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Multiprocessor System for Power System Analysis
Copyright © [FAC Real Time Programming Kyoto. Japan. 1981
MUL TIPROCESSOR SYSTEM FOR POWER SYSTEM ANALYSIS H. Taoka, S. Abe and S. Takeda Central Research Laboratory, Mitsubishi Electric Corporation, Amagasaki, Hyogo, Japan
Abstract. As the technology of computer hardware advances, the speedup of power system analysis becomes more and more necessary. In order to study about future power system analysis by parallel processing, we made a prototype of a multiprocessor system. In this paper, after explaining the parallel processing in power system analysis, we will discuss the hardware and the software of a multiprocessor system including the algorithm of the analysis. We solved the load flow problem as an example of the analysis and compared the multiprocessor system to a conventional sequential machine (COSMO 700-11) in regard to the calculation result. The load flow method used in the multiprocessor system is the Gauss iterative method. Each processor calculates the equations of each node in the power system. As the number of nodes increases, the multiprocessor system becomes superior to the conventional sequential machine (COSMO 700-11) ~n terms of calculation speed. Keywords. Computer architecture; multiprocessor; microprocessor; parallel processor; power system analysis; load flow analysis.
INTRODUCTION
In the actual power system, all of the generators and loads are running parallel. So if we want to calculate the problem in real time while leaving the actual image of the power system, either analog or digital parallel processing machines should be finally used.
The power system is a very large system with generators, loads, transmission lines, transformers and so forth. For the analysis of power systems, digital computers have been used for a long time. Typically for load flow calculation, their network equations have large dimensions and require much time for solving with computers.
From this viewpoint, we made a prototype of a multiprocessor system in order to study future load flow analysis or system simulations by parallel processing.
With the recent advance of computer hardware techniques, the speedup of the analysis is expected, and the use of supercomputers, array processors or parallel processors has been studied by many engineers.
Here we discuss the algorithm of load flow analysis for parallel processing and show the hardware and the software of a multiprocessor system. As an application for power system analysis, we solved the load flow problems and compared the multiprocessor system with a conventional sequential machine (COSMO 700-11) in regard to the calculation results.
One goal is to decrease the time and cost of the analysis which is required by conventional sequential machines. To get good efficiency of analysis, operation and planning, exclusive computers with low cost and high speed are required. Another goal is to realize a realtime simulator for training or security monitoring and to increase the reliability of systems.
PARALLEL PROCESSING FOR POWER SYSTEM ANALYSIS Many kinds of load flow methods have been developed for faster calculation by digital computers.
Supercomputers and array processors are now comming into wide use, and power system engineers (Happ and Pottle, 1979; Podmore and co-workers, 1979; and others) are developing the algorithm for these machines. However, parallel processors have not been commercialized yet and are now in research in the area of power system analysis.
Now, a new generation of computers such as supercomputers, array processors and parallel processors are becoming available. The application of these machines to power system analysis, including load flow calculation, 101
102
H. Taoka, S. Abe and S. Takeda
has recently been studied. Here we explain the character and the application for power system analysis of the new types of computers. The supercomputers have arithmetic units in which arithmetic operations can be broken down into a number of segments. Supercomputers such as the CRAY-I or the CDC STAR-lOO usually have multiple pipes which operate in parallel and assist in achieving the high rates of computational speed. Data references to memory are also pipelined to achieve a satisfactory data rate between memory and the arithmetic units. The largest number of vector processors investigated are the array processors. The array processor requires a host computer and was developed to perform high speed signal processing. These machines have little or no pipe lining and achieve their computational speed by efficient use of parallel arithmetic elements and memory. The parallel processor presently contains research machines consisting of several processors which operate in the multiple instruction multiple data mode (MIMD). In the parallel processor, each processor is able to execute its own instructions on its own data. The super computers are currently few in number and poor results have been obtained from their application. Happ and Pottle (1979) mentioned that their success at solving power system simulation problems depends on raising the efficiency with which they solve sparce linear equations. They approach a new block bordered diagonal form for solving the equation of Ax=b in a power system simulation problem. There are many array processors such as the Floating Point Systems AP-120B or the Data West Real Time Ill. Software for array processors is presently being studied by various potential users (Podmore, 1979; Orem and Tinney, 1979; Lamont and Iveson, 1981). The Bonneville Power Administration has done much work on the AP-120B machine and encouraging results have been obtained (Orem and Tinney, 1979). As mentioned above, the application of supercomputers and array processors for power system analysis has already been studied by many engineers. But parallel processors are still in the experimental stage and only the software for analysis are reported (Brasch and co-workers, 1979; Housos and Wing, 1979). Power system analysis by parallel processing should have cooperation between hardware and software. These problems have not been investigated yet. We chose power system analysis by parallel processing and made the prototype of a multiprocessor system which has several
microprocessors. Through the application for power system analysis, particularly for load flow problems, we studied the hardware and software problems on the multiprocessor system.
