当前位置：文档库 › A Nonlinear-Disturbance-Observer-Based DC-Bus Voltage Control for a Hybrid AC DC Microgrid

A Nonlinear-Disturbance-Observer-Based DC-Bus Voltage Control for a Hybrid AC DC Microgrid

A Nonlinear-Disturbance-Observer-Based DC-Bus V oltage Control for a Hybrid AC/DC Microgrid Chengshan Wang,Senior Member,IEEE,Xialin Li,Li Guo,Member,IEEE,and Yun Wei Li,Senior Member,IEEE

Abstract—DC-bus voltage control is an important task in the op-eration of a dc or a hybrid ac/dc microgrid system.To improve the dc-bus voltage control dynamics,traditional approaches attempt to measure and feedforward the load or source power in the dc-bus control scheme.However,in a microgrid system with distributed dc sources and loads,the traditional feedforward-based methods need remote measurement with communications.In this paper,a nonlinear disturbance observer(NDO)based dc-bus voltage con-trol is proposed,which does not need the remote measurement and enables the important“plug-and-play”feature.Based on this observer,a novel dc-bus voltage control scheme is developed to sup-press the transient?uctuations of dc-bus voltage and improve the power quality in such a microgrid system.Details on the design of the observer,the dc-bus controller and the pulsewidth-modulation (PWM)dead-time compensation are provided in this paper.The effects of possible dc-bus capacitance variation are also consid-ered.The performance of the proposed control strategy has been successfully veri?ed in a30kV A hybrid microgrid including ac/dc buses,battery energy storage system,and photovoltaic(PV)power generation system.

Index Terms—DC–AC bidirectional converter,dc-bus voltage control,hybrid ac/dc microgrid,nonlinear disturbance observer (NDO),plug-and-play.

I.I NTRODUCTION

A HYBRID ac/dc microgrid is regarded as a small scale

power generation,distribution and consumption system with the presence of ac and dc buses,distributed generation(DG) units,energy storage systems,and ac/dc loads[1]–[3].In such a system,the DG units with nonpower frequency output voltage or dc output voltage can be connected into the dc bus through ac–dc converters and dc–dc converters,respectively.The dc subgrid is tied to the ac bus via one or multiple bidirectional dc–ac interlinking converters[4]–[6].Compared to an ac or dc microgrid,a hybrid ac/dc microgrid can take advantage of both

Manuscript received July3,2013;revised September26,2013and Decem-ber23,2013;accepted December26,2013.Date of publication January2, 2014;date of current version July8,2014.This work was supported by the National High Technology Research and Development of China(863Program) (2011AA05A107)and Ph.D.Programs Foundation of Ministry of Education of China(20120032120084).Recommended for publication by Associate Editor Z.Chen.

C.Wang,X.Li,and L.Guo are with the School of Electrical and Engineer-ing Automation,Tianjin University,Tianjin300072,China(e-mail:cswang@ https://www.wendangku.net/doc/8f14019236.html,;xialinlee@https://www.wendangku.net/doc/8f14019236.html,;liguo@https://www.wendangku.net/doc/8f14019236.html,).

Y.W.Li is with the Department of Electrical and Computer Engineering, University of Alberta,Edmonton,AB T6G2V4,Canada(e-mail:yunwei.li@ ualberta.ca).

Color versions of one or more of the?gures in this paper are available online at https://www.wendangku.net/doc/8f14019236.html,.

Digital Object Identi?er

10.1109/TPEL.2013.2297376Fig.1.An Example diagram of a hybrid ac/dc microgrid[1],[2].

DG units and storage systems to meet load demand requirements with less power conversion stages.As a result,the system can operate with improved ef?ciency,economy,and reliability. Fig.1shows an example diagram of a hybrid ac/dc microgrid scheme[1],[2].In the ac subgrid,the bus voltage and frequency are mainly decided by the main ac grid in grid-connected opera-tion and by the supply/demand of the reactive and active power in the autonomous islanding operation.However,with no reac-tive power?ow in the dc subgrid,only the active power distur-bance will lead to the dc-bus voltage?uctuation.The main rea-sons for the power disturbances in the dc subgrid are:1)abrupt change of dc loads;2)DG units and storage systems output power variations;and3)power exchange?uctuations between the dc and ac subgrids.If not controlled properly,the dc-bus voltage variation could trigger dc system protection.Therefore, a suitable dc-bus voltage control strategy plays a key role to en-sure good power quality and stable operation of the dc subgrid or even the whole ac/dc microgrid system.

In general,the dc voltage can be regulated by either the bidi-rectional dc–ac converter or the energy storage systems in a dc subgrid.In most hybrid ac/dc microgrids,the ac subgrid has the capability to support the dc subgrid while maintaining the stability of the ac bus voltage.Thus the bidirectional dc–ac in-verter between the dc and ac subgrids is usually used to ensure a constant dc-bus voltage and maintain the power and energy balance within the dc subgrid[7]–[10].This is also the scenario considered in this paper.

For the dc–ac bidirectional inverter control,the conventional dual-loop control strategy is usually adopted.In such a dual-loop control,the outer dc-bus voltage control loop maintains a constant dc-bus voltage,while the inner current loop is for

0885-8993?2014IEEE.Personal use is permitted,but republication/redistribution requires IEEE permission.

See https://www.wendangku.net/doc/8f14019236.html,/publications standards/publications/rights/index.html for more information.

current https://www.wendangku.net/doc/8f14019236.html,ually,PI controllers are used for the volt-age and current control,especially when the current control is implemented in the synchronous reference frame[11]–[17]. To improve dc-bus voltage control dynamics,feeding forward the disturbance(dc system mismatched current or power in-formation)in the dual-loop control has been proposed to track the mismatched power quickly and reduce the dc-bus voltage ?uctuation[18]–[23].However,these feedforward methods are limited to the condition that the dc–ac converter control scheme can have the information of DGs,energy storage systems,and loads current/power in real time.For a hybrid ac/dc microgrid as shown in Fig.1,it is impractical to have the entire sources or loads information due to the dispersed nature of DGs,en-ergy storage systems and loads.High bandwidth communica-tions between the sources/loads of the dc subgrid and the dc–ac converter will be required in this case,which is against the scalability and plug-and-play feature desired for such an ac/dc microgrid.

More recent methods to improve the dynamics of dc volt-age control without involving the possible remote measure-ment include the constant-frequency asynchronous sigma-delta modulation(CF-ASDM)control[24],the one line-cycle regu-lation approach(OLCRA)and one-sixth line-cycle regulation approach(OSLCRA)based dc-bus voltage control[25].For the CF-ASDM method,the dc-bus voltage is regulated between the high/low bounds by using a hysteresis comparator to gen-erate the current loop reference.The idea is essentially similar to a voltage controller.But how to set the hysteresis band to achieve an accurate regulation of dc voltage and how to prop-erly scale the reference current from the hysteresis comparator is not straightforward.The OLCRA and OSLCRA methods con-trol the dc-bus voltage indirectly through the charge and power balance principle.These methods need accurate information of the dc-bus capacitance to achieve good control accuracy,and therefore,an estimation of the dc-bus capacitance is part of the control scheme.

In this paper,a dc-bus voltage control method based on a nonlinear disturbance observer(NDO)is proposed,where the simple and well-accepted dual-loop control with PI controllers are used together with a disturbance feedforward loop aided by the NDO.The proposed method only uses the dc-bus voltage and instantaneous power through the dc–ac converter and does not require voltage and current information of the sources/loads in the dc subgrid.As a result,the decentralized control with plug-and-play feature is achieved.Based on the developed ob-server,an improved feedforward method is designed by setting a?rst derivative element in series with the feedforward chan-nel to compensate the current loop dynamics and the observer convergence rate.The effects of the possible dc-bus capacitance variation are also analyzed in the dc voltage control scheme. Lastly,considering the dead-time effect to the control perfor-mance of current loop[26],[27],a dead-time compensator is also designed to further improve the performance of the pro-posed feedforward method.The performance of the proposed method has been veri?ed in a30kV A hybrid microgrid system including battery energy storage and photovoltaic(PV)power generation

system.Fig.2.Con?guration of the dc subgrid system.

II.DC S UBGRID/M ICROGRID M ODEL

An example dc subgrid system is illustrated in Fig.2,where all DG units and dc loads are connected to the dc bus.In this system,the PV unit is controlled with maximum power point tracking(MPPT)and its dc–dc converter operates in boost stage. In order to compensate the PV output variation,the dc load changes,and to track the dispatched demands from the central control system[7],[28],the battery energy storage system is adopted and operate with bidirectional energy?ow.The dc–ac converter between the dc subgrid and the ac grid is formed by a three phase pulsewidth-modulation(PWM)voltage-source inverter(VSI)and an LCL?lter.As discussed earlier,this inter-linking inverter controls the dc-bus voltage to be constant and maintain the power and energy balance within the dc subgrid. In this paper,the proposed dc-bus voltage control method is implemented in a system as shown in Fig.2.

In the dc subgrid,as shown in Fig.2,the dynamic differential equation for the capacitor voltage of dc bus can be described as C

du dc

=(i bat+i pv?i load)?i dc(1) where C represents the value of the dc-bus capacitor;u dc,i bat, i pv,i load,and i dc denote the dc-bus voltage,output dc currents of the battery storage system,PV unit,dc load consumption, and the input dc current of the interlinking dc–ac converter, respectively.

The dc/ac converter model in the synchronous dq frame (which is oriented with the grid voltage)can be depicted as

???

e d=L1

di invd

+i invd R1+[v cd+(i invd?i d)R d]+ωL1i invq e q=L1

di invq

+i invq R1+[v cq+(i invq?i q)R d]?ωL1i invd i invd=C f

dv cd

+i d+ωC f v cq

i invq=C f

dv cq

+i q?ωC f v cd

v cd+(i invd?i d)R d=L2

di d

+i d R2+u d+ωL2i q

v cq+(i invq?i q)R d=L2

di q

+i q R2?ωL2i d

(2)

Fig.3.Structure of the traditional dc-bus voltage control system.

where e d and e q are the d-and q-axis components of inverter output voltage;u d is the d-axis component of grid voltage(since the dq frame is oriented with the grid voltage,the q axis compo-nent u q is equal to0);ωis the fundamental angular frequency; L1and L2are the?lter inductances(see Fig.2);R1and R2 denote the equivalent resistances describing the system loss and the parasitic resistances of the?lter inductances;C f and R d are the?lter capacitance and passive damping resistance,respec-tively;i invd and i invq denote the active and reactive components of the converter side current;i d and i q are the active and reactive components of the grid side current;v cd and v cq are the d and q axis components of?lter capacitance voltage.

The traditional dual loop control strategy for dc-bus voltage control is shown in Fig.3,where i o=i bat+i pv?i load.The outer voltage loop usually adopts PI controller to track the refer-ence voltage,while the inner loop is for current tracking with PI controller based on grid voltage oriented control method.If the grid side current(i d and i q)are chosen to be the feedback vari-ables for the current loop,the control equations can be depicted as

?????????

????????e dref=u d+ω(L1+L2)i q+(i dref?i d)k pid+k iid u dr e qref=?ω(L1+L2)i d+(i qref?i q)k pid+k iid u qr

u dr=

i dref?i d

u qr=

i qref?i q

(3)

where k pid and k iid are the proportional and integral gains of the current loop controller,respectively.e dref and e qref represent the reference modulation voltages(which are equal to“e d”and “e q”if the control delay and dead time are not considered). Because the LCL?lter aims to primarily reduce the high-frequency current ripple,and the closed-loop bandwidth of the current control is always designed to be less than the resonant frequency of the LCL?lter[17],the in?uence of the?lter ca-pacitors can be neglected in the latter section for the dc-bus control system design(which is mainly focused on the lower frequency range)[15],[29].As a consequence,the grid voltage, grid side current and the inverter output voltage in dq frame can be expressed as

e d=u d+L(di d/dt)+ωLi q+i d R

e q=L(di q/dt)?ωLi d+i q R

(4)

where L=L1+L2;R=R1+R2.

According(3)and(4),the closed-loop transfer function G c(s) for the current control is obtained in the following equation:

G c(s)=

(k pid s+k iid)

Ls2+(R+k pid)s+k iid

.(5)

TABLE I

S YSTEM P

ARAMETERS

As shown in(5),G c(s)is a typical second-order system

with an additional closed-loop zero,whose damping ratio?and

natural angular frequencyωn are de?ned by

???

2?ωn=

k pid+R

ω2n=

k iid

(6)

Considering the limited overcurrent ability of the power con-

verters,step response overshoot should be avoided in the control

design.From(6),it can be seen that a larger integral gain will

lead to a higher natural frequency and lower damping ratio with

less system damping.With the system parameters shown in Ta-

ble I,when the current control PI parameters are selected as k pid

=1and k iid=20,the following performance of the current loop

can be obtained:?=2.1,ωn=80rad/s,t s=4.4/?ωn=26ms.

When damping ratio?is greater than1,means step response

overshoot will be avoided for the current tracking.While the

settling time t s=26ms means current control loop will need

about26ms to track the reference with zero steady error.

