JPH02136034A - Optimal power load distribution system by neural network - Google Patents

Abstract

PURPOSE:To realize the optimal power load distribution by using a Hopfield network being one of models of a neural network. CONSTITUTION:A load D, a transmission loss L, the maximum and minimum outputs Ui, li of a generator, and a generating cost Ci are inputted to an electric system model condition input part 11. Then, a model for causing the inputted value to correspond to the energy E of a Hopfield network is set in a simulation model setter 12 on the basis of said inputted value. After that, the simulation by the Hopfield network for obtaining the solution of the optimal load distribution corresponding to the minimum value of said energy E is executed in a simulation model execution and control part 13. When said optimal load distribution is obtained, values, which respective generators should output, are outputted from a simulation result output part 14. The output value of each generator is controlled according to said result so that the optimal (the lowest cost) power generation is realized for said load.

Description

[Detailed Description of the Invention] [Summary] The present invention uses a neural network to allocate generator output to loads at the lowest cost in a power system in which a large number of generators and loads are connected via power transmission lines. Concerning an optimal power load distribution system.

[Industrial Application Fields] Electric power is generated by a generator, transmitted to a consumption area via a power transmission line (via a substation), and supplied to a load for consumption. In that case, the output of the generator is adjusted according to the power demand (load) to prevent wasteful power generation and control to prevent shortages.

In such cases, multiple generators are interconnected by power transmission lines and power is supplied to customers in a wide range of regions, and various types of generators are used, each with a generating capacity of 2. There are different types installed depending on cost etc.

Optimal load distribution for the cost of electricity means that a power system network that has many generators with different generation costs and distances from consumption points is configured so that each generator is The purpose is to determine the output of

There are not only differences in power generation such as thermal power, hydropower, and nuclear power, but also
Even in the same type of thermal power generation, the type of fuel is not the same, and each generator has different characteristics such as maximum output and minimum output, and power generation cost is one of such attributes, and in general, the cost per unit output is It varies depending on the generator, and even depending on the output of the same generator. In the IT power line, generators having such various characteristics coexist. Furthermore, even if a generator has a low power generation cost, if it is located far from the consumption area, losses during power transmission will increase and the overall cost may rise. Therefore, the problem of optimal power load distribution is how to adjust the output of each generator in the system to satisfy a given load at the lowest overall cost.

[Conventional technology] Conventionally, there was a method of performing numerical calculations using a computer to perform optimal load distribution for electric power, but now a model for power generation, transmission, and load is set and the optimal power distribution for the load is calculated. In order to do so, there are many parameters that must be considered as described above, and they are interrelated in a complex manner, so even if calculations are performed using a computer, it takes time. It has been difficult to perform load distribution that is cost effective.

[Problem to be solved by the invention] As mentioned above, in the conventional method, it takes time to perform the calculations to perform the optimal load distribution of electric power, and if the calculations are accelerated, the accuracy deteriorates and it is difficult to achieve the optimal distribution. There was a problem that.

An object of the present invention is to provide an optimal power load distribution system that can obtain highly accurate results at high speed.

[Means for Solving the Problems] The present invention performs optimal power load distribution using a Hopfield network, which is one of the neural network models.

The principle for realizing the optimal power load distribution system of the present invention using a Hopfield network will be explained below.

Generally, the cost of a thermal power generator is expressed by the following formula.

C=a P” +b P+c (1) However, P is the generator output, and a, b, and C are constants that depend on each generator.

[Properties of the Hopfield model] As shown in Figure 5, the Hopfield model is a neural network that has a bidirectional connection structure between all neurons.In principle, each neuron is connected to all other neurons, Each is a multi-input, -output element. Each neuron i has an input ■1 and a connection weight Til
It is connected to the input (2) by a weight Ti2, and similarly connected to the input Vi by Tii, and processes a plurality of inputs according to the internal state value U to generate an output value Vi.

As shown in Fig. 5, each neuron i has two types of numerical attributes: an internal state value Ui and an output 4fiVi, and it continuously changes over time depending on the output values of all other neurons as follows. Change.

d U i / d t-ΣjTijVj +Ii
・---(2) Vi = g i (Ui) −
−−・−−−(3) However, Tij is from neuron j to i
The weight of the connection (or connection) to, gi, is the input/output function of neuron i, and Ii is a constant.

