CN106026750A - Power frequency inverter design method - Google Patents

Abstract

The invention discloses a power frequency inverter design method. The method comprises the following steps: an optimal load characteristic expression is deduced according to an optimal loading response waveform; according to the optimal load characteristic expression and expected performance parameters, LC filter parameters are designed; according to an expected performance index and the filter parameters, a sliding mode coefficient is then calculated, and according to the sliding mode coefficient, an error switching coefficient is determined; and finally, according to design efficiency and switching frequency requirements, a smaller hysteresis modulation width is selected, the steady output voltage accuracy of a full-bridge inverter and an output voltage THD in the case of load mutation are simulated and calculated, and whether to meet the standard is analyzed. According to the power frequency inverter design method of the invention, the problems that the existing design method can not get the accurate value of the filter parameter, and parameters of the controller are hard to calculate accurately are solved, the filter and sliding mode parameter design process is simplified, step-by-step formula design of main parameters of the inverter is realized, the design of the inverter is modeled, and the operation is easy and simple.

Description

A kind of method for designing of power frequency inverter

Technical field

The invention belongs to circuit parameter design field, specifically, relate to the method for designing of a kind of power frequency inverter.

Background technology

Power frequency inverter is the important and network interface of distributed power generation and modern power network, and power frequency inverter includes inverter circuit With control circuit two large divisions, inverter circuit is mainly designed to Filter Parameter Design, for international standard, is typically based on filtering skill Art designs；Design on control circuit then uses method design controller architecture and the parameter of control theory, finally realizes inverter and sets Meter.

The wave filter design of existing inverter, based on filtering theory, obtains the constraint equation that filtering parameter is constituted, but cannot Obtain the exact value of certain filtering parameter；Controller is designed with (non-) linear control technique, but design process is loaded down with trivial details, controller Parameter is difficult to accurately calculate.Even if can design, but the load transient characteristic of inverter is how, and whether controller has been given play to The optimal running effect of inverter circuit, has no way of judging.

Summary of the invention

In view of this, the present invention is directed to existing method for designing and cannot obtain the exact value of filtering parameter, controller parameter difficulty With the problem accurately calculated, it is provided that the method for designing of a kind of power frequency inverter, not only determine the concrete number of each parameter Value, also simplify design process.

In order to solve above-mentioned technical problem, the invention discloses the method for designing of a kind of power frequency inverter, specifically include with Lower step:

Step 1, loads response wave shape according to optimum and pushes away to obtain optimal load characteristic expression formula；

${\mathrm{\Δu}}_o^{undershoot}=-{\mathrm{\Δi}}_o{R}_C-\frac{{\[{\mathrm{CR}}_C(E-U_{om})-{\mathrm{L\Δi}}_o\]}^2}{2LC(E-U_{om})}---\left(1\right)$

$t_{si}=\frac{{\mathrm{L\Δi}}_o}{E-U_{om}}(1+\sqrt{\frac{2E}{E+U_{om}}})---\left(2\right)$

In above formula,Represent that output voltage falls；Δi_oRepresent step load change；R_cRepresent filter capacitor series connection etc. Effect resistance；C represents filter capacitor, and E is input voltage, U_omRepresent output voltage amplitude；L represents inductance, t_siRepresent that optimum loads The adjustment time；

Step 2, Filter Parameter Design, change formula (1) and formula (2) left side into maximum permissible voltage magnitude and output respectively The voltage maximum allowable adjustment time, substitute into expected performance parameter, calculate LC filtering parameter；

Step 3, sliding formwork parameter designing, the LC filtering parameter obtained according to expected performance index and step 2, calculate sliding formwork system Number α, and determine error switch coefficient k according to sliding formwork factor alpha₁；

$\mathrm{\α}=\frac{3.5}{P}\{\frac{U_{om}}{L}\[\sqrt{2E(E+U_{om})}-(E+U_{om})\]\}$

In above formula, U_omRepresent output voltage amplitude；P represents inverter rated power；L represents inductance；E is input voltage；

k₁=α k₂, k₂Represent error rate handoff factor；

Step 4, requires to choose less stagnant ring modulation width, emulation measuring and calculating full-bridge inverting according to design efficiency and switching frequency Device steady state output voltage precision, and the output voltage THD when load changing, if meeting design objective, then design complete；No Then, step 4 is repeated.

