An intentional controlled islanding strategy considering island frequency stability for power system with wind-power integrated

Abstract

As the last defense line to avoid cascading failures, intentional controlled islanding (ICI) is of great significance to maintain the stability of power systems. However, with the increasing penetration of renewable energy, the system inertia and primary frequency regulation capacity have significantly decreased, and the adaptability and effectiveness of ICI have also been significantly reduced. Aiming at the above problems, an ICI strategy considering island frequency stability with wind-power integration is proposed. Firstly, a basic model of ICI is constructed through the collaborative optimization of load shedding, generator tripping, and the optimal intentional islanding boundary. Secondly, a frequency response model of the islanded system considering the primary frequency regulation of wind power is established, and the corresponding linear iterative algorithm is proposed. Finally, the established frequency stability constraints are embedded into the ICI model, forming a mixed integer linear program (MILP) model. The results and the effectiveness of islanding frequency control using the proposed strategy is discussed in the IEEE39 system compared with the traditional ICI strategy.

1 Introduction

Driven by the shortage of fossil energy, environmental pollution, and the pressure of carbon emissions, the penetration of renewable energy has been increasing (Breyer et al., 2022; Yang B et al., 2022; Xu et al., 2023). The large-scale grid connection of wind power brings new challenges to the safety and stability of the power system (Fang et al., 2022; Yang H et al., 2022). The dynamic characteristics of wind power units are significantly different from traditional synchronous generators, and the power system’s rotor angle stability characteristics have been profoundly changed (Agarala et al., 2022; Yadav and Saravanan, 2022). On the one hand, the opening space of traditional synchronous machines is occupied, and the system equivalent inertia is reduced, the risk of power system transient instability under large disturbances and extreme faults is correspondingly increasing (Tang et al., 2020; Tang et al., 2022). On the other hand, the primary frequency regulation capability of wind power units and their support to the grid is insufficient (Zhang et al., 2022).

Most of the current research on power system stability focuses on traditional power system. Traditional analysis methods including extended equal area criterion (EEAC), transient energy function and so on (Yang et al., 2006; Yan et al., 2011). In addition, artificial intelligence technology is also gradually being widely used (Fu et al., 2023). Yang conducts a pioneer study for SCUC problems that proposes an expanded sequence-to-sequence (E-Seq2Seq) based data-driven SCUC expert system for dynamic multiple-sequence mapping samples (Yang et al., 2021b). Yang further enhances its self-learning ability on the basis of data-driven method (Yang N et al., 2022a). However, the existing emergency control strategies are not effective enough with large-scale wind power integrated (Fotis et al., 2023; Al Masood et al., 2018). Considering the coexistence of traditional fault conditions and new network attacks during the operation of smart grid, it is urgent to propose some new power system stability control strategies (Zhang et al., 2023).

When a large disturbance triggers a transient instability of the system, through the timely implementation of ICI, the unstable system is separated into several disjoint, internally stable islands (Ding et al., 2017). At present, the research on the ICI problem mainly focuses on the appropriate time (when), the optimal boundary (where), and the execution method (how) three aspects (Ahangar et al., 2020). Since the location of the islanding boundary directly determines the stability characteristics of the islanded system, the “where” problem has become a popular research topic. According to the different objective functions in solving the optimal islanding boundary, the objective functions of the ICI strategy can be divided into: minimizing the unbalanced power of the islands, minimizing the power flow disruption, and other objective functions (Ahangar et al., 2020).

The unbalanced power can be expressed as the algebraic sum of the active power on the switched line, reflecting the frequency deviation of the islanded system (Qiao and Ma, 2022). The lower it is, the more beneficial to the recovery and economic operation of the islanded system (Jin et al., 2023). Sun proposes an ICI strategy based on the OBDD method, and verifies the effectiveness of controlled islanding with the minimum unbalanced power as the objective function (Sun et al., 2003). Xu proposes a three-stage ICI strategy based on graph theory with the same objective function. The solving efficiency is accelerated by determining the controlled islanding boundary through adaptive graph simplification, islanding cut-set search, and islanding scheme checking in turn (Xu and Miao, 2018). Kamali establishes a multi-objective function considering the unbalanced power and transient stability of the island, and an ICI strategy based on the MILP model is proposed to ensure the existence of steady-state operating points of the islanded system (Kamali et al., 2020).

