CN103487186A - Variable frequency water supply system operating efficiency on-line detection method based on grey correlation method - Google Patents

Abstract

The invention provides a variable frequency water supply system operating efficiency on-line detection method based on a grey correlation method. The variable frequency water supply system operating efficiency on-line detection method based on the grey correlation method comprises the following steps: a mathematical model and constraint conditions of output power, frequency disturbance quantity and hydraulic pressure variable quantity are established, so that the mathematical model needed for water supply system operating efficiency on-line detection is formed; frequency small-signal disturbance is conducted under a steady-state condition, an actual pressure change value serves as a reference sequence, and a pressure change value is obtained according to the mathematical model to serve as a comparison sequence; a grey correlation algorithm and a grey correlation degree criterion are adopted for on-line detection of system shaft output power, and then the efficiency of a variable frequency water supply system is obtained. By means of the variable frequency water supply system operating efficiency on-line detection method based on the grey correlation method, on-line output power detection can be realized, a flow sensor is not needed, time for system installation and debugging is shortened, cost for system installation and debugging is lowered, and therefore the system is simpler in structure and lower in cost; a motor and a frequency converter can be effectively protected against low efficiency and failures caused by low frequency operation, therefore, the service life of the system is prolonged, the reliability of the system is improved, and a reliable guarantee is provided for safe and efficient operation of a water pump motor.

Description

Frequency-conversion water supply system operational efficiency online test method based on Grey Incidence

Technical field

The invention belongs to the electromechanical integration measurement and control area, be specifically related to a kind of frequency-conversion water supply system operational efficiency online test method based on Grey Incidence, be particularly useful for air pressure tank frequency conversion water supply facility water pump efficiency and detect.

Background technology

Water pump, as a kind of highly energy-consuming universal machine, is widely used in the every field of industrial and agricultural production and resident living, and the annual electric energy consumed on water pump assembly accounts for total more than 21% of power consumption in the whole nation, accounts for 30%～60% of production cost in water undertaking.The efficiency of water pump and water pump system, even only improve 1%, all can have been brought huge interests to the energy-conservation and environmental protection of China, and the electric energy of water pump consumption 30%～50% is all to save.By adopting frequency conversion control technique can effectively reduce the energy consumption of water pump, 28,200,000,000 kWh that can economize on electricity every year, realize target for energy-saving and emission-reduction.But it is that water pump runs between high efficient area all the time that frequency conversion control technique is realized energy-conservation prerequisite.Yet water supply user's water consumption has randomness and uncertainty on room and time, can not guarantee that water pump operates between high efficient area all the time.Particularly, in the water low ebb time period, because water consumption is very little, frequency converter and pump working are in the low frequency state.Now, motor heat loss and low-frequency vibration are serious, and whole frequency-conversion water supply system energy consumption sharply increases, and system effectiveness is low.Not only can not realize energy-saving and emission-reduction under this operating mode, and pump motor is because long-term low-frequency operation causes mechanical vibration and motor stator winding heating seriously, the safe reliability of reduction system and serviceable life, safe reliability and the production cost supplied water had a negative impact, the even more serious generation that even causes security incident.Thereby it is to deal with problems that the frequency-conversion water supply system operational efficiency detects.

It is that water system realizes the key technical problem that energy-saving and emission-reduction, safe and reliable water supply need emphasis to solve that the frequency-conversion water supply system operational efficiency detects in real time.The frequency-conversion water supply system operational efficiency is pump shaft output power P _outwith the input power power P _inratio.Power supply power input P _inby measuring power input voltage v _inwith input current i _incan obtain, realize comparatively easy.Pump shaft output power P _outneed by measuring hydraulic pressure value p (t) and obtaining with discharge q (t).Hydraulic pressure value p (t) can be recorded by pressure transducer (being generally water pressure gauge), and the measurement of flow q (t) is mainly recorded by following two schemes.

One, flow sensor scheme: by the water outlet at water pump, flow sensor is installed, is realized flow detection; Normally used flow sensor testing agency is mainly vane type, but exists following three kinds of situations can cause flow detection precision and Reliability performance measure not high:

1. supply in the larger situation of water flow velocity, the solid sundries existed in water quality can be clashed into impeller, makes impeller distortion and damaged, causes whole mechanism moment of inertia imbalance, causes flow detection inefficacy or precision and data reliability greatly to reduce; 2. water quality is subject to polluting while presenting acidity or alkalescence, and meeting heavy corrosion impeller mechanism, cause whole mechanism moment of inertia imbalance equally, and flow detection inefficacy or precision and data reliability reduce greatly; 3. the vane type flow detection is rotated by flowing liquid transmission impeller blade, thereby drives the action of associated electrical magnetic mechanism, the turn signal of impeller blade is converted into to the electric signal of different frequency.In the situation that pipeline section is long-pending constant, by the frequency of sampling electric signal, just can measure the flow of liquid.Owing to will considering the restraint conditions such as mechanism's intensity and machining precision and processing cost, the inertia of the rotatable parts such as impeller can not be very little, thereby have a Small flowrate measurement dead zone range, so can not detect such as the low discharge state such as dripping, leak.

