零售市场中电量电价弹性系数分析
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摘要
掌握电力市场中电能需求随电能价格变动的规律（即需求响应规律）对于合
理确定电价与市场开拓是极为重要的。然而，由于当前我国零售电力市场尚未开
放，市场参与者的选择权有限，而且传统的电能销售模式对寻求用户需求对价格
的敏感度（即用户的电量电价弹性系数）分析的技术和信息支持均不完备，致使
电量电价弹性系数的分析具有很大难度。
为解决这一问题，本文首先尝试基于“当前，峰谷分时电价政策的执行，使
用户可以通过选择用电时间，从而间接地选择电能价格”这一现实，针对辽宁省
当前零售市场中的行业用电峰谷分时电价的统计数据，运用了一元线性回归模
型，挖掘出了电量电价弹性系数。又鉴于电量是受多种因素影响的，本文进而对
一些典型行业选用多元线性回归方法进行了分析，给出了电价及相关经济因素对
售电量的影响关系。多元回归模型与前一模型所得到的电价对售电量影响趋势相
近,从而验证了前一模型的可行性。
然而，研究表明，在实际情况下，部分用户某一时刻的用电量不仅与该时刻
的电价有关，还受到相邻时刻的电价影响。因此，本文进一步建立了电量电价弹
性矩阵，分析了由于用户分类及电价分类不同所引起的弹性矩阵结构的不同，并
在此基础上，提出了一种弹性矩阵的简化方法，给出了在我国当前零售端电力市
场中，电量电价弹性矩阵的求取过程，阐明了以月为单位时自弹性系数与交叉弹
性系数间的互补性。该方法不仅可以更好的反映电量电价的实际关系，而且提出
了新的数据处理方法，消除了地区差异和时间周期的影响，从而扩大了可用样本
数。实际应用表明，本文提出的电量电价弹性系数分析方法和模型能够反映当前
市场中的需求规律，具有一定的实用价值。
小样本问题是在我国当前零售电力市场分析中经常遇到的问题，因此，本文
又分析了偏最小二乘回归在小样本多元分析中的优势，及其在零售电力市场中的
应用领域。实例给出了其在配电商成本分析模型中的应用。而应用偏最小二乘回
归求得的成本分析指标，符合实际规律，可以用于对配电商进行评价和分析。
上述方法，已经作为核心算法在辽宁省电力市场分析与决策支持系统——电
量电价关系子系统中得以应用实现。
In order to determine the electricity price reasonably and to extend the power
market, it is important to master the principle that the energy consumption quantity
varies with the price in power market (called Demand Response principle). However,
the current retail power marker in our country has not opened and the option of the
market participants is limited. On the other hand, there are not enough technologies
and data needed by the customer’s price sensitivity analysis (called Price Elasticity of
Demand) in traditional energy sell patterns. All these have complicated the electricity
price elasticity analysis.
To solve this problem, this paper first bases on the fact that the performance of
Time of Use enables users to choose the price indirectly by choosing their using time.
And it digs out the price elasticity by using the simple linear regression method,
according to the industry consumptions in the current retail power market of province
Liaoning. Because the energy consumption quantity is affected by many factors,
multiple regression method has been used for analysis of the typical industries. The
results have reflected the relationship between energy consumption quantity and price
together with other factors. In the aspect of the tendency of price influence on energy
consumption quantity, the same results have been got from above two models. This
has proved the feasibility of the first model.
However, deeper study has proved that the energy consumption quantity is
affected not only by current price, but also by adjacent prices. Therefore, this paper
presents the constructing process of price elasticity matrix of demand, and analyses
the difference of elasticity matrix structure based on different user classes and price
sorts. Then it presents a simplified method for the elasticity matrix, and shows the
calculating process in our current retail power market by an example. The result has
shown that the self-elasticity coefficients and the cross-elasticity coefficients are
compensative. This method can not only reflect the relation between energy
consumption quantity and price more reasonably, but also enlarge the example
number by presenting a new method for data proceeding to remove the effect of place
difference and time cycle. The actual applications have proved that the models
provided in this paper can reflect the Demand Response principle in current retail
market, and own some practical effects.
Considering that the multivariate data analysis with few observations is often
involved in current retail power market, this paper has also analyzed the advantages of
partial least squares regression in multivariate data analysis with few observations and
its application areas in retail power market. And an example is given to show its use
in cost analysis for distribution traders. The results have shown that the calculated
indexes of cost analysis are reasonable and can be used to estimate the distribution
traders.
Above methods have been used as the most important arithmetic in price
subsystem of power system analysis and decision-making system for Liaoning
Province Power Company.