The power flow disruption refers to the sum of the absolute values of the power on the disconnected branches, reflecting the effect of the ICI operation on the transient stability of the islanded system (Badal et al., 2019). Jian comprehensively considers the power flow on transmission lines and the electrical connection between nodes and defines the composite active power flow disruption. Then an ICI method is proposed based on a semi-supervised clustering algorithm to minimize the active power flow disruption (Jian et al., 2014). Isazadeh additionally considers the effect of reactive power flow disruption on the islanding stability, using the self-tuned online fuzzy factors. And weighted time-varying graph structure of the network is used to obtain islanding boundaries (Isazadeh et al., 2015).

With the increasing complexity of power system operation modes, new objective functions and constraints need to be established to guide the determination of islanding sections (Yang et al., 2021a). For example, Kyriacou pursues the reliability of power supply after ICI, and proposes an ICI method with the objective function of the maximum load-carrying capacity using the MILP model (Kyriacou et al., 2017). Ghamsari-Yazdel considers emerging regulation resources such as energy storage facilities and demand response, and establishes a comprehensive objective of minimizing controlling cost and dispatching costs (Ghamsari-Yazdel et al., 2020). Teymouri and Daniar focus on the frequency stability risk and the corresponding controlling cost after executing ICI in low-inertia power systems. Teymouri establishes an ICI strategy considering low-frequency load shedding control to reduce the controlling cost (Teymouri and Amraee, 2019). Daniar considers emergency load shedding control in ICI, which seeks to minimize load shedding while maintaining the system frequency (Daniar et al., 2021). However, the primary frequency control of wind power and the emergency load shedding control is not taken into consideration when the frequency increases (Li et al., 2023b).

In summary, the current research on ICI strategies is still focused on the power supply reliability and transient stability of the islanded system after executing ICI. The frequency stability characteristics of the islanded system and other emergency control strategies coordination are given less consideration (Zhu et al., 2022; Li et al., 2020). With the large-scale integration of wind power with weak frequency regulation capability, the equivalent inertia and primary frequency regulation capability of the islanding system will change significantly after ICI (Javadi et al., 2021; Yang N et al., 2022b). At this time, the unbalanced power generated by ICI may still exceed the maximum capacity of the islanding system, thus triggering multiple rounds of low-frequency load shedding or over-frequency generator tripping, even leading to frequency collapse (Li et al., 2023a).

In this paper, based on the traditional ICI model, the frequency stability constraints considering the participation of wind power in primary frequency modulation is added. First, the basic model of ICI is established. The islanding section, generator tripping, and load shedding are simultaneously taken as decision variables. The minimum generator tripping and load shedding is the goal. The generator coherency constraints, connectivity constraints, and other basic constraints are considered. At the same time, a frequency response model involving wind power is established, a linearized iterative solution algorithm is proposed, and the frequency stability constraints are formed. Finally, by embedding island frequency stability constraints, an ICI strategy considering island frequency stability is proposed, with practical significance and engineering value. The structure diagram of the modeling process is shown in Figure 1.

FIGURE 1

The rest of this paper is organized as follows. In Section 2, the ICI model is constructed including the objective function, the basic constraints, and the method of constructing frequency stability constraint. Case studies and discussions based on the IEEE 39 system are shown in Section 3. The effectiveness of the proposed ICI strategy in maintaining frequency stability and the importance of wind power participation in frequency control are analyzed. Section 4 concludes this study by summarizing the key findings and contributions of this paper.

2 An ICI model considering islanding frequency stability constraints

2.1 Objective function

Since the frequency stability constraints have been considered in the proposed ICI model, it can be assumed that the unbalanced power generated by the execution of ICI will not collapse the island frequency. Therefore, to pursue lower controlling costs, the proposed ICI model takes the minimum load shedding as the objective function:

Where Ω_L, Ω_G, and Ω_w are respectively a set of load nodes, synchronous generator nodes, and wind farm nodes. λ_L,i, λ_G,I, and λ_w,i are the penalty coefficients of shedding load i, tripping synchronizer i and wind farm i respectively. To comprehensively consider the influence of various control measures, the value of each penalty coefficient is set as 1. , , and are respectively the shedding amounts of load i, the tripping amounts of synchronizer i, and wind farm i. This paper argues that only the whole synchronous generator or the whole wind farm can be tripped.

