Based on the iterative bit-filling procedure, a computationally efficient bit and power allocation algorithm is presented. The algorithm improves the conventional bit-filling algorithms by maintaining only a subset of...Based on the iterative bit-filling procedure, a computationally efficient bit and power allocation algorithm is presented. The algorithm improves the conventional bit-filling algorithms by maintaining only a subset of subcarriers for computation in each iteration, which reduces the complexity without any performance degradation. Moreover, a modified algorithm with even lower complexity is developed, and equal power allocation is introduced as an initial allocation to accelerate its convergence. Simulation results show that the modified algorithm achieves a considerable complexity reduction while causing only a minor drop in performance.展开更多
Nowadays, power quality issues are becoming a significant research topic because of the increasing inclusion of very sensitive devices and considerable renewable energy sources. In general, most of the previous power ...Nowadays, power quality issues are becoming a significant research topic because of the increasing inclusion of very sensitive devices and considerable renewable energy sources. In general, most of the previous power quality classification techniques focused on single power quality events and did not include an optimal feature selection process. This paper presents a classification system that employs Wavelet Transform and the RMS profile to extract the main features of the measured waveforms containing either single or complex disturbances. A data mining process is designed to select the optimal set of features that better describes each disturbance present in the waveform. Support Vector Machine binary classifiers organized in a “One Vs Rest” architecture are individually optimized to classify single and complex disturbances. The parameters that rule the performance of each binary classifier are also individually adjusted using a grid search algorithm that helps them achieve optimal performance. This specialized process significantly improves the total classification accuracy. Several single and complex disturbances were simulated in order to train and test the algorithm. The results show that the classifier is capable of identifying >99% of single disturbances and >97% of complex disturbances.展开更多
For future wireless communication systems,Power Domain Non-Orthogonal Multiple Access(PD-NOMA)using an advanced receiver has been considered as a promising radio access technology candidate.Power allocation plays an i...For future wireless communication systems,Power Domain Non-Orthogonal Multiple Access(PD-NOMA)using an advanced receiver has been considered as a promising radio access technology candidate.Power allocation plays an important role in the PD-NOMA system because it considerably affects the total throughput and Geometric Mean User Throughput(GMUT)performance.However,most existing studies have not completely accounted for the computational complexity of the power allocation process when the User Terminals(UTs)move in a slow fading channel environment.To resolve such problems,a power allocation method is proposed to considerably reduce the search space of a Full Search Power(FSP)allocation algorithm.The initial power reallocation coefficients will be set to start with former optimal values by the proposed Lemma before searching for optimal power reallocation coefficients based on total throughput performance.Step size and correction granularity will be adjusted within a much narrower power search range while invalid power combinations may be reasonably discarded during the search process.The simulation results show that the proposed power reallocation scheme can greatly reduce computational complexity while the total throughput and GMUT performance loss are not greater than 1.5%compared with the FSP algorithm.展开更多
To analyze and control complex networks effectively, this paper puts forward a new kind of scheme, which takes control separately in each area and can achieve the network’s coordinated optimality. The proposed algori...To analyze and control complex networks effectively, this paper puts forward a new kind of scheme, which takes control separately in each area and can achieve the network’s coordinated optimality. The proposed algorithm is made up of two parts: the first part decomposes the network into several independent areas based on community structure and decouples the information flow and control power among areas; the second part selects the center nodes from each area with the help of the control centrality index. As long as the status of center nodes is kept on a satisfactory level in each area, the whole system is under effective control. Finally, the algorithm is applied to power grids, and the simulations prove its effectiveness.展开更多
A low complexity Per-Antenna Power Control (PAPC) approach based on Minimum Mean Squared Error (MMSE) detection for V-BLAST is proposed in this paper. The PAPC approach is developed for minimizing the Bit Error Ra...A low complexity Per-Antenna Power Control (PAPC) approach based on Minimum Mean Squared Error (MMSE) detection for V-BLAST is proposed in this paper. The PAPC approach is developed for minimizing the Bit Error Rate (BER) averaged over all substreams when the data throughput and the total transmit power keep constant over time. Simulation results show that the Power-controlled V-BLAST (P-BLAST) outperforms the conventional V-BLAST in terms of BER performance with MMSE detector, especially in presence of high spatial correlation between antennas. However, the additional complexity for P-BLAST is not high. When MMSE detector is adopted, the P-BLAST can achieve a comparable BER performance to that of conventional V-BLAST with Maximum Likelihood (ML) detector but with low complexity.展开更多