Further, in step 2 LC filtering parameter computational methods particularly as follows:

$L=\frac{U_{om}(E-U_{om})}{2P}{(1+\sqrt{\frac{2E}{E+U_{om}}})}^{-1}{t}_s$

$R_C\≤\frac{{\mathrm{\γU}}_{om}^2}{2P}$

$C=\frac{U_{om}({\mathrm{\γU}}_{om}\±\sqrt{{\left({\mathrm{\γU}}_{om}\right)}^2-{(2{\mathrm{PR}}_C/U_{om})}^2})}{2{\mathrm{PR}}_C^2}\·{(1+\sqrt{\frac{2E}{E+U_{om}}})}^{-1}{t}_s$

In above formula, L represents inductance；U_omRepresent output voltage amplitude；E is input voltage, and P represents inverter rated power； t_sRepresent the output voltage maximum allowable adjustment time；R_cRepresent filter capacitor series equivalent resistance；γ represents load regulation；C table Show filter capacitor；

Calculate L and C according to above formula, and choose less R according to constraints_c。

Further, k in step 3₂Value 0.0001.

Further, in step 4, stagnant ring modulation width is less than or equal to maximum output voltage magnitude.

Compared with prior art, the present invention can obtain and include techniques below effect:

(1) present invention is by substep formulation design main circuit filtering parameter and controller parameter, based on optimal load wink State response theory and inverter expected performance index Design L and C of LC wave filter, then based on the most counted L and C, in conjunction with First-order system method for designing gives sliding formwork coefficient formulas, and handoff factor and the method for designing of hysteresis band, solves Existing method for designing cannot obtain the exact value of filtering parameter, controller parameter is difficult to the problem that accurately calculates, not only determines The concrete numerical value of each parameter, also simplify wave filter and sliding formwork parameter designing process；

(2) achieve the substep formulation design of inverter major parameter, make the design medelling of inverter, simple easily behaviour Make, it is not necessary to possessing professional theory knowledge, the general staff possessing basic mathematical knowledge and familiar with computers can more easily grasp.

Certainly, the arbitrary product implementing the present invention it is not absolutely required to reach all the above technique effect simultaneously.

Accompanying drawing explanation

Accompanying drawing described herein is used for providing a further understanding of the present invention, constitutes the part of the present invention, this Bright schematic description and description is used for explaining the present invention, is not intended that inappropriate limitation of the present invention.In the accompanying drawings:

Fig. 1 is the circuit diagram of embodiment of the present invention power frequency inverter；

Fig. 2 is that the optimum of embodiment of the present invention power frequency inverter loads response wave shape figure.

Detailed description of the invention

Embodiments of the present invention are described in detail, thereby to the present invention how application technology hands below in conjunction with embodiment Section solves technical problem and reaches the process that realizes of technology effect and can fully understand and implement according to this.

The method for designing of power frequency inverter of the present invention, its structural representation is as it is shown in figure 1, inverter major design index For: (1) input voltage is E, output voltage amplitude U_om, frequency 50Hz；(2) inverter power P；(3) load regulation γ；(4) Transient state regulating time t_s；(5) total harmonic distortion factor THD≤5%；

Specific design method comprises the following steps:

Step 1, loads response wave shape according to optimum, as in figure 2 it is shown, push away to obtain optimal load characteristic expression formula；

${\mathrm{\Δu}}_o^{undershoot}=-{\mathrm{\Δi}}_o{R}_C-\frac{{\[{\mathrm{CR}}_C(E-U_{om})-{\mathrm{L\Δi}}_o\]}^2}{2LC(E-U_{om})}---\left(1\right)$

$t_{si}=\frac{{\mathrm{L\Δi}}_o}{E-U_{om}}(1+\sqrt{\frac{2E}{E+U_{om}}})---\left(2\right)$

In formula (1) and formula (2),Represent that output voltage falls；Δi_oRepresent step load change；R_cRepresent filtered electrical Hold series equivalent resistance；C represents filter capacitor, and E is input voltage, U_omRepresent output voltage amplitude；L represents inductance, t_siRepresent The optimum loading adjustment time.

