Calculation method of line power loss

Abstract

The present invention discloses a method for calculating line power loss, comprising the steps of: S1. constructing a distributed parameter transmission line model; S2. regarding the transmission line as being composed of a plurality of micro-elements cascaded and superimposed, and calculating the resistance active power loss and the conductance active power loss of any micro-element based on the distributed parameter transmission line model; S3. superimposing the resistance active power losses of all micro-elements to obtain the active power loss on the resistance of the transmission line; superimposing the conductance active power losses of all micro-elements to obtain the active power loss on the conductance of the transmission line. The present invention can eliminate the influence of time asynchronism caused by calculating line loss through voltage and current at both ends, and effectively distinguish the two types of losses, so that the calculation accuracy is further improved.

Description

Technical Field

[0001] The invention relates to the field of power distribution networks, and in particular to a method for calculating line power loss. Background Art

[0002] Line power loss is used in many aspects of the power system, so it puts higher requirements on the accuracy of loss calculation. The traditional line loss calculation method is a simple and rough calculation. In the calculation of cable current carrying capacity, only the load current is used to calculate the cable core heating loss, and the rated voltage is used to calculate the unit dielectric loss. The load current and rated voltage cannot reflect the line current and ground voltage under the actual operation of the cable; in the calculation of power grid line loss rate, the traditional line loss calculation uses different methods to obtain equivalent current, or obtains the power loss on the line through equivalent impedance. This method uses approximate treatment of current I and resistance R, and ignores the influence of ground conductivity, making it difficult to obtain accurate calculation results.

[0003] The power loss of the line can be accurately obtained by measuring the power at both ends of the line and subtracting them. However, since it is difficult to ensure synchronous acquisition in practice, there is a certain time difference and the measured data cannot be used directly. Moreover, this method can only obtain the total power loss of the line and cannot distinguish between the power loss generated by resistance and the power loss generated by conductance. Summary of the invention

[0004] In view of this, the purpose of the present invention is to overcome the defects in the prior art and provide a method for calculating line power loss, which can eliminate the influence of time asynchrony caused by calculating line loss through voltage and current at both ends, and effectively distinguish between the two types of losses, so as to further improve the calculation accuracy.

[0005] The method for calculating line power loss of the present invention comprises the following steps:

[0006] S1. Construct a distributed parameter transmission line model:

[0007]

[0008] Among them, u N (t) is the port voltage at the N end, u M (t) is the port voltage at the M terminal, i M is the port current at the M end, R is the line unit resistance, L is the line unit inductance, C is the line unit capacitance, G is the line unit ground conductance, M is the line port, j is the capacitor order, A(j) is the voltage-voltage residual of the capacitor order j, B(j) is the voltage-current residual of the capacitor order j, and t is the calculation time;

[0009] S2. The transmission line is regarded as a cascade of several micro-elements, and the resistance active power loss and the conductance active power loss of any micro-element are calculated based on the distributed parameter transmission line model;

[0010] S3. The resistance active power losses of all micro-elements are added together to obtain the active power loss on the resistance of the transmission line; the conductance active power losses of all micro-elements are added together to obtain the active power loss on the conductance of the transmission line.

[0011] Furthermore, the active power loss on the transmission line resistance is determined according to the following formula:

[0012]

[0013]

[0014] Among them, R is the unit resistance of the line, Δx is the length of any microelement, i M is the port current, l is the line length, L is the line unit inductance, C is the line unit capacitance, G is the line unit ground conductance, M is the line port, j is the capacitance order, p is the coefficient, i is the order, r is the order, T 2j-1 = Δx 2j-1 The coefficient of 2j = Δx 2j The coefficient of 2(p-j+1)-1 = Δx 2(p -j+1)-1 The coefficient of 2(p-j) = Δx 2(p-j) The coefficient of , t is the calculation time.