理确定电价与市场开拓是极为重要的。然而，由于当前我国零售电力市场尚未开
放，市场参与者的选择权有限，而且传统的电能销售模式对寻求用户需求对价格
的敏感度（即用户的电量电价弹性系数）分析的技术和信息支持均不完备，致使
电量电价弹性系数的分析具有很大难度。
为解决这一问题，本文首先尝试基于“当前，峰谷分时电价政策的执行，使
用户可以通过选择用电时间，从而间接地选择电能价格”这一现实，针对辽宁省
当前零售市场中的行业用电峰谷分时电价的统计数据，运用了一元线性回归模
型，挖掘出了电量电价弹性系数。又鉴于电量是受多种因素影响的，本文进而对
一些典型行业选用多元线性回归方法进行了分析，给出了电价及相关经济因素对
售电量的影响关系。多元回归模型与前一模型所得到的电价对售电量影响趋势相
近,从而验证了前一模型的可行性。
然而，研究表明，在实际情况下，部分用户某一时刻的用电量不仅与该时刻
的电价有关，还受到相邻时刻的电价影响。因此，本文进一步建立了电量电价弹
性矩阵，分析了由于用户分类及电价分类不同所引起的弹性矩阵结构的不同，并
在此基础上，提出了一种弹性矩阵的简化方法，给出了在我国当前零售端电力市
场中，电量电价弹性矩阵的求取过程，阐明了以月为单位时自弹性系数与交叉弹
性系数间的互补性。该方法不仅可以更好的反映电量电价的实际关系，而且提出
了新的数据处理方法，消除了地区差异和时间周期的影响，从而扩大了可用样本
数。实际应用表明，本文提出的电量电价弹性系数分析方法和模型能够反映当前
市场中的需求规律，具有一定的实用价值。
小样本问题是在我国当前零售电力市场分析中经常遇到的问题，因此，本文
又分析了偏最小二乘回归在小样本多元分析中的优势，及其在零售电力市场中的
应用领域。实例给出了其在配电商成本分析模型中的应用。而应用偏最小二乘回
归求得的成本分析指标，符合实际规律，可以用于对配电商进行评价和分析。
上述方法，已经作为核心算法在辽宁省电力市场分析与决策支持系统——电
量电价关系子系统中得以应用实现。
In order to determine the electricity price reasonably and to extend the power
market, it is important to master the principle that the energy consumption quantity
varies with the price in power market (called Demand Response principle). However,
the current retail power marker in our country has not opened and the option of the
market participants is limited. On the other hand, there are not enough technologies
and data needed by the customer’s price sensitivity analysis (called Price Elasticity of
Demand) in traditional energy sell patterns. All these have complicated the electricity
price elasticity analysis.
To solve this problem, this paper first bases on the fact that the performance of
Time of Use enables users to choose the price indirectly by choosing their using time.
And it digs out the price elasticity by using the simple linear regression method,
according to the industry consumptions in the current retail power market of province
Liaoning. Because the energy consumption quantity is affected by many factors,
multiple regression method has been used for analysis of the typical industries. The
results have reflected the relationship between energy consumption quantity and price
together with other factors. In the aspect of the tendency of price influence on energy
consumption quantity, the same results have been got from above two models. This
has proved the feasibility of the first model.
However, deeper study has proved that the energy consumption quantity is
affected not only by current price, but also by adjacent prices. Therefore, this paper
presents the constructing process of price elasticity matrix of demand, and analyses
the difference of elasticity matrix structure based on different user classes and price
sorts. Then it presents a simplified method for the elasticity matrix, and shows the
calculating process in our current retail power market by an example. The result has
shown that the self-elasticity coefficients and the cross-elasticity coefficients are
compensative. This method can not only reflect the relation between energy
consumption quantity and price more reasonably, but also enlarge the example
number by presenting a new method for data proceeding to remove the effect of place
difference and time cycle. The actual applications have proved that the models
provided in this paper can reflect the Demand Response principle in current retail
market, and own some practical effects.
Considering that the multivariate data analysis with few observations is often
involved in current retail power market, this paper has also analyzed the advantages of
partial least squares regression in multivariate data analysis with few observations and
its application areas in retail power market. And an example is given to show its use
in cost analysis for distribution traders. The results have shown that the calculated
indexes of cost analysis are reasonable and can be used to estimate the distribution
traders.
Above methods have been used as the most important arithmetic in price
subsystem of power system analysis and decision-making system for Liaoning
Province Power Company.
引文
[1] 于尔铿，韩放，谢开等，电力市场，北京：中国电力出版社，1998,1~50
[2] Sheen J N, Chen C S, Wang T Y, Response of large industrial customers to
electricity pricing by voluntary time-of-use in Taiwan, IEE, Proc.-Gener. Transm.