Information theoretical results have shown that Distributed Antenna Systems (DAS) can obtain higher capacity than Co-located Antenna Systems (CAS). In this paper,we investigate a downlink port selection and power allo...Information theoretical results have shown that Distributed Antenna Systems (DAS) can obtain higher capacity than Co-located Antenna Systems (CAS). In this paper,we investigate a downlink port selection and power allocation scheme in Distributed Multiple-Input Multiple-Output (D-MIMO) systems,where Distributed Antenna (DA) ports randomly locate in the cell. The contri-bution of this paper can be summarized as two parts. Firstly,we analyze how antenna correlation af-fects power allocation in D-MIMO systems. Secondly,based on large scale fading and antenna corre-lation,a low-complexity port selection and power allocation scheme is proposed. In the proposed scheme,we take both large scale fading and antenna correlation into consideration. Moreover,User Equipment (UE) only needs to feedback the rank of transmit antenna correlation matrix,which will not increase system complexity too much. Simulation results verify the capacity improvement based on the proposed power allocation scheme.展开更多
In order to accurately simulate the game behaviors of the market participants with bounded rationality, a new dynamic Cournot game model of power market considering the constraints of transmission network is proposed ...In order to accurately simulate the game behaviors of the market participants with bounded rationality, a new dynamic Cournot game model of power market considering the constraints of transmission network is proposed in this paper. The model is represented by a discrete differential equations embedded with the maximization problem of the social benefit of market. The Nash equilibrium and its stability in a duopoly game are quantitatively analyzed. It is found that there are different Nash equilibriums with different market parameters corresponding to different operating conditions of power network, i.e., congestion and non-congestion, and even in some cases there is not Nash equilibrium at all. The market dynamic behaviors are numerically simulated, in which the periodic or chaotic behaviors are focused when the market parameters are beyond the stability region of Nash equilibrium.展开更多
A new real and complex-valued hybrid time-delay neural network(TDNN)is proposed for modeling and linearizing the broad-band power amplifier(BPA).The neural network includes the generalized memory effect of input signa...A new real and complex-valued hybrid time-delay neural network(TDNN)is proposed for modeling and linearizing the broad-band power amplifier(BPA).The neural network includes the generalized memory effect of input signals,complex-valued input signals and the fractional order of a complex-valued input signal module,and,thus,the modeling accuracy is improved significantly.A comparative study of the normalized mean square error(NMSE)of the real and complex-valued hybrid TDNN for different spread constants,memory depths,node numbers,and order numbers is studied so as to establish an optimal TDNN as an effective baseband model,suitable for modeling strong nonlinearity of the BPA.A 51-dBm BPA with a 25-MHz bandwidth mixed test signal is used to verify the effectiveness of the proposed model.Compared with the memory polynomial(MP)model and the real-valued TDNN,the real and complex-valued hybrid TDNN is highly effective,leading to an improvement of 5 dB in the NMSE.In addition,the real and complex-valued hybrid TDNN has an improvement of 0.6 dB over the generalized MP model in the NMSE.Also,it has better numerical stability.Moreover,the proposed TDNN presents a significant improvement over the real-valued TDNN and the MP models in suppressing out-of-band spectral regrowth.展开更多
A new method and corresponding numerical procedure are introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method can overcome the ...A new method and corresponding numerical procedure are introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method can overcome the biased and inaccurate faults of graphical linear fitting methods commonly used in current network research. Furthermore, it is verified to have higher goodness-of-fit than graphical methods by comparing the KS (Kolmogorov-Smirnov) test statistics for 10 CNN (Connecting Nearest-Neighbor) networks.展开更多
In this paper, an enhanced greedy bit and power allocation algorithms for orthogonal frequency division multiplexing (OFDM) communication systems are introduced. These algorithms combine low complexity greedy power al...In this paper, an enhanced greedy bit and power allocation algorithms for orthogonal frequency division multiplexing (OFDM) communication systems are introduced. These algorithms combine low complexity greedy power allocation algorithms with a simplified maximum ratio combining (MRC) precoding technique at the transmitter for maximizing the average data throughput of OFDM communication systems. Results of computer simulations show that precoding is an effective technique for improving the throughput performance of the proposed bit and power allocation algorithms.展开更多
Along with the further development of science and technology, computer hardware and the Intemet are in a rapid development, and information technology has been widely used in all fields so that complex problems are si...Along with the further development of science and technology, computer hardware and the Intemet are in a rapid development, and information technology has been widely used in all fields so that complex problems are simply solved. Because of the needs for the development, software starts to mutually integrate with complex power network, making the scale of software increase greatly. Such a growing trend of software promotes soft-ware development to go beyond a general understanding and control and thus a complex system is formed. It is necessary to strengthen the research of complex network theory, and this is a new way to help people study the complexity of software systems. In this paper, the development course of complex dynamic network is introduced simply and the use of complex power network in the software engineering is summarized. Hopefully, this paper can help the crossover study of complex power network and software engineering in the future.展开更多
Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjugate Floquet multipliers coming out of unit circle on the Poincare section. A three-bus system is employed to reveal the relat...Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjugate Floquet multipliers coming out of unit circle on the Poincare section. A three-bus system is employed to reveal the relationship between torus bifurcation and some complex dynamics. Based on theoretical analysis and simulation studies, it is found that torus bifurcation is a typical route to chaos in power system. Some complex dynamics usually occur after a torus bifurcation, such as self-organization, deep bifurcations, exquisite structure, coexistence of chaos and divergence. It is also found that chaos has close relationship with various instability scenarios of power systems. Studies of this paper are helpful to understand the mechanism of torus bifurcation in power system and relationship of chaos and power system instabilities.展开更多
This paper proposes a companding scheme, where small signals are enlarged and large signals are reduced, to reduce the Peak-to-Average Power Ratio(PAPR). Computer simulation results show that the proposed technique ha...This paper proposes a companding scheme, where small signals are enlarged and large signals are reduced, to reduce the Peak-to-Average Power Ratio(PAPR). Computer simulation results show that the proposed technique has two advantages at least when compared with the conventional methods such as partial transmit sequence, selective mapping and the previous companding. First, it gets better PAPR performances with a lower complexity. Second, the scheme achieves greater performances gain with hardly any damnification of OFDM signals in some degree.展开更多
Wireless relay and network coding are two critical techniques to increase the reliability and throughput of wireless cooperative communication systems. In this paper, a complex field network coding (CFNC) scheme wit...Wireless relay and network coding are two critical techniques to increase the reliability and throughput of wireless cooperative communication systems. In this paper, a complex field network coding (CFNC) scheme with the K-th best relay selection (KBS) is proposed and investigated, wherein the K-th best relay is selected to forward the multiplexed signal to the destination. First, the upper bound of the symbol error probability (SEP), the diversity order, and the coding gain are derived for the CFNC scheme with KBS. Then, the coding gain is utilized as the optimized cri- terion to determine the optimal power allocation. It is validated through analysis and simulation that the CFNC scheme with KBS can achieve full diversity only when K=I, while the diversity order decreases with increasing parameter K, and the optimal power allocation can significantly improve the performance of the CFNC scheme with KBS.展开更多
In this paper,a series of major policy decisions used to improve the power grid reliability,reduce the risk and losses of major power outages,and realize the modernization of 21st century power grid are discussed. The...In this paper,a series of major policy decisions used to improve the power grid reliability,reduce the risk and losses of major power outages,and realize the modernization of 21st century power grid are discussed. These decisions were adopted by American government and would also be helpful for the strategic development of Chinese power grid. It is proposed that China should take precaution,carry out security research on the overall dynamic behaviour characteristics of the UHV grid using the complexity theory,and finally provide safeguard for the Chinese UHV grid. It is also pointed out that,due to the lack of matured approaches to controll a cascading failure,the primary duty of a system operator is to work as a "watchdog" for the grid operation security,eliminate the cumulative effect and reduce the risk and losses of major cascading outages with the help of EMS and WAMS.展开更多
It is known that complex networks in nature exhibit some significant statistical features. We notice power law distributions which frequently emerge with respect to network structures of various quantities. One exampl...It is known that complex networks in nature exhibit some significant statistical features. We notice power law distributions which frequently emerge with respect to network structures of various quantities. One example is the scale-freeness which is described by the degree distribution in the power law shape. In this paper, within an analytical approach, we investigate the analytical conditions under which the distribution is reduced to the power law. We show that power law distributions are obtained without introducing conditions specific to each system or variable. Conversely, if we demand no special condition to a distribution, it is imposed to follow the power law. This result explains the universality and the ubiquitous presence of the power law distributions in complex networks.展开更多
基金The National High Technology Research and Devel-opment Program of China (863Program) (No2006AA01Z263)the National Natural Science Foundation of China (No60496311)
文摘Based on the iterative bit-filling procedure, a computationally efficient bit and power allocation algorithm is presented. The algorithm improves the conventional bit-filling algorithms by maintaining only a subset of subcarriers for computation in each iteration, which reduces the complexity without any performance degradation. Moreover, a modified algorithm with even lower complexity is developed, and equal power allocation is introduced as an initial allocation to accelerate its convergence. Simulation results show that the modified algorithm achieves a considerable complexity reduction while causing only a minor drop in performance.
