Splitting Cycle Research Articles

Investigation of control strategies for the hydrogen fueled R-Graz cycle

In the context of large-scale hydrogen power generation, the Graz cycle and its improved version, the R-Graz cycle, exhibits excellent performance and technological feasibility. For such semi-closed, split cycles, apart from the conventional adjustments of fuel consumption and compressor IGV angle, compressor inlet pressure and split ratio are two additional crucial control parameters. In this study, six control strategies are firstly formulated and compared. The results indicate that the control strategy aiming to maintain the turbine inlet temperature outperforms the strategy aiming to maintain the exhaust temperature in terms of efficiency. Among them, the inventory control strategy demonstrates superior efficiency compared to the split ratio and IGV control strategies. Taking into account the advantages of various strategies, a hybrid inventory control strategy suitable for the R-Graz cycle is proposed. Based on this strategy, at 40% load and the ambient temperature of 19 °C, the efficiency reaches 87.06% of the design point, surpassing conventional F-class gas-steam combined cycle units. When the ambient temperature varies, under winter conditions of 10 °C and summer conditions of 30 °C, the full load net efficiency of the cycle reaches 72.06% and 69.60%, respectively. This research holds practical guidance value for the engineering application of the R-Graz cycle and the efficient utilization of hydrogen energy.

Modeling Development of a Receiver–Reactor of Type R2Mx for Thermochemical Water Splitting

Abstract This work reports on the development of a transient heat transfer model for a prototype reactor of type R2Mx for thermochemical water splitting by temperature and pressure swing of ceria. Key aspects of the R2Mx concept, which are also incorporated in the prototype design, include a movable monolithic redox structure combined with a linear transport system, a reduction reactor, as well as a dedicated oxidation reactor. With the model, the operation of the prototype is simulated for consecutive water splitting cycles, in which ceria is reduced in a continuously heated reactor, oxidized in a separate oxidation reactor, and transported in between the reaction zones. A 2D axisymmetric numerical model of the prototype reactor was developed in ansys mechanical. The model includes heat transfer calculations in combination with an approximated simulation of the transport of the redox material during cyclic operation. It incorporates the chemical reaction by means of a modified heat capacity for ceria and accounts for internal radiation heat transfer inside the porous redox material by applying effective heat transfer properties. A parametric analysis has been undertaken to evaluate different modes of operation of the oxidation reactor. Model results are used to size the power demand of the reduction reactor and vacuum pump, to define durations of the process steps, as well as to assess operational parameters with respect to achieved temperatures. Findings suggest that suitable operation of the prototype reactor involves reduction durations ranging from 8 to 10 min and oxidations of 6 to 10 min.

Cobalt-Based Perovskites as Efficient Oxygen Exchange Redox Materials for Solar Thermochemical Application

Solar thermochemical CO2 splitting (STCS) cycles provide the promising routes to generate renewable fuel, fuel precursors, or chemical feedstocks by the utilization of renewable resources like solar thermal energy and CO2 relating to current energy as well as climate change. Perovskites have been proposed as the potential oxygen exchange redox materials for the two-step STCS process due to their greater oxygen release and redox stability. Herein, the oxygen release and redox stability were investigated for the cobalt-based perovskites (SrCoO3-δ and SrCo0.9Zr0.1O3-δ) as the potential STCS candidates. Consequently, the XRD, FT-IR, and Raman confirmed the dual-phase perovskite constitutions of SrCo0.9Zr0.1O3-δ (i.e. SrCoO2.29 and SrZrO3) compared to SrCoO3-δ. The thermogravimetric analysis indicated the incorporation of Zr could facilitate the oxygen release and enhance the phase stability. The near-equilibrium lattice oxygen release and uptake at high temperatures could be observed through the redox performance of SrCo0.9Zr0.1O3-δ at different heating and cooling rates. The results are noteworthy and demonstrate the potential of Zr-enhanced cobalt-based perovskites as the oxygen exchange redox materials for practical solar thermochemical applications.