LOAD FLOW METHODS Here we compare several kinds of load flow methods and discuss the algorithm that is suitable for a multiprocessor system in order to realize the speedup of load flow calculation. Load flow methods (Stott, 1974) classified as follows.
are
roughly
1.
Newton-Raphson method Ward-Hale method (Ward and Hale, 1968) Fast Decoupled Load Flow method (Stott and Alsac, 1974)
2.
Gauss iterative method Gauss-Seidel iterative method
3.
Flow AC method (Takahashi and co-workers, 1968) Flow DC method (Takahashi and co-workers, 1968)
4.
Nonlinear programming method (Sasson, 1969)
Of these methods, the Newton-Raphson method and the Gauss-Seidel iterative method are mainly used. The Newton-Raphson method converges in a few iterations, but requires much memory size and time. The Ward-Hale method is a simplified vers i on of the Newton-Raphson method. It requires less memory size and its calculation algorithm is simple. But it converges slowly and takes more time than the Newton-Raphson method. Stott and Alsac's (1974) Fast Decoupled Load Flow method has constant Jacobian and requires only one inverse matrix calculation. It converges in a few iterations and is faster than the Newton-Raphson method. In general, a load flow method which must solve the simultaneous equations, such as the Newton-Raphson method, spends more time in the inverse matrix calculation than in the iterative calculation. So it is necessary for parallel processing to calculate inverse matrix in parallel to get high speed calculation. The Gauss iterative method and the Gauss-Seidel iterative method have simple algorithms and require small memory size in using an admittance matrix. But they converge very slowly and take more time than the Newton-Raphson method.
Multiprocessor System for Power System Analysis From the viewpoint of the application for parallel processing, the Gauss iterative method has no inverse matrix calculation and requires a few data for the calculation in each node of the power system. In this method, each node can calculate its own equations at one time, and parallel processing is easily realized. We adapted the Gauss iterative method for a multiprocessor system and let each processor correspond to each node. Figure 1 shows the flow chart iterative method.
of
the
Gauss
103
I
M.P.U.
II.p.lo.p.lc n !J fr
.C.
~~~~~~~Q~T.B. ~ C.B. L.P.U.
M.P.U. L .P.U. I • 0. P. C .C. T . B. C. B.
p.
L.P.U.
L.P.U.
:MAIN PROCESSOR UNIT : LOCAL PROCESSOR UNIT I NPUT PORT : OUTPUT PORT : CONTROL 6 INTERRUPT CIRCUIT : TRANSFER BUS : CONTROL BUS
:
Fig. 2.
Multiprocessor system •
>-Y-"E"'S'--_ _ _ _ _ _--,
• , . . 0 ••">': .
12 PV NODE
PO NODE
NO
®:
NO
YES STOP
Fig. 1.
Flow chart of the gauss iterative method.
ARCHITECTURE OF
GENERATOR -+: LOAD
Fig. 3.
IEEE - 14 node system.
data transfer time will the larger the system is, the bus wiring is. So the multiprocessor system will
be shortened. But the more complex flexihility of the be lost.
MULTIPROCESSOR SYSTEM
The multiprocessor system has several Local Processor Units (LPUs), a Main Processor Unit (MPU), a Control Bus and a Transfer Bus, as shown In Fig. 2. The LPUs realize parallel processing, and the MPU controls their calculations, their transfer data, their processing and the I/O devices through the Control Bus. Each LPU corresponds to each node, such as the generator node or the load node. Figure 3 shows an example of the power system. For the analysis of this example, 14 LPUs are needed. Node connection of power systems is usually fixed. For the fixed power system's analysis, a personal bus type is enough. That is to say, a transfer bus can correspond to each node connection, and data will be transfered between only 2 nodes which are connected by the transfer bus. In this type,
So we used a common bus for data transfer. With this typ e , we can easily change the system connection. But, because only one set of data is put on the hus, it takes much t i me for transferring all data. So, in this multiprocessor system, data transfer time is shortened by a First Data Transferring as follows. For transferring data among LPUs, the CPU In the MPU move the block data of LPU numbers among the memory area of the MPU. Then a memory mapped port selector in the MPU chooses the LPU's output port, puts a pair of data on the Transfer Bus, chooses another LPUs' input ports and brings the data into the LPUs. Figure 4 and 5 show the architecture of the MPU and the LPU. Table 1 shows the component parts of the MPU, and Table 2 shows the LPU's. A picture of the multiprocessor system is shown in Fig. 6.
