CN103455081B - Based on the maximum power point tracing method that disturbance is observed - Google Patents

Abstract

The maximum power point tracing method observed based on disturbance disclosed by the invention, first samples to photovoltaic array voltage, line voltage and grid-connected current signal; Next sets up the dynamic model of Single-Stage Grid Connected Solar Inverter System; Finally MPPT maximum power point tracking is carried out to Single-Stage Grid Connected Solar Inverter System.The present invention only need detect photovoltaic array voltage, with grid-connected reference current amplitude signal I _refas the equivalent signal of combining inverter output power; significantly reduce the impact of sample quantization error on MPPT maximum power point tracking algorithm, solve the problem of traditional disturbance observation control strategy poor stability and busbar voltage collapse or output power vibration in the photovoltaic parallel in system of single stage type.

Description

Based on the maximum power point tracing method that disturbance is observed

Technical field

The invention belongs to the renewable technical field of new energy power generation of distributed solar, relate to a kind of MPPT maximum power point tracking control strategy of applicable Single-Stage Grid Connected Solar Inverter System, be specifically related to a kind of maximum power point tracing method observed based on disturbance.

Background technology

The characteristics of output power of photovoltaic cell has very strong non-linear, and its peak power output and peak power output point voltage and electric current are along with the factors vary such as unbalanced degree of temperature, intensity of illumination, illumination.Only have and adopt effective MPPT maximum power point tracking algorithm, the utilization factor of photovoltaic generating system to photovoltaic cell component electric energy could be improved.

At present, the method that photovoltaic generating system realizes MPPT maximum power point tracking has a lot: determine voltage method, disturbance observation, increment conductance method, short-circuit current method etc., but these methods respectively have its relative merits and the scope of application.Common disturbance observation fado is the control strategy of single order, by changing relevant controlled quentity controlled variable, the output power of photovoltaic array or some correlated variabless are changed, by judging that before and after change, next step control mode is determined in the position of these variablees on curve, thus make system works point progressively close to maximum power point.This control mode is feasible in the photovoltaic DC-to-AC converter of twin-stage or off-line type, but in the photovoltaic parallel in system of single stage type its control strategy poor stability, busbar voltage will be caused to collapse or output power vibration, system cannot normally work.

Summary of the invention

The object of this invention is to provide a kind of maximum power point tracing method observed based on disturbance; solve the problem of traditional disturbance observation control strategy poor stability and busbar voltage collapse or output power vibration in the photovoltaic parallel in system of single stage type, and do not affect by algorithm is digitized.

The technical solution adopted in the present invention is: the maximum power point tracing method observed based on disturbance, specifically implements according to following steps:

Step 1: photovoltaic array voltage, line voltage and grid-connected current signal are sampled;

Step 2: the dynamic model setting up Single-Stage Grid Connected Solar Inverter System;

Step 3: MPPT maximum power point tracking is carried out to Single-Stage Grid Connected Solar Inverter System.

Feature of the present invention is also,

Step 2 wherein sets up the dynamic model of Single-Stage Grid Connected Solar Inverter System, specifically implements according to following steps:

With i _pV, i _c, i _outrepresent that photovoltaic array exports the momentary current of momentary current, DC filter capacitor instantaneous charge current and filter capacitor aft section circuit respectively, v _pVrepresent that photovoltaic array exports instantaneous voltage, p _outfor photovoltaic array instantaneous output, then:

$i_{\mathrm{pv}}=i_c+i_{\mathrm{out}}=C\frac{{\mathrm{dv}}_{\mathrm{pv}}}{\mathrm{dt}}+\frac{p_{\mathrm{out}}}{v_{\mathrm{pv}}},$

In conjunction with photovoltaic cell component mathematical model I _z=f (I _ph, V) and=I _ph-ε [exp (ξ V _z)-1] obtain the photovoltaic generating system dynamic model as shown in the formula representing with above formula, in formula,

$\left\{\begin{array}{c}{\stackrel{\·}{v}}_{\mathrm{pv}}=\frac{I_{\mathrm{ph}}}{C}-\frac{\mathrm{\ϵ}}{C}[\exp \left({\mathrm{\ξv}}_{\mathrm{pv}}\right)-1]-\frac{p_{\mathrm{out}}}{{\mathrm{Cv}}_{\mathrm{pv}}},\\ v_{\mathrm{pv}}=v_{\mathrm{pv}}\left(0\right)+{\stackrel{\·}{v}}_{\mathrm{pv}}\end{array}\right.$

