Forward Sweep Research Articles

Aerodynamic Instabilities of Swept Airfoil Design in Transonic Axial-Flow Compressors

This paper investigates the effect of a swept airfoil design on the aerodynamic instabilities of transonic axial-flow compressors based on global stability analysis. An approach aimed at predicting the stall inception point is developed by integrating an improved blade force model and a new mathematical treatment method for steady flow. This approach takes both the concrete blade geometry and complicated base flow into consideration, which promises to provide a highly efficient assessment of the stall margin of a compressor in the design phase. Specifically, the relevant validation is conducted through a typical transonic axial-flow compressor, which shows that the predicted stall inception point agrees well with the experimental result. Furthermore, the compressor is also adopted as a prototype, from which a series of forward- and backward-swept rotors are modeled. Aerodynamic instabilities in the form of eigenvalues for each swept rotor, along with the throttling process, are predicted by solving the developed stall inception model. The comparison of the predicted results for these rotors shows that the backward sweep deteriorates the stall margin; the larger the backward-swept degree, the poorer the compressor stability becomes. However, the forward sweep does not exhibit remarkable and regular influence on the stall margin of the compressor in the present research. A discussion of the predicted results is made from the perspectives of blade loading and passage shock location.

Using forward end-sweep to reduce transonic cantilevered stator losses to improve compressor performance

ABSTRACTThe complicated flows in a transonic cantilevered stator would cause serious aerodynamic losses and reducing these losses would contribute much to improving the overall aerodynamic performance of a compressor. The paper conducts an overview study of the potential aerodynamic losses in a transonic cantilevered stator and presents a systematic numerical study for the effects of forward end sweep on reducing aerodynamic losses. A 2-D stator blade is used to throw light upon the physical mechanism of the forward end sweep on reducing the losses. At the casing region, forward end sweep has led to a redistribution of the blade load along the chordwise direction, higher in the front part and lower in the rear part. This result leads to a lower pressure gradient from the 30% chord location to the trailing edge and can be beneficial for the reduction of the corner separation. At the hub region, on one aspect, forward end sweep reduces both the peak Mach number and the size of the high-Ma region of the blade suction surface, thus decreasing the shock loss near the hub. On the other aspect, it also reduces the peak load and the strength of the leakage vortex, therefore alleviating the flow blockages. Simultaneously, the forward end sweep is applied to a commercial and high-performance multistage compressor to further validate its feasibility. When the technique is applied to the transonic first four stator rows, an improvement of adiabatic efficiency is achieved by ∼ 0.85% and the compressor stable operating range is slightly increased. The results suggest that the forward end-swept transonic cantilevered stators have a significant potential for reducing the stator losses. They would provide guidelines to advance the cantilevered stator design and further improve the compressor aerodynamic performance.Abbreviations: h, stagnation enthalpy; , stagnation pressure; p, static pressure; U, blade rotational speed at tip; V, velocity; , non-dimensional wall distance; , total pressure loss coefficient; , flow coefficient (Vx/U); , stage load coefficient (Δh/U2); , adiabatic efficiency; , total pressure ratio; in, inlet; out, outlet; LE/TE, leading/trailing edge; PS/SS, pressure/suction surface

Transport in Short-Period GaAs/AlAs Superlattices with Electric Domains

AbstractElectronic transport in short-period GaAs/AlAs superlattices with resonant cavities was studied at room temperature. The evolution of tunneling current at forward and backward bias sweep was investigated. The step-like decrease in current at some threshold voltage was referred to moving domain formation. The current hysteresis observed in current-voltage characteristics was explained by changes in electrical domain regimes. The series of maxima in the current-voltage characteristics was attributed to resonant tunneling of electrons through several barriers inside the domain. The change of threshold voltage for the domain formation at the change of the cavity parameters explained by the excitation of high-amplitude oscillations in the cavity which demonstrated the possibility to excite oscillations in the THz cavity by dynamical negative resistance of SLs with domains.