H. Taoka, S. Abe and S . Takeda
104
Fig. 4.
Main Processor Unit. Transfer Bus
Fig. 5.
TABLE 1
Local Processor Unit.
Fi g . 6.
Pictur e of mul tipr ocesso r sys tem.
Component Parts of Main Processor Unit
CPU ROM R A M
AP U D MA 32 BIT PARALLEL INPUT PORT 32 BIT PARALLEL OUTPUT PORT LPU 1/0 PORT SELECTOR INTERRUPT SIGNAL CIRCUIT SERIAL INTERFACE CIRCUIT
z80 8 KBYTE 12 KBYTE Am 9511 Am 9517
, L PU
L P U NO. 2
1 1 1
R A M
A P U 32 BIT PARALLEL INPUT PORT 32 BIT PARALLEL OUTPUT PORT INTERRUPT SIGNAL CIRCUIT
-4)l-----'M
Lt
/i
r-
Fig. 7.
e 1552 (msecl 37 ( mse c)
d
r WAITING ) DATA TRANSFER:
e
RESULT OU TP UT: I OJ 3[msec)
4 ( mse c)
Se qu e nce of lo ad f I o\" ca l culat ion.
fl ow ca l cu l ation of the IEEE-14 node (Fr e ri s and Sasso n, 19 6R) in Fig . 1.
sys t em
4
The load flow me th od adapted in this syst em is the Gauss iterative method using an admittance matrix. Each LPU solves th e eq uations of each node. The Gauss iterative method has a simple algorithm and r e quires only a few data transfers among the LPUs. th e the
)t"J
~
o · - DATA INPU T b ,-, CALCULATl ON'
Th e se qu e nce is as fo ll ows . 1.
Tran s f e r admittanc e data , specifie d power data, specified voltage data and o ther data from th e MPU t o each LPU .
2.
Start th e ca l cu l a ti on of one it e ration at one tim e .
3.
After all LPUs finish th e calcu l a tion, the MPU checks their co n vergence .
4.
If all LPU s converge , go t o Step S. If not, after tr ansfer rin g the data among the LPU s hy a Fast Data Tr ansfe rr i ng , go to Step 2 .
SEQUENCE OF LOAD FLOW CALCULATION
Figure 7 shows processing and
,
"l ,
2
8085 4 KBYTE KBYTE Am 9511
N
obe d
Component Parts of Local Proc esso r Uni t
CPU ROM
==t==-)I
c .
TABLE 2
2
NO . 1 ~.-I--~-==:3H;"----J.~....jI_~
sequence of parallel processing tim e of load
Multiprocessor System for Power System Analysis 5.
Transfer the result from each LPU to the MPU, display the result on the TTY or the CRT, and finish the load flow calculation.
~
105
(msec)
~ 200 a::
(2) / /
w
f-
.....
/
t50
/ /
u.J
Z 0
EVALUATION STUDIES
/ /
tOO
~
Table 3 and Fig. 8 show the result of comparing the multiprocessor system with a conventional sequential machine (COSMO 700-11) in r egard to the calculation time of 4 power systems (Ward and Hale, 1968; Freris and Sasson, 1968).
w 50 ~
f-
Z
8
f-
...J
~
...J
Comparison between Multiprocessor System and COSMO 700-11
0' 0
u
(a)
ITERATION COUNT
6
55 2 . 09
COSMQ-7001 I
TIME
[ 0.97 0.78 ]
(sec )
0.34 ITERATION COUNT MULTIPROCESSOf; SYSTEM
TIME (se c)
(b) 14
30
27 0
373
6 . 55
23 . 62
75 . 74
6.67] ['9 [2 32] [ 15.37 73] 3 .. 53 52 .. 29 0 . 70 1. 57 3 . 72 138
[ 2.17 ~ :~~]
8 . 24
*270
*373
·'6 . 83 *26 . 40
[ 113 .. 40 26] [ 16 6.20] ['5 .. 52] 71 . 08 1 . 01 2 . 17 4 . 12
to
I 20
30
40
50
I
60
70 [node)
(2) COSMO-70011
Calculation time of one iteration.
But the calculation time of one iteration is different between the COSMO 700-11 and the multiprocessor system. It is almost constant in the multiprocessor system, while the COSMO 700-11 requires more time in proportion to the number of nodes, as shown in Fig. 8. Data input and output time increases in proportion to the size of power system for both machines.
-4
ACCURACY: 1.0 X 1.0
It is useful for understanding the changing process of the system to calculate load flow of partially different systems successively.