Enhanced Hydrogen Production in Microwave‐Driven Water‐Splitting Redox Cycles by Engineering Ceria Properties

AbstractSustainable hydrogen, produced from renewable sources such as solar or wind, plays a decisive role in driving industrial decarbonization. Among hydrogen production technologies, steam electrolysis, and solar‐driven thermochemical cycles using reducible solid oxides show promise but face challenges due to high operation temperatures. Microwave‐driven redox chemical looping enables the direct, contactless electrification of the process, reducing the operation temperature and complexity. Previous works showed that microwaves can efficiently drive reduction/water‐splitting cycles using Gd‐doped ceria at low temperatures (<250 °C), but adjustment of material properties is needed. Here, the key properties of materials are explored that affect the redox mechanism by screening a series of doped ceria materials to enhance microwave‐driven hydrogen production. Evaluation of trivalent dopants (La3+, Gd3+, Y3+, Yb3+, Er3+, and Nd3+) reveals that reduction correlates with lattice and electronic properties. The composition Ce0.9La0.1O2‐δ achieves 1.41 mL g−1, the highest hydrogen production among the studied series. Its narrower bandgap allows for reaching higher conductivity upon microwave‐driven reduction at lower temperatures, while a larger ionic lattice size boosts solid‐state oxygen diffusion. Overall, this research remarks on the critical properties of ceria‐based materials that enhance hydrogen production in microwave‐driven water‐splitting cycles, supporting the design of more efficient materials for sustainable chemical production technology.

Insights into the effect of operating parameters and hydrodynamics on hydrolysis reaction in Copper–Chlorine thermochemical water splitting cycle for hydrogen production: Modelling and experimental validation

Copper–Chlorine (Cu–Cl) thermochemical cycle is being explored as one of the promising technologies for large scale production of clean hydrogen from water using nuclear or renewable energy. In this method, water splitting is achieved through a series of reactions in a loop producing only hydrogen and oxygen with complete recycle of all the intermediate copper and chlorine compounds. The first step of the cycle is the hydrolysis reaction wherein steam reacts with solid CuCl2 to form solid Cu2OCl2 (copper oxychloride) and HCl gas. The products enter the subsequent steps of the cycle and are recycled back to complete the loop. Multiple side reactions in the hydrolysis step result in reduced yield and loss of chemicals from the cycle. Efficient reactor design and optimal operating conditions of hydrolysis reactor is imperative towards achieving sustained closed loop operation and reducing the energy demand of Cu–Cl cycle. This paper presents a mathematical model for the simulation of hydrolysis reaction in a bubbling fluidized bed reactor. The one-dimensional model is developed based on modified two-phase theory of fluidization and is coupled with kinetics of multiple side reactions to investigate the effect of operating parameters and hydrodynamics on the conversion and yield of Cu2OCl2. The model results are validated with experimental data in 50 mm and 100 mm semi-batch fluidized bed reactors. The developed model clearly brings out the effect of different process parameters for process optimization and scale-up of the hydrolysis reactor for efficient integration in the cycle.

Towards chemical equilibrium in thermochemical water splitting. Part 2: Re-oxidation

Chemical equilibrium represents the highest efficiency achievable by a thermochemical cycle under specific operational conditions. This study delves into two-step thermochemical water splitting cycles, which dissociate water into hydrogen (H2) and oxygen (O2) via sequential thermal reduction and re-oxidation processes. Building on the thermal reduction analysis presented in Part 1, this paper zeroes in on the re-oxidation reaction within the optimal reactor framework – the counter-current reactor. It elucidates the equilibrium pathway, delineating the progression of chemical equilibrium at each incremental stage of re-oxidation. Using ceria (CeO2) as a model redox-active metal oxide, the investigation analyzes the influence of operational parameters on the re-oxidation reaction. Findings reveal the theoretical feasibility of maintaining near constant temperature (±2.5 °C) during re-oxidation, achieving a total extent of reduction of 0.038 and a hydrogen conversion yield of 32%. While near adiabatic operation is also achievable, practicality is constrained by a maximum total extent of reduction of 6.5·10−3. The study also explores the economic implications of thermochemical water splitting, particularly focusing on the steam-to-hydrogen output ratio. It highlights the severe economic hurdles associated with hydrogen yields below approximately 1%. Furthermore, the investigation reveals that the addition of inert gas to the re-oxidation step offers no significant advantages. Concluding the analysis, a comparative assessment exposes negligible differences in outcomes when substituting carbon dioxide (CO2) for water (H2O) as the oxidant in low-temperature scenarios (800 °C). This comprehensive study not only advances the understanding of re-oxidation dynamics in thermochemical water splitting but also informs practical and economic considerations crucial for the advancement of this technology.