Intrinsic charge carrier mobility in single-crystal OFET by “fast trapping vs. slow detrapping” model

Abstract This study investigates the gate stress-induced mobility discrepancy in p-type single-crystal organic field-effect transistors (OFETs) on an octyltrichlorosilane (OTS)-modified SiO2/Si substrate. During measurements in atmosphere, anti-clockwise hysteresis was observed in the transfer curve, and the mobility calculated from the forward sweep was smaller than that calculated from the reverse sweep. Hysteresis has often been observed for OFETs but the mobility discrepancy has not been clearly understood. We formulated a “fast trapping vs. slow detrapping” model and suggested that the mobility values calculated from the reverse sweep represent the intrinsic property of the material. To verify the validity of this model, we investigated mobility anisotropy of an air-stable organic semiconductor, 2,7-bis(4-methoxyphenyl)benzo[b]benzo[4,5]thieno[2,3-d]thiophene (DBOP-BTBT). By measuring the single-crystal OFET characteristics of many crystals with different orientations, we observed anisotropic hole mobility calculated from the reverse sweep. The mobility along the b-axis, which corresponds to the π-π stacking direction, was 13.9 cm2 V−1 s−1, and that along the a-axis was 6.2 cm2 V−1 s−1. However, we did not see clear anisotropy when mobility was calculated from the forward sweep due to a variation in the data. The threshold voltage from the reverse and the forward sweeps showed isotropic characteristics within the range from −60 to −70 V and from −50 to −60 V, respectively. These results indicate that the numbers of filled traps were different between the reverse and the forward sweeps at the interface, and confirm the validity of our model.

Siting and sizing of distributed generators based on improved simulated annealing particle swarm optimization.

Distributed power grids generally contain multiple diverse types of distributed generators (DGs). Traditional particle swarm optimization (PSO) and simulated annealing PSO (SA-PSO) algorithms have some deficiencies in site selection and capacity determination of DGs, such as slow convergence speed and easily falling into local trap. In this paper, an improved SA-PSO (ISA-PSO) algorithm is proposed by introducing crossover and mutation operators of genetic algorithm (GA) into SA-PSO, so that the capabilities of the algorithm are well embodied in global searching and local exploration. In addition, diverse types of DGs are made equivalent to four types of nodes in flow calculation by the backward or forward sweep method, and reactive power sharing principles and allocation theory are applied to determine initial reactive power value and execute subsequent correction, thus providing the algorithm a better start to speed up the convergence. Finally, a mathematical model of the minimum economic cost is established for the siting and sizing of DGs under the location and capacity uncertainties of each single DG. Its objective function considers investment and operation cost of DGs, grid loss cost, annual purchase electricity cost, and environmental pollution cost, and the constraints include power flow, bus voltage, conductor current, and DG capacity. Through applications in an IEEE33-node distributed system, it is found that the proposed method can achieve desirable economic efficiency and safer voltage level relative to traditional PSO and SA-PSO algorithms, and is a more effective planning method for the siting and sizing of DGs in distributed power grids.

Sensitivity analysis of convergence characteristics in power flow methods for distribution systems

This paper presents an evaluation of the main convergence characteristics of multiphase power flow methods in unbalanced distribution systems. Two widely used methods for solving unbalanced power flows are analyzed: methods based on Newton–Raphson (NR) and methods based on backward forward sweep (BFS). The limits and robustness of the BFS method and NR method are tested in the following aspects: (i) variation of the X/R ratio, (ii) load’s increase up to the convergence limit, (iii) load model impacts (ZIP model), and (iv) voltage regulators modeling impacts. Some models presented in the literature were implemented and tested. Tests are performed on the IEEE 34 and IEEE 123 systems. Analytical explanations are also presented.

Reduced interface losses in inverted perovskite solar cells by using a simple dual-functional phenanthroline derivative

Interface losses at metal/organic interface is a critical issue in organic electronic devices. The interfacial layers play a significant role in enhancing the device performance and the interfacial material design criteria are ongoing challenges to be faced in optimization the device performance. In this work, a simple Phenanthroline derivative Phen-I was synthesized through a quaternization reaction in a high yield without complicated purification process. Besides its good wettability and compatibility of the contact between metal electrode and organic layer, interestingly, Phen-I displays a dual functional property, i.e., it not only lowers the work function of the metallic cathode to increase electron extraction but also can be doped into electron transporting material to enhance the conductivity. The inverted perovskite solar cells (PSCs) with Phen-I as cathode interlayer (CIL) show superior performance both in power conversion efficiency, with a maximum PCE of 18.13%, and devices stability as compared with the control devices. Encouragingly, the best PCE of 19.27% was obtained when the perovskite layer based on FA0.3MA0.7PbI2.7Cl0.3 perovskite system. Meanwhile, the devices with Phen-I as CIL show low J-V hysteresis during the forward and reverse bias sweeping. Subsequent studies demonstrate that the performance of the inverted PSCs also improves to 15.25% using 5% Phen-I:PC61BM as electron transporting layer (ETL). Herein, the interface between the metal electrode and ETL is carefully investigated using a series of electrical and surface potential techniques. These results demonstrate that Phen-I is a dual-functional interlayer material to reduce interface losses, which, highlights the broad promise of this new class of materials for applications in organic electronic devices. Meanwhile, owing to the simple molecular structure, low-cost and solution processible, these intriguing features render Phen-I more suitable for efficient organic electronics in large area printing process.