(a): WARD ~ HALE'S 6 NODE SYSTEM
(b): IEEE -
-«
As the power system becomes larger, total calculation time in the multiprocessor syst em The becomes less than in the COSMO 700-11. multiprocessor system is superior to the conventional sequential machine for the analysis of large power systems.
TIME TOTAL CPU TIME UPPER: DATA INPUT TIME ] MIDDLE: CALCULATION TIME [ LOWER: RESULT OUTPUT TIME SIMULATl NG OAT A
*:
(t)
<
(d) 57
138
53
0 . 43
(c)
;'
(t) MULTIPROCESSOR SYSTEM
Fig. 8. NODE NO .
.., ./
NODE NO.
u
TABLE 3
.., ..,
0
14 NODE SYSTEM
(c): IEEE - 30 NODE SYSTEM
(d): IEEE - 57 NODE SYSTEM
For an example, in the IEEE-14 node system, time required for each step is as follows. 1.
2.
COSMO 700-I! Calculation time of one iteration --- 25.6 * Iteration count -------------- 138 * Calculation time of all iterations --- 3.53 * Total processing time including I/O --- 6.55
CONCLUSIONS
*
Multiprocessor System Calculation time of one iteration --- 41.4 * Iteration count -------------- 138 * Calculation time of all iterations --- 5.71 * Total processing time including I/O --- 8.24
msec sec time sec
*
This multiprocessor system has some special features. The first is high cost performance, using the popular microprocessors. The second is high speed calculation by parallel processing. The third is the special hardware structuring for high speed data transfer among the MPU and the LPUs through a wide common bus. So we can solve the load flow problem very fast.
msec sec time sec
The iteration count of the load flow calculation is mainly influenced by the number of nodes and the character of the power system, and is the same between the COSMO 700-11 and the multiprocessor system because of the same algorithm and the same floating point processing. R TP _ E
We calculated the load flow, starting at a certain state of the system. The calculation time was about 1 to 4 seconds for the 14 node system.
But, on the other hand, there are some defects in this system . First, because each LPU corresponds to each nodes, large number of LPUs are necessary for the analysis of a large power system. Adaptation of network decomposition will settle this problem. A second defect is the use of the Gauss iterative method. In a large power system, this method requires many iterative calculations. It also has the difficulty of convergence in an ill-conditioned power system. And, if the matrix of the equation
106
H. Taoka, S. Abe and S. Takeda
is not pos~t~ve definite, it won't converge. A new algorithm for parallel processing should be developed. In future, we intend to overcome the difficulty of convergence by a new load flow method for parallel processing, and to apply this multiprocessor system for power system simulation or for other problems. REFERENCES Happ, H.H., C. Pottle, and K.A. Wirgan (1979). An assessment of computer technology for large scale power system simulation. 1979 PICA Conference, pp. 316-324. Podmore, R., M. Liveright, and S. Virmani (1979). Application of an array processor for power system network computation. 1979 PICA Conference, pp. 325-331. Orem, F.M., and W.F. Tinney (1979). Evaluation of an array processor for power system applications. 1979 PICA Conference, pp. 345-350. Lamont, J.W., and R.H. Iveson (1981). Array processor applications in power System planning and operation. 7th PSCC, pp. 710-717. Brash, F.M., J.E. Vann Ness, and Sang-Chul Kang (1979). The use of a multiprocessor network for the transient stability problem. 1979 PICA Conference, pp. 337344. Housos, E.C., and O. Wing (1979). Solution of the load flow problem by a parallel optimization method. 1979 PICA Conference, pp. 332-336. Exploring applications of parallel processing to power system analysis problems. EPRI Special Report, EL-566-SR, Oct. 1977. Stott, B. (1974). Review of load-flow calculation method. Proc. IEEE, Vol. 62, No. 7, July 1974, pp. 916-929. Ward, J.B., and H.W. Hale (1968). Digital computer solution of power-flow problems. Proc. lEE, Vol. 115, No. 10, Oct. 1968, pp. 398-404. Stott, B., and O. Alsac (1974). Fast decoupled load flow. IEEE Trans. PAS, Vol. PAS-93, No. 3, May/June 1974, pp. 859-867. Takahashi, K., Y. Sekine, and T. Umezu (1968). Network-flow method applied to load flow calculation. IEEE Trans. PAS, Vol. PAS-87, No. 11, Nov. 1968, pp. 19391949. Sasson, A.M. (1969). Nonlinear programming solutions for the load-flow, minimumloss, and economic dispatching problems. IEEE Trans. PAS, Vol. PAS-88, No. 4, Apr. 1969, pp. 399-409. Freris, L.L., and A.M. Sas son (1968). Investigation of the load-flow problem. Proc. lEE, Vol. 115, No. 10, Oct. 1968, pp. 1459-1469.