Wherein, I _zfor photovoltaic module output current, I _phfor the equivalent photogenerated current of battery component, V _zfor photovoltaic module output voltage, ε=n _pi ₀, n _pfor batteries in parallel connection number of unit, I ₀for the P-N junction reverse saturation current of photovoltaic cell inside equivalent diode, ξ=q/n _ck _ctn _s, q is electronic charge, n _cfor the diode characteristic factor, k _cfor Boltzmann constant, T is photovoltaic cell absolute temperature, n _sfor series-connected cell number of unit.

Step 3 wherein pair Single-Stage Grid Connected Solar Inverter System carries out MPPT maximum power point tracking, specifically implements according to following steps:

(1) acquisition of photovoltaic array output power information:

Owing to controlling to make combining inverter output current real-time follow-up reference current signal by current controller, and line voltage is stable under normal circumstances, so reference current amplitude I _refbe directly proportional to combining inverter output power; Again because combining inverter output power and photovoltaic array output power also exist proportional relationship, therefore use reference current amplitude signal I under stable situation _refreplace the equivalent signal of photovoltaic array output power, this stable situation refer to array actual output voltage trace into reference voltage after situation;

(2) photovoltaic array output voltage control:

Given magnitude of voltage V _refwith sample voltage value V _pVerror regulate through pi regulator, given as grid-connected current amplitude of the output of pi regulator, controls busbar voltage by controlling grid-connected power; Pi regulator passing ratio link k _upwith integral element k _uirealize; G _{inv (s)}the combining inverter link comprising Current Control link, I _refit is the amplitude of the given current signal of this link; I _invgrid-connected output current, it and line voltage v _gridproduct be grid-connected output power P _out; P _outwith V _pVrelation be reduced to: V _pV=f _pVC(V _pV(0), P _out);

(3) adopt disturbance to observe and carry out MPPT maximum power point tracking:

With photovoltaic array output voltage for regulating benchmark, adopt different disturbance bandwidth to carry out disturbance to photovoltaic array reference voltage signal according to different output power grades, and the reference current change in observation contrast disturbance bandwidth is with the direction determining voltage disturbance: V _reffor photovoltaic array reference voltage, V _pVfor photovoltaic array output voltage sampled signal, e _vv _refwith V _pVerror signal, V _refsbe the central point voltage within the scope of voltage disturbance, dV is voltage disturbance amount, J _mxbe forward disturbance bandwidth, LOR represents perturbation direction, I _mfor the maximum I obtained in the disturbance cycle _refvalue, I _refamplitude as grid-connected reference current signal amplitude that is given or active current signal is given; Control to make e by increment type PI _vbe tending towards 0, work as V _pVtenacious tracking V _refafter, with I _refsubstitute photovoltaic array output power as observed quantity; If this I _refvalue is greater than I _mvalue, then by I now _refvalue is assigned to I _m, simultaneously voltage V now _refbe assigned to V _refs, as the central value of voltage disturbance, then with V _refsbased on, continue V _refcarry out the voltage disturbance of dV size, when disturbance quantity dV reaches disturbance upper limit J _mxor disturbance lower limit-J _mxin time, cannot continue to realize disturbance to prevent, must to conversion perturbation direction; If this I _refvalue is less than or equal to I _mvalue, then continue V _refcarry out disturbance; J _mxsize by I _refsize determine, due to the decline along with power, unit I _refchange can cause the change of larger array voltage, along with the decline of power, disturbance bandwidth J _mxalso increase, to cause I thereupon _refchange, carry out observation and comparison, be equivalent to variable step control.

The invention has the beneficial effects as follows:

(1) impact of A/D sampling on MPPT maximum power point tracking algorithm is greatly reduced;

(2) ensure when illumination variation is quite violent, system also can stably to electrical network feedback electric energy, not reason busbar voltage collapse and system is stopped power supply;

(3) steady track error is little.