Free-Form Versus Ruled Inducer Design in a Transonic Centrifugal Impeller

The detailed design of the inducer of a high pressure ratio transonic radial compressor impeller with a design inlet tip relative Mach number of 1.4 is considered. Numerical analysis has been used to compare a datum impeller with ruled inducer design with a number of different free-form design concepts, generated following the same aerodynamic design philosophy. The datum stage and one with a free-form inducer, referred to as “barrelled forward swept,” with forward swept leading edge near the tip and increased chord at midspan, have been manufactured and tested. The tests were performed with the same stationary components, including the casing, vaned diffuser, and the volute. The design with a barrelled forward sweep of the inducer allows the designer more control of the strength and position of the passage shock at the inlet while meeting mechanical constraints. Interestingly, the performance is also enhanced at off-design points at lower tip-speeds. The measurements show that the stage tested with the swept impeller achieves higher efficiency of between 0.5% and 1.6% compared to the datum design, depending on the operating speed. The computational fluid dynamics (CFD) simulations are used to further study the flow at part speeds, in order to explain the causes of the observed performance differences at off design conditions.

β-Ga2O3 Nanomembrane Negative Capacitance Field-Effect Transistors with Steep Subthreshold Slope for Wide Band Gap Logic Applications.

Steep-slope β-Ga2O3 nanomembrane negative capacitance field-effect transistors (NC-FETs) are demonstrated with ferroelectric hafnium zirconium oxide in the gate dielectric stack. Subthreshold slope less than 60 mV/dec at room temperature is obtained for both forward and reverse gate-voltage sweeps with a minimum value of 34.3 mV/dec at the reverse gate-voltage sweep and 53.1 mV/dec at the forward gate-voltage sweep at VDS = 0.5 V. Enhancement-mode operation with a threshold voltage of ∼0.4 V is achieved by tuning the thickness of the β-Ga2O3 membrane. Low hysteresis of less than 0.1 V is obtained. The steep-slope, low hysteresis, and enhancement-mode β-Ga2O3 NC-FETs are promising as an nFET candidate for future wide band gap complementary metal-oxide-semiconductor logic applications.

Mechanisms of Sweep on the Performance of Transonic Centrifugal Compressor Impellers

Transonic centrifugal compressors with high performance are required in the oil and gas industries, modern gas turbine engines, and turbochargers. The sweep of the blades is one of the crucial features that have a significant influence on their performance. This paper numerically investigates mechanisms by which sweep affects the performance of a transonic impeller with twin splitters. Sweep is defined as scaling up or down the shroud chord, and the variation range of the sweep angle has been chosen from −25 to +25°. In the current case, results show that the variation of choke mass flow rate, pressure ratio, and efficiency value is around 1%. If the centrifugal compressor has a higher pressure ratio or a higher front loading, the sweep effect on compressor performance will be even stronger. The essential aerodynamic effect of sweep is the spanwise redistribution of the front loading, resulting in effects on the shock structure, the tip leakage vortex, and the flow separation. On the shroud section, forward sweep restricts the front loading, the shock strength, and the tip leakage vortex, which reduces the loss near the casing. On the hub section, aft sweep suppresses the front loading and the flow separation, which reduces the loss near the hub. It is the delicate balance between controlling the loss near the hub and the loss near the casing that determines the optimal sweep angle design.

Perched landing manoeuvres with a variable sweep wing UAV

A variable sweep wing UAV is developed utilising off the shelf components with a custom mechanism for the wing box. The movement of the wing sweep in flight enables large pitching moments suitable for performing perching manoeuvres. Wind tunnel data is presented that confirms the favourable characteristics expected from sweeping the wing and achieving high pitch rates. Whilst only small sweep changes are required during flight, the design allows up to 30∘ forward sweep for significant pitching moments during the flare.A new collection of controllers is developed based on observations from similar landing techniques performed by birds and hang-gliders onto flat ground. The three-stage landing process takes the aircraft along an approach path, through a roundout procedure during which airspeed decays and concludes with rapid pitch up. Flight test results are presented during which it is found that the airspeed can be reduced to, on average, under 3 m/s in the final moments before landing – well below the stall speed of 9 m/s.