From Fig.3,the dc-bus voltage response can be depicted by

u dc(s)=

(k pu/C)(1+(k iu/k pu s))(1/s)G c(s)k

1+(k pu/C)(1+(k iu/k pu s))(1/s)G c(s)k

U dcref(s)

1/sC

1+(k pu/C)(1+(k iu/k pu s))(1/s)G c(s)k

i o(s)

(7)

where the?rst term in(7)describes the tracking performance of

the voltage controller,while the latter term represents the distur-

bance rejection performance.k pu and k iu are the proportional

Fig.4.Structure of the proposed dc-bus voltage control system.

gain and integral constant of the outer voltage loop controller (τ=k pu /k iu ).G c (s )is the closed-loop transfer function of the inner current loop as shown in (5).k is a scale factor equal to 1.5u d /U dc according to (8),where U dc is the average value of dc-bus voltage.

Neglecting the conversion loss of the converters,the active power p g transferred between the dc subgrid and the ac grid can be expressed by

p g =u dc i dc =1.5u d i d .

(8)

As illustrated in (1),the dc-bus voltage is prone to the power disturbance in the dc microgrid such as abrupt change of dc load (i load ),output variation of DG units and energy storage systems (i bat ,and i pv ).If the control system dynamic response speed needs to be improved to reduce the impact of disturbance current on the dc-bus voltage,the stability margin of the control system has to be sacri?ced,which will be analyzed later.In this paper,an NDO-based dc-bus voltage control strategy is pro-posed.As demonstrated in Fig.4,the proposed control scheme is comprised of three parts:

1)NDO:The NDO is implemented to track the power dis-turbances in the dc subgrid.It also provides reference for both the dead-time compensation in current loop and feedforward control in the voltage loop.

2)V oltage loop:It adopts PI regulator in parallel with an improved power disturbance feedforward control to com-pensate the delay inherently involved in the current loop response and observer convergence rate.

3)Current loop:The current loop is based on the voltage-oriented control with dead-time compensation.The dead-time effect has to be compensated to avoid impacts on the dynamic response of current loop and the dc-bus voltage control performance.

Details on the design of the NDO,voltage loop with feed-forward control,and the current control loop with dead-time compensation are presented in the next section.

III.DC-B US V OLTAGE C ONTROL S TRATEGY

A.Design of an NDO

According to (1),(4)and (8),the second-order system de-picted in (9)(considering active current dynamic equation only)can be used to describe the dc-bus voltage control system

??????du dc dt =?1.5u d i d Cu dc +i o C

di d dt =?R L i d ?ωi q

+e d ?u d

L (9)

where i o =i bat +i pv ?i load .

In order to obtain the standard form for NDO,the following de?nition has been adopted:?

??????????????????

x =[x 1x 2]T =[u dc i d ]T ,u =e d ,d (t )=i o a (x )=?R L i d ?ωi q ?

u d L ,b (x )=1L

g 2(x )= 1C 0 T y =x 1

(10)

where x 1and x 2are state variables,u is the control input,d (t )is the mismatched disturbance,and y is the output.Then,the system (9)can be rewritten as

˙x =f (x )+g 1(x )u +g 2(x )d (t )

y =x 1(11)where f (x )=[?1.5u d x 2/Cx 1a (x )]T ,g 1(x )=[0b (x )]T .

As a consequence,the disturbance in (11)can be estimated by the NDO [30],[31]????

d =z +p (x )

dz dt

=?(l (x )g 2

(x ))z ?l (x )[g 2(x )p (x )+f (x )+g 1(x )u ]

(12)

where?d is the estimation of the disturbance,z is the intermediate state of the nonlinear observer,and p(x)is the observer function needed to be designed,which can be depicted by

p(x)=l1x1+l2x2(13) The observer gains l(x)are then decided by

l(x)=?p(x)

=[l1l2].(14)

Assumption:The disturbance d(t)in system(11)satis?es

????

???d?=sup|d(t)|

t>0

lim

t→∞

dd(t)

(15)

Note that the disturbance i o in dc microgrid is always satis-?ed for this assumption.With the assumption in(15),the error convergence equation can be derived by

de d(t) dt +(l(x)g

(x))e d(t)=0(16)

where e d(t)=d(t)??d(t).

If the observer gains l(x)are selected such that l(x)g2(x)>0, which implies(16)is globally asymptotically stable[30],distur-bance estimation?d of NDO in(12)can track the disturbance d(t) of system(11)asymptotically with time constant1/l(x)g2(x). To simplify the observer design and eliminate the in?uence of other uncertain factors(such as a(x)and u)on the observation, the observer gains can be chosen as l1>0,l2=0.The time con-stant for the novel disturbance observation is C/l1.Generally, the dynamic response of the observer is faster than that of the feedback control system.However,if l1is too large,the system may subject to saturation or noise during implementation. With these considerations,an NDO to track the disturbance i o in(9)can be determined by

???

?? i

=z+l1u dc

l21u dc

1.5u d

Cu dc

l1i d

(17)

where i o is the estimated value of the disturbance i o.

The proposed NDO can estimate the mismatched disturbance in(9),which implies that the disturbances act via the different channel as the control input.On the other side,the NDO can be designed separately from the controller design.If(9)is lin-earized and consider the linear observers presented in[32],[33], more observer gains need to be designed and the implementa-tion of the linear observers is more complicated than that of the NDO(17).

From(16)and(17),the following relationship to describe the observed value and the actual value of disturbance current has been considered:

?i o (s)=

1+T dob s

i o(s)(18)

where T dob=C/l1

Fig.5.DC-bus voltage control block.

B.Voltage Loop with an Improved Feedforward Control

From the power balance point of view,the transients triggered

by the disturbance current i o in the dc subgrid will?rst cause

?uctuations on dc bus.Then,the active current reference value

i dref will be regulated accordingly by the outer voltage loop con-

troller in the traditional dual-loop control structure to stabilize

the dc voltage.As a result,the output current i d of the dc–ac

inverter will lag the variation of i o.When large perturbation

occurs,the dc bus may suffer signi?cant impact.In order to re-

duce the impact,an NDO-based improved feedforward control

loop has been embedded in the dc-bus voltage loop as shown

in Fig.4.The schematic of the voltage loop with the proposed

improved feedforward control is illustrated in Fig.5,where the

dc-bus voltage response can be depicted by

u dc(s)=

(1/sC)G upi(s)G c(s)k

1+(1/sC)G upi(s)G c(s)k

U dcref(s)

sC+G upi(s)G c(s)k

i o(s)

?G fd(s)G c(s)k

sC+G upi(s)G c(s)k

(s).(19)

As the feedforward control has an open-loop nature,its dy-

namic response will be faster than the feedback loop control.

However,if the feedforward value is not so accurate that the

open loop control will result in steady-state mismatch with the

reference.Thus,the PI controller will help to eliminate the errors

between the reference and the feedback.

As can be seen from(18)and(19),if the feedforward transfer

function G fd(s)is designed as

G fd(s)=

1+T dob s

kG c(s)

(20)

the in?uence of the disturbance current i o on the dc-bus volt-

age u dc can be mitigated signi?cantly.In the proposed control

scheme,the disturbance current needed for the feedforward con-

trol is produced from the NDO designed in(17).This is done

without any additional current sensors or communication be-

tween the dc subgrid and the dc–ac converter,and therefore the

system scalability and plug-and-play feature of the DGs within

the dc subgrid are maintained.

Combining(5)and(20),the detailed representation of the

function G fd(s)can be obtained as

G fd(s)=

Ls+R

k pid s+k iid

s+1

(1+T dob s)

[G LD(s)s+1](1+T dob s)(21)

Fig.6.Equivalent circuit of DG/load connected to dc link in the dc subgrid.

where G LD (s )is a lead and lag https://www.wendangku.net/doc/8f14019236.html,ually during the transient,the rate of the disturbance current i o is much higher than the corner frequencies of G LD (s ),and the reduced order of G LD (s )can be used to simplify the analysis

G LD (s )≈

L k pid

.(22)

From the earlier analysis,the feedforward function G fd (s )can be expressed as

G fd (s )=

1+((L/k pid )+T dob )s k =1+T fd s k

(23)

where T fd is called derivative time constant.

It is obvious that the ultimate feedforward function G fd (s )compensates both the tracking time delay of NDO and the re-sponse time of the current loop.A larger proportional gain (k pid )of the current controller,or higher convergence rate of NDO will lead to smaller derivative time constant T fd .

In a practical control system,the output of NDO i o contains

both the estimated value of the disturbance current and high-frequency noise signals.The simple differential operation in (23)will therefore be sensitive to the high-frequency noises.To avoid this noise ampli?cation,a derivative ?lter as shown in (24)can be adopted,which can reduce the sensitivity to high-frequency noise while without affecting much the disturbance estimation ability.In (24),N is the ?ltering coef?cient,which determines the corner frequency of the derivative ?lter

G fd (s )=1

k 1+T fd Ns N +s

.(24)

C.Effects of DC-Bus Capacitance Variations

In an actual dc subgrid,dc loads or the DG units are usually

connected to the dc bus through line impedance (as shown in Fig.2).An equivalent circuit of the DG or load connected to the dc bus is shown in Fig.6,where the DG or load is represented as a capacitance C r (used as voltage stabilizer and ?lter)in parallel with an impedance R eq (which can be negative for DG).This will lead to two possible complications:1)possible resonance caused by the line impedance and dc-bus capacitance [34],and 2)the variation of equivalent dc-bus capacitance [35].In a low voltage microgrid with relatively small capacity,the line/cable resistance R cable could provide damping to the system,and therefore,the uncertainty in the equivalent dc-link capacitance is considered due to connection/disconnection of dc sources and loads.

In order to achieve good performance in both dc-bus volt-age tracking and disturbance rejection,the open loop frequency characteristic of the voltage control should have a phase

margin

Fig.7.Impact of k p u and k iu on the frequency characteristic and the band-width of the control

system.

Fig.8.Feasible region of the dc-bus capacitance value C and the proportional gain k p u when (a)τ=0.1and (b)τ=0.02.

about 45?,wide middle frequency bandwidth,and appropriate cut-off frequency.Considering the stability margin of the control system,the closed-loop control bandwidth and anti-disturbance capability,the relationship between the parameters of the dc-bus voltage controller and the equivalent capacitance is analyzed here.

Fig.7describes the impact of voltage control parameters (k pu and k iu )on the phase margin of the frequency characteristic and the bandwidth of the control system using the model in (7).It can be seen that a larger equivalent proportional gain k pu /C will lead to a wider bandwidth,but result in a smaller phase margin.If the integral gain is larger,the stability margin will be reduced,although the settling time can be shortened.Further,it can be seen from Fig.7that,with τ=k pu /k iu =0.1,in order to ensure a certain bandwidth of dc-bus voltage control systems (such as [50,300](rad/s))and guarantee the phase margin is greater than 45?,the equivalent proportional gain k pu /C can be chosen from 50to 340.

From (7),if the current loop dynamics are neglected,the dc-bus voltage ?uctuation caused by the disturbance current can be depicted as (without the feedforward)

Δu dc (s )=

s 2C +k pu ks +k pu k/τ

Δi o (s ).

(25)

Through the aforementioned analysis,to achieve the given stability margin,the closed-loop control bandwidth range and the dc-bus voltage variations under the disturbance,the feasi-ble region of the dc-bus capacitance value C under different proportional gain k pu of the dc-bus voltage control system can be obtained as shown in Fig.8,where the minimum value of

Fig.9.(a)Root loci of system(27)with C changing from0.01to0.08F.

(b)Performance of the NDO-based dc-bus voltage control under transient with different capacitances.

capacitance is limited by the dc-bus voltage variations under disturbance[36],[37],and the maximum value is limited by the stability margin and the closed-loop control bandwidth.It can be seen from Fig.8that a smaller proportional gain k pu allows larger range of capacitance variation.Furthermore,by compar-ing Fig.8(a)and(b),it can be seen that the integral time constant τof the dc voltage control system has obvious effects on the feasible capacitance variation range.A smaller time constant will signi?cantly reduce this range.

On the other hand,the dc-bus capacitance also has impact on the performance of the NDO as shown in(17),where the estimation of the disturbance current can be depicted as

i o (s)=

kl1

sC0+l1

i d(s)+

l1C0s

sC0+l1

u dc(s)(26)

where C0is the normal value of the capacitance. Therefore,the variation of the dc-bus voltage can be analyzed by(27),at the bottom of this page,from Fig.4and(5),(19)and (26).

When the normal value of the dc-bus capacitance is selected as0.01F for the control system and observer design,the root loci of system(27)and the time-domain performance of the NDO-based dc-bus voltage control under transient with different actual values of the capacitance are shown in Fig.9(a)and(b), respectively.As shown in Fig.9(a),when the difference between the normal value and actual value of the dc-bus capacitance becomes greater,the system will become more oscillatory with reduced damping.In Fig.9(b),obvious oscillation occurs when C is equal to0.04F(four times of the nominal value C0), which will deteriorate the performance of the proposed control system.However,the NDO-based dc-bus control system still has good robustness against the parameters variation.E.g.in the system under study,when the control parameters are selected as described in Section IV(A),the allowed variation range of

the Fig.10.(a)Root loci of system(28)and(29)with L cab le changing from1 to10mH.(b)Performance comparison of the proposed dc-bus voltage control and traditional method.

dc-bus capacitance considering both the dc voltage control and NDO dynamics can be around0.02F(two times of C0).This can be veri?ed through Fig.9(a),where0.02F leads to suf?cient stability margin and good damping of the system response.

