JPH05328614A - Economical load distributing method using parallel processor - Google Patents

Abstract

PURPOSE:To always obtain semi-optimum solution within a short time, in an economical load share among a plurality of generators. CONSTITUTION:Spontaneous reduction of an energy function in a Gaussian machine of hopfield type neural network is related to minimization of an evaluation function (cost function), to map restriction of demand/supply balance between generated power and load to the energy function and restriction of output upper/lower limits of a generator to a neuron input/output function (S1). By considering output change rate restriction of the generator, operational restriction of the generator and an executable region of the generator obtained by using a load estimated data of fixed time to come fetched by the above- mentioned each restriction and a step S2, an economical load is calculated by using a parallel processor by the Gaussian machine (S3). In this way, the output command value of a unit time to come from now is obtained about each generator.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention uses a parallel processor in a central power supply command station in order to perform the most economical load distribution using a neural network for the electric power demand distributed over a plurality of generators. The present invention relates to an economic load distribution method using parallel calculation.

[0002]

2. Description of the Related Art This kind of economic load distribution problem is known as one of optimization problems. The so-called dynamic ELD (Econ) that gives a command to the generators by seeking the optimum economic load distribution for the power demand (load amount) that fluctuates from moment to moment for multiple generators
Omic Load Dispatching) is an online control, so it is necessary to find an optimal solution in a short time using a control computer or the like. However, it is extremely complicated to optimize economic load distribution in consideration of various constraints of the electric power system and generators, which will be described later, and there is a conventional method for obtaining an optimal solution in a short time in consideration of these severe constraints. I didn't. For this reason, conventionally, a dynamic ELD has been studied in which automation is performed in consideration of some constraints, and for a time zone that deviates from these constraints, an operator manually operates based on empirical knowledge.

Further, in order to carry out optimization in consideration of various constraints necessary for economic load distribution, it is necessary to use a nonlinear programming method, but although this method can generally obtain a detailed solution, The calculation usually takes a long time, and in some cases a solution may not be obtained.

On the other hand, in Japan, the responsibility of thermal power generators for supply and demand adjustment is increasing with the increase in the number of nuclear power plants in recent years. In addition, dynamic ELD by a thermal power system is becoming indispensable in consideration of large load fluctuation characteristics such as rising load in the morning and falling load in the daytime. Demand / supply balance constraint of generator, output upper / lower limit constraint, output There is a demand for realization of a dynamic ELD that takes into consideration the rate of change constraint, operational constraint, and the like.

The present invention has been made to solve the above problems, and an object of the present invention is to make it possible to always obtain a suboptimal solution in a short time by parallel calculation of a parallel processor and to control it. An object of the present invention is to provide an economic load distribution method capable of reducing the load on the computer for use.

[0006]

In order to achieve the above object, the present invention provides the most economical load distribution among generators when power is supplied by a plurality of generators to a varying load amount. In the economic load distribution method for carrying out, as shown in FIG. 1, the voluntary decrease of the energy function in the Gaussian machine of the Hopfield neural network is associated with the minimization of the evaluation function for the power generation cost, and the power generation amount and the load amount are The demand-supply balance constraint that requires the equilibrium with is mapped to the energy function, the output upper / lower limit constraint of the generator is mapped to the input / output function of the neuron (step S1), and the output change rate constraint of the generator and the predetermined Operation constraints of the generator that require that the output ahead of time is a value that can be reached from the current output, and the above-mentioned constraints and step S
In consideration of the feasible region in which each generator can be operated for each unit time interval up to the fixed time ahead, which is obtained by using the load prediction data up to the fixed time ahead captured in step 2, the Gaussian machine is used. The economic load is calculated by parallel calculation of parallel processors (at step S3), and the output command value from the present to the unit time ahead is calculated for each generator (at step S4).

[0007]

The present invention has been made paying attention to that the Hopfield neural network can be applied to an optimization problem such as a dynamic ELD by replacing the spontaneous decrease of the energy function with the decrease of the evaluation function (objective function). The economic load distribution problem is mapped to the energy function and the input / output function in the Hopfield neural network, and the optimization problem is solved by relating the decreasing process of the energy function to the minimization of the evaluation function, that is, the cost function. , The most economical load distribution among generators. At this time, a Gaussian machine, which is a probabilistic network, is used to prevent a drop (convergence) to a local optimum solution. In addition, the economic load calculation is performed at a high speed by simultaneously changing the states of a plurality of neurons by parallel calculation of a plurality of processors.

