CN105161258A

CN105161258A - Wide-range current transformer and gas gap length calculation method

Info

Publication number: CN105161258A
Application number: CN201510624166.5A
Authority: CN
Inventors: 李志新; 徐敏锐; 卢树峰; 杨世海; 吴桥; 陈铭明; 赵双双; 陈刚
Original assignee: State Grid Corp of China SGCC; State Grid Jiangsu Electric Power Co Ltd; Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
Current assignee: State Grid Corp of China SGCC; State Grid Jiangsu Electric Power Co Ltd; Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
Priority date: 2015-09-25
Filing date: 2015-09-25
Publication date: 2015-12-16

Abstract

A wide range current transformer and air gap length calculation method proposed by the present invention, wherein the structure of the transformer includes a primary winding, a secondary winding and an iron core, the iron core is composed of a fixed iron core and a movable iron core, and the movable The iron core is separated from the transformer to form an air gap; the structure is simple and easy to realize; when the primary current of the current transformer is large, the magnetization curve of the iron core can be placed in the linear region by adjusting the length of the air gap, effectively solving the problem caused by the iron core. The problem of increased error caused by core saturation reduces core loss; the air gap length calculation method and the current transformer error calculation formula proposed by the present invention are clear, and the calculation and analysis are more convenient.

Description

A Wide Range Current Transformer and Calculation Method of Air Gap Length

技术领域technical field

本发明属于电流互感器领域，尤其涉及一种通过改变铁芯气隙长度拓宽电流互感器量程的结构及其设计方法。The invention belongs to the field of current transformers, and in particular relates to a structure and a design method for widening the measuring range of the current transformer by changing the length of the iron core air gap.

背景技术Background technique

电流互感器广泛应用于电力系统发电、输电、变电、配各环节的电能计量中，将一次侧的大电流转化为统一的二次侧小电流，其性能的优劣极大地影响计量和测控的准确性。由于电网不同地点、不同时间段的电流大小悬殊、从几安到几万安不等，为了便于测量、保护和控制，电流互感器往往需要根据测量的一次电流范围不同制定不同的变比，从而使得二次电流在规定范围之内。Current transformers are widely used in electric energy metering in the power generation, transmission, transformation, and distribution of power systems. They convert the large current on the primary side into a unified small current on the secondary side. The performance of the current transformer greatly affects the measurement and measurement and control. accuracy. Due to the great disparity of current in different locations and different time periods of the power grid, ranging from a few amps to tens of thousands of amps, in order to facilitate measurement, protection and control, current transformers often need to formulate different transformation ratios according to the range of the measured primary current. Make the secondary current within the specified range.

若不考虑铁芯饱和，一次侧电流与二次侧电流之比与一、二次绕组匝数成反比。因此，传统的电流互感器往往在二次绕组不同位置处设置多个抽头，以便于针对不同测量对象选用不同的变比。然而在实际中，受到铁芯材料等因素的制约，固定铁芯结构的电流互感器往往难以同时保证大电流变比和小电流变比时其量测工作点都处于铁芯磁密的线性区，从而导致测量结果不准确，影响测量精度。研究分析可知，当铁芯磁密过小或接近饱和时，电流互感器的工作点都可能进入铁芯非线性特性区域，不仅使得二次电流波形发生畸变，而且电流幅值也会受到影响，产生较大误差。If core saturation is not considered, the ratio of the primary side current to the secondary side current is inversely proportional to the number of turns of the primary and secondary windings. Therefore, traditional current transformers often set multiple taps at different positions of the secondary winding, so as to select different transformation ratios for different measurement objects. However, in practice, due to the constraints of iron core materials and other factors, it is often difficult for a current transformer with a fixed iron core structure to ensure that its measurement operating point is in the linear region of the iron core flux density at the same time when the current transformation ratio is large and the current transformation ratio is small. , resulting in inaccurate measurement results and affecting measurement accuracy. Research and analysis shows that when the magnetic density of the iron core is too small or close to saturation, the operating point of the current transformer may enter the nonlinear characteristic area of the iron core, which not only distorts the secondary current waveform, but also affects the current amplitude. produce large errors.

发明内容Contents of the invention

本发明为了解决现有技术中存在的上述缺陷和不足，提供了一种宽量程电流互感器及气隙长度计算方法，可通过调节气隙长度保证一次电流最大时铁芯磁通密度仍不超过饱和值，铁芯特性始终位于线性区域内。In order to solve the above-mentioned defects and deficiencies in the prior art, the present invention provides a wide-range current transformer and an air gap length calculation method, which can ensure that the core magnetic flux density does not exceed the maximum primary current by adjusting the air gap length. Saturation values, the core characteristic is always in the linear region.

为解决上述技术问题，本发明提供一种宽量程电流互感器，包括一次绕组、二次绕组和铁芯，所述铁芯由固定铁芯和活动铁芯构成，所述活动铁芯从互感器上抽离形成气隙。In order to solve the above technical problems, the present invention provides a wide-range current transformer, including a primary winding, a secondary winding and an iron core, the iron core is composed of a fixed iron core and a movable iron core, and the movable iron core is obtained from the transformer The top is pulled away to form an air gap.