文摘Nowadays, power quality issues are becoming a significant research topic because of the increasing inclusion of very sensitive devices and considerable renewable energy sources. In general, most of the previous power quality classification techniques focused on single power quality events and did not include an optimal feature selection process. This paper presents a classification system that employs Wavelet Transform and the RMS profile to extract the main features of the measured waveforms containing either single or complex disturbances. A data mining process is designed to select the optimal set of features that better describes each disturbance present in the waveform. Support Vector Machine binary classifiers organized in a “One Vs Rest” architecture are individually optimized to classify single and complex disturbances. The parameters that rule the performance of each binary classifier are also individually adjusted using a grid search algorithm that helps them achieve optimal performance. This specialized process significantly improves the total classification accuracy. Several single and complex disturbances were simulated in order to train and test the algorithm. The results show that the classifier is capable of identifying >99% of single disturbances and >97% of complex disturbances.
基金supported in part by the Science and Technology Research Program of the National Science Foundation of China(61671096)Chongqing Research Program of Basic Science and Frontier Technology(cstc2017jcyjBX0005)+1 种基金Chongqing Municipal Education Commission(KJQN201800642)Doctoral Student Training Program(BYJS2016009).
文摘For future wireless communication systems,Power Domain Non-Orthogonal Multiple Access(PD-NOMA)using an advanced receiver has been considered as a promising radio access technology candidate.Power allocation plays an important role in the PD-NOMA system because it considerably affects the total throughput and Geometric Mean User Throughput(GMUT)performance.However,most existing studies have not completely accounted for the computational complexity of the power allocation process when the User Terminals(UTs)move in a slow fading channel environment.To resolve such problems,a power allocation method is proposed to considerably reduce the search space of a Full Search Power(FSP)allocation algorithm.The initial power reallocation coefficients will be set to start with former optimal values by the proposed Lemma before searching for optimal power reallocation coefficients based on total throughput performance.Step size and correction granularity will be adjusted within a much narrower power search range while invalid power combinations may be reasonably discarded during the search process.The simulation results show that the proposed power reallocation scheme can greatly reduce computational complexity while the total throughput and GMUT performance loss are not greater than 1.5%compared with the FSP algorithm.
基金the National Science Foundation of China (No.50525721, 50595411)the National Basic Research Program of China(No.G2004CB217902)
文摘To analyze and control complex networks effectively, this paper puts forward a new kind of scheme, which takes control separately in each area and can achieve the network’s coordinated optimality. The proposed algorithm is made up of two parts: the first part decomposes the network into several independent areas based on community structure and decouples the information flow and control power among areas; the second part selects the center nodes from each area with the help of the control centrality index. As long as the status of center nodes is kept on a satisfactory level in each area, the whole system is under effective control. Finally, the algorithm is applied to power grids, and the simulations prove its effectiveness.
基金This project was supported by the National Natural Science Foundation of China ( 60496314).
文摘A low complexity Per-Antenna Power Control (PAPC) approach based on Minimum Mean Squared Error (MMSE) detection for V-BLAST is proposed in this paper. The PAPC approach is developed for minimizing the Bit Error Rate (BER) averaged over all substreams when the data throughput and the total transmit power keep constant over time. Simulation results show that the Power-controlled V-BLAST (P-BLAST) outperforms the conventional V-BLAST in terms of BER performance with MMSE detector, especially in presence of high spatial correlation between antennas. However, the additional complexity for P-BLAST is not high. When MMSE detector is adopted, the P-BLAST can achieve a comparable BER performance to that of conventional V-BLAST with Maximum Likelihood (ML) detector but with low complexity.