Accompanying drawing explanation

Fig. 1 is the impact that quantization error gathers photovoltaic array output power, wherein (a) is the power collecting waveform under specified illumination condition, b () is the power collecting waveform under 60% specified illumination condition, (c) be under 40% specified illumination condition power collecting waveform, (d) be under 20% specified illumination condition power collecting waveform;

Fig. 2 is photovoltaic array band power source realistic model;

Fig. 3 is DC bus-bar voltage control block diagram;

Fig. 4 is P-V, I-V family curve under two kinds of different modes, and wherein (a) is array voltage and electric current phase multiplication, and (b) is with I _refpower information method of equal value;

Fig. 5 is process flow diagram of the present invention;

Fig. 6 is two class Single-Stage Grid Connected Solar Inverter Systems, and wherein (a) is single-phase single-stage type grid-connected photovoltaic system, and (b) is three-phase single-level formula grid-connected photovoltaic system.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

When MPPT maximum power point tracking algorithm adopts digitized form to realize, the digitizing of some algorithm can cause some to affect on MPPT maximum power point tracking performance, MPPT maximum power point tracking even can be made in some cases to lose efficacy, when not considering noise, quantization error is one of reason causing digitizing MPPT maximum power point tracking algorithm to lose efficacy.

The digital sample resolution of voltage and electric current can be expressed as:

$r_v=\frac{V_{\mathrm{ms}}}{2^{N_c}}$ With $r_i=\frac{I_{\mathrm{ms}}}{2^{N_c}}$ （1）

Wherein, V _mswith I _msbe respectively the sampling range of A/D passage to voltage and electric current, N _cfor A/D Channel-shifted figure place.Quantization error refers to the difference of sample magnitude and actual numerical value.Because common A/D passage all adopts house tail error, so quantization error change along with the consecutive variations indentation of sample objects in sampling range ability, this zig-zag peak value is equal with corresponding sampling resolution, remembers e _qvwith e _qibe respectively the sample quantization error of voltage and electric current, then have:

V _pv=V _pvc+ e _qvwith I _pv=I _pvc+ e _qi(2)

Wherein, V _pVwith I _pVbe respectively photovoltaic array actual output voltage and electric current, V _pVCwith I _pVCbe respectively the sampled value of photovoltaic array output voltage and output current, so exist:

P _pvc=P _pv-(V _pv·e _qi+I _pv·e _qv-e _qv·e _qi)=P _pv-e _qp（3）

Wherein, P _pVwith P _pVCbe respectively as photovoltaic array real output and sampled power, e _qpfor power samples error.Due to V _pVequal consecutive variations in operating voltage range, and e _qvwith operating voltage V _pVlinear change be periodic serrations shape change, e _qiwith working current I _pVlinear change be periodic serrations shape change.

Be 0.2A to current sample resolution, voltage sample resolution is in 1V situation, samples, obtain its P-V family curve and e for the output electricity of different illumination intensity to 50kW photovoltaic array _qpchange curve, as shown in Fig. 1 (a) ~ (d).The P-V curve of Fig. 1 (a) for obtaining under array exports specified power situation, although sampled power value has discontinuous feature, but itself and real power value are substantially identical in operating voltage range, but along with the reduction of intensity of illumination, this coincideing is broken gradually, and multi-peak characteristic even appears in P-V family curve, and illumination is more weak, this multimodal characteristic is more serious, and Fig. 1 (d) shows the P-V family curve obtained at about 20% specified illumination condition down-sampling.The P-V family curve obtained due to the more weak situation down-sampling of illumination has the feature of multi-peak, and traditional MPPT maximum power point tracking algorithm all exports smooth P-V or I-V family curve for following the tracks of foundation with photovoltaic module, so the discontinuous change that the photovoltaic property curve after digital sample presents can affect the efficiency of traditional MPPT maximum power point tracking algorithm, MPPT maximum power point tracking algorithm is even made to lose efficacy.