Deep Level Assessment of n-Type Si/SiO2 Metal-Oxide-Semiconductor Capacitors with Embedded Ge Quantum Dots

Device structures with silicon or germanium nanodots embedded in an oxide matrix may find application in the field of Non-Volatile Memories (NVMs) [1,2] or photonics [3,4]. In the former case, the nanodots can become charged by tunneling of electrons or holes from the silicon substrate through a tunnel oxide. Successful operation requires that the charge does not leak away by the assistance of traps or defects in the material stack. The latter can be probed by techniques like Admittance Spectroscopy [5] or Deep-Level Transient Spectroscopy (DLTS) [2,5]. In the present work we report on a systematic investigation of Metal-Oxide-Semiconductor (MOS) capacitors fabricated on n-type Czochralski silicon substrates and containing Ge nanodots with different size. Ge nanodots with average diameter of 1, 2 or 3 nm have been deposited by Molecular Beam Epitaxy (MBE) on a 5 nm tunnel oxide, thermally grown on n-type Czochralski silicon wafers. An Atomic Force Microscopy (AFM) picture is shown in Fig. 1. Next, 50 nm of SiO2 is deposited. MOS capacitors are prepared by thermal evaporation of 2 mm diameter Al gate contacts, while InGa+In foil ohmic contacts are prepared on the silicon substrate side. The device structure is schematically shown in Fig. 2. Capacitance-Voltage (C-V) characterization is performed at a fixed frequency f=1 MHz, using both a forward and reverse gate voltage sweep. As can be seen in Fig. 3, the presence of the Ge nanodots has a pronounced impact on the C-V characteristics: there is a shift towards positive flat-band voltage, compared with the zero dot reference, a strong increase of the accumulation capacitance and, for the nanodot samples, the hysteresis increases with the increase in nanodot size. For temperature (T-) scan DLTS, the capacitors are mounted in a helium contact gas cryostat cooled with liquid nitrogen. Measurements at different bias pulses from reverse bias (VR) to the pulse bias (VP) are performed in parallel in order to probe the electron traps in different parts of the structure. An example is given in Fig. 4, for the 1 nm nanodots sample. It shows that in deep depletion, there is a broad peak between 150-250 K which could stem from the response of filled interface traps. The increase found at room temperature may originate from minority carrier generation in the depletion region [2,5,6]. When probing closer to the interface, for more positive VR, a pronounced but broad peak around 200 K dominates the spectra. From the Arrhenius plot shown in Fig. 5, it is concluded that it corresponds to the dangling bond (Pb) acceptor level at about 0.31 eV from the conduction band [2,5,6]. Maximum densities are estimated in the range of 5x1011 cm-2eV-1. A comparison of the spectra near the interface for the different samples studied is provided in Fig. 6 and will be discussed in more detail in the conference paper.

Load Flow Analysis for AC/DC Distribution Systems with Distributed Generations

Hybrid AC/DC distribution systems are rapidly growing due to the recent developments in power electronic technologies and increasing deployment of DC output type distributed generations (DGs) in distribution voltage levels. The presence of DGs in DC distribution systems imposes new challenges in load flow calculations. In response, this paper is dealing with the load flow calculation problem in AC/DC distribution systems in the presence of different kinds of DGs. For this purpose, mathematical models of different kinds of DGs are presented, and then, the models are incorporated into the sensitivity matrix method for using in load flow calculations. Since the large number of load buses and the high R/X ratios in the AC part of the system can lead to the divergence of Jacobian matrix based methods, the suggested method is based on backward forward sweep (BFS) method. The proposed method is simulated on a test system equipped with different kinds of DGs and converters and the results are presented.