基金Supported by the National High Technology Research and Development Program of China (863 Program,No.2006AA01Z272 and No.2006AA01Z283)Beijing Municipal Science & Technology Commission (No.D08080100620802)
文摘Information theoretical results have shown that Distributed Antenna Systems (DAS) can obtain higher capacity than Co-located Antenna Systems (CAS). In this paper,we investigate a downlink port selection and power allocation scheme in Distributed Multiple-Input Multiple-Output (D-MIMO) systems,where Distributed Antenna (DA) ports randomly locate in the cell. The contri-bution of this paper can be summarized as two parts. Firstly,we analyze how antenna correlation af-fects power allocation in D-MIMO systems. Secondly,based on large scale fading and antenna corre-lation,a low-complexity port selection and power allocation scheme is proposed. In the proposed scheme,we take both large scale fading and antenna correlation into consideration. Moreover,User Equipment (UE) only needs to feedback the rank of transmit antenna correlation matrix,which will not increase system complexity too much. Simulation results verify the capacity improvement based on the proposed power allocation scheme.
文摘In order to accurately simulate the game behaviors of the market participants with bounded rationality, a new dynamic Cournot game model of power market considering the constraints of transmission network is proposed in this paper. The model is represented by a discrete differential equations embedded with the maximization problem of the social benefit of market. The Nash equilibrium and its stability in a duopoly game are quantitatively analyzed. It is found that there are different Nash equilibriums with different market parameters corresponding to different operating conditions of power network, i.e., congestion and non-congestion, and even in some cases there is not Nash equilibrium at all. The market dynamic behaviors are numerically simulated, in which the periodic or chaotic behaviors are focused when the market parameters are beyond the stability region of Nash equilibrium.
基金The National Natural Science Foundation of China(No.61561052,61701262)the Science and Technology Foundation of Henan Province(No.182102410062,182102210114)the Science and Technology Foundation of Henan Educational Committee(No.17A510018)
文摘A new real and complex-valued hybrid time-delay neural network(TDNN)is proposed for modeling and linearizing the broad-band power amplifier(BPA).The neural network includes the generalized memory effect of input signals,complex-valued input signals and the fractional order of a complex-valued input signal module,and,thus,the modeling accuracy is improved significantly.A comparative study of the normalized mean square error(NMSE)of the real and complex-valued hybrid TDNN for different spread constants,memory depths,node numbers,and order numbers is studied so as to establish an optimal TDNN as an effective baseband model,suitable for modeling strong nonlinearity of the BPA.A 51-dBm BPA with a 25-MHz bandwidth mixed test signal is used to verify the effectiveness of the proposed model.Compared with the memory polynomial(MP)model and the real-valued TDNN,the real and complex-valued hybrid TDNN is highly effective,leading to an improvement of 5 dB in the NMSE.In addition,the real and complex-valued hybrid TDNN has an improvement of 0.6 dB over the generalized MP model in the NMSE.Also,it has better numerical stability.Moreover,the proposed TDNN presents a significant improvement over the real-valued TDNN and the MP models in suppressing out-of-band spectral regrowth.
基金Project supported by the National Natural Science Foundation of China (Nos.70431002, 70401019)
文摘A new method and corresponding numerical procedure are introduced to estimate scaling exponents of power-law degree distribution and hierarchical clustering function for complex networks. This method can overcome the biased and inaccurate faults of graphical linear fitting methods commonly used in current network research. Furthermore, it is verified to have higher goodness-of-fit than graphical methods by comparing the KS (Kolmogorov-Smirnov) test statistics for 10 CNN (Connecting Nearest-Neighbor) networks.
文摘In this paper, an enhanced greedy bit and power allocation algorithms for orthogonal frequency division multiplexing (OFDM) communication systems are introduced. These algorithms combine low complexity greedy power allocation algorithms with a simplified maximum ratio combining (MRC) precoding technique at the transmitter for maximizing the average data throughput of OFDM communication systems. Results of computer simulations show that precoding is an effective technique for improving the throughput performance of the proposed bit and power allocation algorithms.