2.2 Basic constraints

2.2.1 Generator coherency constraints

To ensure the transient stability of the islanding system, the nodes of the system should be assigned to different islands according to the generator coherency results. The transmission lines with nodes belonging to different islands on both sides should be disconnected (You et al., 2004). The generator coherency constraints are given by:

Where Ω_N is the set of system nodes, Ω_K is the set of isolated islands after ICI, and Ω_B is the set of branches. Eq. 2 indicates that a node can only belong to an island. x_i,k is a 0–1 variable, indicating that node i belongs to island k when x_i,k = 1. Eq. 3 is used to judge the line switching state, and a_i,j = 1 means the line is in normal operation. Since is a nonlinear form of multiplication of two 0–1 variables, the auxiliary 0–1 variable t_ij,k is introduced to linearize , as shown in Eqs 4, 5.

2.2.2 Connectivity constraints

After executing the ICI method, all nodes in the island shall be connected to ensure there are no isolated nodes. A common connectivity constraint model is the single-commodity flow model (Ding et al., 2015), which assumes that there is only one virtual source node on the island, and that all other nodes carry a 1 pu virtual load. The balanced virtual power in the island indicates the inner connectivity of the island. The connectivity constraints based on the single-commodity flow model are given by:

Where, is the line virtual power flow from node i to node j. is the virtual generator power on node i. When this node is selected as the virtual source node, its value is greater or equal to 1, otherwise the value is 0. is a set of virtual source nodes. is a set for other virtual load nodes. M is a large number.

2.2.3 Power balance constraints

The power balance of nodes must be ensured first after executing the ICI methods, as shown in Eq. 7.

Where, and respectively represent the set of branches that starting from or ending in node i. P,Q respectively represent the active power and reactive power of generators, while the subscript G,i and w,i respectively represent the synchronous generator i and wind farm i. P_ij, Q_ij respectively represent the line active and reactive power from node i to node j. , respectively represents the initial active and reactive load of node i before executing ICI. φ_i represents the power factor of the load on node i.

2.2.4 Power flow constraints

To avoid the problem that the calculation result of DC power flow is not accurate enough, the AC power flow model is used in the constraints (Nan et al., 2018). The active and reactive power on a transmission line can be expressed as:

Where V_i, V_j is respectively the voltage amplitude of node i and node j at both ends of a line. δ_ij is the phase angle difference of node i and node j after executing ICI. G_ij, B_ij, and respectively represents the line’s conductance, susceptance and susceptance to ground.

The linearized power flow constraints are given by (Kamali et al., 2020):

Where and are the auxiliary variables required for linearization.

2.2.5 Bus voltage amplitude and phase angle constraints

These constraints ensure that the voltage amplitude of each node and the voltage phase Angle difference between the two sides of the line are within the safety limit.

2.2.6 Other basic constraints

Where P, Q respectively represent the active power and reactive power of generators, while the superscript max and min represent the upper and lower limits of power value, the subscripts G,i and w,i respectively represent the synchronous generator i and wind farm i. Q_w,i and φ_w,i are respectively the reactive power output and power factor of wind farm i. According to , the load shedding amount of node i should not be greater than the initial load before executing ICI, and the generator output shall be limited between the upper and lower limits.

2.3 Islanding frequency stability constraints

2.3.1 A frequency response model considering wind power participation

Based on the frequency response model, the frequency stability characteristics of the islanding system with wind power integrated during the ICI process (Javadi et al., 2021; Egido et al., 2009), as shown in Figure 2A. To simplify the analysis, the governor model of the synchronous generator is equivalent to a first-order inertial link, and non-linear links such as output limiting of the governor are retained.

FIGURE 2

At the same time, virtual inertia control combined with droop control is selected as the primary frequency regulation strategy of wind power units.

In Figure 2, T_wi is the time constant of primary frequency regulation, M_wi is the virtual inertial constant, K_wi is the droop control coefficient, M_G is the total inertia of all operational synchronous generators in the system, D is the load damping coefficient, T_Gi is the governor time constant of synchronous generator i, K_Gi is the first frequency modulation coefficient, ΔP_dis is the islanding unbalance power generated during ICI.

