Power Distribution Network Model Research Articles

A Distributed Coordination Method for Coupled Traffic-Power Network Equilibrium Incorporating Behavioral Theory

The increasing penetration of electric vehicles (EVs) gradually evolves the urban transportation network (UTN) and power distribution network (PDN) from being independent to being coupled. To analyze the impact of drivers' behavior on the coupled network, and reveal the relationship between the two networks, a coupled traffic-distribution (CTD) model is proposed, in which the total traveling cost of UTN and the power service cost of PDN is minimized. In the CTD model, A stochastic user equilibrium traffic assignment problem (SUE-TAP) with elastic traffic demand and discrete path selection of drivers is formulated to capture the traffic flow distribution comprised of EVs and gasoline vehicles (GVs). An alternative current optimal power flow (ACOPF) model of PDN is utilized to provide the optimal charging price and scheduling plan. Besides, the SUE-TAP with nonlinear functions is difficult to solve, a novel piecewise linear approximation method is presented to deal with the nonlinear items of the SUE-TAP caused by drivers' traveling cost and traveling tendency incorporating perception. Incorporating the behavioral theory, a distributed coordination method derived from optimal condition decomposition is proposed for the coupled traffic-power network equilibrium. The proposed distributed scheme is examined using a coupled network, which consists of a 20-road UTN and a 33-bus PDN. Numerical results demonstrate the effectiveness and practicability of the proposed model and the distributed coordination method.

Impact of Charging Stations for Electric Vehicles on the Power Distribution Network

Abstract The paper describes the impact of the load increase caused by the connection of electric vehicle (EV) charging stations in the power distribution network. The power distribution network model was created using the professional software tool DIgSILENT PowerFactory (DPF). Analyses were carried out for the cases of connecting a different number of EV charging stations to 0.4 kV busbars of distribution transformer stations (TS). The results of voltage conditions and loading of the most loaded distribution substations are shown. Increasing the load results in an increase in losses in the network, which is particularly significant today since the prices of electrical energy on the market are currently at historically high levels. Distribution System Operator (DSO) should pay attention to the problem of losses increase in the network, and in addition to classic solutions in strengthening the network, the DSO should also consider modern solutions such as the flexibility of new consumers.

Impedance modeling and analysis of multi-stacked on-chip power distribution network in 3D ICs

An accurate impedance modeling of a multi-stacked on-chip power distributed network (PDN) based on through-silicon-vias (TSVs) is vitally important to estimate the electrical performance in three-dimensional integrated circuits (3D ICs). This paper proposes a method for calculating the impedance matrix of the multi-stacked on-chip PDN, which mainly consists of arbitrarily distributed TSVs and grid-type on-chip PDNs. First, a real stack-up structure of a multi-stacked on-chip PDN is separated into discrete components intentionally. Then, the equivalent lumped circuit models of all discrete components are assembled into a whole to build the transmission matrix of the multi-stacked on-chip PDN through the relationship between the nodal voltage and the nodal current. Finally, the impedance matrix can be derived through the transmission matrix. In this paper, the coupling of the arbitrarily distributed TSVs and the distributional effect of the on-chip PDN are considered in the impedance matrix through the transmission matrix method (TMM). The proposed method replaces the simulation of the complex equivalent circuit model with the matrix calculation. The verification results show that the deviation of resonant frequency is about 6 $$\%$$ and the conversation of the simulation time is about 99.9 $$\%$$ compared with the HFSS model. It can accurately and quickly calculate the impedance of the multi-stacked on-chip PDN.

Topology-Based Accurate Modeling of Current-Mode Voltage Regulator Modules for Power Distribution Network Design

Power distribution network (PDN) is essential in electronic systems to provide reliable power for load devices. Thus, modeling of PDNs in printed circuit boards and packages has been extensively studied in the past few decades. However, with the higher integration levels and operation bandwidths of modern voltage regulator module (VRM), there lacks an accurate model for transient load responses based on the widely used current-mode control topology. In this work, a topology-based behavior model, including both the power stage and control loops, is developed for the current-mode buck VRM. A novel method is also proposed to unify the modeling of the continuous and discontinuous conduction modes for transient load responses. Through the measurement-based characterization, the model parameters are optimized to match with the actual design. Furthermore, this model can be applied to both the time-domain and frequency-domain circuit simulations to predict the voltage droop and output impedance, respectively. The accuracy of the model is validated using an evaluation board containing the single-phase and multiphase VRMs. The proposed model for current-mode control VRM can be easily cascaded with other PDN components to enable a combined PDN analysis.