Two, nonshared control unit+Special water pump motor scheme: by the pump motor to special-purpose, carry out the test repeatedly of heat-capacity curve, draw the family curve of pump working in the different flow situation, and using this curve and detect the reference value of flow as system, carry out similarity analysis by detecting the current operation characteristic of pump motor and reference characteristic, thereby the flow value that the system that draws is current, but this method exists serious problem to be exactly:

To the hardware and software of control system require high.Because controller will gather a large amount of data and carry out the characteristic quantity of signal processing and solving system, and carries out similarity analysis with the reference characteristic amount be stored in internal memory, thereby requires high to controller.

Due to system in During Process of Long-term Operation, liquid medium constant, the parameter of electric machine, converter parameter etc. are subject to such environmental effects and senile cause changes, and causes that the operation characteristic quantitative changeization of system is larger, causes precision and the poor reliability measured;

(3) because water system is long-time continuous operation, once thereby water pump break down, can only adopt and the motor of the strict coupling of controller, and can not use the pump motor of other types, thereby cause the operation expense of system high, practicality and poor for applicability.

Thereby the frequency-conversion water supply system operational efficiency detection method fields such as metallurgy, iron and steel, oil, chemical industry, water treatment, mine and resident living water at home has boundless market outlook.

Summary of the invention

The object of the invention is to propose a kind of low cost, the frequency-conversion water supply system operational efficiency online test method based on Grey Incidence that versatility is good, simple in structure.

A kind of frequency-conversion water supply system operational efficiency online test method based on Grey Incidence, is characterized in that, comprises the steps:

(1) with sampling period T _sfor being sampled in interval by hydraulic pressure value, inverter circuit output frequency and the power input of water system pipe network, sampled value is labeled as p (1), f (1) and P for the first time _in(1); Current sampling number is k, makes k=1;

(2) set up hydraulic pressure value array { p (i) }, the inverter circuit output frequency array { f (i) } formed by M element, and power input array { P _in(i) }; I={k-M+1 wherein, k-M+2 ... k}, M is the predefined positive integer that is greater than 1, k is current sampling number; P (i) | _i<=0=0, f (i) | _i<=0=0, P _in(i) | _i<=0=0;

(3) judge that whether water system is in steady state (SS); If so, enter step (4); Otherwise, proceed to step (13);

(4) solve hydraulic pressure mean value

inverter circuit output frequency mean value $\stackrel{\&OverBar;}{F}=\frac{1}{M}\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}f\left(i\right)$ With power input mean value $\stackrel{\&OverBar;}{P_{\mathrm{in}}}=\frac{1}{M}\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}{P}_{\mathrm{in}}\left(i\right);$

(5) the mark current time is the t=0 moment, gives fixing Arbitrary Perturbation Δ F of output frequency;

(6) definition

for t=mT _sshaft power estimated value constantly; M=1 wherein, 2 ..., N,

t _dfor predefined observation interval; Order

wherein initial value for any shaft power estimated value of setting;

Make m=1, second level lowest difference Δ (min)=0, the maximum poor Δ (max)=1 in the second level, resolution ratio γ=0.5;

(7) judgement mT _s>T _dwhether set up, if set up, proceed to step (13); Otherwise, at t=mT _sconstantly, sampling pipe network force value p (m); Obtain

(8) judgement

whether set up, if be false, proceed to step (13); Otherwise, by estimated value

and

Δ F, T _b, ρ, g, P _b, V _b, T and t=mT _sthe substitution formula $\frac{\mathrm{\&Delta;}{p}^g\left(m\right)}{\stackrel{\&OverBar;}{P}}=\frac{(2\stackrel{\&OverBar;}{F}\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{{\stackrel{\&OverBar;}{F}}^2}(1-e^{-\frac{P_{\mathrm{out}}^g\left[m\right]T_b}{\mathrm{\&rho;g}{P}_b{V}_{b}T}t}),$ Obtain pressure surge estimated value Δ p ^g(m);

Wherein, P _bfor water system air pressure tank rated pressure value, V _bfor water system air pressure tank air chamber nominal volume, T _bfor water system air pressure tank rated temperature; T is environment temperature, and ρ is fluid density; G is acceleration of gravity;