Here, in applying the Hopfield type neural network to the dynamic ELD, there are the following problems. Convergence problem to local optimal solution How to give effective initial value How to give various parameters of neural network

In order to solve these problems, the present invention uses a Gaussian machine which suppresses a drop in the local optimal solution by adding stochastic noise and simulated annealing techniques to the Hopfield model. E
The above problem is avoided in combination with the use of a control method that can give an initial value close to the optimum value for the LD problem. Further, the load can be predicted in the dynamic ELD, and the problem due to this can be avoided to some extent in advance. In addition, heuristics are also used when dealing with constraints in order to guide convergence to a global optimum solution in consideration of the various constraints mentioned above.

First, the Hopfield type neural network is an interconnected type, and the dynamic characteristics of the system are described by the following mathematical expression 1. In Equation 1, u _i is the internal state of the neuron, T _{i, j} is the weight of the synaptic connection between the neurons, V _j is the output of the neuron, and I _i
Is a threshold value peculiar to a neuron.

[0011]

[Equation 1]

Further, the output of the neuron is generally expressed by Equation 2
It is described by the input / output function (sigmoid function) of. In Equation 2, μ ₀ is a coefficient that determines the rising of the sigmoid function.

[0013]

[Equation 2]

In the Hopfield, under the condition of T _{i, j} = T _{j, i} , the energy function of the following formula 3 is a Lyapunov function in dynamics, that is, the energy E shown in formula 3 is It was shown that it decreased spontaneously.

[0015]

[Equation 3]

It is the concept of optimization using the Hopfield model that the spontaneous decrease of the energy E is associated with the minimization of the evaluation function (cost function) to solve the optimization problem. Further, although the formula 4 is established by the introduction of the energy E as described above, in practice, the formula 4 is differentiated to obtain the formula 5, and then the formula 6 obtained by modifying the formula 5 is used.

[0017]

[Equation 4]

[0018]

[Equation 5]

[0019]

[Equation 6]

The Gaussian machine is a local optimum solution (local minimum) which is a problem of the Hopfield model.
It was thought to avoid convergence to. In addition, the Gaussian machine is a very general and powerful neuron that includes all the special cases such as Macaroque Pitts, Hopfield, and Boltzmann machine, which have been considered as models of neurons until now. It can be called a model. In the Gaussian machine, the dynamic characteristic of the system is expressed by Equation 7.

[0021]

[Equation 7]

Equation 7 is substantially the same as Equation 1 plus the noise term ε, and this noise term ε follows a Gaussian distribution (normal distribution) with mean = 0 and standard deviation sqrt (8 / π) T.
However, T is a temperature parameter here. This noise term ε also enables movement in the direction of increasing energy. In addition to using simulated annealing using the temperature T, it is possible to escape from the local optimum solution. The formulation of the energy function E is the same as that of the Hopfield model.

[0023]

EXAMPLES Next, examples of the present invention will be described. First, the outline of the dynamic ELD will be described. In a dynamic ELD for a generator, it is important to consider the load variation characteristics and the generator output change rate constraint. To this end, based on the short-term load forecast, after considering the output distribution adequacy for the load up to a certain time ahead (minimum supply and demand imbalance and economical), the next output command value for the generator is determined. The method is also effective in terms of reliability. Therefore, in the present embodiment, after examining the allocation validity of the entire time with respect to the prediction data of the load (13 load bands from 0 minutes to 60 minutes) up to one hour ahead with an interval of 5 minutes, for example, as a unit time, Determine the output command value of the generator 5 minutes from now. By using such a control method, it becomes possible to give an initial value close to the optimum value as described later.

Next, the formulation of the dynamic ELD will be described. The power generation cost of the generator is discontinuous with respect to the amount of power generation depending on the number of mills, the number of burners, etc., but is generally approximated by a quadratic function of the generator output or piecewise linear for simplification. Here, the approximation with the quadratic function of the generator output is used in consideration of the affinity with the neural network. The evaluation function, that is, the cost function is as shown in Expression 8, and the economic load distribution of each generator to all the time zones up to one hour ahead is the evaluation function. Of these, the output of k = 2 (5 minutes ahead) becomes the output command value at the next time point.

[0025]

[Equation 8]

In Equation 8, m is the number of time zones considered (m = 13 in this embodiment), n is the number of generators, and P _ik
Is the amount of power generation of the generator i at time k, and a _i , b _i and c _i are coefficients for P _i .

Further, in the dynamic ELD, it is necessary to satisfy the following constraints (1) to (3). Demand / supply balance constraint In order to generate electric power commensurate with the load, there is a demand / supply balance constraint that the sum of the outputs of all generators in a certain time section is equal to the load amount in that time section, as shown in Equation 9 below. .. Here, the transmission loss is ignored for simplification, but it is actually possible to include the loss in the evaluation function. In Expression 9, L _k is time k
Is the load amount in.