MUL TIPROCESSOR SYSTEM FOR POWER SYSTEM ANALYSIS H. Taoka, S. Abe and S. Takeda Central Research Laboratory, Mitsubishi Electric Corporation, Amagasaki, Hyogo, Japan
Abstract. As the technology of computer hardware advances, the speedup of power system analysis becomes more and more necessary. In order to study about future power system analysis by parallel processing, we made a prototype of a multiprocessor system. In this paper, after explaining the parallel processing in power system analysis, we will discuss the hardware and the software of a multiprocessor system including the algorithm of the analysis. We solved the load flow problem as an example of the analysis and compared the multiprocessor system to a conventional sequential machine (COSMO 700-11) in regard to the calculation result. The load flow method used in the multiprocessor system is the Gauss iterative method. Each processor calculates the equations of each node in the power system. As the number of nodes increases, the multiprocessor system becomes superior to the conventional sequential machine (COSMO 700-11) ~n terms of calculation speed. Keywords. Computer architecture; multiprocessor; microprocessor; parallel processor; power system analysis; load flow analysis.
INTRODUCTION
In the actual power system, all of the generators and loads are running parallel. So if we want to calculate the problem in real time while leaving the actual image of the power system, either analog or digital parallel processing machines should be finally used.
The power system is a very large system with generators, loads, transmission lines, transformers and so forth. For the analysis of power systems, digital computers have been used for a long time. Typically for load flow calculation, their network equations have large dimensions and require much time for solving with computers.
From this viewpoint, we made a prototype of a multiprocessor system in order to study future load flow analysis or system simulations by parallel processing.
With the recent advance of computer hardware techniques, the speedup of the analysis is expected, and the use of supercomputers, array processors or parallel processors has been studied by many engineers.
Here we discuss the algorithm of load flow analysis for parallel processing and show the hardware and the software of a multiprocessor system. As an application for power system analysis, we solved the load flow problems and compared the multiprocessor system with a conventional sequential machine (COSMO 700-11) in regard to the calculation results.
One goal is to decrease the time and cost of the analysis which is required by conventional sequential machines. To get good efficiency of analysis, operation and planning, exclusive computers with low cost and high speed are required. Another goal is to realize a realtime simulator for training or security monitoring and to increase the reliability of systems.
PARALLEL PROCESSING FOR POWER SYSTEM ANALYSIS Many kinds of load flow methods have been developed for faster calculation by digital computers.
Supercomputers and array processors are now comming into wide use, and power system engineers (Happ and Pottle, 1979; Podmore and co-workers, 1979; and others) are developing the algorithm for these machines. However, parallel processors have not been commercialized yet and are now in research in the area of power system analysis.
Now, a new generation of computers such as supercomputers, array processors and parallel processors are becoming available. The application of these machines to power system analysis, including load flow calculation, 101
102
H. Taoka, S. Abe and S. Takeda
has recently been studied. Here we explain the character and the application for power system analysis of the new types of computers. The supercomputers have arithmetic units in which arithmetic operations can be broken down into a number of segments. Supercomputers such as the CRAY-I or the CDC STAR-lOO usually have multiple pipes which operate in parallel and assist in achieving the high rates of computational speed. Data references to memory are also pipelined to achieve a satisfactory data rate between memory and the arithmetic units. The largest number of vector processors investigated are the array processors. The array processor requires a host computer and was developed to perform high speed signal processing. These machines have little or no pipe lining and achieve their computational speed by efficient use of parallel arithmetic elements and memory. The parallel processor presently contains research machines consisting of several processors which operate in the multiple instruction multiple data mode (MIMD). In the parallel processor, each processor is able to execute its own instructions on its own data. The super computers are currently few in number and poor results have been obtained from their application. Happ and Pottle (1979) mentioned that their success at solving power system simulation problems depends on raising the efficiency with which they solve sparce linear equations. They approach a new block bordered diagonal form for solving the equation of Ax=b in a power system simulation problem. There are many array processors such as the Floating Point Systems AP-120B or the Data West Real Time Ill. Software for array processors is presently being studied by various potential users (Podmore, 1979; Orem and Tinney, 1979; Lamont and Iveson, 1981). The Bonneville Power Administration has done much work on the AP-120B machine and encouraging results have been obtained (Orem and Tinney, 1979). As mentioned above, the application of supercomputers and array processors for power system analysis has already been studied by many engineers. But parallel processors are still in the experimental stage and only the software for analysis are reported (Brasch and co-workers, 1979; Housos and Wing, 1979). Power system analysis by parallel processing should have cooperation between hardware and software. These problems have not been investigated yet. We chose power system analysis by parallel processing and made the prototype of a multiprocessor system which has several
microprocessors. Through the application for power system analysis, particularly for load flow problems, we studied the hardware and software problems on the multiprocessor system.