(9) using Δ p (m) as with reference to sequence, Δ p ^g(m) sequence as a comparison, and to Δ p (m), Δ p ^g(m) carry out normalized and obtain corresponding normalization sequence Δ p ₁(m) and

(10) error of calculation sequence

solve Δ p ₁(m),

correlation coefficient ${\mathrm{\&xi;}}_0\left(m\right)=\frac{\mathrm{\&Delta;}\left(\min \right)+\mathrm{\&gamma;\&Delta;}\left(\max \right)}{{\mathrm{\&Delta;}}_0\left(m\right)+\mathrm{\&gamma;\&Delta;}\left(\max \right)};$

(11) solve degree of association r,

ξ wherein ₀(ψ) | _ψ<=0=0;

Judge whether r>=0.95 sets up, if set up, enter step (12); Otherwise more new variables, make

m＝m+1； $P_{\mathrm{out}}^g\left[m\right]=P_{\mathrm{out}}^g[m-1]+\frac{1}{r}\mathrm{sgn}\left(\mathrm{\&Delta;p}\right[(m-1)]-\mathrm{\&Delta;}{p}^g[(m-1)\left]\right),$ Enter step (7);

(12) order computing system efficiency

judge whether to meet η<=η _min, η wherein _minfor predefined inefficient threshold value; If so, illustrative system is in inefficient duty, and inverter output is closed, and exits; Otherwise, enter step (13);

(13) make k=k+1; After this sampling period finishes, sample, and the sampled value of mark hydraulic pressure value, inverter circuit output frequency and power input is p (k), f (k) and P next time _in(k); Return to step (2).

The further setting of the present invention is, described steady state (SS) is defined as:

Calculate the standard deviation of array { p (i) } ${\mathrm{\&sigma;}}_p=\sqrt{\frac{M\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}p{\left(i\right)}^2-{\left(\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}p\left(i\right)\right)}^2}{{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">M</figure-callout>}}^2}}$ And the standard deviation of array { f (i) } ${\mathrm{\&sigma;}}_f=\sqrt{\frac{M\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}f{\left(i\right)}^2-{\left(\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}f\left(i\right)\right)}^2}{{\mathrm{<figure-callout\; id="2"\; label="M"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">M</figure-callout>}}^2}},$ Judge whether to meet: σ simultaneously _p<ε _pand σ _f<ε _f, wherein: ε _pand ε _ffor predefined on the occasion of; If meet, think that water system is in steady state (SS), otherwise, think that water system plays pendulum.

Frequency-conversion water supply system operational efficiency online test method based on Grey Incidence of the present invention has following beneficial effect:

One, frequency-conversion water supply system operational efficiency detection method of the present invention has online output power detection, without flow sensor, has saved system Installation and Debugging required time and cost, makes system architecture simpler, and system cost is lower;

Two, with existing nonshared control unit+Special water pump motor scheme, compare, the present invention detects applicable to the frequency-conversion water supply system operational efficiency of the three-phase alternating current pump motor composition of various models, has versatility widely.Because frequency-conversion water supply system shaft power P _outmeet formula $\frac{\mathrm{\&Delta;p}\left(t\right)}{P}=\frac{(2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{F^2}(1-e^{-\frac{P_{\mathrm{out}}{T}_b}{\mathrm{\&rho;g}{P}_b{V}_{b}T}t}).$ This formula is by parameter Δ p (t), P, Δ F, F, T _b, V _b, P _b, ρ, g, T and t determine output power P _out(Δ p (t), P, Δ F, F, T _b, V _b, P _b, ρ, g, T and t nominal pressure, fluid density, acceleration of gravity, current environmental temperature and time variable when air chamber volume size, the specified operation of air pressure tank when temperature, the specified operation of air pressure tank when inverter circuit output frequency, the specified operation of air pressure tank when hydraulic pressure value, frequency disturbance increment, stable operation when hydraulic pressure departs from undulate quantity, the stable operation of stationary value while being expressed as respectively frequency Δ F disturbance operation, and with the parameter of motor and model without any relation.Thereby detect output power P by this formula _outcan be applied to the interchange pump motor of any model, there is versatility widely.On this basis, then by measuring power supply power input P _incan obtain efficiency $\mathrm{\&eta;}=\frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}\&times;100\%.$

The characteristics such as it is fast that three, frequency-conversion water supply system operational efficiency detection method of the present invention has detection speed, and reliability is high, practical; The inefficiency fault that can effectively protect motor and converter low-frequency operation to cause, the life and reliability of raising system, for pump motor safety, efficient operation provide Reliable guarantee.