[0015] Furthermore, the active power loss on the transmission line conductance is determined according to the following formula:

[0016]

[0017]

[0018] Among them, R is the unit resistance of the line, Δx is the length of any microelement, i M is the port current, l is the line length, L is the line unit inductance, C is the line unit capacitance, G is the line unit ground conductance, M is the line port, j is the capacitance order, p is the coefficient, i is the order, r is the order, H 2j-1 = Δx 2j-1 The coefficient of H 2j = Δx 2j The coefficient of H 2(p-j+1)-1 = Δx 2(p -j+1)-1 The coefficient of H 2(p-j) = Δx 2(p-j)The coefficient of , t is the calculation time.

[0019] Furthermore, it also includes judging whether there is electricity theft and abnormal meter on the line according to the power balance at both ends of each line. When the calculated power of the user line is in an unbalanced state, the power imbalance point is found by calculating the instantaneous phase consistency of the voltage and current on the transition resistance to determine the electricity theft behavior before the meter.

[0020] The beneficial effects of the present invention are as follows: the present invention discloses a method for calculating line power loss, which eliminates the error caused by treating distributed resistance as concentrated resistance by using the idea of ​​"road" instead of the equivalent circuit adopted by the centralized parameter model, and is closer to the operation of the actual line than other methods. The power loss of the entire line can be calculated by using only the voltage and current at one end, eliminating the influence of time asynchrony caused by calculating line loss by using the voltage and current at both ends. At the same time, the factor of conductivity loss, which is often ignored in general line loss calculation, is taken into account, and the two types of losses are effectively distinguished, so that the calculation accuracy is further improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0022] Figure 1 It is a schematic diagram of a single-phase line microelement circuit model of the present invention;

[0023] Figure 2 It is a schematic diagram of the single-phase line micro-element model of the present invention. DETAILED DESCRIPTION

[0024] The present invention is further described below in conjunction with the accompanying drawings, as shown in the drawings:

[0025] The method for calculating line power loss of the present invention comprises the following steps:

[0026] S1. Construct a distributed parameter transmission line model:

[0027]

[0028] Among them, u N (t) is the port voltage at the N end, u M (t) is the port voltage at the M terminal, i M is the port current at the M end, R is the line unit resistance, L is the line unit inductance, C is the line unit capacitance, G is the line unit ground conductance, M is the line port, j is the capacitor order, A(j) is the voltage-voltage residual of the capacitor order j, B(j) is the voltage-current residual of the capacitor order j, and t is the calculation time;

[0029] S2. The transmission line is regarded as a cascade of several micro-elements, and the resistance active power loss and the conductance active power loss of any micro-element are calculated based on the distributed parameter transmission line model;

[0030] S3. The resistance active power losses of all micro-elements are added together to obtain the active power loss on the resistance of the transmission line; the conductance active power losses of all micro-elements are added together to obtain the active power loss on the conductance of the transmission line.

[0031] In this embodiment, the line model established in consideration of the distributed parameter characteristics of the transmission line is called a distributed parameter transmission line model, which can be regarded as a cascade of countless microelements. The distribution characteristics of the line refer to the fact that the current and potential at any point on the line and its adjacent point are not equal at any time when the line is running. Therefore, the current and voltage in the distributed parameter line are not only functions of time t, but also functions of the spatial coordinate x. For actual transmission lines, all electrical parameters on the line have distribution characteristics.

[0032] like Figure 1 In the single-phase line microelement circuit model shown, M is the line head, N is the line end, l is the line length (km), and the distance from any point on the line to the M end is x. R, L, C, and G are the line unit resistance (Ω / km), unit inductance (H / km), unit capacitance (F / km), and D unit conductance (S / km), respectively. At this time, R, L, C, and G are evenly distributed along the transmission line.