Chemical Potential Analysis as an Alternative to the van't Hoff Method: Hypothetical Limits of Solar Thermochemical Hydrogen.

The van't Hoff method is a standard approach for determining reaction enthalpies and entropies, e.g., in the thermochemical reduction of oxides, which is an important process for solar thermochemical fuels and numerous other applications. However, by analyzing the oxygen partial pressure pO2, e.g., as measured by thermogravimetric analysis (TGA), this method convolutes the properties of the probe gas with the solid-state properties of the examined oxides, which define their suitability for specific applications. The "chemical potential method" is here proposed as an alternative. Using the oxygen chemical potential ΔμO instead of pO2 for the analysis, this method does not only decouple gas-phase and solid-state contributions but also affords a simple and transparent approach to extracting the temperature dependence of the reduction enthalpy and entropy, which carries important information about the defect mechanism. For demonstration of the approach, this work considers three model systems; (1) a generic oxide with noninteracting, charge-neutral oxygen vacancy defects, (2) Sr0.86Ce0.14MnO3(1-δ) alloys with interacting vacancies, and (3) a model for charged vacancy formation in CeO2, which reproduces the extensive experimental TGA data available in the literature. The reduction behavior of these model systems obtained from the chemical potential method is correlated with simulated results for the thermochemical water splitting cycle, highlighting the exceptional behavior of CeO2, which originates from defect ionization. The theoretical performance limits for solar thermochemical hydrogen within the charged defect mechanism are assessed by considering hypothetical materials described by a variation of the CeO2 model parameters within a plausible range.

Machine learning-based multi-objective optimization and thermal assessment of supercritical CO2 Rankine cycles for gas turbine waste heat recovery

Technologies for utilizing waste heat for power generation have attracted significant attention in recent years due to their potential to enhance energy efficiency and reduce greenhouse gas emissions. This research focuses on the comparative and optimization analysis of three supercritical carbon dioxide (sCO2) Rankine cycles (simple, cascade, and split) for gas turbine waste heat recuperation. The study begins with parametric analysis, investigating the significant effects of key variables, including turbine inlet temperature, condenser inlet temperature, and pinch point temperature, on the thermal performance of advanced sCO2 power cycles. To identify the most efficient cycle configuration, a multi-objective optimization approach is employed. This approach combines a Genetic Algorithm with machine learning regression models (Random Forest, XGBoost, Artificial Neural Network, Ridge Regression, and K-Nearest Neighbors) to predict cycle performance using a dataset extracted from cycle simulations. The decision-making process for determining the optimal cycle configuration is facilitated by the TOPSIS (technique for order of preference by similarity to the ideal solution) method. The study's major findings reveal that the split cycle outperforms the simple and cascade configurations in terms of power generation across various operating conditions. The optimized split cycle not only demonstrates superior power output but also exhibits enhanced net power output, heat recovery, system and exergy efficiency of 7.99 MW, 76.17 %, 26.86 % and 57.96 %, respectively, making it a promising choice for waste heat recovery applications. This research has the potential to contribute to the advancement and widespread adoption of waste heat recovery in energy technologies boosting system efficiency and economic feasibility. It provides a new perspective for future research, contributing to the improvement of energy generation infrastructure.

An integrated alkali metal thermoelectric converter with sodium hydroxide thermoelectric water splitter and organic Rankine cycle for efficient power and hydrogen production

This study proposes the integration of the NaOH thermochemical water splitting cycle with both an alkali metal thermoelectric converter and an organic Rankine cycle. The objective of the proposed model is to enhance the overall efficiency by utilizing the waste heat generated by the NaOH thermochemical water splitting process and redirecting the heat from the alkali metal thermoelectric converter using bypass when hydrogen demand is low.Performance parameters such as system efficiency, system power, hydrogen production, AMTEC power production, and ORC power production were examined in the study. The results indicated an increase in power and hydrogen production with higher hot-end temperatures, along with an overall reduction in system efficiency for low values of load resistance. The system achieved a maximum efficiency of 53.37%.The system efficiency reached its peak at an AMTEC hot end temperature of 1173 °C, achieving 53.37 % efficiency at an RL value of 1.01 O. When the system operates at its maximum AMTEC power production, the AMTEC modules supply 12.81 kW, while the ORC generates 5.57 kW, and the hydrogen compressor consumes 0.13 kW. The total electrical power generation is 18.38 kW. The findings also indicate that the utilization of the bypass led to a reduction in hydrogen production while increasing the power output of the organic Rankine cycle.