If the effect of the line impedance shown in Fig.6on the system stability can not be ignored,the variation of the dc-bus voltage shown in(27)can be modi?ed to be(28),at the bottom of this page.

Then(28)can be used to analyze the effect of the line impedance on the dc voltage control system with NDO method. The following expression(which is the dc voltage variation with the traditional method)can be used to analyze the effect of the line impedance on the performance of the traditional dc voltage control system:

Δu dc(s)=

(s2L cable C r+sR cable C r+1)(kG upi(s)G c(s)+sC0)+sC r ×Δi s(s).(29) Fig.10(a)shows the comparison of the root loci of system(28) and(29)with L cable changing from1mH to10mH.Especially, the eigenvalues denoted by Eig.1and Eig.2are obtained from (29)and(28),respectively,when the resistance value R cable= 0.1Ωand inductance value L cable=2mH.While,when R cable increased to0.5Ω,eigenvalues denoted by Eig.1and Eig.2will move toward the symbols Eig.3and Eig.4,respectively.It can be seen that:1)when the inductance value L cable becomes greater, the system will become more oscillatory with reduced damping;

2)the resistance R cable could provide damping to the system by comparing the poles positions of Eig.1and Eig.3,or that of Eig.2 and Eig.4;3)under the same condition,the proposed control can provide more damping to the system than the traditional method because by comparing the poles positions of Eig.1and Eig.2,

Δu dc(s)=

1?G c(s)G fd(s)(kl1/sC0+l1)

sC(1?G c(s)G fd(s)(kl1/sC0+l1))+k(G upi(s)G c(s)+G c(s)G fd(s)(sC0l1/sC0+l1))

Δi o(s)(27)

Δu dc(s)=

1?G c(s)G fd(s)(kl1/(sC0+l1))

(s2L cable C r+sR cable C r+1)(kG upi(s)G c(s)+sC0)+(1?G c(s)G fd(s)(kl1/(sC0+l1)))sC r

Δi s(s)(28)

Fig.11.V oltage error vector introduced by dead-time.

or that of Eig.3and Eig.4.The earlier comments1)and2)are consistent with the analysis in[34].In order to further verify comments3),Fig.10(b)shows the time-domain performance comparison of the proposed dc-bus voltage control(28)and traditional method(29)with the disturbance currentΔi s= 1A.As can be seen from Fig.10(b),when the line impedance L cable=5mH and R cable=0.1Ω,the NDO-based control can not only suppress the maximum dc voltage?uctuation,but also reduce the dc voltage oscillations(from0.3V under traditional method to0.18V under the proposed control),which means the proposed method has the ability to reduce the oscillations caused by the line impedance.

Note that for the model considered in this section,the control of sources and loads that connected to the dc link through dc/dc converters are not considered.A full model with the control of other dc/dc converters and the effects of constant power loads (CPLs)are analyzed in the Appendix,where it shows that as long as the NDO and dc/dc converter control are designed properly, the dc-bus voltage control system will have acceptable stability margin and good dynamics using the simpli?ed analysis in this section.

D.Dead-Time Compensation

In a voltage-source converter,the dead-time is implemented in the PWM signals for two switching devices in the same leg. Although the dead-time T d is very small,it causes deviations between the ideal modulation voltages(e dpwm and e qpwm)and the actual output voltages(e d and e q)(see Fig.4),leading to current control performance degradation[26],[27].This cur-rent control dynamics degradation will consequently affect the disturbance feedforward control.

To analyze the dead-time effects,the ac voltages and currents in abc and dq frames are represented in the coordinate frames illustrated in Fig.11,where U and I denote the grid voltage vector and grid side current vector,respectively.δ,θand?are the angles between U and I,between U and a-axis,and between I and a-axis,respectively.Based on the space vector analysis method,voltage error vector concept is adopted to describe the deviations caused by the dead-time[38].As shown in Fig.11, the space is divided into six equal sectors,and the voltage error vector denoted byΔEi(i=1,2,...,6)will change its position 6times in a power frequency cycle.The detailed relationship betweenΔEi and?is depicted in[38].If the6th harmonic component is not considered,the voltage error vector can be de-scribed to be a vector whose amplitude is equal to2u dc T d/(3T s)(where T s is the switching period.),and phase lags behind the grid side current vector I with180?.Therefore,the projections values ofΔEi in dq frame can be derived as

???

ΔE d=?ΔE

i d

+i2q

ΔE q=?ΔE

i q

+i2q

(30)

whereΔE is the amplitude of the voltage error vector.

Due to the voltage errorsΔE d andΔE q,the actual output voltages(e d and e q)obtained from the ideal modulation voltages (e dpwm and e qpwm)can be expressed by

e dpwm+ΔE d=e d

e qpwm+ΔE q=e q.(31) As a result,the response o

f i d should be modi?ed to

i d(s)=G c(s)i dref(s)+

Ls2+(R+k pid)s+k iid

ΔE d(s).

(32) Based on(32),the dc-bus voltage response as shown in(18) should be updated to

u dc(s)

(1/sC)G upi(s)G c(s)k

1+(1/sC)G upi(s)G c(s)k

U dcref(s)

sC+G upi(s)G c(s)k

i o(s)?

G fd(s)G c(s)k

sC+G upi(s)G c(s)k

(s)

?sk

Ls2+(R+k pid)s+k iid

sC+G upi(s)G c(s)k

ΔE d(s).

(33) According to(33),if the variation ofΔE d orΔ(ΔE d)is not equal to zero,the dc-bus voltage will be affected by this term during the transient.From(30),when the inverter delivers a certain reactive power(i q)or the disturbance of dc side results in the inverter power?ow direction,Δ(ΔE d)will not be equal to zero.Especially in the latter scenario,Δ(ΔE d)will reach its maximum value when there is no reactive power output, resulting in serious impact on the dc-bus voltage.

To compensate the dead-time effect and therefore minimize its impact on the dc-bus voltage control,the following compen-sation algorithm is designed based on the earlier analysis:

e dpwm=u d+(i dref?i d)(k pid+k iid/s)+ωL?i q?ΔE d e qpwm=(i qref?i q)(k pid+k iid/s)?ωL?i d?ΔE q.(34) The critical part o

f applying(34)is to obtain the voltage errors ΔE d andΔE q accurately.To do this,the power injected to the dc bus is?rst obtained by usin

g the dc-bus voltage multiplied by the estimated value of the disturbance i o from the NDO.Then, from(8),the required output active current i d of dc–ac to be transferred between the dc and ac subgrids can be determined. Combined wit

h the reactive current

i q,the voltage errorsΔE d andΔE q can be decided by(30).

Fig.12.30kV A hardware setup of the dc subgrid.

IV.V ERIFICATION OF THE C ONTROL S TRATEGY

https://www.wendangku.net/doc/8f14019236.html,boratory Setup Details

To verify the effectiveness of the proposed NDO-based dc-bus voltage control method,a dc subgrid system as illustrated in Fig.2has been built.This dc subgrid is interfaced to the ac grid through a dc–ac converter.The corresponding hard-ware experiment platform is shown in Fig.12,with its sys-tem parameters listed in Table I.In addition,the converters are controlled by a Renesas MCU(M32192F8)+FPGA-based digital controller,with the experimental pro?les observed by a ScopeCorder(YOKOGAW A SL1400).

To emulate the variation of the equivalent dc-link capacitance, two different capacitance values(0.01F and0.02F,respectively) as shown in Table I have been considered.From the theoretical analysis on the feasible region of the dc-bus capacitance and the proportional gain k pu of the dc-bus voltage control system as shown in Fig.8,the parameters of the voltage PI regulator are chosen as:k pu=1,k iu=10.The observer gain l1is chosen to be 10,and the theoretical setting time of NDO error equation(16)is about1ms.According to the parameters chosen earlier,the time constant T fd and the?ltering coef?cient N of the differentiator are4.1ms and200,respectively.

B.Experimental Results

1)Scenario1:In this scenario,the dc-bus capacitance is 0.01F.A disturbance on the system is introduced by controlling the batteries from standby mode to discharging mode(with current reference of30A),while the dc load and PV output are about2.8and2.5kW,respectively.The control performance of conventional PI control and the proposed method have been compared.Because the output power?ow direction of dc–ac converter is changed,this scenario can also be used to verify the performance of the dead-time compensation.

Fig.13shows the theoretical and simulation results with the traditional dual-loop control and the proposed NDO-based dc-bus voltage control method,respectively.The parameters in

the Fig.13.DC voltage variation under disturbance:(a)theoretical results using (33)and(b)simulation results.

PSCAD simulation are the same as in the Table I.The battery voltage is about550V,so with30A current output from the battery,the equivalent disturbance current to dc link i o is22A (with dc voltage at750V),which will cause the dc/ac converter to deliver power to the grid.As discussed earlier in Section III-D, the response of the dc-bus voltage control system will be affected by the voltage errors due to dead-time,which can be analyzed by(33).Fig.13(a)shows the dc-bus voltage response using(31) (only the variation is considered),while Fig.13(b)shows the dc-bus voltage variation(the reference dc-bus voltage is750V) under the transient disturbance.It can be seen that the simulation results obtained in PSCAD are consistent with the theoretical analysis.

Figs.14–16show the experimental results with traditional control and the proposed NDO-based dc-bus voltage control method,respectively.Under the traditional PI control,the dc-bus voltage increased to about787V abruptly,and it took about0.2s to return to the steady-state status,which is consistent with the theoretical analysis and simulation results.With the proposed NDO-based feedforward control method(while without dead-time compensation)as shown in Fig.15,the dc-bus voltage variation has been mitigated signi?https://www.wendangku.net/doc/8f14019236.html,pared with the results in Fig.14,the maximum dc bus has been reduced to 759V with less than28V of voltage?uctuation.The settling time of the dc-bus control system has also been shortened to about30ms.

It can be seen from Figs.14and15,the power is originally balanced in the dc subgrid and the dc–ac inverter”s power is around0.After the disturbance,output power of the dc–ac con-verter is increased to15kW due to the output power variation of the battery energy storage system.So the angle between the grid voltage vector U(d-axis)and the grid side current vector I changes,which causes variation of the voltage errorsΔE d andΔE q;and affects both the performance of current loop and the feedforward control according to(33).Fig.16shows results with the dead-time compensation based on the control scheme described in https://www.wendangku.net/doc/8f14019236.html,paring the results in Figs.15and16,the peak of the dc-bus voltage has been further reduced to755V. As can be seen from the battery current in Figs.14–16,the switching process from battery standby mode to discharging state needs about50ms.This is related to the terminal voltage of the storage system,current references and control parameters of dc–dc controller.

Fig.14.Experimental results under the traditional control scheme.(a)dc-bus voltage:6.25V/div.(b)Battery voltage:3.75V/div.(c)Battery current:5A/div.(d)Phase A voltage:125V/div.(e)Phase A current:12.5A/div.(f)PV voltage:12.5V/div.(g)PV current:1.25A/div.(h)DC load current:0.75

A/div.

Fig.15.Experimental results with NDO-based control and without dead-time compensation.(a)DC-bus voltage:5V/div.(b)Battery voltage:3.75V/div.(c)Battery current:5A/div.(d)Phase A voltage:125V/div.(e)Phase A current:12.5A/div.(f)PV voltage:12.5V/div.(g)PV current:1.25A/div.(h)DC load current:0.75A/div.

Lastly,the performance of the NDO has been shown in Fig.17,which veri?ed that the NDO can track the power dis-turbance effectively.

2)Scenario 2:Compared to the ?rst experiment,the dc-link capacitance has been changed to 0.02F in Scenario 2to verify the control performance under 100%increase of the dc-bus capacitance.The control parameters are selected to be the same in both scenarios.Again the disturbance is introduced by controlling the batteries from standby mode to

discharging

Fig.16.Experimental results with NDO-based control and with dead-time compensation.(a)DC-bus voltage:5V/div.(b)Battery voltage:3.75V/div.(c)Battery current:5A/div.(d)Phase A voltage:125V/div.(e)Phase A current:12.5A/div.(f)PV voltage:12.5V/div.(g)PV current:1.25A/div.(h)DC-load current:0.75

A/div.

Fig.17.

Output of the NDO.

mode (with current reference of 30A),while the dc load and PV output are about 2.8and 2.5kW,respectively.

As seen from Fig.18,the simulation results using PSCAD are consistent with the theoretical analysis under the https://www.wendangku.net/doc/8f14019236.html,pared to Fig.13,the variation of dc-bus capacitance has lit-tle in?uence on the stability of the control system,provided the controller parameters are chosen properly.But the dc-bus volt-age ?uctuation has been reduced to 780V under the traditional PI control due to the larger capacitance used.

Fig.19shows the experimental results with the traditional control,where the dc-bus voltage increased to about 780V during the transient.Due to the increased size of the dc-bus capacitor,the dc-bus voltage ?uctuation has been reduced com-pared to Fig.14,which is consistent with the theoretical analysis

Fig.18.DC voltage variation under disturbance:(a)theoretical results using (33)and (b)simulation

results.