[0033] The distributed parameter transmission line model is constructed according to the following method:

[0034] For a microelement at any point on the line, Kirchhoff's principle gives:

[0035]

[0036] Now divide the MN line into n equal parts, that is, u N =u n , according to the infinitesimal equations (1), (u(x+Δx), i(x+Δx)) is a function of (u(x), i(x)) and its derivatives of various orders (u(x)', i(x)', u(x)", i(x)"...). Then the information of the N-end can be repeatedly deduced from the M-end endpoints through the relational expressions between the inlet and outlet of each infinitesimal element, and the relationship is as follows:

[0037]

[0038] The spatial relationship between point n and the previous point n-1 is as follows:

[0039]

[0040] By repeatedly recursively deducing formula (3) and eliminating the intermediate terms, we can obtain the voltage and current expressions of the line distributed parameter circuit model:

[0041]

[0042] Where: P n ,Q n They are polynomials of various orders regarding R, L, C, G, n, and Δx respectively.

[0043] The current and voltage of the (n-1)th microelement segment are derived as follows:

[0044]

[0045] In the above formula (5), P n (△x r ) indicates that in P n The polynomial expression of degree r containing △x, Q n (△x r ) indicates that in Q n The polynomial expression of degree r containing △x, where (r=0,1,2,3…), and P n (△x 0 )=0,Q n (△x 0 )=0.

[0046] According to (3), (4) and (5), we can deduce:

[0047]

[0048]

[0049] Since Qn does not contain the constant term Qn(△x0), we can get from formula (7):

[0050] P n (Δx)=0 (8)

[0051] Then according to formula (7) and P n (Δx) = 0,

[0052]

[0053] Therefore, by the method of undetermined coefficients, we can obtain:

[0054]

[0055] Similarly, the expressions of Pn(△x3), Qn(△x4), Pn(△x5), Qn(△x6), Pn(△x7) and Qn(△x8)... can be derived successively. Therefore, the expressions of Qn(△x), Pn(△x2), Qn(△x3), Pn(△x4), Qn(△x5), Pn(△x6)... can also be derived. The distributed parameter transmission line model summarized by mathematical induction is as follows:

[0056]

[0057] In this embodiment, based on the equation (11) corresponding to the above distributed parameter transmission line model, let:

[0058]

[0059] For any xth infinitesimal element in a line of length l, then

[0060]

[0061] Theoretically, if the voltage and current at one end of the line are known (u M (t), i M (t) or u N (t), i N (t)), the voltage u at any point on the line can be obtained using formula (14) x (t) and current i x (t), when x = n, because n → ∞, the voltage and current at the other end of the line can be obtained. The derivation of this model is based on the idea of ​​circuit theory rather than wave theory, but it is consistent with wave theory. Taking into account the distributed parameter characteristics of the line, the model is extremely accurate.

[0062] Theoretical description of uniform transmission line: a transmission line is considered to be composed of countless micro-elements cascaded together, such as Figure 2 As shown. For any infinitesimal element Δx, the active power loss of the resistor ΔP R =i 2 (x, t)RΔx, the active power loss per unit conductance is ΔP G =u 2 (x+Δx,t)GΔx.

[0063] Because the electromagnetic field is formed very quickly, approximately equal to the speed of light, the time difference can be ignored, that is, at any time t, the active power loss on the resistor R in the transmission line is the active power ΔP of all micro-resistances R The active power loss on the conductance is the active power ΔP of all infinitesimal conductances. GIn steady state, this method can derive the expression of instantaneous power p(t) of any phase. Using the instantaneous power and three-phase power formula, the expression of active power in three-phase transmission and distribution lines can be derived.

[0064] The line active loss obtained by this method is not only much more accurate than the general method of calculating line loss, but also can accurately identify the active loss on resistance and the active loss on conductivity.