АНАЛИЗ АДАПТИВНЫХ СИСТЕМ УПРАВЛЕНИЯ ДОРОЖНЫМ ДВИЖЕНИЕМ

This paper describes state-of-the-art adaptive control systems both in Split Cycle Offset Optimization (SCOOT), Optimization Policies for Adaptive Control (OPAC), Real-Time Hierarchical Optimized Distributed and Effective System (RHODES), Adaptive Control System-Lite (ACS-Lite), and worldwide. Urban road conditions and traffic signal timing to accommodate traffic volume changes and minimize stops and delays are controlled by adaptive traffic control systems on roadways. Based on the research objectives and comparing the positive aspects of past experiences will help traffic engineers and decision makers to select the most effective adaptive control system.

Continuous multiphase Bunsen reactor of iodine-sulfur thermochemical water splitting cycles for hydrogen production: Experimental, Modelling and Design Insights

Thermochemical water splitting cycles (TWSCs) hold promise for sustainable H2 production in future energy systems, with Iodine-Sulfur (IS) and Nickel-Iodine-Sulfur (NIS) processes standing out as efficient options. The core of both these processes lies in the Bunsen reaction, underscoring the need to identify optimal operational conditions and plant solutions for this crucial reaction section. Thus, in this study, a continuous counter-current flow Bunsen reactor fed with 5 NL h−1 of SO2 was constructed and tested. An inventive aspect was the introduction of solid I2 pellets from the top to enhance saturation at the liquid-liquid interface between sulfuric and hydriodic product phases, promoting segregation. This ingenious design achieved nearly complete SO2 conversion and optimal H2SO4 and HI concentrations in the respective product phases, while avoiding undesirable byproduct formation. The study further advanced the modelling of the experimental reactor by employing innovative kinetic and liquid-liquid equilibrium description approaches, and demonstrating exceptional validation accuracy of R2 = 0.9988. Additionally, with the aim of obtaining design charts as a potential tool for Bunsen reactor design, a microscopic model describing the gas phase trend along bubble or packed Bunsen-type reactors was developed. The model’s dimensionless analysis revealed a characteristic times ratio (Bu) comprehensively describing all the phenomena occurring to the gas phase within the Bunsen reaction section, and identified an optimal Bu value of 0.4 for pure SO2 gas inlet. Overall, the study's innovative strategies and models contribute significantly to the advancement of Bunsen reactor engineering.

Impact of operation parameters and lambda input signal during lambda-dithering of three-way catalysts for low-temperature performance enhancement

A synthetic exhaust gas bench was dynamically operated to investigate the impact of temperature, amplitude, split cycle, mean lambda, gas hourly space velocity, and oxygen storage capacity on average pollutant conversion and product selectivity of three-way catalysts in periodic operation. As temperature and amplitude increase and oxygen storage capacity decreases, the optimal frequency for maximum pollutant conversion increases. This is consistent with faster desorption of CO and O2 from the catalyst, yielding free surface sites. Regarding the formation of secondary products, the optimal frequency for maximum pollutant conversion does not always correspond to minimal N2O and NH3 emissions. The split cycle variation reveals the enhancement of C3H8 and NO conversion after both lean-rich and rich-lean switches and C3H6 and CO conversion after rich-lean switches at the optimal frequency. As periodic operation does not affect existing engine settings or operating conditions, it is a cost-effective control strategy for meeting future emission limits.

Thermodynamic analysis on CSP integrated cerium oxide (CeO2 − CeO1.72/1.83) water splitting cycle for hydrogen production