Adaptive Droop Control of the VSC-MTDC Distribution Network Considering Power–Voltage Deviation

In order to realize the unbalanced power optimally allocated and the DC voltage stably controlled after disturbance, an adaptive droop control method considering power and voltage deviation is proposed based on the traditional voltage–power droop control of a voltage source converter-based multi-terminal direct current (VSC-MTDC) distribution network. The inherent constraint that the unbalanced power is proportionally distributed according to its capacity under the traditional droop control is broken in the proposed method to realize the reasonable transfer of unbalanced power and to reduce the overload risk of smaller capacity VSCs; the “dead zone” is appropriately set to relax the operating range of the VSC to a certain extent by a power deviation factor being introduced in the droop characteristic curve. The corresponding MATLAB/Simulink simulation model of the five-terminal DC power distribution network is established and compared with the electromagnetic transient model under the traditional droop control. Finally, the simulation results verify the effectiveness and control effects of the proposed control method.

Planning of active power distribution network based on source-network-load collaborative optimization

With the fast development of renewable energy generation, the randomness and volatility seriously threaten the stability of the power system. In order to improve the consumption rate of renewable energy and the economic benefit, the source-network-load collaborative optimization is put forward and widely used in the power system. And the active power distribution network which consists of the energy storage devices and flexible load is the best carrier to realize it. Based on the active power distribution network planning, this paper firstly designs an economic index covering construction cost and operation cost as the optimization objective. Then with the physical constraints consisting of the physical features of generation units, energy storage devices and flexible load, the source-network-load collaborative optimization model of active power distribution network is established. Finally, a case of city distribution network is presented to verify the effect of source-network-load collaborative optimization and the efficiency of the optimization model.

Test Method and Data Application of Physical Model of Power Distribution Network

This paper states the test method and data application of a kind of physical model of power distribution network. After the establishment of distribution automation physical simulation laboratory, the equipment in the platform is effectively controlled and reasonable test procedures are designed. The detailed solution is to record the test process during the physical simulation test.In the design of this test method, the main difficulty is that the data of each equipment at each stage in the system shall be recorded completely during the whole process for physical reduction of transient fault, and to design the interface with the power system simulation software; otherwise, the meaning of the test will be discounted heavily. The on-site operating environment of the distribution network can be restored furthest, all details in the test process can be presented to the testers clearly and intuitively, and the test data can be expanded and applied to provide strong support for technical research and analysis of distribution automation in this way.

Modeling of Loaded Nonuniform Grid Power Distribution Network With Arbitrary Shapes

This article presents an equivalent circuit modeling method for the impedance calculation of the loaded power distribution network (PDN). The topology of the proposed equivalent circuit is based on the modal field analysis of the PDN, so that the elements in the circuit possess certain physical meaning. The element values in the equivalent circuit are extracted from a circuit perspective. Using the proposed equivalent circuit and the interpolation method, the calculation efficiency of the proposed method is greatly improved. Compared with the traditional mode method which is limited for the modeling of the regular-shaped PDN, the proposed equivalent circuit method can be used for the modeling of both grid-type and plane PDNs with nonuniform, irregular-shaped, and shorting via-loaded structures. To verify the accuracy of the proposed equivalent circuit, two different samples are simulated and fabricated, and the impedance obtained from the measurement shows good agreements with that obtained from the proposed method.

Analysis of Nonlinear Power Distribution Network and Estimation of Jitter Transfer Functions Based on Output Buffer Pseudo Open Drain Termination

With increasing data rates of links, jitter budget allowable for the channel keeps decreasing, and precisely estimating jitter becomes very important to have confidence in designing a robust communication system. Current analysis of jitter transfer function assumes a linear or approximately linear power distribution network, but the linearity of power distribution network can be distorted by driver states or load conditions at the end of signal channel. In order to estimate power supply induced jitter accurately, both the receiver termination mode and the interconnection parameters of channel should be considered. In this paper, the nonlinearity of power distribution network caused by termination mode and its effect on jitter are discussed. The emphasis is given to the pseudo open drain termination, which is the popular scheme used in DDR4. Then, an analytical calculation method of transfer functions relating power supply noise to jitter is proposed, in which the nonlinear power distribution network model including the output buffers, signal channels, and pseudo open drain terminations is used to derive the analytical expressions. Simulation results demonstrate that the proposed analytical estimation method achieves good agreement with ADS simulated results under a real case power distribution network.