[0065] For the n-element single-phase line model, we get:

[0066]

[0067] so:

[0068]

[0069] Formula (16) is derived by taking the common factors B(j) and the square of B(j). For example, the idea of ​​summing the superposition limit is used to derive the above formula. For the convenience of derivation, B(j) and the square of B(j) are summed separately, and the formula is

[0070]

[0071] ①Derivation of C(j):

[0072] Expand formula (15)

[0073]

[0074] After the expansion of equation (17), it is actually the sum of the (2j)th order polynomial of Δx and the (2j+1)th order polynomial of the first (n-1) terms, Δx 2j-1 The product of the (2j-1) term in the coefficients of is actually a (2j-1)-order polynomial of n, Δx 21 The product of the 2j terms in the coefficients is actually a 2j-order polynomial of n, using the combination number formula:

[0075]

[0076] The formula for the number of combinations is

[0077]

[0078] At the same time, because nΔx=l, l is the total length of the line, when the uniform transmission line is composed of an infinite number of concentrated parameter circuit elements cascaded, Δx→0, n→∞, then

[0079]

[0080] Therefore, substitute formula (19) and formula (20) into formula (18):

[0081]

[0082] ②Derivation of D(j):

[0083] From formula (15) and (16), we can get

[0084]

[0085] Expand formula (16) to include Δx p The expression of p = 2, 3, 4…, 4(n-1), where any coefficient has a p-order polynomial containing n-1() because after the square expansion of B(j), the lowest order value of Δx is p = 4j-2, and the highest order value is p = 4j, (∑B(j)) 2 In the expanded set, the lowest order value of Δx is p = 2, the highest order value is p = 4j, and Δx 2j-1 and Δx 2j The coefficient T 2j-1 and T 2j Any term Δx in the set with the same coefficient p The coefficient of T a T b , p=a+b, p is any combination of any two sums of 1, 2, ..., (2j-1), (2j). Continuing the derivation, we get

[0086]

[0087] According to the high-order polynomial summation formula (20) and formula (23)

[0088]

[0089] Among them, p1, p2, ... pk, a1, a2, ... ak-1, t1, t2, ... tk+1 are arbitrary constants. So

[0090]

[0091] Combining formulas (15), (21) and (25), the active power loss of the line considering the distributed characteristic resistance is:

[0092]

[0093]

[0094] Among them, R is the unit resistance of the line, Δx is the length of any microelement, i Mis the port current, l is the line length, L is the line unit inductance, C is the line unit capacitance, G is the line unit ground conductance, M is the line port, j is the capacitance order, p is the coefficient, i is the order, r is the order, T 2j-1 = Δx 2j-1 The coefficient of 2j = Δx 2j The coefficient of 2(p-j+1)-1 = Δx 2(p -j+1)-1 The coefficient of 2(p-j) = Δx 2(p-j) The coefficient of , t is the calculation time;

[0095] The power loss of the line considering the distributed conductance is the same as the derivation principle of the resistance. According to the single-phase line model with n infinitesimal elements, p G1 (t)=[u 1 (t)] 2 GΔx,p G2 (t)=[u 2 (t)] 2 GΔx,……,p Gn (t)=[u n (t)] 2 GΔx, so p G (t) = p G1 (t)+p G2 (t)+……+p Gn (t),

[0096] From formula (13), we can know

[0097]

[0098] Right now

[0099]

[0100]

[0101]

[0102] so

[0103]

[0104] Formula (31) is extracted with the common factors A(j) and the square of A(j). The above formula is derived by using the idea of ​​summing the superposition limit. Let

[0105]

[0106] ①Derivation of C(j):

[0107] Expand formula (33)

[0108]

[0109] The expanded form of formula (34) is the sum of the first n terms of the (2j)th order polynomial and the (2j+1)th order polynomial of n. Using the combination number formula (18), its expansion formula (19) and the uniform transmission line cascaded by infinite number of lumped parameter circuit elements formula (21), we can get

[0110]

[0111] ②Derivation of D(j):

[0112]

[0113] Expand formula (35) to include Δx p The expression of p = 2, 3, 4…, 4n-2, any of which has a polynomial of order p containing n, then

[0114]

[0115] According to the high-order polynomial summation formula and formula (14),

[0116]

[0117] Combining formulas (32), (35) and (38), the active power loss of the line considering the distributed characteristic conductance is:

[0118]

[0119]