LOAD FLOW METHODS Here we compare several kinds of load flow methods and discuss the algorithm that is suitable for a multiprocessor system in order to realize the speedup of load flow calculation. Load flow methods (Stott, 1974) classified as follows.
are
roughly
1.
Newton-Raphson method Ward-Hale method (Ward and Hale, 1968) Fast Decoupled Load Flow method (Stott and Alsac, 1974)
2.
Gauss iterative method Gauss-Seidel iterative method
3.
Flow AC method (Takahashi and co-workers, 1968) Flow DC method (Takahashi and co-workers, 1968)
4.
Nonlinear programming method (Sasson, 1969)
Of these methods, the Newton-Raphson method and the Gauss-Seidel iterative method are mainly used. The Newton-Raphson method converges in a few iterations, but requires much memory size and time. The Ward-Hale method is a simplified vers i on of the Newton-Raphson method. It requires less memory size and its calculation algorithm is simple. But it converges slowly and takes more time than the Newton-Raphson method. Stott and Alsac's (1974) Fast Decoupled Load Flow method has constant Jacobian and requires only one inverse matrix calculation. It converges in a few iterations and is faster than the Newton-Raphson method. In general, a load flow method which must solve the simultaneous equations, such as the Newton-Raphson method, spends more time in the inverse matrix calculation than in the iterative calculation. So it is necessary for parallel processing to calculate inverse matrix in parallel to get high speed calculation. The Gauss iterative method and the Gauss-Seidel iterative method have simple algorithms and require small memory size in using an admittance matrix. But they converge very slowly and take more time than the Newton-Raphson method.
Multiprocessor System for Power System Analysis From the viewpoint of the application for parallel processing, the Gauss iterative method has no inverse matrix calculation and requires a few data for the calculation in each node of the power system. In this method, each node can calculate its own equations at one time, and parallel processing is easily realized. We adapted the Gauss iterative method for a multiprocessor system and let each processor correspond to each node. Figure 1 shows the flow chart iterative method.
of
the
Gauss
103
I
M.P.U.
II.p.lo.p.lc n !J fr
.C.
~~~~~~~Q~T.B. ~ C.B. L.P.U.
M.P.U. L .P.U. I • 0. P. C .C. T . B. C. B.
p.
L.P.U.
L.P.U.
:MAIN PROCESSOR UNIT : LOCAL PROCESSOR UNIT I NPUT PORT : OUTPUT PORT : CONTROL 6 INTERRUPT CIRCUIT : TRANSFER BUS : CONTROL BUS
:
Fig. 2.
Multiprocessor system •
>-Y-"E"'S'--_ _ _ _ _ _--,
• , . . 0 ••">': .
12 PV NODE
PO NODE
NO
®:
NO
YES STOP
Fig. 1.
Flow chart of the gauss iterative method.
ARCHITECTURE OF
GENERATOR -+: LOAD
Fig. 3.
IEEE - 14 node system.
data transfer time will the larger the system is, the bus wiring is. So the multiprocessor system will
be shortened. But the more complex flexihility of the be lost.
MULTIPROCESSOR SYSTEM
The multiprocessor system has several Local Processor Units (LPUs), a Main Processor Unit (MPU), a Control Bus and a Transfer Bus, as shown In Fig. 2. The LPUs realize parallel processing, and the MPU controls their calculations, their transfer data, their processing and the I/O devices through the Control Bus. Each LPU corresponds to each node, such as the generator node or the load node. Figure 3 shows an example of the power system. For the analysis of this example, 14 LPUs are needed. Node connection of power systems is usually fixed. For the fixed power system's analysis, a personal bus type is enough. That is to say, a transfer bus can correspond to each node connection, and data will be transfered between only 2 nodes which are connected by the transfer bus. In this type,
So we used a common bus for data transfer. With this typ e , we can easily change the system connection. But, because only one set of data is put on the hus, it takes much t i me for transferring all data. So, in this multiprocessor system, data transfer time is shortened by a First Data Transferring as follows. For transferring data among LPUs, the CPU In the MPU move the block data of LPU numbers among the memory area of the MPU. Then a memory mapped port selector in the MPU chooses the LPU's output port, puts a pair of data on the Transfer Bus, chooses another LPUs' input ports and brings the data into the LPUs. Figure 4 and 5 show the architecture of the MPU and the LPU. Table 1 shows the component parts of the MPU, and Table 2 shows the LPU's. A picture of the multiprocessor system is shown in Fig. 6.