Optimal Active Energy Loss with Feeder Routing and Renewable Energy for Smart Grid Distribution

Electric power is the main energy source for a modern society. Good management of electric power cycle is essential for a sustainable society. The electric power cycle is composed of Generation, Transmission, Distribution, and Consumption. Smart Grid (SG) is a system that integrated traditional grids with Information and Communication Technology (ICT). In addition, SG has the ability to integrate electrical power supply from both to main power substation and Distributed Generation (DG), which compensates for the power demand during peak times. However, SG still has a similar problem to the original grid in terms of active power loss, from electric current injecting through the transmission line. This paper solves the active power loss problem by feeder routing using the Adjusting Dijkstra's Cost Method, follow by deciding the allocation position and sizing of DG by the use of Evolutionary Computing, namely Harmony Search (HS), Artificial Bee Colony (ABC), and Particle Swarm Optimization (PSO). The experiments evaluate the performance of the algorithm using power flow analysis, Backward / Forward Sweep Method, on the IEEE 33 bus system. From the experimental results, PSO provides the best performance. The overall active power loss in the cases of 3 DGs was reduced from 202.67 to 52.29 kW, representing a reduction of 74.20%.

Head Accelerations Associated with Six Standard Judo Throws and Break Falls

The contact sport of judo involves throwing an opponent in a variety of ways, with potential risk of concussive head impacts. When being thrown, a judo practitioner executes a break fall, theoretically protecting the head from injury. However, little research has directly measured head accelerations of a person executing a break fall in response to various throws in judo. PURPOSE: Quantify and compare head accelerations associated with six standard judo throws and corresponding break falls. METHODS: In random and repeated design, 14 judo martial artists (13 male, 1 female; age = 28 ± 9 yrs; stature = 177 ± 6.7 cm; mass = 80.3 ± 9.4 kg; rank = brown or black belt) performed five sets of six standard judo throws & corresponding break falls. The six throws were layback throw (tomoe-nage), hand throw (tai-otoshi), leg sweep (harai-tsuri-komi-ashi), shoulder throw (seoi-nage), forward leg sweep (deashi-braai), and thigh throw (uchi-mata). The participant being thrown wore a headband-mounted tri-axial accelerometer, measuring linear (g) and rotational accelerations (krad•s-2) of the head when performing a break fall corresponding with one of the six throws. Minimum threshold for registering acceleration was 16 g. RESULTS: Repeated measures one-way ANOVA and post hoc compared magnitude and frequency of accelerations of the head when performing a break fall corresponding with each of the six throws. When utilizing the linear acceleration criterion >80 g for risk of concussion, as suggested by some experts, none of the six judo throw/break fall combinations resulted in a significant head impact (incidence rate = 0%). However, when comparing all registered accelerations above 16 g threshold, hand throw (1 impact, 1.4 % incidence rate, 27.94 g, 2.8 krad•s-2), forward leg sweep (1 impact, 1.4 % incidence rate, 20.58 g, 1.59 krad•s-2), and thigh throw (7 impacts, 10% incidence rate, 28.16 ± 4.92 g, 3.94 ± 1.83 krad•s-2) had higher frequency of occurrence and magnitude of acceleration than other throws (p<0.01). Thigh throw had highest incidence rate of any throw (p< 0.01). CONCLUSION: The judo thigh throw (and break fall) had the highest incidence of sub-concussive head accelerations in the category of 20-40 g. However, none of the judo throws and associated break falls resulted in any impact considered high risk for concussion.

Improved Algorithm for Load Flow Analysis of Radial Distribution System

Objectives: In this paper an improved algorithm for load flow analysis of Radial Distribution Systems (RDS) is presented. The algorithm incorporates probabilistic variations of line and load data along with composite loads. Methodology: The algorithm uses Simple Backward and Forward Sweep based method for solving RDS and has further been modified to solve distribution systems with Distributed Generation (DG). Findings: This Improved algorithm for load flow analysis is tested on standard RDS and considerable promising results have been delivered for the system having Distributed Generator for improving the voltage profile and reduce the losses. Novelty/Improvement: The results obtained are exemplary that confirms usefulness of the algorithm and can have significant impact on future planning and operation purposes of unbalanced RDS.