Considering that the response speed of the wind power unit is much higher than that of the synchronous machine under the converter control, the response delay of the wind power unit’s primary frequency regulation can be ignored. Therefore, T_Gi >> T_wi≈0.

After equivalent aggregation of the inertia response of the synchronous generator and the virtual inertia control of the wind power unit, the total inertia of the system is given by:

The frequency response model of the system after simplified aggregation is shown in Figure 2B. Its dynamic equation is shown as:

Where, N_G and N_w are respectively the number of synchronous generators and wind power units which are not tripped in the islanding system after executing ICI.

2.3.2 Islanding frequency stability constraints

Before establishing the islanding frequency stability constraints, the unbalanced power of the island must be solved first. The calculation process is shown as:

The load shedding condition is shown in Eq. 15, where is the remaining load of node I in the island k. x_i,k is a 0–1 variable, and x_i,k = 1 indicates that load node i belongs to the island k. and in - are respectively represent the active power output of synchronous generator i and wind power unit i in the island k. The power balance equation is shown as , where and are respectively the short power and surplus power. According to , the power shortage and surplus cannot exist simultaneously on an island. = 0 indicates that there is no power surplus in island k, = 1 indicates that there is no power shortage in island k.

2.3.2.1 Maximum rate of change of frequency (ROCOF) constraints

At the moment of the ICI method execution, due to the frequency regulation dead zone and control delay, the primary frequency regulation control of the wind power units and the synchronous generators are started, and the islanding system can only rely on the inertia of the units to hinder the frequency change. At this time, the primary frequency regulation power ΔP_Gi(t) and ΔP_wi(t) are 0, and the ROCOF reaches the maximum, as given by:

The maximum ROCOF constraints are shown as:Where M_sys,k is the system inertia of island k, as shown in Eq. 22. T_j,i and S_G,i are respectively the inertial time constant and the unit capacity of the synchronous generator. T_w,i and S_w,i are respectively the virtual inertia time constant and the capacity of the wind power units. f_N is the rated frequency of the system. and are the sets of synchronous generators and wind power units in island k respectively, determined by the coherency results; ROCOF_max is set as 2 Hz/s.

2.3.2.2 Transient frequency deviation constraints

Eq. 14 is discretized, and the time step between two adjacent discrete quantities is Δt (typical value is 0.05 s or 0.1 s), can be rewritten as:Where Δf_k,n is the frequency deviation of the island k relative to the frequency dead zone at number n step, ΔP_Gi,n and ΔP_wi,n are the primary frequency regulation power of synchronous generator i and the droop control power of wind farm i at number n step respectively.

Since there is a nonlinear term of the multiplication of two variables in , auxiliary variables and are defined to help linearize:

When generators or wind farms are tripped, the respective auxiliary variable is equal to 0. Otherwise, when the generators and wind farms are normally operated, the respective auxiliary variable is equal to the product of unit inertia and frequency deviation.

Based on the above derivations, the linear expressions of are given by:

The primary frequency regulation power of the synchronous generator in Figure 2 can be discretized and modeled as:Where, f_db,k is the frequency regulation dead zone of island k, is the initial active power output of synchronous generator i. According to , the primary frequency regulation power is determined by the dynamic model of the governor only when the generator is operating normally and the active power does not exceed the limit. When the active power exceeds the limit, the primary frequency regulation power is determined by the output limit. When the generator is tripped, the primary frequency regulation power is 0.

The linear expressions of are given by:Where, represents the dynamic characteristics of the low-order governor of synchronous generator i at the number n step without amplitude limits. and are respectively the upper and lower limits of the primary frequency regulation power of synchronous machine i. and are both 0–1 variables, = 1 ( = 1) indicates that the primary frequency regulation power of synchronous machine i at the number n step exceeds the upper limit (lower than the lower limit). The frequency regulation dead zone is determined according to , the upper and lower limits are set as −0.033 Hz and 0.033 Hz respectively.

The droop control characteristics of wind farm are:Where is the initial active power output of wind farm i.