[0028]

[Equation 9]

Upper and Lower Limits of Output of Generator Since the output range of the generator is limited by the number of burners, the number of mills, etc., there are upper and lower limits of output as shown in Formula 10. Note that in Equation 10, P
_{min, i} indicates the minimum output of the generator i, and P _{max, i} indicates the maximum output of the generator i.

[0030]

[Equation 10]

Limitation of output change rate of generator The generator cannot rapidly change its output due to thermal stress of the boiler and other factors. Therefore, the output that can be changed in the unit time is defined as the following Expression 11, and this becomes the output change rate constraint. In Expression 11, dP _{max, i} represents the maximum output change rate of the generator i.

[0032]

[Equation 11]

Operational Constraints Each generator has a current output, which cannot be changed. Therefore, there is a constraint that the output of the generator thereafter is limited to a range that can be reached from the current output, which can be expressed by Equation 12. In Expression 12, PG _i is the current output of the generator i.

[0034]

[Equation 12]

By using the above-mentioned constraints and the load prediction data up to one hour ahead, the upper limit α _max and the lower limit α _min of the feasible region in which each generator can operate in each time zone are
It can be obtained by the following sequential calculation. First, k
For = 1, the upper and lower limits of the output of each generator are given by Expression 13 in consideration of the above operation constraint.

[0036]

[Equation 13]

For the other time zones (k = 2 to 13), the upper limit of the output can be obtained by the sequential calculation by the formula 14 on the premise of the formulas 15 and 16.

[0038]

[Equation 14]

[0039]

[Equation 15]

[0040]

[Equation 16]

Regarding the lower limit α _{ik, min} of the output, min and max and -dP _max and d of each variable of the above equations.
Similar calculation can be performed by replacing P _max . Here, the feasible region indicates whether or not it is possible to cope with the load variation with the maximum efficiency, considering the performance unique to the generator with respect to the load amount. Therefore, when the upper and lower limit values of the feasible region are reversed and the state of the following Expression 17 is reached, the reversed amount Δα _ik = α _{ik, max} −α _{ik, min} is subtracted from L _k. Let a new L _k . Then, Δα _ik is registered as an already known mismatch at this point. This feasible region is added as a constraint on the generator output.

[0042]

[Equation 17]

Next, the formulation of the dynamic ELD using the Hopfield type neural network will be described.
Basically, the ELD problem is defined on the neural network by transforming the ELD problem described above into the form of the energy function of Expression 3.

First, how to handle the evaluation function and various constraints will be described. Evaluation function and supply / demand balance constraint The evaluation function and supply / demand balance are considered by the energy function. Although the evaluation function is used as it is, with respect to the supply and demand balance constraint, Expression 9 is transformed into the second term on the right side of Expression 18 in accordance with the energy function. In addition, in Formula 18, A and B are constants.

[0045]

[Equation 18]

By using the energy function E shown in Expression 18, it is possible to maintain the symmetry of the weight coefficient of the neural network. Further, the diagonal term is negative, and for the dynamic ELD which is a continuous problem, this guarantees the convergence to the local solution.

Upper / Lower Limit Constraints on Output of Generator Here, Equation 19 is obtained by using a method for improving the sigmoid function.

[0048]

[Formula 19]

Operational constraints Operational constraints are considered by fixing the output value of the neuron that represents the current time point. The maximum output change rate constraint and feasible region of the generator The change rate constraint is considered by obtaining the modification amount Δu of u in the partial differential equation so as to satisfy the following formula. That is, Equations 20 and 21 are obtained from Equations 2 and 11, and Equation 22 is obtained in consideration of the constraint from k + 1.

[0050]

[Equation 20]

[0051]

[Equation 21]

[0052]

[Equation 22]

Next, the feasible area obtained by the equation 14 is
As in the formula 22, the constraint of u is set, and the formula 23, the formula 24,
Equation 25 is obtained.

[0054]

[Equation 23]

[0055]

[Equation 24]

[0056]

[Equation 25]

From the above, u _ik takes into account the expressions 22 to 25, and the modified u _ik is obtained within the range of the following expression 26.
It should be noted that β _{ik, min} and β _{ik, max} in Formula 26 are given by Formula 2
7 is represented by Expression 28.

[0058]

[Equation 26]

[0059]

[Equation 27]

[0060]

[Equation 28]

For fairly severe loads, β _{ik, max}
<Β _{ik, min} , but in this case u
_ik is forcibly set to the value shown in Expression 29.