Embodiment

The invention provides a kind of frequency-conversion water supply system operational efficiency detection method based on Grey Incidence, mainly adopted frequency-conversion water supply system efficiency mathematical model.

A) pump shaft output power mathematical model

The water system sketch as shown in Figure 1, mainly comprises water intaking water source, non-return valve 1, pump motor M, air pressure tank 3, tensimeter 4, temperature sensor 5, outlet water control valve 2, inverter circuit 6, controller 7, the detection of power supply power input etc.Add thick line in Fig. 1 and mean power lead, the direction of arrow means the power direction of transfer.The water intaking water source is mainly tap water pipe network or deep-well, pool, rivers and lakes etc.; Non-return valve 1 major function is while preventing that water pump is out of service, the aqueous reflux backwater source in user's webmaster; Pump motor M carries the Zhong network of rivers, water source user by the impeller blade High Rotation Speed; The function of air pressure tank 3 is to stablize hydraulic pressure, prevents the harm of water hammer accident to pipe network; Temperature sensor 5 is for detection of the system Current Temperatures; Tensimeter 4 is for detection of the hydraulic pressure of water system; The power input pick-up unit is for detection of the power of input power; Outlet water control valve 2 is for opening or stopping supplying water to the user; Controller 7 is mainly realized the input of correlation parameter, the sampling of correlated variables, the demonstration of running status and the operation of system control program; The controlled quentity controlled variable that inverter circuit 6 sends by receiving controller, the inversion output to input power, realize the pump motor variable frequency regulating speed control; Input power 8 provides electric energy to whole system.

Variable declaration is as follows: q ₁(t) be inflow; q ₂(t) be aquifer yield; T (t) is ambient temperature value; The hydraulic pressure value that p (t) is pipe network; P _out(t) be the pump shaft output power; F (t) is the inverter circuit output frequency value; P _in(t) be the power supply power input; η is system effectiveness; v ₁(t) be air pressure tank air chamber volume; p _a(t) be the air pressure tank air chamber pressure; v ₂(t) be air pressure tank hydroecium volume; S is the air pressure tank sectional area; V _zfor the air pressure tank cumulative volume; P _bfor air pressure tank air chamber rated pressure value; V _bfor air pressure tank air chamber nominal volume; T _bfor the air pressure tank rated temperature; T is time variable; ρ is fluid density; G is acceleration of gravity.

During the water system stable state: force value is P, and the inverter circuit output frequency is F, and the Inlet and outlet water flow is Q, and environment temperature is T, and air pressure tank air chamber volume is V ₁, the hydroecium volume is V ₂, the air pressure tank air chamber pressure is p _a(0), the unit of above-mentioned all amounts is international unit.Definition t=0 is the last moment of system with frequency F stable operation constantly, exists:

$\left\{\begin{array}{c}{q}_1\left(0\right)=Q\\ q_2\left(0\right)=Q\\ f\left(0\right)=F\\ p_a\left(0\right)=P-\mathrm{\&rho;g}\frac{V_2}{S}\\ p\left(0\right)=P\\ v_1\left(0\right)=V_1\\ v_2\left(0\right)=V_2\\ T\left(0\right)=T\end{array}\right.$

Suppose at [0, T _d] running frequency of water pump is in the time: f (t)=F+ Δ F, Δ F is the frequency disturbance increment, T _dfor being greater than 0 time value, according to varying in size of water system power, artificially determine in advance; Hydraulic pressure value is p (t)=P+ Δ p (t), the water pressure fluctuations value that Δ p (t) causes for Δ F; The inflow of water pump is q ₁(t)=Q+ Δ q ₁(t), Δ q ₁(t) the flow of inlet water undulating quantity caused for Δ F; The aquifer yield of water pump is q ₂(t)=Q+ Δ q ₂(t), Δ q ₂(t) the water flow undulating quantity caused for Δ F; From University Of Chongqing's Master's thesis " research and design based on PLC tea place constant pressure spriukler irrigation control system ", the pass between water feeding of water pump flow, hydraulic pressure and motor running frequency is:

$\frac{q_1\left(t\right)p\left(t\right)}{\mathrm{\&eta;}}=\frac{m_1{k}_u^2\frac{R_2}{S}f{\left(t\right)}^2}{{(R_1+\frac{R_2}{S})}^2+{({\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">X</figure-callout>}}_{1\mathrm{\&sigma;}}+{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">X</figure-callout>}}_{2\mathrm{\&sigma;}})}^2}---\left(1\right)$

Wherein: the efficiency that η is water pump, the i.e. ratio of motor useful power and shaft power;

S is revolutional slip;