Fig.19.Experimental results under the traditional control scheme.(a)DC-bus voltage:6.25V/div.(b)Battery voltage:3.75V/div.(c)Battery current:5A/div.(d)Phase A voltage:125V/div.(e)Phase A current:12.5A/div.(f)PV voltage:12.5V/div.(g)PV current:1.25A/div.(h)DC-load current:0.75A/div.

and simulation results.With the proposed NDO-based feedfor-ward control method (while without dead-time compensation)as shown in Fig.20,the maximum dc bus has been reduced to 759V with less than 21V compared with the results in Fig.18.The settling time of the dc-bus control system has also been shortened signi?cantly.Fig.21shows the results with the dead-time compensation based on the control scheme described in https://www.wendangku.net/doc/8f14019236.html,paring the results in Figs.20and 21,the peak of the dc-bus voltage has been reduced to 757V .The performance of the NDO has been shown in Fig.22,which can track the power disturbance effectively.This result in Fig.22is also consistent with Fig.9,where the NDO response starts to become a bit oscillatory when the capacitance is increased to 0.02F.

Overall,it can be seen that the designed control system has a good robustness to deal with the parameters uncertainty of the system,and there is a good match among the theoretical analysis,simulations,and experimental results.

V .C ONCLUSION

A simple NDO-based dc-bus voltage control strategy was proposed in this paper,which is especially suitable for a

hy-

Fig.20.Experimental results with NDO-based control and without dead-time compensation.(a)DC-bus voltage:5V/div.(b)Battery voltage:3.75V/div.(c)Battery current:5A/div.(d)Phase A voltage:125V/div.(e)Phase A current:12.5A/div.(f)PV voltage:12.5V/div.(g)PV current:1.25A/div.(h)DC-load current:0.75

A/div.

Fig.21.Experimental results with NDO-based control and with dead-time compensation.(a)DC-bus voltage:5V/div.(b)Battery voltage:3.75V/div.(c)Battery current:5A/div.(d)Phase A voltage:125V/div.(e)Phase A current:12.5A/div.(f)PV voltage:12.5V/div.(g)PV current:1.25A/div.(h)DC-load current:0.75A/div.

brid ac/dc microgrid or a dc microgrid.With the proposed con-trol strategy,high bandwidth communications between the dc source/loads and the dc–ac converter can be avoided,which is key for the system scalability and maintaining the plug-and-play feature of the DGs.Based on the estimated results from NDO,the proposed dc-bus voltage control method with improved feed-forward and dead-time compensation can signi?cantly reduce

Fig.22.Output of the

NDO.

Fig.23.

Con?guration of the dc subgrid system for full model analysis.

the dc-bus control settling time and mitigate the dc-bus voltage variations.The effects of equivalent dc-bus capacitance varia-tion are also considered in this paper.The experimental results from a 30kV A dc subgrid have shown the effectiveness of the proposed control strategy.

A PPENDIX

Without loss of generality,assume that the dc microgrid in-cludes two dc–dc converters for the system stability analysis,which operate in boost stage and buck stage,respectively,as shown in Fig.23.Speci?cally,the boost dc–dc converter is controlled by current regulation and transmit power from the source to the dc bus,which is typical for a PV unit or battery storage system interface in discharging mode (note that the bat-tery charging mode will be same as the buck dc–dc converter and therefore a bidirectional dc–dc converter is not used here).On the other hand,the buck dc–dc converter acting as a line-regulating converter (LRC)to supply power for the constant power loads (CPLs)is controlled by voltage regulation [5],[9],[39].

From Fig.23,the average state model of the boost dc–dc converter can be depicted as

u s =L 1di 1dt +(1?d 1)u dc

u s i 1=u dc i o 1(A1)

where u s ,i 1and i o 1denote the dc source voltage,the inductor current and output dc currents of the boost dc–dc converter,respectively,L 1is ?lter inductance,and d 1is the duty cycle.When the current loop adopts the PI controller,the duty cycle can be obtained as

??d 1=(i 1ref ?i 1)k pi1+k ii1u 1r

u 1r

=i 1ref ?i 1

(A2)

where i 1ref is the current reference,k pi1and k ii1are the propor-tional gain and integral constant of the current loop controller,respectively,u 1r is the integral state of the current PI controller.When the models in (A1)and (A2)are linearized,the resulting current response can be depicted by

Δi 1=

U dc (k pi1s +k ii1)

L 1s 2+k pi1U dc s +k ii1U dc Δi 1ref

(1?D 1)s

L 1s 2+k pi1U dc s +k ii1U dc

Δu dc

(A3)

where Δdenotes small disturbance,U dc is the steady-state dc voltage,D 1is the steady-state duty cycle.

Therefore,the closed-loop transfer function G i (s )in (A4)for the current control can be used to analyze the stability of the boost dc–dc converter

G i (s )=

U dc (k pi1s +k ii1)

L 1s 2+k pi1U dc s +k ii1U dc

(A4)

In a similar way,the average state model of the buck dc–dc converter can be depicted as

???????

??????

u o =?L 2di 2dt +d 2u dc i 2=C 2du o dt +P L u o +u dc R o u o i 2=?u dc i o 2(A5)where u o ,i 2and i o 2denote the dc source voltage,the inductor current and output dc currents of the buck dc–dc converter,respectively,L 2and C 2are the ?lter inductance and capacitance,respectively,d 2is the duty cycle,the loads includes a resistor R o and a CPL P L .

When the buck dc–dc converter adopts the dual-loop control with two PI controllers,the duty cycle can be drawn by

??????????????????i 2ref =(u oref ?u o )k pu2+k iu2u 2ur u 2ur =u oref ?u o s

d 2=(i 2ref ?i 2)k pi2+k ii2u 2r u 2r

=i 2ref ?i 2

(A6)

where u2ref is the voltage reference,i2ref is the current refer-ence;k pu2and k iu2,k pi2,and k ii2are the proportional gain and integral constant of the voltage loop and current loop controllers, respectively;u2ur and u2r are the integral states of the voltage and current PI controllers,respectively.

When the models in(A5)and(A6)are linearized the resulting load voltage response can be depicted by(A7),at the bottom of this page,whereΔdenotes small disturbance,U o is the steady-state voltage,D2is the steady-state duty cycle.

Thus,the closed-loop transfer function G uo(s)in(A8),at the bottom of this page,for the current control can be used to analyze the stability of the buck dc–dc converter.

When considering the effect of the dc–dc converters control systems on the dc-bus voltage control system stability,the com-plete signal model in(A9),at the bottom of this page,can be built through Fig.5and(A1)–(A8).

From(A9),the effect of the boost dc–dc converter,buck dc–dc converter,and the NDO on the system stability can be studied by eigenvalue analysis.The comparisons of the eigenvalues of in (A9)and the loci of the characteristic equations[which are cal-culated from characteristic equations of boost dc–dc converter in(A4),buck dc–dc converter in(A8),and dc-bus voltage con-trol system in(19)]with variation of different parameters(such as k pi1,k pu2,P L,and the NDO gain l1)are shown in Figs.24, 25,and26,respectively.In these?gures,the symbol“×”,“+”,“o,”and“?”denote the eigenvalues of the characteristic ma-trix of the complete signal model in(A9),and the loci of the characteristic equations in(19),(A8),and(A4),respectively.

Δu o=

(k pi2s+k ii2)(k pu2s+k iu2)U dc

(k pi2s+k ii2)(k pu2s+k iu2)U dc+s2+(C2s?P L

U2o

R o

)s[L2s2+(k pi2s+k ii2)U dc]

Δu oref

D2s2

(k pi2s+k ii2)(k pu2s+k iu2)U dc+s2+(C2s?P L

U2o

R o

)s[L2s2+(k pi2s+k ii2)U dc]

Δu dc(A7)

G uo(s)=

(k pi2s+k ii2)(k pu2s+k iu2)U dc

(k pi2s+k ii2)(k pu2s+k iu2)U dc+s2+(C2s?P L

U2o

R o

)s[L2s2+(k pi2s+k ii2)U dc]

(A8)

???????????????????????????????????????????????????????????????????????????????????????????????????C

dΔu d c

U s

U d c

Δi1?

U o

U d c

Δi2?

U d c

Δu o?

R d c

Δu d c?

1.5U d

U d c

Δi d

dΔi d

=?Δi d(R+k p i)+(Δu d c?Δu d cref)k p u k p i+Δu u d cr k iu k p i+Δu d r k ii+k p i

(Δz+l1Δu d c)+k p i

T fd s

Δz+k p i

T fd s

l1Δu d c dΔu d r

=(Δu d c?Δu d cref)k p u+Δu u d cr k iu?Δi d+

(Δz+l1Δu d c)+

T fd s

Δz+

T fd s

l1Δu d c

dΔu u d cr

=Δu d c?Δu d cref

dΔi1

=?(1?D1)Δu d c+[(Δi1ref?Δi1)k p i1+Δu1r k ii1]U d c

dΔu1r

=Δi1ref?Δi1

dΔi2

=?Δu o+D2Δu d c+[((Δu oref?Δu o)k p u2+k iu2Δu2u r)k p i2?Δi2k p i2+k ii2Δu2r)]U d c

dΔu2r

=(Δu oref?Δu o)k p u2+k iu2Δu2u r?Δi2

dΔu o

=Δi2?

Δu o

R o

P L

U o U o

Δu o

dΔu2u r

=Δu oref?Δu o

dΔz

Δz?

l21Δu d c

l1Δi d

(A9)

https://www.wendangku.net/doc/8f14019236.html,parison of the eigenvalues of in (A9)(“x”)and the loci of the characteristic equations in (A8)(“o”),(19)(“+”),and in (A4)(“?”),with the current loop gain k p i1of the boost dc–dc converter changed from 0.0005to

0.003.

https://www.wendangku.net/doc/8f14019236.html,parison of the eigenvalues of in (A9)(“x”)and the loci of the characteristic equations in (A8)(“o”),(19)(“+”),and in (A4)(“?”),with (a)the CPL of the buck dc–dc converter changed from 100W to 1000W and (b)the voltage loop gain k p u 2of the buck dc–dc converter changed from 0.2to

A.Effect of the Boost DC–DC Converter on the System Stability

As seen from Fig.24,with the current loop gain k pi1of the dc–dc boost converter varies from 0.0005to 0.003,loci of the characteristic equation of the boost dc–dc converter in (A4)are

consistent with the eigenvalue trajectory of the characteristic matrix of the complete model in (A9).This means the dynamics of the dc-bus voltage control considering the full model under the variation of the dc–dc boost converter control parameters is similar to those for the boost converter control in (A4).There-fore,if the boost dc–dc converter control is designed properly,its effect on the dc-bus voltage control can be minimized,and the simpli?ed model in (19)can be used for the control scheme design.

B.Effect of the Buck DC–DC Converter on the System Stability

As shown in Fig.25(a),if the CPL of the buck dc–dc con-verter increased,the high-frequency loci of the characteristic equation of buck dc–dc converter in (A8)will move toward to the right,and the system will become more oscillatory with reduced damping,which have been validated in [5].Observing the eigenvalue trajectory of the characteristic matrix of the com-plete signal model in (A9),the same conclusion can be drawn.By comparison,the effect of the CPL on the dynamics of the dc-bus voltage control is similar to the buck dc–dc converter control system in (A8).Fig.25(b)shows the comparison when the voltage loop gain k pu2of the buck dc–dc converter changes from 0.2to 2.Both the variation trajectories denoted by “x”and “o”are consistent.Therefore,if the buck dc–dc converter con-trol is designed properly,its effect on the dc-bus voltage control can also be minimized,and the simpli?ed model in (19)can be used for the dc-bus control design.

C.Effect of the NDO on the System Stability

As seen from the loci comparison in Fig.26,if the gain l 1of the NDO has chosen to be too small,especially the triangle (denoted by “x”and “+”)and square (denoted by “x”and “?”)regions in the zoomed in part of Fig.26(b),the gain l 1of the NDO will affect the dynamics (not stability)of dc-bus voltage control and boost dc–dc control systems,e.g.,when a small gain (l 1=1)is used,the dc-bus voltage control becomes more oscillatory.On the other hand,if l 1is too large the system stability margin will be smaller with the poles moving toward the right.However,it is important to note that for the NDO design in Section III,to ensure the dynamic response of the observer is always faster than that of the feedback control system (l 1cannot be too small)and with the consideration that a too large l 1will cause saturation or noise during implementation,the gain l 1of the NDO also need to be design properly.As a result,this properly designed NDO gain should not affect the dc microgid stability margin and damping.

Through the analysis in this Appendix,it shows that as long as the NDO and dc/dc converter control are designed properly,the dc-bus voltage control system will have acceptable stability margin and good robustness against,and the simpli?ed analysis in Section III will be suf?cient for the design of the control scheme.However,if the detailed effects of dc/dc converter con-trol and the NDO design for the full system are desired,the methodology presented in the Appendix can be adopted.

R EFERENCES

[1]P.C.Loh,D.Li,Y.K.Chai,and F.Blaabjerg,“Hybrid AC–DC microgrids

with energy storages and progressive energy?ow tuning,”IEEE Trans.

Power Electron.,vol.28,no.4,pp.1533–1542,Apr.2013.

[2]P.C.Loh,D.Li,Y.K.Chai,and F.Blaabjerg,“Autonomous operation of

hybrid microgrid with AC and DC subgrids,”IEEE Trans.Power Electron., vol.28,no.5,pp.2214–2222,May2013.

[3]J.M.Guerrero,J.C.Vasquez,J.Matas,L.G.De Vicuna,and M.Castilla,

“Hierarchical control of droop-controlled AC and DC microgrids—A gen-eral approach toward standardization,”IEEE Trans.Ind.Electron.,vol.58, no.1,pp.158–172,Jan.2011.