Solar thermochemical CeO2-based H2O splitting cycle was thermodynamically analyzed to ascertain the optimal thermal reduction (TH) and re-oxidation (TL) temperatures and evaluate the solar-to-fuel conversion efficiency (ηsolar−to−fuel) of the cycle. The equilibrium composition of CeO2, CeO1.72,CeO1.83 and O2 exhibited that the thermal reduction initiated at 1400 K thereby attaining 100 % TR at 2734 K. The observed variations in Gibbs free energy (ΔG) correspond to the feasibility of the re-oxidation step of CeO1.83 and CeO1.72 at 1050 K and 1200 K respectively. It was reported that the absorption efficiency of solar reactor (ηabs−solar−reactor−WS) decreases from 95.6 % to 37 %, as the TH increases from 1400 K to 2734 K. The results show that ηsolar−to−fuel reached the maximum value of 7.45 % for CeO1.72 and 7.69 % for CeO1.83 at 61.72 % TR of CeO2 without heat recuperation. Further, the ηsolar−to−fuel attained the maximum value of 14.92 % and 13.54 % for CeO1.83 and CeO1.72, respectively at the %TR of CeO2 of 80 % with 50 % heat recuperation. The solar-to-fuel conversion efficiency (ηsolar−to−fuel) further can be increased with the optimization of oxygen partial pressure (PO2) and molar flow rate of reduction regents (Ar or N2).

H2 producing hybrid solar thermochemical ZnSO4/ZnO water splitting cycle: Thermodynamic efficiency analysis

This investigation reports the thermodynamic efficiency analysis of a hybrid ZnSO4/ZnO water-splitting cycle. The data required for efficiency calculations are gathered from HSC Chemistry Software. The prime goal is to examine the effects of the thermal energy needed for heating inert sweep gas and separating the gaseous components in the cycle on the solar-to-fuel energy conversion efficiency. Complete dissociation of ZnSO4 into ZnO, SO2, and O2 is considered. Besides, a comprehensive re-oxidation of ZnO in the presence of SO2 and H2O is assumed. A thermodynamic process model, which includes reduction and oxidation reactors, two separators, multiple gas-to-gas heat exchangers, two heaters, and one ideal H2/O2 fuel cell, is developed and used to analyze the efficiency. The energy required for the separation of inert/O2/SO2 gas mixture is observed to be one of the significant contributors to the energy needed to drive the ZnSO4/ZnO WS cycle. The solar power required (989.9 kW) is recorded to be the lowest for the inert gas molar flow rate equal to 10 mol/s. Because of the low solar energy requirement, the maximum solar-to-fuel energy conversion efficiency (28.4 %) is attained at the thermal reduction temperature of 1445 K.

Hydrogen production using hybrid six-step copper-chlorine thermochemical cycle: Energy and exergy analyses

The hybrid thermochemical copper-chlorine (Cu–Cl) cycle for water splitting, developed as a novel approach to produce green hydrogen, has gained greater attention. A series of close-loop reactions makes the process environmentally friendly. A newly developed hybrid six-step Cu–Cl cycle consists of thermochemical, electrochemical, and a unit operation of spray drying. The present paper analyzes the configuration of the six-step Cu–Cl cycle thermodynamically. Studies on many factors are carried out to determine the cycle's total energy and exergy efficiency. The modeling and simulation of the six-step process was done by Aspen Plus. The six-step cycle was found to have an energy and exergy efficiency of 38.94 % and 52.74 %, respectively. The effect on exergetic efficiency with ambient temperature and cycle temperature variation was also investigated. The enhancement in the effectiveness of six steps Cu–Cl cycle could be possible from the current study analysis using thermal recovery and minimizing exergy destructions.

Process splitting analysis and thermodynamic optimization of the Allam cycle with turbine cooling and recompression modification

Allam cycle is an advanced semi-closed supercritical carbon dioxide (sCO2) power cycle that utilizes hydrocarbon fuels with nearly zero carbon emission. Different from other closed power cycles, in the Allam cycle, the oxy-fuel combustion products are directly mixed with the working fluid and the turbine blade cooling is necessary for the high cycle temperature above 1000 °C; moreover, the heat integration might be applied to the Allam cycle to improve the thermodynamic performance, making the Allam cycle complex and hard to conduct the process and parameter optimization. To deepen the understanding on the performance of the Allam cycle with turbine cooling and recompression modification, a novel splitting analytical method is developed that the Allam cycle is split into the closed cycle and open process, and the closed cycle is further split into the simple host cycle and two equivalent power cycles. Using the constructed splitting analytical models, the influences of the turbine cooling and the recompression modification on the net efficiency are clearly evaluated by the split cycles, and the highest efficiency of the Allam cycle is optimized to be 49.92 % (higher heating value) as the coolant temperature and recompression mass flow rate are 320 °C and 439.5 kg/s, respectively.