Energy E is defined as an index representing the state of the Hopfield network as follows.

E = -1/2 gi Σj TijViVj
-gil l1Vi - (4) It is known that a major feature of the Hopfield network is that the energy E converges to a local minimum value as follows.

dE/dt = d/dt(-1/2Σi Σj Tij
ViVj−Σ1liVi) =−1/2Σl Σj Tij (Vj(dVi/d
t)+Vi(dVj/dt) l-gi ll(dVi
/dt)=-1/2Σi dVi/dt (Σj
(TijVj+Tj 1Vj)+2 1i 1 =-1/2Σi dVi/dt (2Σj TijVj
+21i)=-gi dVi/dt (Σj TijV
j+l1l-1Σ1(dVi/dt) (dUi/dt
)--gi(d(gi(Ui))/dt)(dUi/
dt) - Σi gi' (Di) (dUi/dt)"
Here, if gi (Lli) is a monotonically increasing function, then gi
'(LII)≧0. Therefore, the following formula holds.

dE/dL≦0 −・・−・−−−−(5) That is,
E is simple t) [less. On the other hand, the output value V of each neuron
If i is a public domain, E is bounded below by definition, so E converges to its minimum point.

Normally, the following sigmoid (S-shaped) function is used as the input/output function gi so that the output value of the neuron takes a value from 0 to 1.

gi([14)=1/2(1+tanh(old/u,))
--------(6) Here, uo is a constant.

As shown in FIG. 6, this function satisfies both the monotonically increasing property and the official property of Vi, so the energy E converges to a minimum value.

[Numerical expression]

Most pump field network systems utilize the fact that the output value of the neuron ultimately converges to O or 1, but in order to be applicable to power distribution, the neuron must have an arbitrary real value as the final output value. By using a network that can take numerical values, a large numerical value can be expressed with a single neuron. The possibilities of this method are explained below.

First, energy E can be expressed for any neuron k as follows.

E = -1/2Σi Σj Tij Vi Vj
-gi Ii Vi=-1/2 Tkk Vk”
-(Σ j≠k Tkj VjLIk)Vk-1/2Σ
ink Σ jf−k TijViVj−Σ i≠
kIiVi=-1/27kk(Vk+(Σ j -I-
k TkjVj+Ik)/Tkk)”1/2 Σj
≠kvj (Σj ≠k Tij Vj+ 21i)
+(Σj≠k Tkj VJ + Ik)2/2Tk
k ----(7) Therefore, the relationship between the energy E and the output value Vk to the neuron when the output value Vj (j≠k) of all neurons other than the neuron is fixed, and the relationship between the energy E and the minimum value It can be seen from equation (7) that the relationship between the VkO values when

In Figure 7, α=-(Σj ≠k Tkj Vj+
Ik) β-α/Tkk, and fl and ul represent the lower limit and upper limit of the value of the input/output function gk (Uk), respectively. If there is no upper or lower limit (e.g. 11=-■, U1
=+■) means ff1l and ul in the minimum value column means divergence. For example, for a sigmoid function between 0 and 1, 11-
0, ul=1.

According to Figure 7, if Tkk <Q, then the energy curve on the E<Vk plane is a concave quadratic curve, and since the energy E converges to its minimum value with time, the input/output function gk to the neuron is Even if we do not guarantee the officialness of , the neural network converges to its official minimum. Therefore, as an input/output function, exp(t
l), exp("7Ll), etc. (value range is O to ■), any positive number can be expressed by the output value of the neuron.

In order to perform a simulation to determine the output of each generator that satisfies the load at a certain point in time with the minimum cost, we first create an electric power system with generators and load points at multiple nodes as shown in Figure 8. Assume something.

[Principle of simulation]

First, as a power system model, a plurality of nodes are connected by power transmission lines as shown in FIG. 8, and each node has a power station 1, 2, etc.
Assume a configuration in which . . . i and loads, , L, .

Next, as constraints on this power system, ■total output,■
The method for formulating maximum output, minimum output, and minimum cost will be explained below.

■If the total output load is calculated and the power transmission loss is L, equation (8) must be satisfied.

D+L−ΣtPt ·−·−(B) However, Pi represents the output of generator i.

In the system shown in Figure 8, the power transmission loss can be expressed as follows.