[4]H.Zhou,T.Bhattacharya, D.Tran,T.S.Terence Siew,and

A.M.Khambadkone,“Composite energy storage system involving bat-

tery and ultracapacitor with dynamic energy management in microgrid applications,”IEEE Trans.Power Electron.,vol.26,no.3,pp.923–929, Mar.2011.

[5] A.Kwasinski and C.N.Onwuchekwa,“Dynamic behavior and stabiliza-

tion of DC microgrids with instantaneous constant-power loads,”IEEE Trans.Power Electron.,vol.26,no.3,pp.822–833,Mar.2011.

[6]S.Anand,B.G.Fernandes,and J.M.Guerrero,“Distributed control to

ensure proportional load sharing and improve voltage regulation in low-voltage DC microgrids,”IEEE Trans.Power Electron.,vol.28,no.4, pp.1900–1912,Apr.2013.

[7]H.Fakham,D.Lu,and B.Francois,“Power control design of a battery

charger in a hybrid active PV generator for load-following applications,”

IEEE Trans.Ind.Electron.,vol.58,no.1,pp.85–93,Jan.2011.

[8]https://www.wendangku.net/doc/8f14019236.html,go and M.L.Heldwein,“Operation and control-oriented modeling

of a power converter for current balancing and stability improvement of dc active distribution networks,”IEEE Trans.Power Electron.,vol.26, no.3,pp.877–884,Mar.2011.

[9] A.A.A.Radwan and Y.A.-R.I.Mohamed,“Linear active stabilization

of converter-dominated DC microgrids,”IEEE Trans.Smart Grid,vol.3, no.1,pp.203–215,Mar.2012.

[10]H.-S.Kim,M.-H.Ryu,J.-W.Baek,and J.-H.Jung,“High-ef?ciency iso-

lated bidirectional AC–DC converter for a DC distribution system,”IEEE Trans.Power Electron.,vol.28,no.4,pp.1642–1653,Apr.2013. [11]S.A.Khajehoddin,M.-K.Ghartemani,P.-J.Jain,and A.Bakhshai,“DC-

bus design and control for a single-phase grid-connected renewable con-verter with a small energy storage component,”IEEE Trans.Power Elec-tron.,vol.28,no.7,pp.3245–3253,Jul.2013.

[12] A.Timbus,M.Liserre,R.Teodorescu,P.Rodriguez,and F.Blaabjerg,

“Evaluation of current controllers for distributed power generation sys-tems,”IEEE Trans.Power Electron.,vol.24,no.3,pp.654–662,Mar.

2009.

[13] F.Blaabjerg,R.Teodorescu,M.Liserre,and A.V.Timbus,“Overview

of control and grid synchronization for distributed power generation sys-tems,”IEEE Trans.Power Electron.,vol.53,no.5,pp.1398–1407,Oct.

2006.

[14]J.Dannehl,C.Wessels,and F.W.Fuchs,“Limitations of voltage-oriented

PI current control of grid-connected PWM recti?ers with LCL?lters,”

IEEE Trans.Ind.Electron.,vol.56,no.2,pp.380–387,Feb.2009. [15]M.Liserre,F.Blaabjerg,and S.Hansen,“Design and control of an LCL-

?lter-based three-phase active recti?er,”IEEE Trans.Ind.Appl.,vol.41, no.5,pp.1281–1290,Sep./Oct.2005.

[16]J.Dannehl,F.W.Fuchs,and P.B.Th?gersen,“PI state space current

control of grid-connected PWM converters with LCL?lters,”IEEE Trans.

Power Electron.,vol.25,no.9,pp.2320–2328,Sep.2010.

[17]N.R.Nargari and G.Joos,“Performance investigation of a current-

controlled voltage regulated PWM recti?er in rotating and stationary frames,”IEEE Trans.Ind.Electron.,vol.42,no.4,pp.396–401,Aug.

1995.

[18]J.Yao,H.Li,Y.Liao,and Z.Chen,“An improved control strategy of

limiting the DC-link voltage?uctuation for a doubly fed induction wind generator,”IEEE Trans.Power Electron.,vol.23,no.3,pp.1205–1212, May2008.

[19] A.Sato and T.Noguchi,“V oltage-source PWM recti?er–inverter based on

direct power control and its operation characteristics,”IEEE Trans.Power Electron.,vol.26,no.5,pp.1559–1566,May2011.

[20] D.Dong,I.Cvetkovic, D.Boroyevich,W.Zhang,R.Wang,and

P.Mattavelli,“Grid-interface bidirectional converter for residential dc distribution systems—Part one:High-density two-stage topologys,”IEEE Trans.Power Electron.,vol.28,no.4,pp.1651–1665,Apr.2013. [21]M.Hagiwara and H.Akagi,“An approach to regulating the DC-link

voltage of a voltage-source BTB system during power line faults,”IEEE Trans.Ind.Appl.,vol.41,no.5,pp.1263–1270,Sep./Oct.2007.[22] B.-G.Gu and K.Nam,“A DC-link capacitor minimization method through

direct capacitor current control,”IEEE Trans.Ind.Appl.,vol.42,no.2, pp.573–581,Mar./Apr.2006.

[23] B.Parkhideh and S.Bhattacharya,“Vector-controlled voltage-source-

converter-based transmission under grid disturbances,”IEEE Trans.Power Electron.,vol.28,no.2,pp.661–671,Feb.2013.

[24] C.-H.Chang,F.-Y.Wu,and Y.-M.Chen,“Modularized bidirectional grid-

connected inverter with constant-frequency asynchronous sigma–delta modulation,”IEEE Trans.Ind.Electron.,vol.59,no.1,pp.4088–4099, Nov.2012.

[25]T.-F.Wu,C.-H.Chang,L.-C.Lin,G.-R.Yu,and Y.-R.Chang,“DC-bus

voltage control with a three-phase bidirectional inverter for DC distribution systems,”IEEE Trans.Power Electron.,vol.28,no.4,pp.1890–1898, Apr.2013.

[26]T.Itkonen,J.Luukko,A.Sankala,and https://www.wendangku.net/doc/8f14019236.html,akkonen,“Modeling and

analysis of the dead-time effects in parallel PWM two-level three-phase voltage-source inverters,”IEEE Trans.Power Electron.,vol.24,no.11, pp.2446–2454,Nov.2009.

[27]S.-H.Hwang and J.-M.Kim,“Dead time compensation method for

voltage-fed PWM inverter,”IEEE Trans.Energy Convers.,vol.25,no.1, pp.1–10,Mar.2010.

[28] D.Chen and L.Xu,“Autonomous DC voltage control of a DC microgrid

with multiple slack terminals,”IEEE Trans.Power Syst.,vol.27,no.4, pp.1897–1904,Nov.2012.

[29]M.H.Bierhoff and F.W.Fuchs,“Active damping for three-phase PWM

recti?ers with high-order line-side?lters,”IEEE Trans.Ind.Electron., vol.56,no.2,pp.371–379,Feb.2010.

[30]J.Yang,S.Li,and X.Yu,“sliding-mode control for systems with mis-

matched uncertainties via a disturbance observer,”IEEE Trans.Ind.Elec-tron.,vol.60,no.1,pp.160–168,Jan.2013.

[31]W.-H.Chen,“Disturbance observer based control for nonlinear systems,”

IEEE Trans.Mechatr.,vol.9,no.4,pp.706–710,Dec.2004.

[32]S.Li,J.Yang,W.H.Chen,and X.Chen,“Generalized extended state

observer based control for systems with mismatched uncertainties,”IEEE Trans.Ind.Electron.,vol.59,no.12,pp.4792–4801,Dec.2012. [33]P.Pasi,N.Pasi,and B.P.Juha,“Observer-based output voltage control for

DC power distribution purposes,”IEEE Trans.Power Electron.,vol.28, no.4,pp.1914–1925,Apr.2013.

[34]P.Karlsson and J.Svensson,“DC bus voltage control for a distributed

power system,”IEEE Trans.Power Electron.,vol.18,no.6,pp.1405–1412,Nov.2003.

[35]M.Davari and Y.Mohamed,“Robust multi-objective control of VSC-

based DC-voltage power port in hybrid AC/DC multi-terminal micro-grids,”IEEE Trans.Smart Grid,vol.4,no.3,pp.1597–1612,Sep.2013.

[36]M.K.Ghartemani,S.A.Khajehoddin,P.Jain,and A.Bakhshai,“A sys-

tematic approach to DC-bus control design in single-phase grid-connected renewable converters,”IEEE Trans.Power Electron.,vol.28,no.7, pp.3158–3166,Nov.2013.

[37]S.A.Khajehoddin,M.K.-Ghartemani,P.Jain,and A.Bakhshai,“DC-bus

design and control for a single-phase grid-connected renewable converter with a small energy storage component,”IEEE Trans.Power Electron., vol.28,no.7,pp.3245–3253,Nov.2013.

[38]M.G.Wu,R.X.Zhao,and X.Z.Tang,“Dead-time effects analysis and

compensation of SPWM and SVPWM inverter,”in Proc.CSEE,Jun.

2006,vol.26,no.12,pp.101–105.

[39] D.Marx,P.Magne,B.N.Mobarakeh,S.Pierfederici,and B.Davat,“Large

signal stability analysis tools in DC power systems with constant power loads and variable power loads—A review,”IEEE Trans.Power Electron., vol.27,no.4,pp.1773–1785,Nov.

2012.

Chengshan Wang(SM’11)received the Ph.D.de-

gree in electrical engineering from Tianjin Univer-

sity,Tianjin,China,in1991.

He is currently a Professor with the School of

Electrical Engineering and Automation,Tianjin Uni-

versity.His current research interests include distribu-

tion system analysis and planning,distributed genera-

tion system and microgrid,and power system security

analysis.

Xialin Li was born in Hunan,China,in1986.He received the B.S.degree in electrical engineering in2009from Tianjin University,Tianjin,China, where he is currently working toward the Ph.D.de-gree in the Department of Electrical Engineering and Automation.

His current research interests include stability and

control of the distributed generations and

microgrids.

Li Guo(M’11)received the B.Sc.and Ph.D.degrees in electrical engineering from South China Univer-sity of Technology,Guangdong,China,in2002and 2007,respectively.

He is currently an Associate Professor at Tian-jin University,Tianjin,China.His current research interests include the optimal planning and design of microgrid,the coordinated operating strategy of microgrid,and the advanced energy management

system.

Yun Wei Li(S’04–M’05–SM’11)received the B.Sc.

degree in electrical engineering from Tianjin Univer-

sity,Tianjin,China,in2002,and the Ph.D.degree

from Nanyang Technological University,Singapore,

in2006.

In2005,Dr.Li was a Visiting Scholar with Aal-

borg University,Denmark.From2006to2007,he

was a Postdoctoral Research Fellow at Ryerson Uni-

versity,Canada.In2007,he worked at Rockwell Au-

tomation Canada and later joined the Department of

Electrical and Computer Engineering,University of

Alberta,Canada,in the same year.He is currently an Associate Professor at the

University of Alberta,Edmonton,Canada.His current research interests include

distributed generation,microgrid,renewable energy,high-power converters,and

electric motor drives.

Dr.Li is currently an Associate Editor for the IEEE T RANSACTIONS ON

P OWER E LECTRONICS and the IEEE T RANSACTIONS ON I NDUSTRIAL E LECTRON-ICS.He was also a Guest Editor for the IEEE T RANSACTIONS ON I NDUSTRIAL E LECTRONICS Special Session on Distributed Generation and Microgrids.He

received the2013Richard M.Bass Outstanding Young Power Electronics En-

gineer Award from the IEEE Power Electronics Society.