Wherein, the derivation of formula (1) and formula (2) is as follows:

According to Fig. 1 and Fig. 2, push away the transient state expression formula of capacitance current is

$i_C=\left\{\begin{array}{cc}-{\mathrm{\Δi}}_o+\frac{E-U_{0m}}{L}t,& t\∈\[t_0,t_2\]\\ -{\mathrm{\Δi}}_o+\frac{2E}{L}{t}_2-\frac{E+U_{om}}{L}t,& t\∈\[t_2,t_{si}\]\end{array}\right.---(TD-1)$

Wherein, Δ i_oFor load loading capacity, Δ i_o>0。

From formula (TD-1), the capacitance current in transient process is divided into two stages: linearly increasing stage and linearly subtracting Few stage.

1. the optimum output voltage that loads falls

According to Fig. 2 and Shi (TD-1), output voltage when step load change amount is bigger fallsFor

${\mathrm{\Δu}}_o^{undershoot}=-{\mathrm{\Δi}}_o{R}_C-\frac{{\[{\mathrm{CR}}_C(E-U_{om})-{\mathrm{L\Δi}}_o\]}^2}{2LC(E-U_{om})}---(TD-2)$

Formula (TD-2) (i.e. formula (1)), describe optimum output voltage magnitude and step load change amount, filter capacitor inductance, The relation of filter capacitor ESR.

2. optimum loading adjustment time (t_si)

I. after step load change, electric capacity stops discharging time t₁

By i_C(t₁)=0, can obtain

$t_1=\frac{{\mathrm{L\Δi}}_o}{E-U_{om}}---(TD-3)$

From formula (TD-3), Optimal Stop discharging time t after loading₁With input voltage, output voltage, inductance value and negative Carry transition amount relevant, but unrelated with filter capacitor.

Ii. time t is adjusted_si

According to transient capacitance current waveform in Fig. 2, can be by the quantity of electric charge S of electric capacity release in transient process_Δ1With supplementary Quantity of electric charge S_Δ2It is expressed as

$\left\{\begin{array}{c}{S}_{\mathrm{\Δ}1}=\frac{1}{2}(t_1-t_0){\mathrm{\Δi}}_o\\ S_{\mathrm{\Δ}2}=\frac{1}{2}(t_{si}-t_1)i_C\left(t_2\right)\end{array}\right.---(TD-4)$

According to Fig. 2, association type (TD-1) and formula (TD-3), (TD-4) is converted into

$\left\{\begin{array}{c}{S}_{\mathrm{\Δ}1}=\frac{{\mathrm{L\Δi}}_o^2}{2(E-U_{om})}\\ S_{\mathrm{\Δ}2}=\frac{(E^2-U_{om}^2)(E-U_{om})t_{si}^2-2{\mathrm{L\Δi}}_o(E^2-U_{om}^2)t_{si}+L^2{\mathrm{\Δi}}_o^2(E+U_{om})}{4LE(E-U_{om})}\end{array}\right.---(TD-5)$

In order to ensure at t_siMoment capacitance terminal voltage is equal to steady state output voltage U_om, electric capacity is at [t₁,t_si] supplement electric charge Amount is necessarily equal to electric capacity at [t₀,t₁The quantity of electric charge of release, i.e. S during]_Δ1=S_Δ2, formula (TD-5) obtain:

$t_{si}=\frac{{\mathrm{L\Δi}}_o}{E-U_{om}}(1+\sqrt{\frac{2E}{E+U_{om}}})---(TD-6)$

Formula (TD-6) (i.e. formula (2)) indicates optimum loading adjustment time t_siWith filter inductance, incremental loading, input voltage And steady state output voltage u_oBetween relation, these parameters define single-phase full bridge power frequency changer load (Δ i_o＞ 0) feelings The fastest response speed that can reach under condition.