[0062]

[Equation 29]

By handling each constraint and the behavior of the stochastic neural network, it becomes possible to gradually converge to a solution that is close to an optimal solution that can be executed.

Next, how to give the simulation initial value at each time section (at the time when a unit time elapses, that is, every 5 minutes) will be described. As the simulation initial value in each time section of the simulation, a value obtained by shifting the predicted command value by the previous ELD by one time zone can be used as shown in FIG. Therefore, the previous k = 2 output command value becomes the current k = 1 value, that is, the operation constraint. According to this method, the initial value of k = 13 disappears, but only at the time of k = 13, the initial value is obtained by the equal λ method considering the output change rate constraint from k = 12 and the feasible region.

Therefore, the output upper and lower limit values used for the equal λ method at k = 13 are as follows. Upper limit value = min (P _{i, 12} + dP _{max, i} , P _{max, i} , α
_{max, 13} ) Lower limit = max (P _{i, 12} −dP _{max, i} , P _{min, i} , α
_{min, 13} ) Actually, the load prediction error is included, but since the load prediction is performed fairly accurately, it is considered that the above method can give an initial value that is fairly close to the optimal solution. Therefore, this initial value setting method prevents a drop in the local optimum value and increases the possibility of convergence to a global optimum solution.

The Hopfield neural network is based on individual (asynchronous) state change of each neuron, and the state change of each neuron is basically obtained by parallel calculation. Therefore, it is possible to calculate the economic load distribution among the generators in parallel by using, for example, a MIMD type parallel processor. In a general simulation, since the simulation is performed by sequential calculation, a method of randomly determining a neuron whose state is to be changed is dealt with, but in the present invention, when changing the state of each neuron, Expression 27, Expression 28, etc. are used. Therefore, all the generator outputs in the target time zone and the output of the target generator in the −1 time point and the +1 time point are required. Therefore, if the neurons whose states are to be changed are selected from time zones that are not adjacent to each other, the states of those neurons can be changed in parallel. Therefore, considering the time zones from 5 minutes to 60 minutes ahead that are not adjacent to each other, parallel calculation is possible for up to 6 (eg, k = 2, 4, 6, 8, 10, 12) time zones. In principle, parallel calculation is possible with up to 6 processors.

Next, the conditions of the actual simulation will be described. As the specifications of the generator, the equivalent three-generator system shown in Table 1 below, which is a contraction of the generator of the actual system, was used.

[0068]

[Table 1]

As the load pattern, a pattern for two hours (pattern 1, pattern 2) shown in FIG. 3 simulating a rise in the morning to a fall in the day was used. In each simulation, load prediction data from the present time to one hour ahead was used.

As the initial value of the simulation, at the beginning of the simulation, 0 minutes to 60 minutes before each pattern.
The simulation was started on the assumption that a load having the same value as that of 0 minutes was simulated in each minute. By using the same load, it is not necessary to consider the output change rate constraint.
Therefore, it is possible to obtain the optimum solution by the equal λ method considering only the supply and demand balance and use this as the simulation initial value.

In this simulation, as shown in FIG. 7, four processors 101, 102, 103, 104 are used.
(For the sake of convenience, these are referred to as "main", "sub 1", "sub 2", and "sub 3". Each processor has a brand name "Transputer": INMOS T-800 25Hz) connected in a star shape, and the main The processor 101 is connected to the host computer 100 to control the parallel processor as a whole and to communicate with the host computer 100, and also to change the state of the neuron together with the sub processors 102, 103 and 104. I also made it possible to calculate.

In this simulation, programming was carried out by using C language which is capable of parallel computation for a parallel processor, and parallel computation was performed. In addition, as a result of trial and error, the following parameters were used in Equations 18 and 19. A = 0.1, B = 1.0, μ ₀ = 5.0

In the dynamic ELD, the problem to be handled by the neural network changes depending on the load data.
The load to which the method is applied in the statistical data and load prediction up to now can be predicted with high accuracy, and the above parameters can be adjusted in advance. The dynamic ELD by the formulation described here can also be solved by quadratic programming. Actually, the quadratic programming is not suitable for online calculation because it takes a long time to execute, but here the solution by the quadratic programming is taken as the detailed solution, and the results of this method and the quadratic programming are It should be compared.