变电所母线桥的动稳定校验

变电所母线桥的动稳定校验随着用电负荷的快速增长，许多变电所都对主变进行了增容，并对相关设备进行了调换和校验，但往往会忽视主变母线桥的动稳定校验，事实上此项工作非常重要。当主变增容后，由于阻抗发生了变化，短路电流将会增大许多，一旦发生短路，产生的电动力有可能会对母线桥产生破坏。特别是户内母线桥由于安装时受地理位置的限制，绝缘子间的跨距较长，受到破坏的可能性更大，所以应加强此项工作。下面以我局35kV/10kv胡店变电所#2主变增容为例来谈谈如何进行主变母线桥的动稳定校验和校验中应注意的问题。 1短路电流计算图1为胡店变电所的系统主接线图。(略) 已知#1主变容量为10000kVA，短路电压为7.42%，#2主变容量为12500kVA，短路电压为7.48%(增容前短路电压为7.73%)。取系统基准容量为100MVA，则#1主变短路电压标么值 X1＝7.42/100×100×1000/10000＝0.742， #2主变短路电压标么值 X2＝7.48/100×100×1000/12500＝0.5984 胡店变电所最大运行方式系统到35kV母线上的电抗标么值为0.2778。 ∴#1主变与#2主变的并联电抗为： X12=X1×X2/(X1+X2)＝0.33125；最大运行方式下系统到10kV母线上的组合电抗为： X＝0.2778+0.33125＝0.60875

∴10kV母线上的三相短路电流为：Id=100000/0.60875*√3*10.5，冲击电流：I sh=2.55I =23032.875A。 d 2动稳定校验 (1)10kV母线桥的动稳定校验：进行母线桥动稳定校验应注意以下两点： ①电动力的计算，经过对外边相所受的力，中间相所受的力以及三相和二相电动力进行比较，三相短路时中间相所受的力最大，所以计算时必须以此为依据。 ②母线及其支架都具有弹性和质量，组成一弹性系统，所以应计算应力系数，计及共振的影响。根据以上两点，校验过程如下：已知母线桥为8×80mm2的铝排，相间中心线间距离为210mm，先计算应力系数： ∵频率系数N f＝3.56，弹性模量E＝7×10.7 Pa，单位长度铝排质量M＝1.568kg/m，绝缘子间跨距2m，则一阶固有频率: f’=(N f/L2)*√(EI/M)=110Hz 查表可得动态应力系数β＝1.3。 ∴单位长度铝排所受的电动力为： f ph＝1.73×10-7I sh2/a×β＝568.1N/m ∵三相铝排水平布置，∴截面系数W＝bh2/6＝85333mm3，根据铝排的最大应力可确定绝缘子间允许的最大跨距为： L MAX=√10*σal*W/ f ph=3.24m ∵胡店变主变母线桥绝缘子间最大跨距为2m，小于绝缘子间的最大允许跨距。

华师秋《高等数学文》在线作业

华师16秋《高等数学(文)》在线作业

————————————————————————————————作者：————————————————————————————————日期：

一、单选题（共 20 道试题，共 40 分。） V 1. y=xsin3x,则y=( )。 . (-os3x+3sin3x)x . (sin3x+3xos3x)x . (os3x+sin3x)x . (sin3x+xos3x)x 标准答案： 2. f(x)在某点连续是f(x)在该点可微的（） . 充分条件 . 必要条件 . 充分必要条件 . 既非充分又非必要条件标准答案： 3. x→5时，函数|x-5|/(x-5)的极限是（） . 0 . ∞ . 1 . 不存在标准答案： 4. 当x→0时，ln(1+x)与x比较是（）。 . 高阶无穷小量 . 等价无穷小量 . 非等价的同阶无穷小量 . 低阶无穷小量标准答案： 5. 当x→0时，下列变量为无穷大量的是（）。 . xsinx . sinx/x . ^x . (1+sinx)/x 标准答案： 6. 极值反映的是函数的（）性质。 . 局部 . 全体 . 单调增加 . 单调减少标准答案： 7. （）是函数f(x)=1/2x的原函数。 . F(x)=ln2x . F(x)=-1/x^2 . F(x)=ln(2+x) . F(x)=lnx/2 标准答案： 8. 若f(x)是奇函数，g(x)是偶函数，且f[g(x)]有意义，则f[g(x)]是（）

. 奇函数 . 非奇非偶函数 . 偶函数或奇函数标准答案： 9. 曲线y=(4+x)/(4-x)在点（2,3）的切线的斜率是（）。 . 2 . -2 . 1 . -1 标准答案： 10. 曲线y=f(x)在点(x0,f(x0))的切线存在是函数y=f(x)在x0处可导的 . 充分条件 . 必要条件 . 充分必要条件 . 既非充分又非必要条件标准答案： 11. 如果函数f(x)的定义域为（-1,0），则下列函数中，（）的定义域为（0,1）. f(1-x) . f(x-1) . f(x+1) . f(x2-1) 标准答案： 12. 偶函数的定义域一定是( )。 . 包含原点的区间 . 关于原点对称 . (-∞,+∞) . 以上说法都不对标准答案： 13. 函数y=x^2+1在区间[-2,1]上的最大值是（）。 . 1 . 2 . 5 . 不存在标准答案： 14. 设函数f(x)=|x|，则函数在点x=0处() . 连续且可导 . 连续且可微 . 连续不可导 . 不连续不可微标准答案： 15. 曲线y=xlnx-x在x=处的切线方程是（）。 . y=-x- . y=x-

母线电动力及动热稳定性计算

母线电动力及动热稳定性计算 1 目的和范围本文档为电气产品的母线电动力、动稳定、热稳定计算指导文件，作为产品结构设计安全指导文件的方案设计阶段指导文件，用于母线电动力、动稳定性、热稳定性计算的选型指导。 2 参加文件表1 3 术语和缩略语表2 4 母线电动力、动稳定、热稳定计算 4.1 载流导体的电动力计算 4.1.1 同一平面内圆细导体上的电动力计算

? 当同一平面内导体1l 和2l 分别流过1I 和2I 电流时（见图1），导体1l 上的电动力计算 h F K I I 4210 π μ= 式中 F ——导体1l 上的电动力（N ） 0μ——真空磁导率，m H 60104.0-?=πμ； 1I 、2I ——流过导体1l 和2l 的电流（A ）； h K ——回路系数，见表1。图1 圆细导体上的电动力表1 回路系数h K 表两导体相互位置及示意图 h K 平行 21l l = ∞=1l 时，a l K h 2= ∞≠1l 时，?? ? ???-+=l a l a a l K h 2)(12 21l l ≠ 22 2) ()(1l a m l a l a K h ++-+= 22)()1(l a m +-- l a m =

? 当导体1l 和2l 分别流过1I 和2I 电流时，沿1l 导体任意单位长度上各点的电动力计算 f 124K f I I d μ= π 式中 f ——1l 导体任意单位长度上的电动力（m N ）； f K ——与同一平面内两导体的长度和相互位置有关的系数，见表2。表2 f K 系数表

4.1.2 两平行矩形截面导体上的电动力计算两矩形导体（母线）在b ＜＜a ，且b ＞＞h 的情况下，其单位长度上的电动力F 的计算见表3。当矩形导体的b 与a 和h 的尺寸相比不可忽略时，可按下式计算 712 210x L F I I K a -=? 式中 F -两导体相互作用的电动力，N ； L -母线支承点间的距离，m ； a -导体间距，m ； 1I 、2I -流过两个矩形母线的电流，A ； x K -导体截面形状系数；表3 两矩形导体单位长度上的电动力 4.1.3 三相母线短路时的电动力计算

高等数学B(二)教学大纲

《高等数学B（二）》教学大纲本课程依据全校理工类专业2015版人才培养方案，理工类本科数学基础课程教学基本要求制定，也依据了2015年教育部高等学校大学数学课程教学指导委员会关于大学数学课程教学的基本要求。课程名称：高等数学B（二）课程代码：BB-2 课程管理：数理学院（或部）高等数学教研室教学对象：全校理工类专业教学时数：总时数64 学时，其中理论教学64 学时，实验实训0 学时。课程学分：4.0 课程开设学期：2 课程性质：专业基础课课程衔接：（1）先修课程初等数学（2）后续课程概率论与数理统计一、课程教学目标及要求通过本课程的学习，要使学生获得空间解析几何与向量代数、多元函数微分学、多元函数积分学、常微分方程及无穷级数等基本概念、基本理论和基本运算技能，为学习后继课程和进一步获得数学知识奠定必要的数学基础。要求学生理解数学的基本概念和基本定理，培养学生的抽象思维能力和逻辑思维能力。熟悉高等数学的基本公式和基本方法，掌握常用公式和方法，提高计算能力。二、教学内容及要求第六章空间解析几何与向量代数（一）教学目标使学生掌握向量概念及有关运算；掌握平面方程、空间直线方程的各种形式；熟悉平面与平面、直线与直线、平面与直线之间的交角公式及平行、垂直条件；掌握常用的二次曲面的标准方程及其图形。（二）知识点及要求第一节向量及其线性运算 1、理解空间直角坐标系，向量的概念及其表示。 2、掌握向量的线性运算，向量的模与方向余弦的计算。第二节数量积与向量积 1、理解两向量的数量积与向量积的概念。 2、掌握向量的数量积和向量积的运算。第三节平面及其方程 1、理解平面的点法式方程，平面的一般方程，两平面的夹角。 2、掌握平面方程及其求法，平面与平面间几何位置的判定。第四节空间直线及其方程 1、理解空间直线的一般方程、对称式方程与参数方程，两直线的夹角，直线与平面的夹角。 2、掌握空间直线方程及其求法，会利用直线、平面相互关系（平行、垂直、相交

高压电缆热稳定校验计算书

筠连县分水岭煤业有限责任公司井下高压电缆热稳定性校验计算书巡司二煤矿编制：机电科筠连县分水岭煤业有限责任公司

井下高压电缆热稳定校验计算书一、概述：根据《煤矿安全规程》第453条及456条之规定，对我矿入井高压电缆进行热稳定校验。二、确定供电方式我矿高压供电采用分列运行供电方式，地面变电所、井下变电所均采用单母线分段分列供电方式运行，各种主要负荷分接于不同母线段。三、井下高压电缆明细：矿上有两趟主进线，引至巡司变电站不同母线段，一趟931线，另一趟925线。井下中央变电所由地面配电房10KV输入。入井一回路：MYJV22-8.7/10KV 3*50mm2--800m(10KV) 入井二回路：MYJV22-8.7/10KV 3*50mm2--800m(10KV) 四、校验计算 1、井下入井回路高压电缆热稳定性校验已知条件：该条高压电缆型号为，MYJV22-8.7/10KV 3*50mm2 ,800m，电缆长度为800m=0.8km。（1）计算电网阻抗查附表一，短路电流的周期分量稳定性为电抗：X=0.072*0.8=0.0576Ω；电阻：R=0.407*0.8=0.3256 Ω； (2)三相短路电流的计算

A Z I 5.174693305 .0310000 3v 3=?== ∞ （3）电缆热稳定校验由于断路器的燃弧时间及固有动作时间之和约为t=0.05S; 查附表二得热稳定计算系数取K=142; 故电缆最小热值稳定截面为 23mm 51.2705.0142/5.17469t )/(min ===∞）（K I S Smin<50mm 2 故选用 MYJV 22 -8.7/10KV 3*50 电缆热稳定校验合格，符合要求。附表一：三相电缆在工作温度时的阻抗值（Ω/Km ）电缆截面S （mm 2 ） 4 6 10 16 2 5 35 50 70 95 120 150 185 240 交联聚乙烯 R 4.988 3.325 2.035 1.272 0.814 0.581 0.407 0.291 0.214 0.169 0.136 0.11 0.085 X 0.093 0.093 0.087 0.082 0.075 0.072 0.072 0.069 0.069 0.069 0.07 0.07 0.07 附表二不同绝缘导体的热稳定计算系数绝缘材料芯线起始温度（° C ）芯线最高允许温度（°C ）系数K 聚氯乙烯 70 160 115（114）普通橡胶 75 200 131 乙丙橡胶 90 250 143（142）油浸纸绝缘 80 160 107 交联聚乙烯 90 250 142

高等数学2课程教学大纲

高等数学A2 课程教学大纲课程编号：10009B6 学时：90 学分：5 适用对象：理学类、工科类本科专业先修课程：高等数学A1 考核要求：闭卷考试，总成绩=平时成绩20%+期末成绩80% 使用教材及主要参考书：同济大学数学系主编，《高等数学》（下册），高等教育出版社，2002 年, 第五版黄立宏主编，《高等数学》（上下册），复旦大学出版社，2006 年陈兰祥主编，《高等数学典型题精解》，学苑出版社，2001 年陈文灯主编，《考研数学复习指南（理工类）》，世界图书版公司2006年李远东、刘庆珍编，《高等数学的基本理论与方法》，重庆大学出版社，1995年钱吉林主编，《高等数学辞典》，华中师范大学出版社，1999 年一、课程的性质和任务高等数学课程是高等学校理工科各专业学生的一门必修的重要基础理论课，为学习后继课程（如大学物理等）奠定必要的基础，是为培养我国社会主义现代化建设所需要的高质量、高素质专门人才服务的。二、教学目的与要求通过本课程的学习，使学生获得向量代数和空间解析几何、多元函数微分学、多元函数积分学、无穷级数（包括傅立叶级数）等方面的基本概念、基本理论和基本运算技能。在传授知识的同时，要通过各个教学环节逐步培养学生具有抽象思维能力、逻辑推理能力、空间想象能力和自学能力，还要特别注意培养学生具有比较熟练的运算能力和综合运用所学知识去分析问题和解决问题的能力。三、学时分配

第八章多元函数微分法及其应用18 第九章重积分16 第十章曲线积分与曲面积分16 第十一章无穷级数18 总复习 6 四、教学中应注意的问题 1. 考虑学生的差异性，注意因材施教； 2. 考虑数学学科的抽象性，注意数形结合； 3. 考虑数学与现实生活的关系，注意在教学中多讲身边的数学, 使学生树立“学数学是为了用数学”的观点，培养学生“用数学”的好习惯。五、教学内容第七章：空间解析几何与向量代数 1 ?基本内容：向量及其线性运算，数量积，向量积，曲面及其方程，空间曲线及其方程，平面及其方程，空间直线及其方程。 2 ?教学基本要求： (1)理解空间直角坐标系、理解向量的概念及其表示； (2)掌握向量的运算(线性运算、点乘法、叉乘法、)了解两个向量垂直、平行的条件； (3)掌握单位向量，方向余弦、向量的坐标表达式以及用坐标表达式进行向量运算的方法； (4)平面的方程和直线的方程及其求法，会利用平面、直线的相互关系解决有关问题 (5)理解曲面的方程的概念，了解常用二次曲面的方程及其图形，了解以坐标轴为旋转的旋转曲面及母线平行于坐标轴的柱面方程； (6)了解空间曲线的参数方程和一般方程； (7)了解曲面的交线在坐标平面上的投影。 3 ?教学重点与难点: 教学重点：向量的运算（线性运算、点乘法、叉乘法），两个向量垂直、平行的条件，向量方向余弦、向量的坐标表达式以及用坐标表达式进行向量运算，平面的方程和直线的方程及其求法，曲面方程的