Step 2, Filter Parameter Design

When formula (1) and formula (2) left side are changed into respectively maximum permissible voltage magnitude and output voltage maximum allowable adjustment Between, substitute into expected performance parameter, calculate LC filtering parameter；

The computational methods of described LC filtering parameter particularly as follows:

$L=\frac{U_{om}(E-U_{om})}{2P}{(1+\sqrt{\frac{2E}{E+U_{om}}})}^{-1}{t}_s---\left(3\right)$

$R_C\≤\frac{{\mathrm{\γU}}_{om}^2}{2P}---\left(4\right)$

$C=\frac{U_{om}({\mathrm{\γU}}_{om}\±\sqrt{{\left({\mathrm{\γU}}_{om}\right)}^2-{(2{\mathrm{PR}}_C/U_{om})}^2})}{2{\mathrm{PR}}_C^2}\·{(1+\sqrt{\frac{2E}{E+U_{om}}})}^{-1}{t}_s---\left(5\right)$

In formula (3)-formula (5), L represents inductance；U_omRepresent output voltage amplitude；E is input voltage, and P represents inverter volume Determine power；t_sRepresent the output voltage maximum allowable adjustment time；R_cRepresent filter capacitor series equivalent resistance；γ represents that load is adjusted Whole rate；C represents filter capacitor；

Calculate L and C according to formula (3)-formula (5), and choose less R according to constraints_c。

Wherein, the derivation of formula (3)-formula (5) is as follows:

By transient state regulating time t_sSubstitution formula (2), can obtain inductance is:

$L=\frac{E-U_{om}}{{\mathrm{\Δi}}_{omax}}{(1+\sqrt{\frac{2E}{E+U_{om}}})}^{-1}{t}_s---(TD-7)$

In formula (TD-7), Δ i_omaxIt is inverter from unloaded transition to fully loaded maximum load current instantaneous transition amount.

Assume that bearing power factor, close to 1, according to the inverter power of design objective, obtains

${\mathrm{\Δi}}_{omax}=\frac{P}{U_{om}/\sqrt{2}}\·\sqrt{2}=\frac{2P}{U_{om}}---(TD-8)$

Bring formula (TD-8) into formula (TD-7), obtain

$L=\frac{U_{om}(E-U_{om})}{2P}{(1+\sqrt{\frac{2E}{E+U_{om}}})}^{-1}{t}_s---(TD-9)$

According to the concept of voltage regulation factor, obtain in conjunction with design objective and formula (1)

$\left|{\mathrm{\Δu}}_{omax}\right|={\mathrm{\Δi}}_{omax}{R}_C+\frac{{\[{\mathrm{CR}}_C(E-U_{om})-{\mathrm{L\Δi}}_{omax}\]}^2}{2LC(E-U_{om})}={\mathrm{\γU}}_{om}---(TD-10)$

Trying to achieve filter capacitor according to formula (TD-10) is

$C=\frac{L({\mathrm{\γU}}_{om}\±\sqrt{{\left({\mathrm{\γU}}_{om}\right)}^2-{\left(R_C{\mathrm{\Δi}}_{omax}\right)}^2})}{R_C^2(E-U_{om})}---(TD-11)$

From formula (TD-11), certainly exist γ U_om-R_CΔi_omax>=0, convolution (11) can obtain

$R_C\≤\frac{{\mathrm{\γU}}_{om}^2}{2P}---(TD-12)$

Formula (TD-12) is the relation that the equivalent series resistance of filter capacitor must is fulfilled for.

Bring formula (TD-8) and formula (TD-9) into formula (TD-11) to obtain

$C=\frac{U_{om}({\mathrm{\γU}}_{om}\±\sqrt{{\left({\mathrm{\γU}}_{om}\right)}^2-{(2{\mathrm{PR}}_C/U_{om})}^2})}{2{\mathrm{PR}}_C^2}\·{(1+\sqrt{\frac{2E}{E+U_{om}}})}^{-1}{t}_s---(TD-13)$

Step 3, sliding formwork parameter designing

The LC filtering parameter obtained according to expected performance index and step 2, calculates sliding formwork factor alpha, and according to sliding formwork factor alpha Determine error switch coefficient k₁；

$\mathrm{\α}=\frac{3.5}{P}\{\frac{U_{om}}{L}\[\sqrt{2E(E+U_{om})}-(E+U_{om})\]\}---\left(6\right)$

In above formula, U_omRepresent output voltage amplitude；P represents inverter rated power；L represents inductance；E is input voltage；

It is considered that filtering parameter understands change at random, sliding formwork coefficient value 2 α in reality；Choose k again₂For fractional value (as 0.0001), in the maximum load moment so that k₂x₂With maximum permissible voltage magnitude γ U_omKeep with (low) order of magnitude, this Carve x₂=2P/ (CU_om), obtain k₂, thus according to k₁=α k₂Obtain k₁, k₂Represent error rate handoff factor.