Segmentation method based modeling and analysis of a glass package power distribution network (PDN)

Segmentation method based modeling and analysis of a glass package power distribution network (PDN)

Fast and Accurate Power Distribution Network Modeling of a Silicon Interposer for 2.5-D/3-D ICs With Multiarray TSVs

In this paper, we first propose power distribution network (PDN) model of the perforated power and ground (P/G) planes including substrate effects and multiarray through-silicon vias (TSVs) for a silicon interposer. Since it is almost impossible to simulate a high metal density perforated PDN structure, we first suggest a modeling methodology for P/G perforated planes to reduce simulation time significantly with a high accuracy. To obtain the PDN impedance of a silicon interposer faster, we convert the perforated planes to solid planes with a dielectric mixture. The capacitance (C) and conductance (G) component of perforated P/G planes are precisely estimated based on the conformal mapping method. From the estimated C and G, the physical dimension and material properties of the dielectric mixture of solid P/G planes are determined, respectively. Because silicon interposer PDN consists of a periodic structure, we design and analyze the unit cell of a PDN thoroughly. From the unit cell analysis, the electrical characteristic of an entire PDN for a silicon interposer is successfully estimated. The PDN impedance of the proposed solid and perforated P/G planes and simulation time to obtain each PDN impedance are compared and evaluated, respectively. The proposed methodology is validated by a full 3-D electromagnetic (EM) simulation in the frequency range from 0.01 to 20 GHz. We also proposed models of multiarray P/G TSVs that can be applied to the various P/G patterns for a silicon interposer. From the inductance matrix considering current directions, the self- and mutual inductances of TSVs are accurately calculated. Because quasi-transverse electromagnetic mode is propagated through TSVs and the substrate dielectric of a silicon interposer can be regarded as a uniform dielectric, the capacitance and conductance of TSVs can be calculated from the inductance matrix. The proposed model of multiarray TSVs is also analyzed and verified by EM simulations in the frequency range from 0.01 to 20 GHz with a high accuracy.

Detection for Non-Technical Loss by Smart Energy Theft With Intermediate Monitor Meter in Smart Grid

In this paper, to detect non-technical loss (NTL) of meter manipulating/malfunctioning and bypassing at the same time, we propose the intermediate monitor meter (IMM)-based power distribution network model with the concept of unit networks (UNs) dividing the network into smallest and independent networks to analyze the power flow in detail and effectively detect the NTL. We then propose an NTL detection algorithm to solve linear system of equations (LSE) constructed by energy balance analysis with IMMs and the collector, and describe the hardware architecture of IMMs. Simulation results show that the proposed NTL detection algorithm successively detects the honesty of energy consumers as well as the energy loss from bypassing. Furthermore, it is observed the proposed detection framework is time-efficient and detection accuracy is at least 95% when variability of meter reading value is 80%.

Fast Algorithm for Minimizing the Number of decap in Power Distribution Networks

In this paper, fast capacitor assignment algorithms capable of finding a decoupling solution scheme with a minimum number of components that meets a predefined target impedance with a semi-arbitrary shape within a few seconds to an hour for a given power distribution network (PDN) are proposed. The proposed algorithms also provide identification of shadowed decap ports in a PDN based on an inductance matrix extraction from the given PDN model. Elimination of those shadowed decap ports with the proposed algorithms enables more effective layouts and cost savings on PCB designs.

A New Search Algorithm of MBD Based on Spider Web and Its Application in Power Distribution Network Fault Diagnosis

To reduce the spatial complexity and search time of minimum hitting sets in model-based diagnosis (MBD), a new algorithm for searching minimum hitting sets of MBD is proposed in this paper, which can use the characteristics of minimum hitting sets and the idea of spider prey in biology. We call it cobweb search algorithm. In the algorithm, the generation of visit spiders and search strategy are proposed, and the visit spider that can find the visit path of cobweb to search all minimum hitting sets within a cobweb is constructed. Based on the experiment comparisons, Cobweb search algorithm has better performance than other algorithms of searching minimum hitting sets. As an example, a 14-node power distribution network model is constructed. The diagnosis process with MBD is introduced and analyzed in detail, at the same time the cobweb search algorithm is applied in power distribution network fault diagnosis. The experiment results verify the effectiveness and superiority of the proposed algorithm.

Plane-Pair PEEC Model for Power Distribution Networks With Sub-Meshing Techniques

We present an improved plane-pair partial element equivalent circuit (PEEC) model for power distribution network modeling based on the PEEC formulation. The model can include via connections, decoupling capacitor macro-models, and discontinuities such as holes in the plane-pairs. An efficient approximate inductance sub-meshing model is described for large printed circuit plane-pairs with complex geometries and numerous vias. The modified nodal analysis (MNA) used leads to a flexible circuit solution where we can compute inductances, resistances, impedances, or other circuit models, including dc solutions. The MNA equations include effective optimizations such as the placement of capacitors. Today, a large class of methods are available based on numerous formulations including finite-difference time-domain, finite-element method, integral equation model, and cavity models. Each of the approaches has its own type of problems for which it is most suitable.