热稳定性校验(主焦

井下高压开关、供电电缆动热稳定性校验一、-350中央变电所开关断路器开断能力及电缆热稳定性校验 1 23 G 35kV 2 Uz%=7.5△P N.T =12kW △P N.T =3.11kW S N.T =8MVA 6kV S1点三相短路电流计算： 35kV 变压器阻抗： 2 22.1. u %7.5 6.30.37()1001008z N T N T U Z S ?===Ω? 35kV 变压器电阻：2 22.1.22. 6.30.0120.007()8 N T N T N T U R P S =?=?=Ω 35kV 变压器电抗：10.37()X = ==Ω 电缆电抗：02(x )0.415000.08780 0.66()1000 1000i L X ??+?== =Ω∑ 电缆电阻：02(x )0.11815000.118780 0.27()1000 1000 i L R ??+?== =Ω∑ 总阻抗： 21.370.66) 1.06( Z ==Ω S1点三相短路电流：(3)1 3.43()d I KA === S2点三相短路电流计算： S2点所用电缆为MY-3×70+1×25，长400米，变压器容量为500KV A ，查表的：(2)2d I =2.5KA

S2点三相短路电流：32 d d =2.88I I KA = 1、架空线路、入井电缆的热稳定性校验。已知供电负荷为3128.02KV A ，电压为6KV ，需用系数0.62，功率因数cos 0.78φ=，架空线路长度1.5km ，电缆长度780m (1)按经济电流密度选择电缆，计算容量为 3128.020.62 2486.37cos 0.78 kp S KVA φ?= ==。电缆的长时工作电流Ig 为239.25 Ig === A 按长时允许电流校验电缆截面查煤矿供电表5-15得MYJV42-3×185-6/6截面长时允许电流为479A/6kV 、大于239.25A 符合要求。 (2)按电压损失校验，配电线路允许电压损失5%得 60000.1300Uy V ?=?=，线路的实际电压损失 109.1L U COS DS φφ?====，U ?小于300V 电压损失满足要求 (3)热稳定性条件校验，短路电流的周期分量稳定性为电缆最小允许热稳定截面积： 3 2min d =S I mm 其中：i t ----断路器分断时间，一般取0.25s ； C----电缆热稳定系数，一般取100，环境温度35℃，电缆温升不超过120℃时，铜芯电缆聚乙烯电缆熔化温度为130℃，电

全球汽车车型中英文对照表

全球汽车车型中英文对照表车型（中文）车型（英文）车型（中文）车型（英文）奥迪奥迪AUDI伊兰特ELANTRA 宝马宝马BMW特拉卡Terracan 迷你Mini途胜Tucson mini One mini One御翔NF 奔驰奔驰benz雅绅特Accent 东风雪铁龙东风雪铁龙DONGFENG CITROEN 圣达菲SantaFe 爱丽舍Elysee酷派coupe 毕加索Picasso君爵XG 世嘉quatre特杰Trajet 凯旋triomphe美佳Matrix 大众(上汽)大众(上汽)VW(Shangha i) 雅科仕EQUUS 波罗Polo维拉克斯Veracruz 帕萨特领驭PASSAT悦达起亚起亚KIA 高尔GOL千里马桑塔纳SANTANA赛拉图CERATO 途安Touran嘉华Carnival 大众(一汽)大众(一汽)faw-volksw agen 远舰Optima 捷达JETTA RIO RIO 宝来BORA索兰托SORENTO 高尔夫Golf佳乐Carens 开迪Caddy狮跑Sportage 速腾 Sagitar Sagitar欧迪玛Optima 迈腾magotan 阿尔法-罗米欧阿尔法-罗米欧Alfa Romeo 甲壳虫beetle保时捷保时捷porsche 辉腾Phaeton新款Boxster porsche Boxster 康比Combi卡宴Cayenne VR6VR6卡曼cayman 途锐Touareg宾利宾利Bentley 面包车multivan雅致Arnage 高尔夫Golf GTI欧陆飞驰Continental Flying Spur 辉腾Phaeton大陆Continental GT 东风标致东风标致Dongfeng 大陆Continental

华中师范大学人才培养方案

历史学专业本科人才培养方案★专业编号：832 历史学专业本科人才培养方案一、专业培养目标及基本要求培养目标：本专业依据“研教双优”人才培养模式培养具有良好的政治思想素质、有较强的学习和研究能力、扎实的专业技能的一流师资和应用型人才。基本要求：扎实掌握本专业的基本理论和基本知识，了解本专业的发展趋势和新进展；具有科学的思维方法和探索精神，具备一定的科学研究能力和专业技能。具体要求毕业生应获得以下几方面的知识和能力： 1．在大学平台课的基础上，掌握历史学的基本理论和中国历史、世界历史比较系统的基本知识； 2．通过专业学习和训练，形成一定的历史学研究能力； 3．较熟悉地掌握古汉语和一门外国语，能阅读中外历史文献和资料； 4．了解相关学科基本理论，具有较强的综合应用能力； 5．掌握科学的教育理论和教学方法，具备教师基本技能。二、主要课程中国古代史、中国近代史、中国现代史、中华人民共和国史、历史科学概论、世界古代史、世界中世纪史、世界近代史、世界现代史、世界当代史、中国史学史、西方史学史、中国历史地理、中国历史文选、教育学、心理学等。三、学制 4年四、授予学位历史学学士五、教学时间分配表（续表）

六、课程教学学时、学分分布表注：专业类必修课指学科基础必修课与专业必修课；专业类选修课指学科基础选修课与专业选修课七、课程计划表（续表）

（续表）

（续表）（续表）

八、说明 1．本专业必须修满教学计划规定的167学分方可毕业。其中通识教育必修课35学分，通识教育选修课12学分，专业必修课67学分，专业选修课34学分，实践环节19学分，必修课学分不能以选修课学分代替； 2．教师教育课程分必修、选修共20学分，必修课为教育学基础3学分、心理学基础3学分、教师口语1学分、教师书法1学分、多媒体技术与应用2学分、现代教育技术2学分、历史教学技能训练1学分、历史学科教学论2学分，共15学分；选修课5学分（教育、心理类3学分，学科教育类2学分）； 3．本专业学生必须选修12个学分的综合素质课。其中必须理科类不得少于4学分，艺体类不少于2学分，其他6学分建议从文学院、政法学院、经济学院、管理学院、美术学院、音乐学院等院选修； 4．专业实践包括第二学年暑期专业考察（2学分）和第三学年暑期专业研究实践“历史记忆中的家乡”（2学分）； 5．本专业共开设双学位课程49学分。修满双学位课程28学分，可申请本专业辅修结业证书；修满42学分并完成辅修论文及答辩，可申请本专业双学位学士证书； 6．学生需同时修满规定的专业课程学分和素质拓展学分方可毕业。素质拓展学分要求：学生需获取20个必修学分，10个选修学分，具体修取办法见教学管理规章制度中的相关规定。

上海理工大学高等传热学试题及答案

1.试求出圆柱坐标系的尺度系数，并由此导出圆柱坐标系中的导热微分方程。 2 .一无限大平板，初始温度为T 0；τ>0时，在x = 0表面处绝热；在x = L 表面以对流方式向温度为t f 的流体换热。试用分离变量法求出τ>0时平板的温度分布（常物性）。（需求出特征函数、超越方程的具体形式，范数（模）可用积分形式表示）。（15分） , 3.简述近似解析解——积分法中热层厚度δ的概念。答：近似解析解：既有分析解的特征：得到的结果具有解析函数形式，又有近似解的特征：结果只能近似满足导热解问题。在有限的时间内，边界温度的变化对于区域温度场的影响只是在某一有限的范围内，把这个有限的范围定义为热层厚度δ。 4.与单相固体导热相比，相变导热有什么特点答：相变导热包含了相变和导热两种物理过程。相变导热的特点是 1.固、液两相之间存在着移动的交界面。 2.两相交界面有潜热的释放（或吸收） | 对流部分（所需量和符号自己设定） 1 推导极坐标系下二维稳态导热微分方程。 2 已知绕流平板流动附面层微分方程为 y u y u V x u u 22??=??+??ν 取相似变量为： x u y νη∞ = x u f νψ∞= 写出问题的数学模型并求问题的相似解。 3 已知绕流平板流动换热的附面层能量积分方程为： ?=∞?? =-δ00)(y y t a dy t t u dx d 当Pr<<1时，写出问题的数学模型并求问题的近似积分解及平均Nu （取三次多项式）。 4 ] O x

5写出常热流圆管内热充分发展流动和换热问题的数学模型并求出速度和温度分布及Nu x.辐射 1．请推导出具有n个表面的净热流法壁面间辐射换热求解公式，并简要说明应用任一种数值方法的求解过程。 2．试推导介质辐射传递方程的微分形式和积分形式，要求表述出各个步骤和结果中各个相关量的含义。 3．根据光谱辐射强度表示下面各量：1）光谱定向辐射力；2）定向辐射力；3）光谱辐射力；4）辐射力；5）辐射热流量。要求写清各量的符号、单位。 4．说明下列术语（可用数学表达式）（每题4分） a)光学厚度 b)漫有色表面 c)? d)兰贝特余弦定律 e)光谱散射相函数 f)定向“灰”入射辐射

高压电缆热稳定校验计算书

*作品编号：DG13485201600078972981* 创作者：玫霸* 筠连县分水岭煤业有限责任公司井下高压电缆热稳定性校验计算书巡司二煤矿

编制：机电科筠连县分水岭煤业有限责任公司井下高压电缆热稳定校验计算书一、概述：根据《煤矿安全规程》第453条及456条之规定，对我矿入井高压电缆进行热稳定校验。二、确定供电方式我矿高压供电采用分列运行供电方式，地面变电所、井下变电所均采用单母线分段分列供电方式运行，各种主要负荷分接于不同母线段。三、井下高压电缆明细：矿上有两趟主进线，引至巡司变电站不同母线段，一趟931线，另一趟925线。井下中央变电所由地面配电房10KV输入。入井一回路：MYJV22-8.7/10KV 3*50mm2--800m(10KV) 入井二回路：MYJV22-8.7/10KV 3*50mm2--800m(10KV) 四、校验计算 1、井下入井回路高压电缆热稳定性校验已知条件：该条高压电缆型号为，MYJV22-8.7/10KV 3*50mm2 ,800m，电缆长度为800m=0.8km。（1）计算电网阻抗查附表一，短路电流的周期分量稳定性为

电抗：X=0.072*0.8=0.0576Ω；电阻：R=0.407*0.8=0.3256 Ω； (2)三相短路电流的计算（3）电缆热稳定校验由于断路器的燃弧时间及固有动作时间之和约为t=0.05S; 查附表二得热稳定计算系数取K=142; 故电缆最小热值稳定截面为 Smin<50mm2故选用 MYJV22 -8.7/10KV 3*50 电缆热稳定校验合格，符合要求。附表一：三相电缆在工作温度时的阻抗值（Ω/Km）

汽车名中英对照

汽车品牌及车型中英名对照 ?本田 HONDA ?本田飞度（fit） ?本田思迪/锋范（city） ?本田思域（civic） ?本田雅阁（accord） ?本田思铂睿（spirior） ?本田奥德赛（Odyssey） ?时韵(小型MPV) ? CRV ? STEPWGN(7座MPV)、Element、Pilot(SUV)、Ridgeline(皮卡)、S2000(跑车). ? ?别克 BUICK ?别克凯越（Excelle） ?别克君威（Regal） ?别克君越（LaCROSSE） ?别克林荫大道（Park Avenue） ?别克荣御（Royaum） ?别克昂科雷（Enclave） ? GL8 ?英朗XT（Excelle XT) ?赛欧（sail） ? ?长安汽车 :Changan ?长安奔奔（Benben） ?长安志翔（Zhixiang） ?长安杰勋（Jiexun） ?悦翔 ?长安之星 ?长安星光35 ?奥拓（Alto） ? ?长城汽车 GreatWALL ?长城赛弗（safe） ?长城风骏（Wingle） ?长城精灵（Peri） ?长城炫丽（florid） ?长城哈弗（Hover） ?长城酷熊（coolbear） ?长城嘉誉（Cowry） ?长城爱迪尔（Idea） ? ?大众 VOLKSWAGEN ?大众高尔（gol） ?大众波罗（polo） ?大众高尔夫（golf） ?大众捷达（Jetta） ?大众宝来（Bora） ?大众速腾（Sagitar） ?大众朗逸（Lavida) ?大众桑塔纳（Santana） ?大众帕萨特（Passat） ?大众迈腾（Magotan)