L; ΣJRj (Σiαij P i)” −・−(
9) However, Rj represents the resistance value of each part of the network (power transmission line) j, and αij represents a constant determined from the impedance of each branch. From equations (8) and (9), the following equation is obtained.

D0Σj Rj (gi α1jPi)” =Σi P
1-(10) ■ Maximum output and minimum ratio crab The output Pi of each power generation Iai is the minimum output li and the maximum output u
i, subject to the following constraints.

iI≦Pi≦u i −−−−−−−−−(11) ■Minimum cost: If the power generation cost of generator i is C1, gi Ci −
+ min −−−−−−−−−(12) (min is the minimum value), and this formula is
) from Σ1(aiPi” +biPi+ci) −+m i
n---(13) However, ai, bi, and ci are constants determined depending on the generator i.

Next, a method of expressing the above constraints as constraints in Hopfield's work will be described.

First, if the output Pi of each generator i is represented by the output value Vi of the neuron i, each of the above constraints is expressed as follows.

(2) By simply converting P→V from the total output formula (lO), it can be replaced with the constraint condition as shown in the following formula.

(D+ΣjRj(gi α1jVi)”−Σ1Vi)2
→ min −1・−(10') In order to solve an optimization problem using a Hompfield network, the constraint conditions of the problem must be associated with the energy range of the network and the energy scale reduction function of the network can be used. to find the optimal solution to the problem. However, since the left side of equation (10') is a quartic equation, the energy E of the Hopfield model
(quadratic expression of Vi) cannot be made.

By the way, in reality, the power transmission loss is quite small compared to the total load, so the power transmission loss is ignored and assumed to be L-0), and the following constraint conditions are used to determine the constraint conditions.

(D−ΣtV i)” −+min
(14) Instead of formula (10''), the output value Vi is once obtained under the constraint condition of formula (14), and the power transmission loss L'' for that output is calculated from formula (9). Next, the output Vi is calculated again using the following equation, which is a modification of equation (8).

(D+L' -Σ1Vi)2-+ min -(8
°) From this Vt, calculate the power transmission loss °'' again from (9) 2. Repeat this until the difference between L' and '' becomes negligibly small (the value of L is extremely small compared to the total load). (because the number of repetitions is small), the output value Vi under this constraint can be obtained.

■Maximum output and minimum output There are ways to express inequalities in Honbfield network using Slanok variables, but in the present invention, the output Pi of each generator i is expressed by the output value of one neuron, and each neuron The input/output function gi is a sigmoid function, and the lower limit is the maximum output ui and the minimum output 1 of the generator.
This constraint condition is expressed by setting it to 1.

gi(ui) = (ui −1i) (1+ tan
h (to Di 8))/2+Ai-・-・−−−−1−−
・----1--・----(15) Here, uo is an appropriate constant.

■Since the power generation cost of each generator on the left side of the minimum cost equation (13) is non-negative if the output satisfies equation (11), it can be used as a constraint condition for the neural network as shown in the following equation. Can be done.

gi (ai Vi"+bi Vi+ci) = m i
n---(13') The above constraints can be expressed as a whole by weighting the individual constraints (8') and (13') as follows.

A (D+L-Σ1Vi)"+BΣ1(ai Vi"+
bi Vi +ci) → min −1−−
-------------(16) In this formula, A,
B is a parameter value set based on an experimental value.

[Configuration of neural network]

In order to solve the problem using the energy minimization function of the Hopfield network, if we associate the problem constraint shown in equation (16) with the network energy E shown in equation (4), we get the following: The connection weight Ti'
is determined.

Tij= −A Bai −−−−−(17)
Tij=−A ・−−−・−(18) 1
i = ^(D +L) -B b i /2 ---
(19) ΔUi=(Σj Tij+(i) Δt= [
−A(ΣjVj −D −L)−B(aiVi+bi/
2)) Δt −・・−−−−−−−−−−(20)
V i =gi(Lli) = (ui −1i) (1+ tanh(Ui/u
o))/2+l 1−−−1−−−−−−−−−・・
(15) The above equation (15) is used together with equation (20) for neuron calculations, so it will be reprinted here.

In this way, it can be correlated to the equation (4) of the energy E, so by finding the minimum point using the Hopfield network, the power of each generator for optimal load distribution can be obtained as the output value of each neuron. be able to.