W-element RLGC matrices calculation for power distribution planes modeling using MCTL matrix method

The ever-increasing demands of advanced computing and communication have been driving the semiconductor technology to change with each passing day following Moore’s law. As a consequence, advanced electronic packages have been developed and predictive modeling of Power Distribution Network (PDN) becomes more and more important. In this paper, we present an efficient methodology for predictive modeling of multilayered PDNs. This methodology is based on Multi-Conductor Transmission Line (MCTL) which will be modeled by W-Elements. Equations of RLGC Matrices will be given and effective self and mutual inductance will be proposed to efficiently describe the inductive interactions among coupled signal lines. Test structures were designed and simulated up to 50 GHz. A good correlation was obtained between model and full-wave solver based on the method of Moments. The proposed model substantially reduces the CPU run time and memory resources that requires only few seconds and small memory for which the EM solver would have taken several minutes, or even hours, and much more memory.

From the Editor's Desk

This issue features articles on software in the context of the history of intellectual property, the first in a two-part series on the challenge of writing contemporary history by James Cortada, an exploration of the transition from analog to digital methods in the modeling of electrical power distribution networks, an article on computing prime numbers on the ENIAC and EDSAC, and a firsthand account of the IBM Advanced Computer Systems (ACS) project of the mid-to-late 1960s by Brian Randell.

Power Distribution Network Modeling using Block-based Approach

A power distribution network (PDN) is a network that provides connection between the voltage source supply and the power/ground terminals of a microprocessor chip. It consists of a voltage regulator module, a printed circuit board, a package substrate, a microprocessor chip as well as decoupling capacitors. For power integrity analysis, the board and package layouts have to be transformed into an electrical network of resistor, inductor and capacitor components which may be expressed using the S-parameters models. This modeling process generally takes from several hours up to a few days for a complete board or package layout. When the board and package layouts change, they need to be re-extracted and the S-parameters models also need to be re-generated for power integrity assessment. This not only consumes a lot of resources such as time and manpower, the task of PDN modeling is also tedious and mundane. In this paper, a block-based PDN modeling is proposed. Here, the board or package layout is partitioned into sub-blocks and each of them is modeled independently. In the event of a change in power rails routing, only the affected sub-blocks will be reextracted and re-modeled. Simulation results show that the proposed block-based PDN modeling not only can save at least 75% of processing time but it can, at the same time, keep the modeling accuracy on par with the traditional PDN modeling methodology.

Modeling and Measurement of Power Supply Noise Effects on an Analog-to-Digital Converter Based on a Chip-PCB Hierarchical Power Distribution Network Analysis

In this paper, a model of power supply noise (PSN) effects on an analog-to-digital converter (ADC) in a hierarchical structure is proposed. The ADC performance is determined by not only on-chip characteristics but also off-chip characteristics. Therefore, chip-package-printed circuit board (PCB) coanalysis and comodeling are required to accurately evaluate the performance of the ADC. We propose the comodel which allows the estimation and analysis of PSN effects on the ADC including off-chip characteristic. The proposed model includes three separate submodels: a power distribution network (PDN) model from the power/ground of the PSN source to the ADC power/ground, an on-chip circuit model from the ADC power/ground to the ADC inputs, and an ADC behavioral model from the ADC inputs to the factor of the effective number of bits (ENOB), which is one of the ADC performance factors. By applying a segmentation method for the PDN model, an analytical model for the on-chip circuit model, and a MATLAB model for the ADC behavioral model, fast, precise, and broadband estimations of the PSN effects are achieved. To validate the proposed models, an ADC was fabricated by a 0.13-μm CMOS process and wire bonded to the designed PCB. The ENOB of the ADC was measured by sweeping the PSN's frequency from 1 MHz up to 3 GHz, which was injected into the PCB to discover which noise frequency is critical to an ADC designed with a chip-PCB hierarchical structure. The results estimated by the proposed model correlated well with the cosimulated and measured results. The proposed modeling procedure saves the chip, package, and PCB designers time and computation resources to achieve high-quality analog devices or mixed-mode systems and provides an intuitive understanding of the noise effect.

Modeling and Analysis of Power Distribution Networks in 3-D ICs

This paper addresses the modeling and analysis problems for power distribution networks (PDNs) in 3-D ICs. An on-chip distributed model is proposed for 3-D power grids, in which the details of metal layers are considered. The distributed model is demonstrated to be essential to identifying the unique noise behavior of 3-D PDNs. A lumped model is proposed based on the distributed model. The lumped model features the connection impedance between tiers and is proven to be useful for designers to understand the global effects of 3-D PDNs. Based on the models, an analysis flow is designed for 3-D PDNs in both frequency domain and time domain. With the analysis flow, the electrical characteristics of 3-D PDNs are studied systematically for the first time. The frequency-domain analysis identifies the global and local resonance phenomena in 3-D PDNs that are distinct from those in 2-D PDNs. The physical mechanisms behind the resonance phenomena are investigated. The time-domain analysis predicts the worst-case supply noise based on distributed current constraints. The “Rogue Wave” concept is introduced to explain the spatial and temporal relations of the worst-case on-chip noise responses in 3-D PDNs.