Electrochemical Studies of Ru+4O2 Reactions with Lithium at Low Voltages

Nanostructured pyramidal shape ruthenium oxide (Ru+4O2) was studied electrochemically using cyclic voltammetry (CV) and cyclic charge-discharge (CCD) experiments. The experiments were performed at five different cut-off voltages (4.0 to 1.5, 1.0, 0.80, 0.4, and 0.1 V) versus Li/Li+. CCD experiments performed from 4.0 to 1.5 V and 4.0 to 1.0 V showed a plateau at approximately 2.1 V that corresponds to 100 and 350 mAh g-1, respectively, with no significant formation of solid electrolyte interface (SEI). Insertion and de-insertion of lithium ions in the crystalline lattice of Ru+4O2 were determined to be the dominant mechanism. CV experiments performed in the same voltage range showed a reduction and an oxidation peak at 2.1 and 2.5 V, respectively, that corroborated the CCD experiments. When the cut off voltage was set below 0.80 V, the CV showed two peak currents at ~1.0 V (Ru0/Li2O) and ~0.6 V (SEI) during the first forward potential sweep. The SEI disappeared during the second cycle and beyond. On the other hand, during the reverse potential sweep two peak currents are observed at ~1.2 V and ~2.7 V. The latter represents the oxidation of Ru0 to Ru+4 and the peak at 1.2 V is assigned to the decomposition of the SEI. The CCD experiment revealed a total capacity of approximately 1200 mAh g-1 (~6 Li+ per mol of Ru+4O2), which was determined in the voltage range from 4.0 to 0.1 V. However, the expected capacity is 806 mAh g-1 (4 Li+ per mol of Ru+4O2) as described by the conversion reaction of lithium with Ru+4O2 (Ru+4O2 + 4Li++4e- <--->Ru0 + 2Li2O). Therefore, there is an excess capacity of ~600 mAh g-1. To understand the source of the excess capacity, CCD experiments were performed in the range of 2.0 to 0.1 V vs. Li/Li+ which revealed that the material is behaving as a capacitor. CV experiments performed in the same voltage range supported the CCD experiments. The calculated storage capacity in this range is only 90 mAh g-1. This value is too small to explain the amount of excess capacity observed in this material. The most possible scenario for the excess capacity is pseudo-capacitive and interfacial storage.

Matrix Backward Forward Sweep for Unbalanced Power Flow in αβ0 frame

A Backward/Forward Sweep (BFS) algorithm for power flow calculations adapted to matrix formulation in the αβ0 reference frame is presented in this paper. The novelty of the work is the definition of a BFS solver with the following characteristics: matrix formulation in αβ0 frame, valid for unbalanced three phase or single phase systems and capable of handling transformers and distributed generators; Slack, PQ or PV nodes. The matrix formulation avoids the difficulties of load-flow methods presented in the literature: lack of generalization for arbitrary network topologies and transformer connections; the αβ0 stationary reference frame makes the algorithm easily applicable to distribution systems; and finally, the BFS algorithm is an efficient, robust and fast solver. The IEEE Node Test Feeders will be used to provide test systems under several configurations. Comparison to a direct algorithm will demonstrate the improvements in robustness, efficiency and computation time.

Short-circuit analysis in large-scale distribution systems with high penetration of distributed generators

In this paper a short-circuit computation U+0028 SCC U+0029 procedure for large-scale distribution systems with high penetration of distributed generators based on contemporary technologies is proposed. The procedure is suitable for real-time calculations. Modeling of modern distributed generators differs from the modeling of traditional synchronous and induction generators. Hence, SCC procedures found on the presumption of distribution systems with only traditional generators are not suitable in nowadays systems. In the work presented in this paper, for computation of the state of the system with short-circuit, the improved backward U+002F forward sweep U+0028 IBFS U+0029 procedure is used. Computation results show that the IBFS procedure is much more robust than previous SCC procedures, as it takes into account all distribution system elements, including modern distributed generators.

Optimal power flow in distribution network considering spatial electro‐thermal coupling effect

The conductor resistance changes in accordance with the conductor temperature, in turn the line thermal capacity limit and power flow are influenced by its spatial characteristics of line routes and surrounding weather conditions. In light of the significant difference of spatial characteristics of line routes and weather conditions in different regions covered by distribution network, a novel optimal power flow (OPF) model in distribution network considering spatial electro-thermal coupling effect is proposed to integrate heat transfer constraints and electro-thermal coupling constraints into normal distribution network operation constraints. To address the computational complexity of the proposed model, the line thermal capacity limit is calculated firstly using the spatial steady-state heat balance equation. Then, a genetic algorithm combined with an extended back/forward sweep method is presented to solve the distribution system OPF problem, in which the heat balance equation is embedded in the forward sweep stage of the power flow calculation. Consequently, line temperatures, resistances, and power flows are dynamically updated during the iterative procedure. A 14-bus system with nine regions shows that the spatial electro-thermal coupling effect has a significant impact on the result of power flow and the optimal dispatch of the distributed generation in the distribution network.