Accurate estimation of precipitation from satellite precipitation products (PPs) over the complex topography and diverse climate of Pakistan with limited rain gauges (RGs) is an arduous task. In the current study, we assessed the performance of two PPs estimated from soil moisture (SM) using the SM2RAIN algorithm, SM2RAIN-CCI and SM2RAIN-ASCAT, on the daily scale across Pakistan during the periods 2000–2015 and 2007–2015, respectively. Several statistical metrics, i.e., Bias, unbiased root mean square error (ubRMSE), Theil’s U, and the modified Kling–Gupta efficiency (KGE) score, and four categorical metrics, i.e., probability of detection (POD), false alarm ratio (FAR), critical success index (CSI), and Bias score, were used to evaluate these two PPs against 102 RGs observations across four distinct climate regions, i.e., glacial, humid, arid and hyper-arid regions. Total mean square error (MSE) is decomposed into systematic (MSEs) and random (MSEr) error components. Moreover, the Tropical Rainfall Measurement Mission Multi-Satellite Precipitation Analysis (TRMM TMPA 3B42v7) was used to assess the performance of SM2RAIN-based products at 0.25° scale during 2007–2015. Results shows that SM2RAIN-based product highly underestimated precipitation in north-east and hydraulically developed areas of the humid region. Maximum underestimation for SM2RAIN-CCI and SM2RIAN-ASCAT were 58.04% and 42.36%, respectively. Precipitation was also underestimated in mountainous areas of glacial and humid regions with maximum underestimations of 43.16% and 34.60% for SM2RAIN-CCI. Precipitation was overestimated along the coast of Arabian Sea in the hyper-arid region with maximum overestimations for SM2RAIN-CCI (SM2RAIN-ASCAT) of 59.59% (52.35%). Higher ubRMSE was observed in the vicinity of hydraulically developed areas. Theil’s U depicted higher accuracy in the arid region with values of 0.23 (SM2RAIN-CCI) and 0.15 (SM2RAIN-ASCAT). Systematic error components have larger contribution than random error components. Overall, SM2RAIN-ASCAT dominates SM2RAIN-CCI across all climate regions, with average percentage improvements in bias (27.01% in humid, 5.94% in arid, and 6.05% in hyper-arid), ubRMSE (19.61% in humid, 20.16% in arid, and 25.56% in hyper-arid), Theil’s U (9.80% in humid, 28.80% in arid, and 26.83% in hyper-arid), MSEs (24.55% in humid, 13.83% in arid, and 8.22% in hyper-arid), MSEr (19.41% in humid, 29.20% in arid, and 24.14% in hyper-arid) and KGE score (5.26% in humid, 28.12% in arid, and 24.72% in hyper-arid). Higher uncertainties were depicted in heavy and intense precipitation seasons, i.e., monsoon and pre-monsoon. Average values of statistical metrics during monsoon season for SM2RAIN-CCI (SM2RAIN-ASCAT) were 20.90% (17.82%), 10.52 mm/day (8.61 mm/day), 0.47 (0.43), and 0.47 (0.55) for bias, ubRMSE, Theil’s U, and KGE score, respectively. TMPA outperformed SM2RAIN-based products across all climate regions. SM2RAIN-based datasets are recommended for agricultural water management, irrigation scheduling, flood simulation and early flood warning system (EFWS), drought monitoring, groundwater modeling, and rainwater harvesting, and vegetation and crop monitoring in plain areas of the arid region.

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This paper proposes a DC fault protection strategy for large multi-terminal HVDC (MTDC) network where MMC based DC-DC converter is configured at strategic locations to allow the large MTDC network to be operated interconnected but partitioned into islanded DC network zones following faults. Each DC network zone is protected using either AC circuit breakers coordinated with DC switches or slow mechanical type DC circuit breakers to minimize the capital cost. In case of a DC fault event, DC-DC converters which have inherent DC fault isolation capability provide 'firewall' between the faulty and healthy zones such that the faulty DC network zone can be quickly isolated from the remaining of the MTDC network to allow the healthy DC network zones to remain operational. The validity of the proposed protection arrangement is confirmed using MATLAB/SIMULINK simulations.

This paper develops a small-signal impedance model of modular multilevel converters (MMCs) using harmonic statespace (HSS) method and studies the stability in a multiple converter scenario. In order to simplify analysis on the coupling characteristics between different frequencies in MMCs, the proposed model is developed in the positive-negative-zero (PN0) sequence-frame, where the zero-sequence current in three-phase three-wire system is directly set to zero without introducing complicated method. A simple 2 by 2 admittance matrix in PN0frame is extracted from the MMC small-signal model for ease of system stability analysis. Using the developed impedance model, the multi-infeed interaction factor (MIIF) measure is adopted to analyze the most significant interactions for multi-infeed converter systems to be prioritized. Different outer-loop controllers are adopted and compared in the analysis to illustrate the effect of different control modes on converter impedance and system stability. Analytical studies and time-domain simulation results are provided to validate the proposed model and stability analysis.