As a result of the simulation, for pattern 1 in FIG. 3, the results of the present method and the quadratic programming method, which is a detailed solution, were completely in agreement. FIGS. 4 to 6 show changes in the output command value (collected only of command values 5 minutes ahead) of each generator for the pattern 2 in FIG. Here, Fig. 4 shows the characteristics of Unit 1, Fig. 5 shows the characteristics of Unit 2, and Fig. 6 shows the characteristics of Unit 3. In the characteristic lines of each figure, the solid line is based on this method using the Gaussian machine, and the broken line is the secondary plan. It is by law.

Qualitatively explaining these figures,
As a whole, the most economical Unit 3 is used as much as possible. In addition, since Unit 1 is uneconomical, it is not used as much as possible from the beginning, and the maximum output of Unit 1 is reduced when the load drops. Also, since Unit 3 is economical, it is fully used from the beginning, and the load drop is absorbed only by other generators. Looking at the output command value, between 55 and 75 minutes, this method is slightly more uneconomical than the quadratic programming method, but it is a quasi-optimal solution that is very close to the optimal solution without causing a supply-demand imbalance. Is being output. In addition, it is completely 2 for other time zones.
It can be seen that it is consistent with the next programming method.

As a result of the simulation, it was found that the average time required for neuron calculation can be shortened by the parallel calculation, and in particular, the maximum calculation time required for convergence can be shortened. FIG. 8 shows the transition of the average calculation time and the maximum calculation time required for changing the number of processors and the state of neurons. Since random numbers are used in the present invention, FIG. 8 is obtained from many simulation results. As is clear from this figure, the average calculation time and the maximum calculation time become shorter as the number of processors increases. The processor used this time has four links for communication with other processors, and when communicating with five or more processors, it is necessary to communicate via an intermediate processor. It is possible that the overhead will increase. In this simulation, only four processors are considered, but considering the communication overhead, it is considered that four parallel processors are close to the optimum number.

Each processor calculates each neuron state change. Even when the number of generators increases and a real-scale problem is dealt with, the amount of calculation for each state change of each neuron executed by each processor does not change. Due to the increase in the number of neurons handled, the state change does not occur until convergence. It only increases the total number of neurons that should not be retained. Therefore, the tendency shown in FIG. 8 can be considered as a general characteristic regardless of the number of generators for which load distribution should be performed.

In this simulation,
The load up to 1 hour ahead is different in each time section,
You will be solving different problems on the same network every time. However, as shown here, it outputs a suboptimal solution that does not cause supply-demand imbalance, and it can be said that the reliability of this method is high.

[0079]

As described above, according to the present invention, the Hopfield type neural network using the Gaussian machine is applied to the dynamic ELD, various constraints are taken into consideration, and the energy function is reduced spontaneously. Since the economic load distribution is calculated using the process, it is possible to always obtain the most economical load distribution between generators in a short period of time without burdening the control computer etc. it can. Further, by using a Gaussian machine which is a probabilistic network, it is possible to prevent a drop in the local optimum solution, and it becomes possible to perform load distribution with high accuracy. In particular, since parallel calculation by a parallel processor is possible, it is suitable to apply the present invention to online business of a power system that requires high-speed calculation.

[Brief description of drawings]

FIG. 1 is a flowchart showing a processing process of the present invention.

FIG. 2 is a diagram showing how to give a simulation initial value in each time section.

FIG. 3 is an explanatory diagram of load patterns used in the simulation.

FIG. 4 is an explanatory diagram of simulation results.

FIG. 5 is an explanatory diagram of simulation results.

FIG. 6 is an explanatory diagram of simulation results.

FIG. 7 is an explanatory diagram of a parallel processor.

FIG. 8 is a diagram showing the relationship between the number of processors and the maximum and average calculation times required to change the neuron state.

[Explanation of symbols]

 S1, S2, S3, S4 Step 100 Host computer 101, 102, 103, 104 Processor

Claims (1)

[Claims] 1. An economic load distribution method for carrying out the most economical load distribution among generators when power is supplied from a plurality of generators to a varying load amount, wherein a Hopfield neural network is used. The voluntary decrease of the energy function in the Gaussian machine is related to the minimization of the evaluation function related to the power generation cost, and the demand-supply balance constraint that requires the balance between the power generation amount and the load amount is mapped to the energy function. Limit constraint is mapped to the input / output function of the neuron, and the output change rate constraint of the generator, the operational constraint of the generator that requires that the output after a predetermined time is a value that can be reached from the current output, Execution is possible in which each generator can be operated at each unit time interval up to the above-mentioned fixed time, calculated using constraints and load prediction data up to the fixed time Considering the region, the economic load calculation by the Gaussian machine is executed by parallel calculation by a plurality of processors, and the output command value from the present to the unit time ahead is calculated for each generator. Load distribution method.