After linearization, the wind farm i droop control power is shown as:Where, represents the droop characteristics of wind farm i at the number n step without amplitude limits. and are respectively the upper and lower limits of droop control power of wind farm i. and are both 0–1 variables, = 1 ( = 1) means that the droop control power of wind farm i exceeds the upper limit (lower than the lower limit) at the number n step, and the actual droop control power of wind farm i is forced at (). and are both 0 means that the droop control power does not exceed the limit, which is equal to .

The frequency deviation curve of island k can be calculated by using -, - and -. To ensure that the island frequency meets the requirements, it is only necessary that the frequency deviation of island k at each step time does not exceed the limit, as shown in:Where, Δf_d,max and Δf_d,min are respectively the upper and lower limits of the transient frequency deviation. In order to avoid triggering the low-frequency load shedding or over-frequency generator tripping, Δf_d,max and Δf_d,min are set at −0.75 Hz and 0.6 Hz respectively.

2.3.2.3 Quasi-steady state frequency deviation constraints

In the quasi-steady state stage, the frequency of the island system does not change, then is shown as:Where, Δf_d,max is the quasi-steady state frequency deviation of island k, ΔP_Gi,s and ΔP_wi,s are the droop control power of synchronous generator i and wind farm i in quasi-steady state stage respectively. The expressions are respectively given by:

The expressions after linearization with auxiliary variables are:

Where, , , , , , and are all auxiliary variables to help linearization.

The quasi-steady state frequency deviation of island k can be calculated directly by combining and -. Therefore, the quasi-steady state frequency deviation constraint of island k is:

Considering the capacity of the island system after executing ICI may be small, the Δf_s,min and Δf_s,max are set as −0.5 Hz and 0.5 Hz respectively. The values of parameters are derived from the power system operation standards.

In summary, the proposed ICI model of wind power integrated system considering frequency stability constraints is a MILP model, which can be quickly solved in MATLAB by using commercial solvers such as GUROBI (Ringkjøb et al., 2018).

3 Simulations

Based on the modified IEEE39 system (Pai, 1989), the accuracy of the frequency response model proposed and its discretized linear iterative solution algorithm is verified. And the effectiveness of the proposed ICI model in maintaining the frequency stability of the islanding system is proved. The modified system model is shown in Figure 3. There are 14 generators and 50 lines in the system. The total load power is 6,097.1 MW, and the wind power penetration rate of the system reaches 44.2%. Synchronous generator G01 is not configured with a governor, G10 is configured with an IEEEG3 governor, and other synchronous machines are configured with an IEEEG1 governor. The relevant parameters are all typical values in DigSILENT software. All of the six wind farms participate in the primary frequency regulation control. During the simulation, the proposed frequency response discretization algorithm and the ICI model are solved in MATLAB by using the GUROBI solver, while the dynamic simulation is calculated by DigSILENT.

FIGURE 3

3.1 Accuracy verification of discrete frequency response algorithm

First, a frequency step disturbance is applied to the speed control system of each synchronous generator, and then the step response of the governor is fitted with a first-order inertia link based on the least square method (Egido et al., 2009) to obtain the low-order model of each speed control system. The primary frequency regulation control parameters of the synchronous machine and the wind farm are shown in Table 1.

The following two disturbance cases are set to simulate some small disturbance scenarios such as load fluctuation and large disturbance scenarios such as line switch.

FIGURE 4

3.2 Validation of an ICI model considering island frequency stability

A three-phase fault is created on Bus3 at t = 1 s and the fault is removed at t = 1.6 s. After clearing the fault, the rotor angle of each unit (the wind farm is replaced by the voltage phase angle of the grid-connected bus) and the voltage curve of the grid-connected bus are shown in Figure 5.

FIGURE 5

After the system is disturbed, the rotor angle of synchronous generators G08, G09, and G10, as well as the grid-connected bus voltage phase angle of wind farms G11 and G13 continue to increase. The bus voltage fluctuates periodically in a wide range and over 180° at t = 1.73 s. The system is unstable and separated into two groups {G08∼G11 and G13} (island 1) and {G1∼G7, G12 and G14} (island 2). It is necessary to implement the ICI method to separate the original system into two islands.

Four different ICI strategies are shown as follows:

FIGURE 6

FIGURE 7

FIGURE 8

4 Conclusion

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