Distrib, 1995, 142(2): 157~166
[3] 王 建 新 ， 彭 巨 等 ， 电 力 市 场 营 销 分 析 中 的 两 类 建 模 问 题 ， 电 力 需 求 侧 管
理,2001,3(2):24~27
[4] Bushnell James, Mansur Erin. The impact of retail rate deregulation on electricity
consumption in San Diego, University of California Energy Institute, Technical
report, 2001,1~42
[5] 曹世光,慈义,电力需求预测模型研究,中国电力, 1997,30(11):16~18
[6] Daniel S. Kirschen, Goran Strbac, Factoring the Elasticity of Demand in Electricity
Prices, IEEE TRANSACTIONS ON POWER SYSTEMS, MAY
2000,15(2):612~617
[7] Y.Q.He, A.K.David, Time-of-use electricity pricing based on global optimization
for generation expansion planning, Proceedings of the 4th International
Conference on Advances in Power System Control, Operation and Management,
November 1997
[8] Rajesh Rajaraman, The effect of demand elasticity on security prices for the PoolCo
and multi-lateral contract models, IEEE, August 1997, 12(3): 1177～1184
[9] A.K.David, Y.Z.Li, Consumer rationality assumptions in the real-time pricing of
electricity. IEE, JULY 1992, 139(4)：315 -322
[10] Mika Rasanen, Jukka Ruusunen, Identification of consumers' price responses in
the dynamic pricing of electricity, IEEE, 1995,2：1182 -1187
[11] 古扎拉蒂著，计量经济学，中国人民大学出版社,2000
48
[12] 蒋平 ,任开 军等 ，多 元 组 内回 归 分 析 的 模 型 及 其 算 法.模 糊系 统 与数 学 ,
2002,16(3):99~103
[13] 辽宁统计年鉴，辽宁省人民政府主办，2000～2001
[14] 李扬，王治华，卢毅，李军红，张长沪，峰谷分时电价的实施及大工业用户的
相应，电力系统自动化，2001，25（8）：45~48
[15] 钱绍圣,测量不确定度,清华大学出版社,2002
[16] 曹妨,韩放,杨以涵等,实时电价的意义与实现,电网技术,1995,19(10):56~59
[17] Caves D W, Herriges J A, Windle R J, Customer response to
interruptible and curtailable rates, EPRI, Christensen L R
Associates Inc., Technical report, 1988
[18] Daniel S.Kirschen, Demand-side view of electricity markets, IEEE Transactions on
Power Systems, May 2003, 18(2): 520~529
[19] A.K.David, Y.Z.Li. Effect of inter-temporal factors on the real time pricing of
electricity, IEEE Transactions on Power Systems, February 1993, 8(1): 44~52
[20] J-N Sheen, C-S Chen, T-Y Wang, Response of large industrial customers to
electricity pricing by voluntary time-of-use inTaiwan, IEE Proc-Gener. Transm.
Distrib, March 1995, 142(2): 157~166
[21] J-N Sheen, C-S Chen, J-K Yang, Time of use pricing for load management
programs in Taiwan power company, IEEE Transactions on Power Systems,
February 1994, 9(1): 388~396
[22] A.K.David, Y.Z.Li. A comparison of system response for different types of real
time pricing, IEE International Conference on Advances in Power System Control,
Operation and Management, Hong Kong, November 1991.385~390
[23] S.Rahman, Rinaldy, An efficient load model for analyzing demand side
management impacts, IEEE Transactions on Power Systems, August 1993, 8(3):
1219~1226
[24] Michele Benini, Mirko Marracci, Paolo Pelacchi, Day-ahead market price
volatility analysis in deregulated electricity markets, Power Engineering Society
49
Summer Meeting, IEEE, July 2002, 3: 1354 ~1359
[25] Gerard L.Doorman, Ivar Wangensteen, Demand side provision of peaking capacity
and reserves in Deregulated power systems, Power Engineering Society Winter
Meeting, IEEE, Jan 2000, 3: 1766~1771
[26] J.G.Roos, I.E.Lane, Industrial power demand Response analysis for one-part
real-time pricing, IEEE Transactions on Power Systems, February 1998, 13(1):
159~164
[27] Rajesh Rajaraman, Jayant V.Sarlashkar, Fernando L.Alvarado. The effect of
demand elasticity on security prices for the poolco and multi-lateral contract
models, IEEE Transactions on Power Systems, August 1997, 12(3): 1177~1184
[28] 张恒喜，郭基联，朱家元，虞健飞，小样本多元数据分析方法及应用，西安：
西北工业大学出版社,2002,22~43
[29] 王惠文，偏最小二乘回归方法及其应用，北京：国防工业出版社,1999,201~223
[30] 张伏生，汪鸿，韩涕，孙晓强等，基于偏最小二乘回归分析的短期负荷预测，
电网技术，2003，27(3)：36~40
[2] Sheen J N, Chen C S, Wang T Y, Response of large industrial customers to
electricity pricing by voluntary time-of-use in Taiwan, IEE, Proc.-Gener. Transm.