The above explanation is to realize an optimal power load distribution system at a specific point in time, but next, it is possible to realize a time-series simulation by repeating load distribution one after another for loads that change over time. is possible. At this time, points to consider are resetting the weights between each constraint condition and setting the initial value of the neuron. In this case, this can be done by simply not resetting the weights between the constraint conditions, and by using the immediately previous load distribution result (final neuron value) as the neuron value for the load distribution simulation at the next time point.

FIG. 1 shows a basic configuration diagram of the present invention.

In FIG. 1, 11 is a power system model condition input section;
2 is a simulation model setting section, 13 is a simulation model execution control section, and 14 is a simulation result output section.

[Function] In Fig. 1, the system model serving as the constraint conditions described in the above principle explanation, load D, transmission loss network resistance Rj, impedance constant αij), maximum/minimum output of the generator, power generation cost C1 etc. are input into the power system model condition input section 11. Next, based on the input values, the simulation model setting unit 12 sets a model to be associated with the energy E equation of the Hopfield network.

Next, the simulation model execution control unit 13 executes a simulation using a Hopfield network to find a solution for optimal load distribution corresponding to the minimum value of energy E.

When the simulation model execution control unit 13 determines the optimal load distribution corresponding to the minimum value of the energy E, the simulation result output unit 14 outputs the value Vi that each generator i should output. By controlling the output value of each generator according to this result, optimal (lowest cost) power generation for the load can be achieved.

[Example] FIG. 2 shows a processing flow diagram of an embodiment of the present invention.

When the simulation starts, in step 20, the network with transmission loss = O is calculated using equations (17) to (
19). Next, the state of each neuron l (i
Set the initial value of jiUi (Step 21), and set the output value Vi of each neuron i to the state L! Calculation from the i value U1 is performed in step 22. In that case, the formula Vi=gi (U
Use i).

Next, in step 23, one neuron is arbitrarily selected and set as neuron i, and the change ΔUi in the state value of that neuron i is calculated from equation (20) (step 24), and the new state value Ui - current state ( iiLJi+ΔUi and new output value V
Calculate i-gi (new state value Ui) (step 25)
.

In this way, the new output value ■
1 (via step 27), and after updating all neurons once (step 126), the network energy E is calculated from equation (4) (step 128). Once the result is obtained, it is necessary to determine whether the differences between the energy value E of the last few times and the current E value are all small. The output and the loss of one power transmission member are determined from equation (9) (step 30). Next, in step 31, it is determined whether the total load + total power transmission loss (total power loss) ζ total power generation holds true, and if so, the simulation is terminated and the output value Vi of each neuron at that time is optimally distributed. value.

If the equation in step 31 does not hold, correct the value of power transmission loss (using equations (8) and (9)), find a network with the corrected values from equations (17) to (19), The network is used for subsequent processing, and the process returns to step 23.

FIG. 3 is an explanatory diagram of the overall operation of the embodiment. Thin lines in the figure represent control movements, and double lines represent data movements.

Referring to FIG. 3, when the system starts operating, it enters a load information input waiting state 40, and waits for load information indicating the load amount for each load point to be input. This load information can be input at regular intervals.

When the load information is input, simulation processing is started, and the configuration 41 of the neural network is executed in accordance with the load information and each value stored in the constant table 43. This network configuration is expressed by the above equations (17) to (19).
Corresponds to the operation of When the network is configured, the numerical values of the constituent elements are stored in the network configuration table 44. Next.

The number of network configuration tables 44 (direction) is used to enter the state of calculation 42 by the neural network and execute the calculation.The contents are as shown in the processing flow of FIG. 2.In this process, the number of network configuration tables 44
4, data is read from and written to the Vi/U i value table 45. The output value of each generator representing the finally obtained optimal power load distribution is V
The i/U i value is obtained as the vi value stored in the i value table 45. Each value on these tables is displayed on a display or the like.

FIG. 4 is a diagram showing an example of the configuration of a table, in which ``A'' to ``C'' represent an example of the configuration of the constant table 43 in FIG.
A, is a generator constant table representing the power system model;
is the impedance constant table of the network path, C is the resistance value table of the network bus, 2 is the network configuration table in Fig. 3, and ■ is the multiple weights of each neuron (Ii!(T i t, T i j
) is stored in the weight table, and ■ represents the dark value table (Ii) in which the dark value (I i) of each neuron is stored. These tables are allocated to each area of memory (not shown), and although not shown, constants A and B (formula (17)
- (20)) and an area (registration area) where a load value is set.