R ₁, R ₂, X _{1 σ}, X _{2 σ}, m ₁,

intrinsic parameter for pump motor;

Because pump motor adopts variable frequency regulating speed control, so s remains unchanged substantially.Order:

$\frac{m_1{k}_u^2\frac{R_2}{S}}{{(R_1+\frac{R_2}{S})}^2+{({\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">X</figure-callout>}}_{1\mathrm{\&sigma;}}+{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">X</figure-callout>}}_{2\mathrm{\&sigma;}})}^2}=k---\left(2\right)$

K is only relevant with the structural parameters of motor own, with flow, pressure independent.So formula can be reduced to:

$\frac{q_1\left(t\right)p\left(t\right)}{\mathrm{\&eta;}}=\mathrm{kf}{\left(t\right)}^2---\left(3\right)$

Make k '=η k., when t=0, have:

QP＝k′F ² (4)

At t ∈ [0, T _d], by q ₁(t)=Q+ Δ q ₁(t), f (t)=F+ Δ F and p (t)=P+ Δ p (t) substitution formula (3):

(Q+Δq ₁(t))(P+Δp(t))=k′(F+ΔF) ² (5)

Launch (5), and arrange:

PQ+QΔp(t)+PΔq ₁(t)+Δq ₁(t)Δp(t)＝k′(F ²+2FΔF+ΔF ²) (6)

(4) substitution (6) can be obtained:

QΔp(t)+PΔq ₁(t)+Δq ₁(t)Δp(t)＝k′(2FΔF+ΔF ²) (7)

Due to T _dless with the value of Δ F, and the mathematical model of water system contains the large inertial element of single order, thereby system aquifer yield q ₂(t) at t ∈ [0, T _d] change in the time very little, can be approximated to be constant, i.e. q ₂(t)=Q.Thereby at time [0, T _d] in, the value of the Δ p (t) that Δ F causes is less, so exist:

|Δp(t)|＜＜P (8)

So arranging (7) obtains:

QΔp(t)+PΔq ₁(t)＝k′(2FΔF+ΔF ²) (9)

Formula (9) can be obtained divided by (4):

$\frac{\mathrm{\&Delta;}{q}_1\left(t\right)}{Q}+\frac{\mathrm{\&Delta;p}\left(t\right)}{P}=\frac{2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2}{F^2}---\left(10\right)$

Air pressure tank kinetics equation: at t ∈ [0, T _d], the volume change of air pressure tank hydroecium is:

${\mathrm{\&Delta;v}}_2\left(t\right)={\&Integral;}_0^t(q_1\left(t\right)-q_2\left(t\right))\mathrm{dt}$

$={\&Integral;}_0^t(Q+\mathrm{\&Delta;}{q}_1\left(t\right)-Q)\mathrm{dt}---\left(11\right)$

$={\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}$

So, t ∈ [0, T _d] the hydroecium volume is:

$v_2\left(t\right)={\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">V</figure-callout>}}_2+{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}---\left(12\right)$

Because V remains unchanged, thereby the air chamber volume is:

$v_1\left(t\right)=V_1-{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}---\left(13\right)$

Suppose [0, the T at t ∈ _d] in the time, environment temperature T remains unchanged, from equation for ideal gases:

$\frac{p_a\left(t\right)}{p_a\left(0\right)}=\frac{V_1}{v_1\left(t\right)}---\left(14\right)$

(13) substitution (14) is obtained:

$\frac{p_a\left(t\right)-p_a\left(0\right)}{p_a\left(0\right)}=\frac{{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}{V_1-{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}---\left(15\right)$

Make △ p _a(t)=p _a(t)-p _a(0) be air pressure tank air chamber pressure variable quantity:

$\mathrm{\&Delta;}{p}_a\left(t\right)=\frac{p_a\left(0\right){\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}{V_1-{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}---\left(16\right)$

And the pressure variety caused by the hydroecium volume change is:

$\mathrm{\&Delta;}{p}_s\left(t\right)=\frac{\mathrm{\&rho;g}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}{S}---\left(17\right)$

So, the variation in water pressure amount

$\mathrm{\&Delta;p}\left(t\right)=\mathrm{\&Delta;}{p}_a\left(t\right)+\mathrm{\&Delta;}{p}_s\left(t\right)$

$=\frac{p_a\left(0\right){\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}{V_1-{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}+\frac{\mathrm{\&rho;g}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}}{S}---\left(18\right)$

If parameter T _dchoose rationally, meet

:

$\mathrm{\&Delta;p}\left(t\right)=\frac{p_a\left(0\right)+\mathrm{\&rho;g}\frac{V_1}{\mathrm{<figure-callout\; id="1"\; label="S\; V"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">S</figure-callout>}}}{V_{}}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}---\left(19\right)$