Wherein, the derivation of formula (6) is as follows:

By maximum allowable for output voltage adjustment time t_sBring formula (TD-14) into,

$\mathrm{\α}=7t_s^{-1}---(TD-14)$

Convolution (2), is converted into formula (TD-14)

$\mathrm{\α}=\frac{7}{{\mathrm{L\Δi}}_{omax}}\[\sqrt{2E(E+U_{om})}-(E+U_{om})\]---(TD-15)$

Bring formula (TD-8) into formula (TD-15), obtain

$\mathrm{\α}=\frac{3.5}{P}\{\frac{U_{om}}{L}\[\sqrt{2E(E+U_{om})}-(E+U_{om})\]\}---(TD-16)$

Derive complete.

Step 4, requires to choose less stagnant ring modulation width, emulation measuring and calculating full-bridge inverting according to design efficiency and switching frequency Device steady state output voltage precision, and the output voltage THD when load changing, if meeting design objective, then design complete；No Then, step 4 is repeated.

In step 4, stagnant ring modulation width is less than or equal to maximum output voltage magnitude.

The realization approach of the present invention: based on desired design index and optimal load transient response Decoupling design power frequency inverter Thought, analyze power frequency inverter optimal load transient response response process, derivation optimal load transient response expression formula, it is retouched State the relation of optimal load transient response and two expected performance indexs.C parameter and the L of LC wave filter can be calculated accordingly Parameter.Again as a example by sliding formwork control, use the method for designing of first-order system to give the computing formula of sliding formwork coefficient, select the most again Take handoff factor k₂For decimal (such as 0.0001), can determine that handoff factor k according to sliding formwork coefficient₁, finally according to design efficiency and opening Close frequency requirement and appropriately choose the width of stagnant ring manipulator.So far, a power frequency inverter design is complete.

Embodiment

Experiment condition: single-phase full bridge power frequency inverter section major parameter is: (1) input direct voltage 60V, output AC Voltage 24Sin2 π 50t (V)；(2) filter capacitor 500 μ F, R_C=5m Ω, filter inductance 40 μ H, load resistance 0.5 Ω～zero load. Assume to load and having transition between load and zero load with 100Hz.

Using above-mentioned method for designing, optimum loading experiment result is as shown in table 1 with formula result of calculation:

The optimum loading characteristic formula of table 1 contrasts with numerical simulation

Wherein,

As shown in Table 1, when the output voltage magnitude that load current step loading causes is less than the 5% of crest voltage (1.2V), the deviation ratio of output voltage magnitude is less than 10% (9.665%), and optimum load time deviation ratio is less than 10% (6.05%), optimal load transient response formula result of calculation is the most identical with experimental result.As Δ i_oDuring >=36A, output electricity Pressure magnitude is higher than the 5% of crest voltage, and relatively large deviation occurs in optimum loading characteristic formula result of calculation.If it is intended to expand public affairs The formula scope of application, can add correction term and improve result of calculation accuracy.

The method for designing of power frequency inverter of the present invention, is joined by substep formulation design main circuit filtering parameter and controller Number, and inverter expected performance index Design theoretical based on optimal load transient response L and C of LC wave filter, then based on it Before counted L and C, give sliding formwork coefficient formulas in conjunction with first-order system method for designing, and handoff factor and stagnant ring width The method for designing of degree.Not only determine the concrete numerical value of each parameter, also simplify design process, somewhat possess basic mathematical The people of computing knowledge familiar with computers can grasp rapidly.

As employed some vocabulary in the middle of description and claim to censure special component or method.Art technology Personnel are it is to be appreciated that same composition may be called with different nouns in different regions.This specification and claims are not In the way of the difference of title is used as distinguishing composition." comprising " as mentioned by the middle of description and claim in the whole text is One open language, therefore " comprise but be not limited to " should be construed to." substantially " refer in receivable range of error, this area Technical staff can solve described technical problem in the range of certain error, basically reaches described technique effect.Description is follow-up It is described as implementing the better embodiment of the present invention, for the purpose of right described description is the rule so that the present invention to be described, not In order to limit the scope of the present invention.Protection scope of the present invention is when being as the criterion depending on the defined person of claims.