H. Taoka, S. Abe and S . Takeda
104
Fig. 4.
Main Processor Unit. Transfer Bus
Fig. 5.
TABLE 1
Local Processor Unit.
Fi g . 6.
Pictur e of mul tipr ocesso r sys tem.
Component Parts of Main Processor Unit
CPU ROM R A M
AP U D MA 32 BIT PARALLEL INPUT PORT 32 BIT PARALLEL OUTPUT PORT LPU 1/0 PORT SELECTOR INTERRUPT SIGNAL CIRCUIT SERIAL INTERFACE CIRCUIT
z80 8 KBYTE 12 KBYTE Am 9511 Am 9517
, L PU
L P U NO. 2
1 1 1
R A M
A P U 32 BIT PARALLEL INPUT PORT 32 BIT PARALLEL OUTPUT PORT INTERRUPT SIGNAL CIRCUIT
-4)l-----'M
Lt
/i
r-
Fig. 7.
e 1552 (msecl 37 ( mse c)
d
r WAITING ) DATA TRANSFER:
e
RESULT OU TP UT: I OJ 3[msec)
4 ( mse c)
Se qu e nce of lo ad f I o\" ca l culat ion.
fl ow ca l cu l ation of the IEEE-14 node (Fr e ri s and Sasso n, 19 6R) in Fig . 1.
sys t em
4
The load flow me th od adapted in this syst em is the Gauss iterative method using an admittance matrix. Each LPU solves th e eq uations of each node. The Gauss iterative method has a simple algorithm and r e quires only a few data transfers among the LPUs. th e the
)t"J
~
o · - DATA INPU T b ,-, CALCULATl ON'
Th e se qu e nce is as fo ll ows . 1.
Tran s f e r admittanc e data , specifie d power data, specified voltage data and o ther data from th e MPU t o each LPU .
2.
Start th e ca l cu l a ti on of one it e ration at one tim e .
3.
After all LPUs finish th e calcu l a tion, the MPU checks their co n vergence .
4.
If all LPU s converge , go t o Step S. If not, after tr ansfer rin g the data among the LPU s hy a Fast Data Tr ansfe rr i ng , go to Step 2 .
SEQUENCE OF LOAD FLOW CALCULATION
Figure 7 shows processing and
,
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2
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N
obe d
Component Parts of Local Proc esso r Uni t
CPU ROM
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c .
TABLE 2
2
NO . 1 ~.-I--~-==:3H;"----J.~....jI_~
sequence of parallel processing tim e of load
Multiprocessor System for Power System Analysis 5.
Transfer the result from each LPU to the MPU, display the result on the TTY or the CRT, and finish the load flow calculation.
~
105
(msec)
~ 200 a::
(2) / /
w
f-
.....
/
t50
/ /
u.J
Z 0
EVALUATION STUDIES
/ /
tOO
~
Table 3 and Fig. 8 show the result of comparing the multiprocessor system with a conventional sequential machine (COSMO 700-11) in r egard to the calculation time of 4 power systems (Ward and Hale, 1968; Freris and Sasson, 1968).
w 50 ~
f-
Z
8
f-
...J
~
...J
Comparison between Multiprocessor System and COSMO 700-11
0' 0
u
(a)
ITERATION COUNT
6
55 2 . 09
COSMQ-7001 I
TIME
[ 0.97 0.78 ]
(sec )
0.34 ITERATION COUNT MULTIPROCESSOf; SYSTEM
TIME (se c)
(b) 14
30
27 0
373
6 . 55
23 . 62
75 . 74
6.67] ['9 [2 32] [ 15.37 73] 3 .. 53 52 .. 29 0 . 70 1. 57 3 . 72 138
[ 2.17 ~ :~~]
8 . 24
*270
*373
·'6 . 83 *26 . 40
[ 113 .. 40 26] [ 16 6.20] ['5 .. 52] 71 . 08 1 . 01 2 . 17 4 . 12
to
I 20
30
40
50
I
60
70 [node)
(2) COSMO-70011
Calculation time of one iteration.
But the calculation time of one iteration is different between the COSMO 700-11 and the multiprocessor system. It is almost constant in the multiprocessor system, while the COSMO 700-11 requires more time in proportion to the number of nodes, as shown in Fig. 8. Data input and output time increases in proportion to the size of power system for both machines.
-4
ACCURACY: 1.0 X 1.0
It is useful for understanding the changing process of the system to calculate load flow of partially different systems successively.