Distrib, 1995, 142(2): 157~166
[3] 王 建 新 ， 彭 巨 等 ， 电 力 市 场 营 销 分 析 中 的 两 类 建 模 问 题 ， 电 力 需 求 侧 管
理,2001,3(2):24~27
[4] Bushnell James, Mansur Erin. The impact of retail rate deregulation on electricity
consumption in San Diego, University of California Energy Institute, Technical
report, 2001,1~42
[5] 曹世光,慈义,电力需求预测模型研究,中国电力, 1997,30(11):16~18
[6] Daniel S. Kirschen, Goran Strbac, Factoring the Elasticity of Demand in Electricity
Prices, IEEE TRANSACTIONS ON POWER SYSTEMS, MAY
2000,15(2):612~617
[7] Y.Q.He, A.K.David, Time-of-use electricity pricing based on global optimization
for generation expansion planning, Proceedings of the 4th International
Conference on Advances in Power System Control, Operation and Management,
November 1997
[8] Rajesh Rajaraman, The effect of demand elasticity on security prices for the PoolCo
and multi-lateral contract models, IEEE, August 1997, 12(3): 1177～1184
[9] A.K.David, Y.Z.Li, Consumer rationality assumptions in the real-time pricing of
electricity. IEE, JULY 1992, 139(4)：315 -322
[10] Mika Rasanen, Jukka Ruusunen, Identification of consumers' price responses in
the dynamic pricing of electricity, IEEE, 1995,2：1182 -1187
[11] 古扎拉蒂著，计量经济学，中国人民大学出版社,2000
48
[12] 蒋平 ,任开 军等 ，多 元 组 内回 归 分 析 的 模 型 及 其 算 法.模 糊系 统 与数 学 ,
2002,16(3):99~103
[13] 辽宁统计年鉴，辽宁省人民政府主办，2000～2001
[14] 李扬，王治华，卢毅，李军红，张长沪，峰谷分时电价的实施及大工业用户的
相应，电力系统自动化，2001，25（8）：45~48
[15] 钱绍圣,测量不确定度,清华大学出版社,2002
[16] 曹妨,韩放,杨以涵等,实时电价的意义与实现,电网技术,1995,19(10):56~59
[17] Caves D W, Herriges J A, Windle R J, Customer response to
interruptible and curtailable rates, EPRI, Christensen L R
Associates Inc., Technical report, 1988
[18] Daniel S.Kirschen, Demand-side view of electricity markets, IEEE Transactions on
Power Systems, May 2003, 18(2): 520~529
[19] A.K.David, Y.Z.Li. Effect of inter-temporal factors on the real time pricing of
electricity, IEEE Transactions on Power Systems, February 1993, 8(1): 44~52
[20] J-N Sheen, C-S Chen, T-Y Wang, Response of large industrial customers to
electricity pricing by voluntary time-of-use inTaiwan, IEE Proc-Gener. Transm.
Distrib, March 1995, 142(2): 157~166
[21] J-N Sheen, C-S Chen, J-K Yang, Time of use pricing for load management
programs in Taiwan power company, IEEE Transactions on Power Systems,
February 1994, 9(1): 388~396
[22] A.K.David, Y.Z.Li. A comparison of system response for different types of real
time pricing, IEE International Conference on Advances in Power System Control,
Operation and Management, Hong Kong, November 1991.385~390
[23] S.Rahman, Rinaldy, An efficient load model for analyzing demand side
management impacts, IEEE Transactions on Power Systems, August 1993, 8(3):
1219~1226
[24] Michele Benini, Mirko Marracci, Paolo Pelacchi, Day-ahead market price
volatility analysis in deregulated electricity markets, Power Engineering Society
49
Summer Meeting, IEEE, July 2002, 3: 1354 ~1359
[25] Gerard L.Doorman, Ivar Wangensteen, Demand side provision of peaking capacity
and reserves in Deregulated power systems, Power Engineering Society Winter
Meeting, IEEE, Jan 2000, 3: 1766~1771
[26] J.G.Roos, I.E.Lane, Industrial power demand Response analysis for one-part
real-time pricing, IEEE Transactions on Power Systems, February 1998, 13(1):
159~164
[27] Rajesh Rajaraman, Jayant V.Sarlashkar, Fernando L.Alvarado. The effect of
demand elasticity on security prices for the poolco and multi-lateral contract
models, IEEE Transactions on Power Systems, August 1997, 12(3): 1177~1184
[28] 张恒喜，郭基联，朱家元，虞健飞，小样本多元数据分析方法及应用，西安：
西北工业大学出版社,2002,22~43
[29] 王惠文，偏最小二乘回归方法及其应用，北京：国防工业出版社,1999,201~223
[30] 张伏生，汪鸿，韩涕，孙晓强等，基于偏最小二乘回归分析的短期负荷预测，
电网技术，2003，27(3)：36~40