文摘Along with the further development of science and technology, computer hardware and the Intemet are in a rapid development, and information technology has been widely used in all fields so that complex problems are simply solved. Because of the needs for the development, software starts to mutually integrate with complex power network, making the scale of software increase greatly. Such a growing trend of software promotes soft-ware development to go beyond a general understanding and control and thus a complex system is formed. It is necessary to strengthen the research of complex network theory, and this is a new way to help people study the complexity of software systems. In this paper, the development course of complex dynamic network is introduced simply and the use of complex power network in the software engineering is summarized. Hopefully, this paper can help the crossover study of complex power network and software engineering in the future.
基金Supported by the Special Fund of the National Fundamental Research (No. 2004CB217904)National Natural Science Foundation of China (No. 50595413)Program for New Century Excellent Talents in Universities, Fok Ying Tung Education Foundation (No.104019 )Foundation for the Authors of National Excellent Doctoral Dissertation (No. 200439) ,Key Project of Chinese Ministry of Education (No. 10047).
文摘Torus bifurcation is a relatively complicated bifurcation caused by a pair of complex conjugate Floquet multipliers coming out of unit circle on the Poincare section. A three-bus system is employed to reveal the relationship between torus bifurcation and some complex dynamics. Based on theoretical analysis and simulation studies, it is found that torus bifurcation is a typical route to chaos in power system. Some complex dynamics usually occur after a torus bifurcation, such as self-organization, deep bifurcations, exquisite structure, coexistence of chaos and divergence. It is also found that chaos has close relationship with various instability scenarios of power systems. Studies of this paper are helpful to understand the mechanism of torus bifurcation in power system and relationship of chaos and power system instabilities.
文摘This paper proposes a companding scheme, where small signals are enlarged and large signals are reduced, to reduce the Peak-to-Average Power Ratio(PAPR). Computer simulation results show that the proposed technique has two advantages at least when compared with the conventional methods such as partial transmit sequence, selective mapping and the previous companding. First, it gets better PAPR performances with a lower complexity. Second, the scheme achieves greater performances gain with hardly any damnification of OFDM signals in some degree.
基金supported by the Major State Basic Research Development Program of China(973 Program No.2012CB316100)the National Natural Science Foundation of China(Nos.61032002/61271246)the 111 Project(No.111-2-14)
文摘Wireless relay and network coding are two critical techniques to increase the reliability and throughput of wireless cooperative communication systems. In this paper, a complex field network coding (CFNC) scheme with the K-th best relay selection (KBS) is proposed and investigated, wherein the K-th best relay is selected to forward the multiplexed signal to the destination. First, the upper bound of the symbol error probability (SEP), the diversity order, and the coding gain are derived for the CFNC scheme with KBS. Then, the coding gain is utilized as the optimized cri- terion to determine the optimal power allocation. It is validated through analysis and simulation that the CFNC scheme with KBS can achieve full diversity only when K=I, while the diversity order decreases with increasing parameter K, and the optimal power allocation can significantly improve the performance of the CFNC scheme with KBS.
文摘In this paper,a series of major policy decisions used to improve the power grid reliability,reduce the risk and losses of major power outages,and realize the modernization of 21st century power grid are discussed. These decisions were adopted by American government and would also be helpful for the strategic development of Chinese power grid. It is proposed that China should take precaution,carry out security research on the overall dynamic behaviour characteristics of the UHV grid using the complexity theory,and finally provide safeguard for the Chinese UHV grid. It is also pointed out that,due to the lack of matured approaches to controll a cascading failure,the primary duty of a system operator is to work as a "watchdog" for the grid operation security,eliminate the cumulative effect and reduce the risk and losses of major cascading outages with the help of EMS and WAMS.
文摘It is known that complex networks in nature exhibit some significant statistical features. We notice power law distributions which frequently emerge with respect to network structures of various quantities. One example is the scale-freeness which is described by the degree distribution in the power law shape. In this paper, within an analytical approach, we investigate the analytical conditions under which the distribution is reduced to the power law. We show that power law distributions are obtained without introducing conditions specific to each system or variable. Conversely, if we demand no special condition to a distribution, it is imposed to follow the power law. This result explains the universality and the ubiquitous presence of the power law distributions in complex networks.