Will

substitution formula (19), and arrange:

$\mathrm{\&Delta;p}\left(t\right)=\frac{P-\mathrm{\&rho;g}\frac{V_2}{S}+\mathrm{\&rho;g}\frac{V_1}{\mathrm{<figure-callout\; id="1"\; label="S\; V"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">S</figure-callout>}}}{V_{}}{\&Integral;}_0^t{\mathrm{\&Delta;q}}_1\left(t\right)\mathrm{dt}---\left(20\right)$

By formula (20), can be obtained:

$\frac{P-\mathrm{\&rho;g}\frac{\mathrm{<figure-callout\; id="1"\; label="V\; S\; V"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">V</figure-callout>}}{S}}{V_{}}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}<\mathrm{\&Delta;p}\left(t\right)<\frac{P+\mathrm{\&rho;g}\frac{\mathrm{<figure-callout\; id="1"\; label="V\; S\; V"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">V</figure-callout>}}{S}}{V_{}}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}---\left(21\right)$

Wherein: V=V ₁+ V ₂.Due to

the hydraulic pressure produced corresponding to the air pressure tank vertical height, normally much smaller than actual lift (the constant pressure water supply lift is generally more than 14m), so

so have:

$\mathrm{\&Delta;p}\left(t\right)\&ap;\frac{\mathrm{<figure-callout\; id="1"\; label="P\; V"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">P</figure-callout>}}{V_{}}{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{dt}---\left(22\right)$

(22) substitution (10) arrangement can be obtained:

$\frac{\mathrm{\&Delta;}{q}_1\left(t\right)}{Q}+\frac{{\&Integral;}_0^t\mathrm{\&Delta;}{q}_1\left(t\right)\mathrm{<figure-callout\; id="1"\; label="dt\; V"\; filenames="HDA00003798550500011.png"\; state="\{\{state\}\}">dt</figure-callout>}}{V_{}}=\frac{2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2}{F^2}---\left(23\right)$

So equation (23) is about Δ q ₁(t) a Differential Equation with Constant Coefficients, can separate:

$\mathrm{\&Delta;}{q}_1\left(t\right)=\frac{Q(2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{F^2}{e}^{-\frac{Q}{V_1}t}---\left(24\right)$

Simultaneous formula (24) and (10) can obtain:

$\mathrm{\&Delta;p}\left(t\right)=\frac{P(2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{F^2}(1-e^{-\frac{Q}{V_1}t})---\left(25\right)$

Suppose that air pressure tank is without Leakage Gas, from equation for ideal gases:

$\frac{P_b\&times;V_b}{T_b}=\frac{P\&times;V_1}{T}---\left(26\right)$

Simultaneous formula (25) and (26), and arrange:

$\mathrm{\&Delta;p}\left(t\right)=\frac{P(2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{F^2}(1-e^{-\frac{\mathrm{QP}{T}_b}{P_b{V}_{b}T}t})---\left(27\right)$

Due to the pump shaft output power

substitution formula (27) also arranges:

$\frac{\mathrm{\&Delta;p}\left(t\right)}{P}=\frac{(2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{F^2}(1-e^{-\frac{P_{\mathrm{out}}{T}_b}{\mathrm{\&rho;g}{P}_b{V}_{b}T}t})---\left(28\right)$

By inequality (8), can be obtained, at t ∈ [0, T _d], the constraint condition that formula (28) is set up:

$\left|\frac{(2F\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{F^2}(1-e^{-\frac{P_{\mathrm{out}}{T}_b}{\mathrm{\&rho;g}{P}_b{V}_{b}T}t})\right|<<1---\left(29\right)$

Due to parameter P, F, Δ F, ρ, g, P _b, V _b, T _bbe observable quantity and known quantity with T, thereby pass through test pressure disturbance quantity Δ p (t) at t ∈ [0, T _d] value just can calculate the shaft power P of system when stable state _outsize.

B) frequency-conversion water supply system efficiency calculation

By parameter P, F, Δ F, ρ, g, P _b, V _b, T _b, T and Δ p (t) substitution formula (28) just can calculate the shaft power P of system when stable state _out.So efficiency eta is:

$\mathrm{\&eta;}=\frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}\&times;100\%---\left(30\right)$

The frequency-conversion water supply system efficiency eta can be tried to achieve in simultaneous (28) and (30).

