefore, it is necessary and important to further incorporate the equivalent reactance parameters of TCSCs in the APSSR expression, which is generally established in the space of node active power injections. In this paper, a rapid construction method of APSSRs incorporating the equivalent reactances of TCSCs is proposed. Firstly, applicability and efficiency of the conventional APSSR construction method for power systems with TCSCs are analyzed. Further, with equivalent disconnection of TCSC branches, the effect of TCSC equivalent reactances on the distribution of active power flow through changing the structure parameters is treated as modifying node active power injections. On this basis, explicit expressions of APSSRs with a single TCSC equivalent reactance parameter and double TCSC equivalent reactance parameters are derived, respectively. Moreover, by deducing the general formula of APSSRs with multiple TCSC equivalent reactance parameters, the feasibility of the proposed method for power systems with multiple TCSCs is analyzed. Eventually, via benchmarks with different scales and a different number of TCSCs, validity and superiorities of the proposed method in computational efficiency are demonstrated.