The present invention is based on the maximum power point tracing method that disturbance is observed, Fig. 6 is hardware circuit of the present invention basis, and wherein C is DC side filter capacitor, and L is AC filter inductance, specifically implements according to following steps:

Step 1: photovoltaic array voltage, line voltage and grid-connected current signal are sampled;

Step 2: the dynamic model setting up Single-Stage Grid Connected Solar Inverter System;

Because line voltage is normally stable, and do not change with the change of grid-connected current, so the amplitude size of grid-connected current is directly proportional to the output power of combining inverter, namely be that controlled quentity controlled variable can be equivalent to output power with grid-connected current be controlled quentity controlled variable, so the realistic model of photovoltaic array band power source load as shown in Figure 2 can be set up, ignore the pressure drop of anti-reverse charging diode, the voltage at electric capacity C two ends is equal with photovoltaic array voltage, with i _pV, i _c, i _outrepresent that photovoltaic array exports the momentary current of momentary current, DC filter capacitor instantaneous charge current and filter capacitor aft section circuit respectively, v _pVrepresent that photovoltaic array exports instantaneous voltage, p _outfor photovoltaic array instantaneous output, then exist:

$i_{\mathrm{pv}}=i_c+i_{\mathrm{out}}=C\frac{{\mathrm{dv}}_{\mathrm{pv}}}{\mathrm{dt}}+\frac{p_{\mathrm{out}}}{v_{\mathrm{pv}}}---\left(4\right)$

In conjunction with photovoltaic cell component mathematical model (I _z=f (I _ph, V) and=I _ph-ε [exp (ξ V _z)-1]) can obtain with formula (4) the photovoltaic generating system dynamic model that represents such as formula (5).In formula,

$\left\{\begin{array}{c}{\stackrel{\·}{v}}_{\mathrm{pv}}=\frac{I_{\mathrm{ph}}}{C}-\frac{\mathrm{\ϵ}}{C}[\exp \left({\mathrm{\ξv}}_{\mathrm{pv}}\right)-1]-\frac{p_{\mathrm{out}}}{{\mathrm{Cv}}_{\mathrm{pv}}},\\ v_{\mathrm{pv}}=v_{\mathrm{pv}}\left(0\right)+{\stackrel{\·}{v}}_{\mathrm{pv}}\end{array}\right.---\left(5\right)$

Wherein, I _zfor photovoltaic module output current, I _phfor the equivalent photogenerated current of battery component, V _zfor photovoltaic module output voltage, ε=n _pi ₀(n _pfor batteries in parallel connection number of unit, I ₀p-N junction reverse saturation current for photovoltaic cell inside equivalent diode), ξ=q/n _ck _ctn _s(q is electronic charge, n _cfor the diode characteristic factor, k _cfor Boltzmann constant, T is photovoltaic cell absolute temperature, n _sfor series-connected cell number of unit).

Step 3: MPPT maximum power point tracking is carried out to Single-Stage Grid Connected Solar Inverter System.

This novel disturbance observation is on the basis of stable busbar voltage, change reference voltage level, observation output power value after feedback voltage is equal with given voltage, and follow the trail of with the peak power output realizing pair array for foundation changes given voltage with this point voltage value and this point output power value.First to guarantee the stable of busbar voltage in normal system operation, under the prerequisite that busbar voltage is stable, go regulation output electric current to control to feed back to the power of electrical network again.So just, can ensure when illumination variation is quite violent, system also can stably to electrical network feedback electric energy, not reason busbar voltage collapse and system is stopped power supply.Specifically be divided into again following step:

(1) acquisition of photovoltaic array output power information

Owing to controlling to make combining inverter output current real-time follow-up reference current signal by current controller, and line voltage is stable under normal circumstances, so reference current amplitude I _refbe directly proportional to combining inverter output power.Again because combining inverter output power and photovoltaic array output power also exist proportional relationship, therefore reference current amplitude signal I can be used completely under stable situation _refreplace the equivalent signal of photovoltaic array output power, this stable situation refer to array actual output voltage trace into reference voltage after situation.

Fig. 4 is P-V and the I-V family curve that two kinds of different modes obtain.Wherein, Fig. 4 (a) is sampled light photovoltaic array output voltage and output current, by the P-V family curve drawn after multiplying; Fig. 4 (b) is with grid-connected reference current amplitude signal I _refreplace the I-V family curve of photovoltaic array output power.Visible by contrasting, when illumination variation, the curvilinear characteristic of two kinds of waveforms is basically identical, thus demonstrates and use variable I _refreplace the feasibility of photovoltaic array output power.From Fig. 4 (a), obviously see that P-V family curve exists multiple sawtooth like shape peak value, be unfavorable for the tracing control of maximum power point; Have the single peak feature of relative smooth from Fig. 4 (b), I-V family curve, be applicable to very much being used as tracking target, therefore the present invention is with I _refphotovoltaic array output power is replaced to realize MPPT maximum power point tracking.