The invention provides a kind of frequency-conversion water supply system operational efficiency online test method based on Grey Incidence, comprise the steps:

(1) with sampling period T _sfor being sampled in interval by hydraulic pressure value, inverter circuit output frequency and the power input of water system pipe network, sampled value is labeled as p (1), f (1) and P for the first time _in(1); Current sampling number is k, makes k=1;

(2) set up hydraulic pressure value array { p (i) }, the inverter circuit output frequency array { f (i) } formed by M element, and power input array { P _in(i) }; I={k-M+1 wherein, k-M+2 ... k}, M is the predefined positive integer that is greater than 1, k is current sampling number; P (i) | _i<=0=0, f (i) | _i<=0=0, P _in(i) | _i<=0=0;

(3) judge that whether water system is in steady state (SS).Steady state (SS) is defined as: the standard deviation of calculating M sampled pressure value p (t)

and the standard deviation of inverter circuit output frequency f (t)

judge whether to meet: σ simultaneously _p<ε _pand σ _f<ε _f(wherein: ε _p, ε _ffor set on the occasion of, can be set according to real system, such as getting 0.1 or 0.2).If meet, think that water system is in steady state (SS), enter step (4); Otherwise water system plays pendulum, proceed to step (13).

(4) solve hydraulic pressure mean value

inverter circuit output frequency mean value with power input mean value

(5) be designated as t=0 constantly with blaze now, give fixing Arbitrary Perturbation Δ F of output frequency,

(6) definition for t=mT _s(m=1,2 ..., N) moment shaft power estimated value, order

wherein

initial value for any shaft power estimated value of setting; For without loss of generality,

value is larger.N is defined as t _dfor predefined observation interval;

Make m=1; Definition second level lowest difference Δ (min)=0, the maximum poor Δ (max)=1 in the definition second level, definition resolution ratio γ=0.5.

(7) judgement mT _s>T _dwhether set up, if set up, proceed to step (13); Otherwise, at t=mT _sconstantly, sampling pipe network force value p (m); Obtain

(8) judgement

whether set up.Be false, proceed to step (13); Otherwise, by estimated value

and

, Δ F, T _b, ρ, g, P _b, V _b, T and t=mT _sthe substitution formula $\frac{\mathrm{\&Delta;}{p}^g\left(m\right)}{\stackrel{\&OverBar;}{P}}=\frac{(2\stackrel{\&OverBar;}{F}\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{{\stackrel{\&OverBar;}{F}}^2}(1-e^{-\frac{P_{\mathrm{out}}^g\left[m\right]T_b}{\mathrm{\&rho;g}{P}_b{V}_{b}T}t}),$ Obtain pressure surge estimated value Δ p ^g(m).

(9) using Δ p (m) as with reference to sequence, Δ p ^g(m) sequence as a comparison, and to Δ p (m), Δ p ^g(m) carry out normalized and obtain corresponding normalization sequence: Δ p ₁(m) and

(10) error of calculation sequence solve Δ p ₁(m), correlation coefficient ξ ₀(m), ${\mathrm{\&xi;}}_0\left(m\right)=\frac{\mathrm{\&Delta;}\left(\min \right)+\mathrm{\&gamma;\&Delta;}\left(\max \right)}{{\mathrm{\&Delta;}}_0\left(m\right)+\mathrm{\&gamma;\&Delta;}\left(\max \right)}.$

(11) solve degree of association r:

(wherein: ξ ₀(ψ) | _ψ<=0=0).

Judge whether r>=0.95 sets up.Set up, enter step (12); Otherwise, new variables more:

m＝m+1； $P_{\mathrm{out}}^g\left[m\right]=P_{\mathrm{out}}^g[m-1]+\frac{1}{r}\mathrm{sgn}\left(\mathrm{\&Delta;p}\right[(m-1)]-\mathrm{\&Delta;}{p}^g[(m-1)\left]\right),$ Enter step (7).

(12) estimated value

be exactly system actual axle output power P _out.Computing system efficiency:

judge whether actual output efficiency meets η<=η _min(wherein: η _minfor the inefficient threshold value of setting, can be set according to real system, such as being set as 30% or 40% etc.).If so, illustrative system is in inefficient duty, and inverter output is closed, and exits.Otherwise, enter step (13).

(13) make k=k+1; After this sampling period finishes, sample, and the sampled value of mark hydraulic pressure value, inverter circuit output frequency and power input is p (k), f (k) and P next time _in(k); Return to step (2).

