Evaluating grid strength under uncertain renewable generation
Introduction
Integration of inverter-based renewable energy resources (IB-RERs) like wind and solar in North American power grid has surpassed 100 GW in 2016 [1]. While the IB-RERs supply clean energy to electricity customers, they pose many challenges in grid planning and operation. The IB-RERs provide expected real and reactive power based on the electronic controls, which separate the power source from the grid. The predominant control strategy for contemporary IB-RERs is grid-following, where a phase-locked loop tracks the voltage at the point of interconnection (POI), which is, in general, assumed to be stiff [1], with which an output current is generated to achieve power set points. An associated challenge with high instantaneous penetrations of grid-following IB-RERs is the reduction of synchronous generation that forms the basis of this stiff grid assumption, which results in a weak grid. Under weak grid conditions, the grid voltage is sensitive to active and reactive power disturbances, which may result in potential voltage stability and grid reliability issues. Such weak grid issues are becoming prominent due to the variability and uncertainty of renewable generation [2].
Potential weak grid issues are usually analyzed and identified based on grid strength assessment. In the assessment, short-circuit ratio (SCR) is an index recommended by North American Electric Reliability Corporation (NERC) to quantify the grid strength [1], [3]. The commonly used SCR calculation method ignores the interactions among IB-RERs and thus may cause an inaccurate estimation of grid strength at POIs for IB-RERs [1], [4]. To consider the effect of IB-RERs interactions on grid strength, several new methods have been developed, such as the weighted short-circuit ratio (WSCR) method developed by the Electric Reliability Council of Texas (ERCOT) [4] and the composite short-circuit ratio (CSCR) method developed by GE Energy Consulting [5]. Both CSCR and WSCR methods do not consider the real electrical network connections among IB-RERs, and therefore do not reflect the actual strength of the grid at the POIs. Moreover, both these methods mainly provide the aggregated strength of a power grid in the area where the IB-RERs are interconnected electrically close, but they do not calculate the strength of the grid at each individual POI in the specific area. To overcome those shortcomings, various metrics have been proposed, such as the site-dependent short-circuit ratio (SDSCR) method is proposed in [6], network response short-circuit ratio (NRSCR) [7], generalized short-circuit ratio (gSCR) [8], and hybrid multi-infeed effective short-circuit ratio (HMIESCR) [9]. The gSCR and HMIESCR are proposed for grid strength analysis in multi-infeed HVDC (MIDC) systems, while the SDSCR and NRSCR are mainly proposed for grid strength assessment in power systems with high penetration of renewable resources. In addition, the SDSCR has further been extended to effective site-dependent short circuit ratio (ESDSCR), which considers the impact of interconnected capacitors at POIs on grid strength in power systems with high penetration of renewable resources [10].
With the intermittent nature of renewable generation resulting from uncertain weather conditions, grid strength may change with uncertain renewable generation. Thus, quantifying the impact of uncertain renewable generation on grid strength will be critical to prevent the potential weak grid issues via grid planning and operation, especially in an IB-RER-dominated grid. Traditionally, the uncertainty evaluation can be evaluated using Monte Carlo simulation (MCS) [11], [12], [13]. However, the MCS typically repeats deterministic grid strength analysis by using a massive number of renewable generation samples to render the uncertainty characteristics of the results.
To improve simulation efficiency, this paper proposes an uncertainty evaluation algorithm to quantify the impact of uncertain renewable generation on grid strength based on the probabilistic collocation method (PCM). The PCM has been studied for uncertainty analysis in numerous power system studies [14], [15], [16], [17], [18]. The proposed algorithm can use the probability distributions of renewable generation to quantify the probabilistic characteristics of grid strength through a set of orthogonal polynomials to approximate the original models. The calculation is made to determine the parameters in the approximation functions which can obtain the desired precision of results using a small number of simulations. Therefore, the proposed algorithm significantly reduces the computational burden and outperforms MCS thousands of times in terms of simulation efficiency. To further enhance the accuracy of the proposed algorithm, the K-means clustering technique is introduced to the PCM for selecting the representative approximation samples to describe the probabilistic characteristics of uncertain renewable generation. The major contributions of this paper are summarized as follows.
(1) An uncertainty evaluation algorithm is proposed to quantify the impact of uncertain renewable generation on grid strength by integrating the PCM with grid strength assessment. Since the PCM can obtain accurate results using a small set of simulations, this method can potentially be used to save computational cost without compromising the result accuracy compared to the MCS simulation.
(3) The K-means clustering technique is introduced to the PCM to select the representative approximation samples for improving the approximation accuracy for grid strength analysis under uncertain renewable generation.
(3) The efficacy of the proposed algorithm is validated on the modified IEEE 9-bus and IEEE 39-bus systems.
The rest of this paper is organized as follows. In Section 2, grid strength assessment is discussed. In Section 3, the principle of PCM is introduced. Section 4 presents our proposed method for quantifying the impact of uncertain renewable generation on grid strength. The efficacy of the proposed method is demonstrated in Section 5. In Section 6, the conclusions are drawn.
Section snippets
Grid strength assessment
Grid strength assessment can help grid engineers identify and understand “weak” grid issues for reliably planning and operating the power grid. Grid strength is a measure of an electrical power system that evaluates the change in voltage and operating conditions, following a disturbance in the power system [19]. The strength of a power grid at POI is commonly quantified by SCR, which is the ratio of the short circuit capacity at the POI to the rated capacity or injected power from the IB-RER. A
Probability collocation method (PCM)
PCM is an uncertainty modeling approach using Gaussian quadrature to map the relationship between the uncertain input parameters and the output. In the PCM, the relationship between the uncertain parameter and the output response is represented through polynomial equation to identify a good set of simulations for correctly and robustly determining the mapping. The PCM model is derived based on the concept of orthogonal polynomials [15].
Uncertainty assessment method for grid strength analysis
To evaluate the strength of the power system under uncertain renewable generation, the ESDSCR-based method is integrated with the PCM, which probabilistically models the impact of uncertain renewable generation based on their historical data and evaluates the probabilistic results instead of deterministic values.
System description
The proposed method for quantifying the impact of uncertain renewable generation on grid strength is validated on the modified IEEE 9-bus and IEEE 39-bus systems. In the modified IEEE 9-bus system as shown in Fig. 4, the two synchronous generators at buses 2 and 3 are replaced with two solar farms with 100 MW and 50 MW rated power, respectively. The values of the parameters for the beta pdf and the orthogonal polynomials for the respective irradiance of the solar farms are listed in Table 1,
Conclusion
This paper presented an approach to analyze the impact of uncertain renewable generation on grid strength by integrating the PCM with the ESDSCR-based method. In the proposed approach, the ESDSCR-based method was used for grid strength assessment, while the PCM was used to establish the approximation polynomial functions with multiple input variables for modeling the impact of uncertain renewable generation. To improve the approximation accuracy of the PCM, K-means clustering technique was
CRediT authorship contribution statement
Manisha Maharjan: Methodology, Software, Visualization, Investigation, Validation, Writing – original draft. Almir Ekic: Data curation, Software. Mari Beedle: Writing – review & editing. Jin Tan: Writing – review & editing. Di Wu: Conceptualization, Supervision, Writing – review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
The authors would like to thank Emily L Barrett from PNNL for her valuable suggestions on the manuscript. The authors express their gratitude to the funding provided to support this study from National Science Foundation (NSF), USA EPSCoR RII Track-4 Program under the grant number OIA2033355. The findings and opinions expressed in this article are those of the authors only and do not necessarily reflect the views of the sponsors.
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