(2) photovoltaic array output voltage control strategy

In order to make photovoltaic array output voltage tracing preset voltage, control block diagram as shown in Figure 3 can be adopted to control it.In Fig. 3, given magnitude of voltage V _refwith sample voltage value V _pVerror regulate through pi regulator, given as grid-connected current amplitude of the output of pi regulator is control busbar voltage by controlling grid-connected power in this way; Pi regulator is passing ratio link k _upwith integral element k _uirealize; G _{inv (s)}the combining inverter link comprising Current Control link, I _refit is the amplitude of the given current signal of this link; I _invgrid-connected output current, it and line voltage v _gridproduct be grid-connected output power P _out; P _outwith V _pVrelation can describe by formula (5), be reduced to: V _pV=f _pVC(V _pV(0), P _out).The method realizes in the mode of outer voltage current inner loop, and inner ring controlled frequency is fast, and to realize the fast track to set-point, outer shroud control cycle is slower in relative to inner ring to realize and the decoupling zero of inner ring, due to P _outrate of change and V _pVrate of change be oppositely correlated with, so the local linear that can realize the Linear Control of grid-connected current and busbar voltage respectively by the method controls.

(3) realization of modified disturbance observation method

Novel disturbance observation: with photovoltaic array output voltage for regulating benchmark, different disturbance bandwidth is adopted to carry out disturbance to photovoltaic array reference voltage signal according to different output power grades, and the reference current change in observation contrast disturbance bandwidth is with the direction determining voltage disturbance, specific implementation flow process as shown in Figure 5.In figure, V _reffor photovoltaic array reference voltage, V _pVfor photovoltaic array output voltage sampled signal, e _vv _refwith V _pVerror signal, V _refsbe the central point voltage within the scope of voltage disturbance, dV is voltage disturbance amount, J _mxbe forward disturbance bandwidth, LOR represents perturbation direction, I _mfor the maximum I obtained in the disturbance cycle _refvalue, and I _refamplitude as grid-connected reference current signal amplitude that is given or active current signal is given.Control to make e by increment type PI _vbe tending towards 0, work as V _pVtenacious tracking V _refafterwards (such as delay count j1>=10), with I _refsubstitute photovoltaic array output power as observed quantity.If this I _refvalue is greater than I _mvalue, then by I now _refvalue is assigned to I _m, simultaneously voltage V now _refbe assigned to V _refs, as the central value of voltage disturbance, then with V _refsbased on, continue V _refcarry out the voltage disturbance of dV size, when disturbance quantity dV reaches disturbance upper limit J _mxor disturbance lower limit-J _mxin time, cannot continue to realize disturbance to prevent, must to conversion perturbation direction; If this I _refvalue is less than or equal to I _mvalue, then continue V _refcarry out disturbance.J _mxsize by I _refsize determine, due to the decline along with power, unit I _refchange can cause the change of larger array voltage, so along with the decline of power, disturbance bandwidth J _mxalso should increase, to cause I thereupon _refchange, thus can carry out observation and comparison, this is equivalent to variable step and controls.

Its steady track error of disturbance observation of the present invention is little, particularly when in miniwatt situation, its quiescent potential closely maximum power point voltage, along with the increase of output power, voltage disturbance scope reduces gradually, and under steady state conditions, its operating voltage is more close to the maximum power point voltage of photovoltaic array.Although the sampling of power is still by the impact of quantization error, but it does not have multi-peak characteristic, so this algorithm can not produce because of the power of illumination depart from its maximum power point tracking error phenomenon far away, solve tracking error phenomenon under the steady state conditions caused due to quantization error.

Claims (1)

1., based on the maximum power point tracing method that disturbance is observed, it is characterized in that, specifically implement according to following steps:

Step 1: photovoltaic array voltage, line voltage and grid-connected current signal are sampled;

Step 2: the dynamic model setting up Single-Stage Grid Connected Solar Inverter System;

Specifically implement according to following steps:

With i _pv, i _c, i _outrepresent that photovoltaic array exports the momentary current of momentary current, DC filter capacitor instantaneous charge current and filter capacitor aft section circuit respectively, v _pvrepresent that photovoltaic array exports instantaneous voltage, p _outfor photovoltaic array instantaneous output, then:

$i_{pv}=i_c+i_{out}=C\frac{{\mathrm{dv}}_{pv}}{dt}+\frac{p_{out}}{v_{pv}},$

In conjunction with photovoltaic cell component mathematical model I _z=f (I _ph, V) and=I _ph-ε [exp (ξ V _z)-1] obtain the photovoltaic generating system dynamic model as shown in the formula representing with above formula, in formula,

$\left\{\begin{array}{c}{\stackrel{\·}{v}}_{pv}=\frac{I_{ph}}{C}-\frac{\mathrm{\ϵ}}{C}\[\exp \left({\mathrm{\ξv}}_{pv}\right)-1\]-\frac{p_{out}}{{\mathrm{Cv}}_{pv}}\\ v_{pv}=v_{pv}\left(0\right)+{\stackrel{\·}{v}}_{pv}\end{array}\right.,$

Wherein, wherein C is DC side filter capacitor, I _zfor photovoltaic module output current, I _phfor the equivalent photogenerated current of battery component, V _zfor photovoltaic module output voltage, ε=n _pi ₀, n _pfor batteries in parallel connection number of unit, I ₀for the P-N junction reverse saturation current of photovoltaic cell inside equivalent diode, q is electronic charge, n _cfor the diode characteristic factor, k _cfor Boltzmann constant, T is photovoltaic cell absolute temperature, n _sfor series-connected cell number of unit;

Step 3: MPPT maximum power point tracking is carried out to Single-Stage Grid Connected Solar Inverter System;

Specifically implement according to following steps:

(1) acquisition of photovoltaic array output power information:

Owing to controlling to make combining inverter output current real-time follow-up reference current signal by current controller, and line voltage is stable under normal circumstances, so reference current amplitude I _refbe directly proportional to combining inverter output power; Again because combining inverter output power and photovoltaic array output power also exist proportional relationship, therefore use reference current amplitude signal I under stable situation _refreplace the equivalent signal of photovoltaic array output power, this stable situation refer to array actual output voltage trace into reference voltage after situation;

(2) photovoltaic array output voltage control:

Given magnitude of voltage V _refwith sample voltage value V _pVerror regulate through pi regulator, given as grid-connected current amplitude of the output of pi regulator, controls busbar voltage by controlling grid-connected power; Pi regulator passing ratio link k _upwith integral element k _uirealize; G _{inv (s)}the combining inverter link comprising Current Control link, I _refit is the amplitude of the given current signal of this link; I _invgrid-connected output current, it and line voltage v _gridproduct be grid-connected output power P _out; P _outwith V _pVrelation be reduced to: V _pV=f _pVC(V _pV(0), P _out);

(3) adopt disturbance to observe and carry out MPPT maximum power point tracking:

With photovoltaic array output voltage for regulating benchmark, adopt different disturbance bandwidth to carry out disturbance to photovoltaic array reference voltage signal according to different output power grades, and the reference current change in observation contrast disturbance bandwidth is with the direction determining voltage disturbance: V _reffor given magnitude of voltage, V _pVfor sample voltage value, e _vv _refwith V _pVerror signal, V _refsbe the central point voltage within the scope of voltage disturbance, dV is voltage disturbance amount, J _mxbe forward disturbance bandwidth, LOR represents perturbation direction, I _mfor the maximum I obtained in the disturbance cycle _refvalue, I _refas the amplitude of the given current signal of this link; Control to make e by increment type PI _vbe tending towards 0, work as V _pVtenacious tracking V _refafter, with I _refsubstitute photovoltaic array output power as observed quantity; If this I _refvalue is greater than I _mvalue, then by I now _refvalue is assigned to I _m, simultaneously voltage V now _refbe assigned to V _refs, as the central value of voltage disturbance, then with V _refsbased on, continue V _refcarry out the voltage disturbance of dV size, when disturbance quantity dV reaches disturbance upper limit J _mxor disturbance lower limit-J _mxin time, cannot continue to realize disturbance to prevent, and must convert perturbation direction; If this I _refvalue is less than or equal to I _mvalue, then continue V _refcarry out disturbance; J _mxsize by I _refsize determine, due to the decline along with power, unit I _refchange can cause the change of larger array voltage, along with the decline of power, disturbance bandwidth J _mxalso increase, to cause I thereupon _refchange, carry out observation and comparison, be equivalent to variable step control.