Claims (2)

1. the frequency-conversion water supply system operational efficiency online test method based on Grey Incidence, is characterized in that, comprises the steps:

(1) with sampling period T _sfor being sampled in interval by hydraulic pressure value, inverter circuit output frequency and the power input of water system pipe network, sampled value is labeled as p (1), f (1) and P for the first time _in(1); Current sampling number is k, makes k=1;

(2) set up hydraulic pressure value array { p (i) }, the inverter circuit output frequency array { f (i) } formed by M element, and power input array { P _in(i) }; I={k-M+1 wherein, k-M+2 ... k}, M is the predefined positive integer that is greater than 1, k is current sampling number; P (i) | _i<=0=0, f (i) | _i<=0=0, P _in(i) | _i<=0=0;

(3) judge that whether water system is in steady state (SS); If so, enter step (4); Otherwise, proceed to step (13);

(4) solve hydraulic pressure mean value

inverter circuit output frequency mean value $\stackrel{\&OverBar;}{F}=\frac{1}{M}\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}f\left(i\right)$ With power input mean value $\stackrel{\&OverBar;}{P_{\mathrm{in}}}=\frac{1}{M}\underset{i=k-M+1}{\overset{k}{\mathrm{\&Sigma;}}}{P}_{\mathrm{in}}\left(i\right);$

(5) the mark current time is the t=0 moment, gives fixing Arbitrary Perturbation Δ F of output frequency;

(6) definition

for t=mT _sshaft power estimated value constantly; M=1 wherein, 2 ..., N,

t _dfor predefined observation interval; Order

wherein

initial value for any shaft power estimated value of setting;

Make m=1, second level lowest difference Δ (min)=0, the maximum poor Δ (max)=1 in the second level, resolution ratio γ=0.5;

(7) judgement mT _s>T _dwhether set up, if set up, proceed to step (13); Otherwise, at t=mT _sconstantly, sampling pipe network force value p (m); Obtain

(8) judgement whether set up, if be false, proceed to step (13); Otherwise, by estimated value

and

Δ F, T _b, ρ, g, P _b, V _b, T and t=mT _sthe substitution formula $\frac{\mathrm{\&Delta;}{p}^g\left(m\right)}{\stackrel{\&OverBar;}{P}}=\frac{(2\stackrel{\&OverBar;}{F}\&times;\mathrm{\&Delta;F}+\mathrm{\&Delta;}{F}^2)}{{\stackrel{\&OverBar;}{F}}^2}(1-e^{-\frac{P_{\mathrm{out}}^g\left[m\right]T_b}{\mathrm{\&rho;g}{P}_b{V}_{b}T}t}),$ Obtain pressure surge estimated value Δ p ^g(m);

Wherein, P _bfor water system air pressure tank rated pressure value, V _bfor water system air pressure tank air chamber nominal volume, T _bfor water system air pressure tank rated temperature; T is environment temperature, and ρ is fluid density; G is acceleration of gravity;

(9) using Δ p (m) as with reference to sequence, Δ p ^g(m) sequence as a comparison, and to Δ p (m), Δ p ^g(m) carry out normalized and obtain corresponding normalization sequence Δ p ₁(m) and

(10) error of calculation sequence

solve Δ p ₁(m),

correlation coefficient ${\mathrm{\&xi;}}_0\left(m\right)=\frac{\mathrm{\&Delta;}\left(\min \right)+\mathrm{\&gamma;\&Delta;}\left(\max \right)}{{\mathrm{\&Delta;}}_0\left(m\right)+\mathrm{\&gamma;\&Delta;}\left(\max \right)};$

(11) solve degree of association r,

ξ wherein ₀(ψ) | _ψ<=0=0;

Judge whether r>=0.95 sets up, if set up, enter step (12); Otherwise more new variables, make

m＝m+1； $P_{\mathrm{out}}^g\left[m\right]=P_{\mathrm{out}}^g[m-1]+\frac{1}{r}\mathrm{sgn}\left(\mathrm{\&Delta;p}\right[(m-1)]-\mathrm{\&Delta;}{p}^g[(m-1)\left]\right),$ Enter step (7);

(12) order

computing system efficiency

judge whether to meet η<=η _min, η wherein _minfor predefined inefficient threshold value; If so, illustrative system is in inefficient duty, and inverter output is closed, and exits; Otherwise, enter step (13);

(13) make k=k+1; After this sampling period finishes, sample, and the sampled value of mark hydraulic pressure value, inverter circuit output frequency and power input is p (k), f (k) and P next time _in(k); Return to step (2).

2. the frequency-conversion water supply system operational efficiency online test method based on Grey Incidence according to claim 1, is characterized in that, described steady state (SS) is defined as:

Calculate the standard deviation of array { p (i) }

and the standard deviation of array { f (i) }

judge whether to meet: σ simultaneously _p<ε _pand σ _f<ε _f, wherein: ε _pand ε _ffor predefined on the occasion of; If meet, think that water system is in steady state (SS), otherwise, think that water system plays pendulum.

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