This system can deal with the load that changes over time by repeatedly distributing the load one after another. At that time, the points that need to be taken into consideration are the problems of resetting the weights between each constraint condition and setting the initial value of the neuron. This is achieved by using this as the initial value of the neuron in the distribution simulation.

Next, the results of simulation examples based on specific numerical values using the power load distribution system according to the present invention will be explained using FIGS. 9 to 13.

Figure 9 is a diagram showing the model to be simulated, Figure 10 is a diagram showing the attributes of the generator, Figure 11 is a diagram showing the optimal value of the generator determined by the neural network, and Figure 12 is a diagram at a specific point in time. Fig. 13 shows an example of a time series simulation.

The power system model in FIG. 9 has four nodes each with a load and two generators. Each generator is #11.
#12. #21. Each number #22... is blanked out, and the attributes of the generator, ie, output (maximum output/minimum output), 5 power generation cost, and power generation cost/output are shown in FIG.

5000KW and 5000K for load 1 to load 4 respectively
W, 10,000KW, 10,000 enemies (total 300
Figure 12 shows a part of the simulation screen for calculating the output of each generator when 0. Figure 11 shows the power generation cost per unit.

A in FIG. 12 shows the state of convergence of the energy E at a specific time, the vertical axis represents the energy value, and the horizontal axis represents the elapsed calculation time of the neural network. B.

shows how the total output of the generator, the total power generation cost, and the total transmission loss ti change and converge as the calculation time of the neural network passes. In addition, C0 is the output (P) of one of the generators 42 (indicated by #42) among the generators connected to the node, and the cost per unit output light (C/P) is determined by the elapsed calculation time of the neural network. Represents change and final value.

Figure 13 shows a simulation when the load fluctuates over time. In this example, the load at each load point is applied every hour from 11:00 to 17:00, and the output of each generator is calculated for that load. ing.

A represents changes in the total load, total output of the generator, total power generation cost, and total power transmission loss at each time. B is generator #11. #31, #32, #41,
#42 shows the change in cost per unit output light at each time, and C9 shows the output (P) of generators #11 and #32 and the cost per unit output light (C
/P) is shown. According to these results, we were able to achieve a highly satisfactory optimal load distribution.

[Effects of the Invention] According to the present invention, by simulating optimal power load distribution using a neural network, calculation results can be changed quickly, highly accurate results (optimal numerical values) can be obtained, and The overall power generation cost of a power network consisting of a large number of generators depending on the load can be reduced.

13. Simulation model execution control section 14: Simulation result output section

[Brief explanation of the drawing]

Fig. 1 is a diagram showing the basic configuration of the present invention, Fig. 2 is a processing flow diagram of the embodiment, Fig. 3 is an explanatory diagram of the overall operation of the embodiment, Fig. 4 is a diagram showing an example of the structure of a table, and Fig. 5 is a diagram showing the configuration of the Hopfield 2 y network, Figure 6 is a diagram showing an example of the input/output function of a neuron, Figure 7 is a diagram showing the relationship between energy E and neuron output value Vk, and Figure 8 is a model of a power system. Figure 9 shows the model to be simulated, Figure 10 shows the attributes of the generator, Figure 1
FIG. 1 is a diagram showing the optimum value of the generator determined by a neural network, FIG. 12 is a diagram showing an example of simulation at a specific time, and FIG. 13 is a diagram showing an example of time series simulation. In Figure 1, 11: Power system model condition input section 12: Simulation model setting section

Claims (1)

[Claims] In an optimal power load distribution system using a Hopfield network, which is one of the neural network models, a power system model and the output (P_i) of each generator (i)
, maximum/minimum power generation (u_i, l_i), power generation cost (
A power system model condition input section into which C_i), total load (D), and transmission loss (L) are input, and a total output, A simulation model setting section that sets up a model that includes constraints such as maximum output, minimum output, and minimum cost; and a simulation model setting section that sets each neuron using parameters (A, B) included in the model obtained in the simulation model setting section. Optimal power load using a neural network, characterized in that the optimal output (Vi) of each generator corresponding to the total load is determined by determining the connection weights for inputs and performing energy minimization processing of the Hopfield network. allocation system.