Also, it should be noted term " includes ", " comprising " or its any other variant are intended to nonexcludability Comprise, so that include that the commodity of a series of key element or system not only include those key elements, but also include the most clearly Other key elements listed, or also include the key element intrinsic for this commodity or system.In the feelings not having more restriction Under condition, statement " including ... " key element limited, it is not excluded that in the commodity including described key element or system also There is other identical element.

Described above illustrate and describes some preferred embodiments of invention, but as previously mentioned, it should be understood that invention is not It is confined to form disclosed herein, is not to be taken as the eliminating to other embodiments, and can be used for other combinations various, amendment And environment, and can be carried out by above-mentioned teaching or the technology of association area or knowledge in invention contemplated scope described herein Change.And the change that those skilled in the art are carried out and change are without departing from the spirit and scope of invention, the most all should weigh appended by invention In the protection domain that profit requires.

Claims (4)

1. the method for designing of a power frequency inverter, it is characterised in that specifically include following steps:

Step 1, loads response wave shape according to optimum and pushes away to obtain optimal load characteristic expression formula；

${\mathrm{\Δu}}_o^{undershoot}=-{\mathrm{\Δi}}_o{R}_C-\frac{{\[{\mathrm{CR}}_C(E-U_{om})-{\mathrm{L\Δi}}_o\]}^2}{2LC(E-U_{om})}---\left(1\right)$

$t_{si}=\frac{{\mathrm{L\Δi}}_o}{E-U_{om}}(1+\sqrt{\frac{2E}{E+U_{om}}})---\left(2\right)$

In above formula,Represent that output voltage falls；Δi_oRepresent step load change；R_cRepresent filter capacitor series equivalent electricity Resistance；C represents filter capacitor, and E is input voltage, U_omRepresent output voltage amplitude；L represents inductance, t_siRepresent that optimum loads to adjust Time；

Step 2, Filter Parameter Design, change formula (1) and formula (2) left side into maximum permissible voltage magnitude and output voltage respectively The maximum allowable adjustment time, substitute into expected performance parameter, calculate LC filtering parameter；

Step 3, sliding formwork parameter designing, the LC filtering parameter obtained according to expected performance index and step 2, calculate sliding formwork factor alpha, And determine error switch coefficient k according to sliding formwork factor alpha₁；

$\mathrm{\α}=\frac{3.5}{P}\{\frac{U_{om}}{L}\[\sqrt{2E(E+U_{om})}-(E+U_{om})\]\}$

In above formula, U_omRepresent output voltage amplitude；P represents inverter rated power；L represents inductance；E is input voltage；

k₁=α k₂, k₂Represent error rate handoff factor；

Step 4, requires to choose less stagnant ring modulation width according to design efficiency and switching frequency, and emulation measuring and calculating full-bridge inverter is steady State output voltage precision, and the output voltage THD when load changing, if meeting design objective, then design complete；Otherwise, Repeat step 4.

The method for designing of power frequency inverter the most according to claim 1, it is characterised in that LC filtering parameter in step 2 Computational methods particularly as follows:

$L=\frac{U_{om}(E-U_{om})}{2P}{(1+\sqrt{\frac{2E}{E+U_{om}}})}^{-1}{t}_s$

$R_C\≤\frac{{\mathrm{\γU}}_{om}^2}{2P}$

$C=\frac{U_{om}({\mathrm{\γU}}_{om}\±\sqrt{{\left({\mathrm{\γU}}_{om}\right)}^2-{(2{\mathrm{PR}}_C/U_{om})}^2})}{2{\mathrm{PR}}_C^2}\·{(1+\sqrt{\frac{2E}{E+U_{om}}})}^{-1}{t}_s$

In above formula, L represents inductance；U_omRepresent output voltage amplitude；E is input voltage, and P represents inverter rated power；t_sTable Show the output voltage maximum allowable adjustment time；R_cRepresent filter capacitor series equivalent resistance；γ represents load regulation；C represents Filter capacitor；

Calculate L and C according to above formula, and choose less R according to constraints_c。

The method for designing of power frequency inverter the most according to claim 1, it is characterised in that k in step 3₂Value 0.0001.

The method for designing of power frequency inverter the most according to claim 1, it is characterised in that stagnant ring modulation width in step 4 Less than or equal to maximum output voltage magnitude.