High-entropy perovskite oxides for direct solar-driven thermochemical CO2 splitting

The global energy crisis and climate change have fueled interest in solar-driven thermochemical CO2 splitting as a potential solution. However, conventional materials like CeO2 encounter limitations attributable to their low solar absorptivity and CO yield (even at high reduction temperatures), exerting a detrimental influence on both solar energy utilization and process efficiency. This study proposes high-entropy A-site doped perovskites as a potential solution for efficient solar thermochemical CO2 splitting. The increased configurational entropy enhances the solar thermal CO2 splitting cycles by decreasing oxygen vacancy formation energy and lattice oxygen migration energy barrier. This is supported by experimental results, where Sm0.25Sr0.25Ca0.25La0.25MnO3 achieved a maximum CO yield of 764.76 μmol g−1 with low temperature difference between the reduction and oxidation steps, marking an important progress in solar thermal CO2 splitting cycles. The study demonstrates the potential of high-entropy perovskites for direct solar energy harvesting with high spectrum absorption coefficients and sustainable CO2 utilization.

Redox Performance and Optimization of the Chemical Composition of Lanthanum–Strontium–Manganese-Based Perovskite Oxide for Two-Step Thermochemical CO2 Splitting

The effects of substitution at the A- and B sites on the redox performance of a series of lanthanum–strontium–manganese (LSM)-based perovskite oxides (Z = Ni, Co, and Mg) were studied for application in a two-step thermochemical CO2 splitting cycle to produce liquid fuel from synthesis gas using concentrated solar radiation as the proposed energy source and CO2 recovered from the atmosphere as the prospective chemical source. The redox reactivity, stoichiometry of oxygen/CO production, and optimum chemical composition of Ni-, Co-, and Mg-substituted LSM perovskites were investigated to enhance oxygen/CO productivity. Furthermore, the long-term thermal stabilities and thermochemical repeatabilities of the oxides were evaluated and compared with previous data. The valence changes in the constituent ionic species of the perovskite oxides were studied and evaluated by X-ray photoelectron spectroscopy (XPS) for each step of the thermochemical cycle. From the perspectives of high redox reactivity, stoichiometric oxygen/CO production, and thermally stable repeatability in long-term thermochemical cycling, Ni0.20-, Co0.35-, and Mg0.125-substituted La0.7Sr0.3Mn perovskite oxides are the most promising materials among the LSM perovskite oxides for two-step thermochemical CO2 splitting, showing CO productivities of 387–533 μmol/g and time-averaged CO productivities of 12.9–18.0 μmol/(min·g) compared with those of LSM perovskites reported in the literature.

Surface tension effects on cryogenic liquid injection dynamics in supercritical environment

The injection of cryogenic fluids into environments where the prevailing conditions are supercritical in comparison to the critical point of the injected cryogenic fluid is encountered in cryogenic rocket engines, and novel engine architectures such as the recuperated split cycle engine. The physical characteristics of cryogens injected into supercritical environment are rather unclear. While surface tension is usually assumed to be absent/negligible for supercritical fluids, recent experimental research has identified the existence of surface tension and its effects on liquid hydrocarbons in supercritical environment. This research work proposes an alternative computationally simple adaptive surface tension algorithm for the simulation of a liquid injected into supercritical environment. The numerical simulations presented here correspond to single- and binary-specie cases of iquid nitrogen and liquid methane respectively, undergoing phase transition post their injection into supercritical conditions. Following a critical review of related numerical works, this paper begins with a brief explanation of the physics behind the surface tension effect in a binary-fluid interface in which a supercritical fluid is involved and we present why this effect is of relevance to supercritical cryogenic jets? Then, the rationale and specifics of the the new modelling framework based on adaptive surface tension is discussed along with its implications. The results of the numerical simulations of low-temperature vs near-critical temperature iquid nitrogen and liquid methane injection dynamics revealed the drastically different fluid- and thermo-dynamics at play in these two cases. The role of surface tension at these conditions is also explored.

Split Cycle: a new Condorcet-consistent voting method independent of clones and immune to spoilers

We propose a Condorcet-consistent voting method that we call Split Cycle. Split Cycle belongs to the small family of known voting methods satisfying the anti-vote-splitting criterion of independence of clones. In this family, only Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, in contrast to other clone-independent methods, Split Cycle mitigates both “spoiler effects” and “strong no show paradoxes.”