?大众开迪（Candy） ?大众途安（Touran） ?大众途欢（tiguan） ?大众甲壳虫（beetle） ?大众尚酷（Scirocco） ?大众辉腾（Phaeton） ?大众途锐（Touareg） ? ?道奇 Dodge ?道奇酷博（Caliber） ?道奇锋哲（avenger） ?道奇酷威（Journey） ? ?东南汽车 Southeast Automobile ?东南菱悦（lingyue） ?东南菱帅（Lioncel） ?东南菱动（lingdong） ?东风 DONGFENG ?东风风行（Fengxing） ?东风奥丁（Oting） ? ?菲亚特 Fait ?菲亚特派朗（perla） ?菲亚特派力奥（Palio） ?菲亚特西耶那（Siena 国外叫Albea）?菲亚特周末风（Palio Weekend）?菲亚特朋多（Grande Punto） ?菲亚特领雅（Linea） ?菲亚特博悦（Bravo） ? ?丰田 TOYOTA ?丰田威驰（vios） ?丰田雅力士（Yaris） ?丰田卡罗拉/花冠（corolla） ?丰田凯美瑞（Camry） ?丰田锐志（reiz） ?丰田皇冠（Crown） ?丰田汉兰达（Highlander） ?丰田普拉多（PRADO) ?丰田普瑞维亚(PREVIA) ?丰田兰德酷路泽（LAND CRUISER）?巡洋舰（Land cruiser ） ?霸道（Prado） ? RAV4 ?福特 FORD ?福特嘉年华（Fiesta） ?福特福克斯（focus） ?福特蒙迪欧（Mondeo） ?福特致胜（Mondeo） ?福特S-MAX ? ?福田汽车 Forten ?福田迷迪（midi） ? ?哈飞 HAFEI ?民意 ?中意 ?松花江

华中师范大学教育学专业参考书目

华中师范大学教育学专业参考书目华中师范大学教育学考研参考书目，鉴于出现很多想报考教育学硕士研究生的同学们，苦于找不到参考的书籍这一情况，凯程教育第一时间整理了如下书籍，希望对考研的同学们提供点帮助。随着越来越多的人加入考研大军，研究生就业问题近年来也成为热点话题。官方发布的研究生总体就业率高达95%以上，但有的专业首次就业率甚至低至5.56%。究竟什么才是真实的情况，也许永远也无法知道，但多几个渠道了解信息，或许能在作决定时提供帮助。七成高校研究生就业率超95％凯程考研以"专业、负责、创新、分享"的办学理念，突出"高命中率、强时效性、全面一条龙服务"的特色，成为考研学子选择专业课辅导的首选。10年来已有千余位考生在凯程的帮助下顺利考取全国著名高校，引发业界强烈关注。主要参考书目教育经济与管理专业（教育学院）《教育学》王道俊、王汉澜主编，人民教育出版社1999年版《当代教育学》袁振国，教育科学出版社《教育投入与产出》王善迈，河北教育出版社《教育经济学新编》范先佐，人民教育出版社2010年版《学校管理学新编》萧宗六、余白，华中师范大学出版社《新编教育管理学》修订版，吴志宏、魏志春等主编，华东师范大学出版社注：311教育学专业基础综合考试大纲由国家统一制订课程与教学论（历史学院）《历史教育学》王铎全上海教育出版社《中学历史教学法》于友西高等教育出版社

课程与教学论复试科目参考书目（数据与统计学院）《数学教育学》，吴宪芳、华中师范大学出版社或《中学数学教材教法》总论，十三院校协编、高等教育出版社课程与教学论、教育硕士（物理科学与技术学院）《力学》漆安慎等高等教育出版社（《力学》潘武明科学出版社）《电磁学》赵凯华高等教育出版社（《电磁学》陈义成科学出版社）《光学教程》姚启均高等教育出版社《中学物理新课程教学概论》主编：阎金铎，郭玉英，北京师范大学出版集团2008年2月《现代基础物理教育学》主编：李来政何熊智，华中师范大学出版社2004年8月《大学物理实验》主编：熊永红等科学出版社2007年8月有机化学、物理化学、分析化学、无机化学、高分子化学与物理、农药学（化学学院）《物理化学》万洪文詹正坤主编高等教育出版社（面向21世纪教材）《物理化学解题指南》陈平初、詹正坤、万洪文编，高等教育出版社《物理化学》南京大学傅献彩等编著（第四版），高等教育出版社《有机化学》（上下册）尹冬冬主编高等教育出版社《有机化学》五所师大合编，曾昭琼主编第三版上下册，高教出版社，北京《有机化学实验》五所师大合编，曾昭琼主编第三版，高教出版社，北京生物化学：（生命科学学院）《生物化学教程》王镜岩等，高等教育出版社，2008年

华中师范大学高等数学C真题

院（系）：专业：年级：学生姓名：学号： --- -- -- --- -- -- -- --- -- -- -- --- -- -- -- --- -- -- -- -- -- -- 密 -- -- -- -- --- -- -- -- --- -- -- -- --- -- -- - 封 --- -- -- --- -- -- -- --- -- -- -- -- -- 线 ---- -- -- -- --- -- -- -- --- -- -- -- --- -- -- -- --- -- -- -- --- -- -- -- --

第 1 页(共页)

------------------------------------------------- 密 ---------------------------------- 封 ----------------------------- 线 ---------------------------------------------------------

第 2 页(共页)

------------------------------------------------- 密 ---------------------------------- 封 ----------------------------- 线 ---------------------------------------------------------

第 3 页(共页)

传热学上海理工大学硕士研究生入学考试试题

2004年上海理工大学硕士研究生入学考试试题考试科目：传热学准考证号：得分：一、问答题(每题5分) 1. 一无内热源平板沿厚度x方向发生一维稳态导热，其一侧表面上的温度梯度 =30 ℃/m，导热系数λ1=40W/(m.℃)，如果其另一侧表面上的导热系数λ2=50W/(m.℃)，问这一侧表面上的温度梯度是多少? 2. 解释毕渥准则数Bi的物理含义，并说明为什么用Bi判别非稳态导热问题能否采用集总参数法求解。 3. 图1.1示出了常物性、有均匀内热源、二维稳态导热问题局部边界区域的网格配置，试用元体平衡法建立节点0关于温度t的有限差分方程式（设，所需参数的符号自己设定）。 4. 当条件相同时，物体在空气中冷却快还是在水中冷却快？这一现象说明对流换热与什么因素相关？ 5. 试用简图表示流体沿平板流动时速度边界层的发展并说明速度边界层内分成哪些区域？ 6. 试解释普朗特数Pr的物理意义,并示意性的画出Pr>1时的速度边界层和热边界层厚度沿板长的变化(速度边界层和热边界层要画在同一图上以便比较)。 7. 说明温度附面层的概念及附面层能量微分方程在物理上忽略了哪部分换热。 8. 在应用管内旺盛紊流实验关联式时，当流体与换热壁面温差较大时需要对计算结果修正，为什么? 9. 试说明为什么一个细长圆柱水平放置时自然对流换热一般大于竖直放置时的自然对流换热？ 10.在稳定膜态沸腾过程中，为什么换热系数随增加而迅速上升？

11.试说明大气中CO2含量增高为什么会出现大气温室效应？二、计算题 1. （10分）一直径为5cm的钢球，其初始温度为500℃，突然被置于温度为 30℃的空气中。设钢球表面与周围环境的对流换热系数为10 W/m2℃，试计算钢球非稳态导热的时间常数及其被冷却到300℃所需的时间。已知钢球的比热为c=0.48kJ/kg℃, ρ=7753kg/m3, λ=33W/m℃。 2. （20分）长10m、外径133mm的水平管道通过一大房间，房间壁面及其内的空气温度均为30℃。若管道表面温度为90℃、黑度为0.9，求管道的散热量（自然对流换热的努塞尔特数用下式计算）。3. （22分）如图2所示为一半径R=1m的半球，球冠3绝热。底面1和2的温度分别为500℃和100℃，黑度都为0.9，求底面1和2间的辐射散热量。 4. （23分）温度为95℃的热空气流经一内径100mm、厚度6mm的圆管，管壁导热系数为22 W/m℃。管外环境温度为30℃，管外壁与环境的总换热系数为10 W/m2℃。若管内空气质量流量为407kg/h，求管出口空气温度降低到65℃时的管长(不需考虑修正)。三、理论题 1.（8分）一厚度为2δ的无内热源薄平板，其导热系数和初始温度分别为 λ和t0，突然被插在温度为t f的流体中。平板表面与流体的换热系数为h，给出问题的完整数学描述。 2. （12分）绕流平板换热的附面层积分方程为：平板温度为t W，来流速度和温度分别为u∞和t∞，若Pr<<1，可以忽略速

案例--变电所母线桥的动稳定校验

案例--变电所母线桥的动稳定校验朱时光修改下面以35kV/10kv某变电所#2主变增容为例来谈谈如何进行主变母线桥的动稳定校验和校验中应注意的问题。 1短路电流计算图1为某变电所的系统主接线图。(略) 已知#1主变容量为10000kVA，短路电压为7.42%，#2主变容量原为1000为kVA 增容为12500kVA，短路电压为7.48%。取系统基准容量为100MVA，则#1主变短路电压标么值 X1＝7.42/100×100×1000/10000＝0.742， #2主变短路电压标么值 X2＝7.48/100×100×1000/12500＝0.5984 假定某变电所最大运行方式系统到35kV母线上的电抗标么值为0.2778。 ∴#1主变与#2主变的并联电抗为： X12=X1×X2/(X1+X2)＝0.33125；最大运行方式下系统到10kV母线上的组合电抗为： X＝0.2778+0.33125＝0.60875 ∴10kV母线上的三相短路电流为：Id=100000/0.60875*√3*10.5=9.04KA，冲击电流：I s h=2.55I d=23.05KA。 2动稳定校验

(1)10kV母线桥的动稳定校验：进行母线桥动稳定校验应注意以下两点： ①电动力的计算，经过对外边相所受的力，中间相所受的力以及三相和二相电动力进行比较，三相短路时中间相所受的力最大，所以计算时必须以此为依据。 ②母线及其支架都具有弹性和质量，组成一弹性系统，所以应计算应力系数，计及共振的影响。根据以上两点，校验过程如下：已知母线桥为8×80mm2的铝排，相间中心线间距离A为210mm，先计算应力系数： 6Kg/Cm2， ∵频率系数N f＝3.56，弹性模量E＝0.71×10 -4kg.s2/cm2，绝缘子间跨距2m，单位长度铝排质量M＝0.176X10 截面惯性矩J=bh3/12=34.13c m4或取惯性半径（查表）与母线截面的积， ∵三相铝排水平布置，∴截面系数W＝bh2/6＝8.55Cm3，则一阶固有频率: f0=(3.56/L2)*√(EJ/M)=104(Hz) 查表可得动态应力系数β＝1.33。 ∴铝母排所受的最大机械应力为： σMAX＝1.7248×10-3I s h2（L2/Aw）×β＝270.35 kg/c m2<σ允许=500 根据铝排的最大应力可确定绝缘子间允许的最大跨距为：（简化公式可查表） L MAX=1838√a/ I s h=366(c m) ∵某变主变母线桥绝缘子间最大跨距为2m，小于绝缘子间的最大允许跨距。

利亚纳a维修手册电喷系统

K14B利亚纳维修手册（电喷系统）德尔福MT22.1发动机管理系统目录 1.2. 系统功能介绍 ............................................................................................................................................. 2.3.电子节流阀体功能限制模式 ....................................................................................................................... 3.8．油压调节器 ................................................................................................................................................ 4.2. 故障指示灯（MI）说明 (18) 5.1. 燃油及润滑油 (29)

6.2. 发动机故障指示灯 .....................................................................................................................................

1. 系统介绍 1.1. 系统特点 K14B利亚纳的德尔福MT22.1发动机管理系统基于扭矩和电子节气门控制，其特征是电脑闭环控制、多点燃油顺序喷射、无分电器顺序点火和三元催化器后处理。系统主要功能包括： - 发动机气体热力学空气流量及温度计算； - 发动机扭矩输出控制模式； - 整车主电源继电器控制； - 闭环控制多点燃油顺序喷射； -无回油供油方式的控制； - 燃油油泵工作控制； - ECM内置点火驱动模块，无分电器式顺序点火； - 点火模式为顺序点火； - 线性EGR控制(选用)； - 爆震控制； - 电子节气门控制控制； - 即插即用式空调控制； - 冷却液箱风扇控制； - 碳罐电磁阀控制； - 系统自诊断功能； - 过电压保护； - 即插即用式ECM防盗控制(防盗器需经德尔福认证)； 1.2. 系统功能介绍发动机气体热力学模型空气流量计算 ECM通过进气温度压力传感器对进入气缸的空气流量进行计算，并通过控制供油量，使空燃比符合各工况的要求。扭矩控制模式系统根据油门踏板位置传感器，估算输出扭矩，对发动机的输出动力进行控制。曲轴位置基准及转速测量系统根据曲轴位置传感器信号判断曲轴位置及测量发动机转速，精确控制发动机点火及喷油正时。发动机各缸工作顺序判断

A Nonlinear-Disturbance-Observer-Based DC-Bus Voltage Control for a Hybrid AC DC Microgrid

变电所母线桥的动稳定校验

华师秋《高等数学文》在线作业

母线电动力及动热稳定性计算

最新对比导购稿日系美系家轿大PK三厢利亚纳A6对比新赛欧

高等数学B(二)教学大纲

高压电缆热稳定校验计算书

高等数学2课程教学大纲

热稳定性校验(主焦

全球汽车车型中英文对照表

华中师范大学人才培养方案

上海理工大学高等传热学试题及答案

高压电缆热稳定校验计算书

汽车名中英对照

华中师范大学教育学专业参考书目

华中师范大学高等数学C真题

传热学上海理工大学硕士研究生入学考试试题

案例--变电所母线桥的动稳定校验

利亚纳a维修手册电喷系统