(a): WARD ~ HALE'S 6 NODE SYSTEM
(b): IEEE -
-«
As the power system becomes larger, total calculation time in the multiprocessor syst em The becomes less than in the COSMO 700-11. multiprocessor system is superior to the conventional sequential machine for the analysis of large power systems.
TIME TOTAL CPU TIME UPPER: DATA INPUT TIME ] MIDDLE: CALCULATION TIME [ LOWER: RESULT OUTPUT TIME SIMULATl NG OAT A
*:
(t)
<
(d) 57
138
53
0 . 43
(c)
;'
(t) MULTIPROCESSOR SYSTEM
Fig. 8. NODE NO .
.., ./
NODE NO.
u
TABLE 3
.., ..,
0
14 NODE SYSTEM
(c): IEEE - 30 NODE SYSTEM
(d): IEEE - 57 NODE SYSTEM
For an example, in the IEEE-14 node system, time required for each step is as follows. 1.
2.
COSMO 700-I! Calculation time of one iteration --- 25.6 * Iteration count -------------- 138 * Calculation time of all iterations --- 3.53 * Total processing time including I/O --- 6.55
CONCLUSIONS
*
Multiprocessor System Calculation time of one iteration --- 41.4 * Iteration count -------------- 138 * Calculation time of all iterations --- 5.71 * Total processing time including I/O --- 8.24
msec sec time sec
*
This multiprocessor system has some special features. The first is high cost performance, using the popular microprocessors. The second is high speed calculation by parallel processing. The third is the special hardware structuring for high speed data transfer among the MPU and the LPUs through a wide common bus. So we can solve the load flow problem very fast.
msec sec time sec
The iteration count of the load flow calculation is mainly influenced by the number of nodes and the character of the power system, and is the same between the COSMO 700-11 and the multiprocessor system because of the same algorithm and the same floating point processing. R TP _ E
We calculated the load flow, starting at a certain state of the system. The calculation time was about 1 to 4 seconds for the 14 node system.
But, on the other hand, there are some defects in this system . First, because each LPU corresponds to each nodes, large number of LPUs are necessary for the analysis of a large power system. Adaptation of network decomposition will settle this problem. A second defect is the use of the Gauss iterative method. In a large power system, this method requires many iterative calculations. It also has the difficulty of convergence in an ill-conditioned power system. And, if the matrix of the equation
106
H. Taoka, S. Abe and S. Takeda
is not pos~t~ve definite, it won't converge. A new algorithm for parallel processing should be developed. In future, we intend to overcome the difficulty of convergence by a new load flow method for parallel processing, and to apply this multiprocessor system for power system simulation or for other problems. REFERENCES Happ, H.H., C. Pottle, and K.A. Wirgan (1979). An assessment of computer technology for large scale power system simulation. 1979 PICA Conference, pp. 316-324. Podmore, R., M. Liveright, and S. Virmani (1979). Application of an array processor for power system network computation. 1979 PICA Conference, pp. 325-331. Orem, F.M., and W.F. Tinney (1979). Evaluation of an array processor for power system applications. 1979 PICA Conference, pp. 345-350. Lamont, J.W., and R.H. Iveson (1981). Array processor applications in power System planning and operation. 7th PSCC, pp. 710-717. Brash, F.M., J.E. Vann Ness, and Sang-Chul Kang (1979). The use of a multiprocessor network for the transient stability problem. 1979 PICA Conference, pp. 337344. Housos, E.C., and O. Wing (1979). Solution of the load flow problem by a parallel optimization method. 1979 PICA Conference, pp. 332-336. Exploring applications of parallel processing to power system analysis problems. EPRI Special Report, EL-566-SR, Oct. 1977. Stott, B. (1974). Review of load-flow calculation method. Proc. IEEE, Vol. 62, No. 7, July 1974, pp. 916-929. Ward, J.B., and H.W. Hale (1968). Digital computer solution of power-flow problems. Proc. lEE, Vol. 115, No. 10, Oct. 1968, pp. 398-404. Stott, B., and O. Alsac (1974). Fast decoupled load flow. IEEE Trans. PAS, Vol. PAS-93, No. 3, May/June 1974, pp. 859-867. Takahashi, K., Y. Sekine, and T. Umezu (1968). Network-flow method applied to load flow calculation. IEEE Trans. PAS, Vol. PAS-87, No. 11, Nov. 1968, pp. 19391949. Sasson, A.M. (1969). Nonlinear programming solutions for the load-flow, minimumloss, and economic dispatching problems. IEEE Trans. PAS, Vol. PAS-88, No. 4, Apr. 1969, pp. 399-409. Freris, L.L., and A.M. Sas son (1968). Investigation of the load-flow problem. Proc. lEE, Vol. 115, No. 10, Oct. 1968, pp. 1459-1469.