[0120] Among them, R is the unit resistance of the line, Δx is the length of any microelement, i M is the port current, l is the line length, L is the line unit inductance, C is the line unit capacitance, G is the line unit ground conductance, M is the line port, j is the capacitance order, p is the coefficient, i is the order, r is the order, H 2j-1 = Δx 2j-1 The coefficient of H 2j = Δx 2j The coefficient of H 2(p-j+1)-1 = Δx 2(p -j+1)-1 The coefficient of H 2(p-j) = Δx 2(p-j) The coefficient of , t is the calculation time;

[0121] Therefore, if the voltage and current uM(t) and iM(t) at the line head M are known, the time domain expression of the active power loss on the resistance R and the conductance G can be obtained using formulas (26) and (39). The superposition of the two terms is the time domain expression of the active power loss on the transmission line. That is, if the voltage and current at any end of the line (M or N) are known, the power loss of the entire line can be calculated.

[0122] In this embodiment, the power supply and power consumption recorded by the main meter, the dedicated transformer user power meter and the substation power meter in the distribution network are the data sources for calculating the 10kV line loss or line loss rate. If an electric meter is abnormal or the user steals electricity beyond the meter, the calculated value of the line loss cannot reflect the actual situation. If the line loss rate deviation is not significant, it is difficult to find abnormal meters or electricity theft. In addition to errors in measurement, calculation, and time stamping caused by aging components, meter abnormalities may also be caused by users privately modifying or interfering with the meter to steal electricity.

[0123] The power balance at both ends of each line can be used to determine whether there is electricity theft and abnormal metering on the line. When the calculated power of the user line is in an unbalanced state, the power imbalance point is found by calculating the instantaneous phase consistency of the voltage and current on the transition resistor to determine the electricity theft before the meter.

[0124] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A method for calculating line power loss, Features: The steps include: S1. Construct a distributed parameter transmission line model: Among them, u N is the port voltage at the N terminal, u M is the port voltage at the M terminal, i M is the port current at the M end, R is the line unit resistance, L is the line unit inductance, C is the line unit capacitance, G is the line unit ground conductance, M is the line port, j is the capacitor order, A(j) is the voltage residual of the capacitor order j, B(j) is the current residual of the capacitor order j, and t is the calculation time; M is the beginning of the line, N is the end of the line, i N is the port current at the N end, Δx is a microelement length at any point on the line, and divides the MN line into n equal parts; S2. The transmission line is regarded as a cascade of several micro-elements, and the resistance active power loss and the conductance active power loss of any micro-element are calculated based on the distributed parameter transmission line model; S3. The resistance active power losses of all micro-elements are added together to obtain the active power loss on the resistance of the transmission line; the conductance active power losses of all micro-elements are added together to obtain the active power loss on the conductance of the transmission line.

2. The method for calculating line power loss according to claim 1, Features: The active power loss on the transmission line resistance is determined according to the following formula: Where l is the line length, j is the capacitor order, p is the coefficient, i is the order, r is the order, T 2j-1 = Δx 2j-1 The coefficient of 2j = Δx 2j The coefficient of 2(p-j+1)-1 = Δx 2(p-j+1)-1 The coefficient of 2(p-j) = Δx 2(p-j) The coefficient of .

3. The method for calculating line power loss according to claim 1, Features: The active power loss on the transmission line conductance is determined according to the following formula: Where l is the line length, j is the capacitor order, p is the coefficient, i is the order, r is the order, H 2j-1 = Δx 2j-1 The coefficient of H 2j = Δx 2j The coefficient of H 2(p-j+1)-1 = Δx 2(p-j+1)-1 The coefficient of H 2(p-j) = Δx 2(p-j) The coefficient of .

4. The method for calculating line power loss according to claim 1, Features: It also includes judging whether there is electricity theft and abnormal metering on the line based on the power balance at both ends of each line. When the calculated power of the user line is in an unbalanced state, the power imbalance point is found by calculating the instantaneous phase consistency of the voltage and current on the transition resistance to determine the electricity theft behavior before the meter.

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