**1. Introduction**

Growing concerns for climate change, energy security, increasing fuel prices for non-renewable generation sources, price reduction for renewable sources like wind and solar power are driving power systems to have a larger share of renewables all over the world. Due to large onshore and offshore developments, wind power is set to become the leading source of electricity in Europe after 2030 [1]. Around 52.6 GW of wind power capacity was installed globally in 2017, increasing the net installed capacity to 539.6 GW [1]. Increase in the share of renewables is also phasing out the conventional generations like coal based power plants, which brings many new challenges in operation and stability of the power system. Some of these challenges include a decrease in inertia, active and reactive power fluctuations, network congestion, etc. This article deals with reactive power reserve and support from wind power plants (WPP). The reactive power reserves conventionally provided by exciter of synchronous generator reduces when replaced by WPPs. This can cause voltage stability issues. This issue is further pronounced in weak grids where WPPs are connected to the grid through long lines. The need for analysis of reactive power support from WPP is especially essential when the grid is in a stressed condition. However, integration of hundreds of WPPs in large power system analysis is very complex and computationally intensive. Therefore, simplified representations of WPPs accurate enough to reflect capabilities and limitations of the converter based wind turbines (WTs) are required to analyze future power systems.

In power system stability analysis, long-term voltage stability is defined as a slow phenomenon involving slow acting equipment like tap-changing transformers, thermostatically controlled loads, generator limiters etc., such that the network is unable to provide adequate reactive power support (at least at certain nodes or areas in the power system) [2,3]. Traditionally, realistic representations of synchronous generators along with automatic voltage regulators have been used to model the capabilities and limits of reactive power resources in long-term voltage stability studies [2]. A similar reactive power resource model for WPPs needs to be developed for future power systems dominated by converter connected power generations. In this article, WPP reactive power capability is developed for an accurate representation of maximum reactive power generation and absorption capability of IEC 61400-27-1 [4] Type 4 WT (full rated converter based WT) based WPPs.

Several studies have been carried out over the years, where WPP reactive power capability has been used for power system analyses. Reactive power capability has been used to determine the voltage dependent reactive current limitation for modelling of WT by Bech [5] and Sørensen et al. [6]. In power system operation studies, reactive power capabilities of WPPs have been used for load flow studies in [7,8]. Zhang et al. have applied reactive power capability curves of IEC 61400-27-1 Type 3 (also known as doubly fed induction generator (DFIG)) WT for loss minimisation in WPP [9]. Inclusion of Type 3 WTs in optimal power flow for loss minimisation of distribution network have been investigated by Meegahapola et al. [10]. System flexibility studies have been performed by Stankovíc and S*o*¨der to determine the reactive power capability of distribution systems with distributed wind generations [11]. Network planning studies including the reactive power capability of WPPs have been done by Ugranli and Karatepe [12]. Reactive power reserve managemen<sup>t</sup> of WPPs considering the maximum capability of WTs have been proposed by Martínez et al. [13]. Voltage control at the point of common coupling (PCC) considering reactive power capability of WPPs have been investigated by Kim et al. [14] and Karbouj et al. [15]. Reactive power capability of WPPs have also been applied for voltage stability studies. Dynamic voltage stability studies incorporating capability curves have been done by Meegahapola et al. [16]. Londero et al. [17] and Amarasekara et al. [18] have considered WT capability curves to analyze the long-term voltage stability of a power system with wind power generation. Vijayan et al. [19] have developed a voltage stability assessment method depicting that the inclusion of a WT capability curve can result in a larger power transfer margin of the system. Reactive power capability curves have also been applied for studies on ancillary services. For example, Ullah et al. have developed a generalized reactive power cost model for WPPs based on Type 4 WTs [20]. Voltage support as an ancillary service from WPPs using capability curves (for both dynamic and steady-state) have been studied by Karbouj and Rather [15].

Modelling of capability curves can be broadly categorized into: (i) WT capability curves and (ii) WPP capability curves. Lund et al. [21] have derived the steady-state capability of Type 3 WT considering rotor current, rotor voltage and stator current limitation as well as the effect of switching of coupling of DFIG stator on the capability curve. Engelhardt et al. [22] have derived capability of Type 3 WTs considering the generator and converter current limitation, losses in the machine and converter, saturation of flux, converter output voltage limitation, etc. Ullah et al. [20] have derived an analytical expression to compute reactive power capability of Type 4 WTs.

There has been limited work for representing capability curve of a WPP. Generally, there are two methods used in literature for modelling a WPP capability curve:


All these existing methodologies described in literature cannot be applied for simulating large power systems with numerous WPPs because of the following reasons:


Therefore, authors have developed a new reactive power capability model in this article which estimates reactive power close to the detailed model while requiring less parameters and computation time. The objective of this article is to develop a reactive power capability model of WPP considering the WPP collection system. The developed model considers active power generation from the WPP as well as voltage dependency at the PCC. Inclusion of the collection system assures that the active and reactive power losses in the collection system are taken into account while computing WPP capability curves. Reduced the number of parameters enables fast real-time calculation of reactive power availability of any WPP. The capability curve of WPPs is dependent on various parameters such as the number of WTs, collection system configuration and length of array cables. Sensitivity studies are performed in order to realize the impact of aforementioned parameters on the WPP capability curve. The accuracy of the proposed model is compared against the WPP detailed model and scaled WT model for different simulated case studies of real WPPs. Furthermore, all these methodologies are applied on a simulated power system model to exemplify the efficacy of the proposed model.

Organisation of the article is as follows: Section 2 describes the methodology for modelling of WPP reactive power capability. In Section 3, case studies are presented and discussed to understand effects of various parameters on WPP reactive power capability. Application of the reactive power capability model for power system studies is also shown in this section. Finally, conclusive remarks are reported in Section 4.