优选地，所述活动铁芯包括至少1块活动铁芯单元，所述活动铁芯单元从互感器上抽离形成气隙。Preferably, the movable iron core includes at least one movable iron core unit, and the movable iron core unit is pulled away from the transformer to form an air gap.

优选地，所述活动铁芯单元个数为电流互感器量程个数减1，其中电流互感器量程个数至少为2。Preferably, the number of movable iron core units is the number of measuring ranges of current transformers minus 1, wherein the number of measuring ranges of current transformers is at least two.

一种宽量程电流互感器气隙长度计算方法，包括以下步骤：A method for calculating the air gap length of a wide-range current transformer, comprising the following steps:

步骤一，根据铁芯的周长L_t计算出气隙长度g与固定铁芯长度L_f和活动铁芯长度L_a关系：Step 1. Calculate the relationship between the air gap length g, the fixed iron core length L _f and the movable iron core length L _a according to the circumference L _t of the iron core:

L_t＝L_f+L_a+g＝πDL _t = L _f + L _a + g = πD

其中，D为铁芯的直径；Among them, D is the diameter of the iron core;

步骤二，电流互感器一次电流量程为0～I_{1_max}，铁芯材料在非饱和区域允许的最大磁通密度为B_max，且在0～B_max范围之内，铁芯的相对磁导率为μ_r，则气隙长度g为：Step 2, the primary current range of the current transformer is 0~I _{1_max} , the maximum magnetic flux density allowed by the iron core material in the unsaturated region is B _max , and within the range of 0~B _max , the relative magnetic permeability of the iron core is μ _r , then the air gap length g is:

$g g = = \frac{{N N}_{11} {I I}_{11__m m a a x x}}{{B B}_{m m a a x x}} \cdot \cdot \frac{{μ μ}_{r r} {μ μ}_{00}}{(({μ μ}_{r r} - - 11))} - - \frac{{ωSN ωSN}_{11}^{22}}{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '}} \cdot \cdot \frac{{μ μ}_{r r} {μ μ}_{00}}{(({μ μ}_{r r} - - 11))} - - \frac{{L L}_{t t}}{(({μ μ}_{r r} - - 11))}$

其中，N₁为一次侧绕组匝数；μ₀为空气磁导率；ω为电流角频率；S为电流互感器铁芯截面积；Z₂′为二次侧绕组内阻抗折算到一次侧的值；Z_L′为二次侧负载阻抗折算到一次侧的值。Among them, N ₁ is the number of turns of the primary side winding; μ ₀ is the air permeability; ω is the current angular frequency; S is the cross-sectional area of the current transformer iron core; Z ₂ ′ is the internal impedance of the secondary side winding converted to the primary side value; Z _L ′ is the value converted from the load impedance of the secondary side to the primary side.

优选地，所述步骤二的计算过程具体为：Preferably, the calculation process of the second step is specifically:

一次侧电流范围为0～I_{1_max}，则对应二次侧电流范围为0～I_{2_max}，根据磁动势守恒得出下式：The primary side current range is 0～I _{1_max} , and the corresponding secondary side current range is 0～I _{2_max} , and the following formula is obtained according to the conservation of magnetomotive force:

${N N}_{11} {I I}_{11__m m a a x x} - - {N N}_{22} {I I}_{22__max max} \frac{{B B}_{max max}}{{μ μ}_{r r} {μ μ}_{00}} (({L L}_{t t} - - g g)) + + \frac{{B B}_{m m a a x x}}{{μ μ}_{00}} g g$

其中，N₂为二次侧绕组匝数；Among them, N ₂ is the number of turns of the secondary side winding;

利用电流互感器等效电路求解可知：Using the equivalent circuit of the current transformer to solve it, we can know that:

${N N}_{11} {I I}_{11__max max} \frac{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '}}{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '} + + {Z Z}_{m m}} = = \frac{{B B}_{max max}}{{μ μ}_{r r} {μ μ}_{00}} (({L L}_{t t} - - g g)) + + \frac{{B B}_{max max}}{{μ μ}_{00}} g g$

其中，Z_m为励磁阻抗，将Z_m的表达式带入上式得出：Among them, Z _m is the excitation impedance, Substituting the expression for Z _m into the above formula yields:

$g g = = \frac{{N N}_{11} {I I}_{11__m m a a x x}}{{B B}_{m m a a x x}} \cdot &Center Dot; \frac{{μ μ}_{r r} {μ μ}_{00}}{(({μ μ}_{r r} - - 11))} - - \frac{{ωSN ωSN}_{11}^{22}}{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '}} \cdot &Center Dot; \frac{{μ μ}_{r r} {μ μ}_{00}}{(({μ μ}_{r r} - - 11))} - - \frac{{L L}_{t t}}{(({μ μ}_{r r} - - 11))} . .$

优选地，所述计算方法还包括误差计算过程。Preferably, the calculation method further includes an error calculation process.

优选地，误差计算过程为，一次侧电流量程为0～I_{1_max}，气隙长度为g时，该状态下电流互感器的误差为：Preferably, the error calculation process is, when the primary side current range is 0 to I _{1_max} and the air gap length is g, the error of the current transformer in this state for:

$\overset{\cdot \cdot}{ϵ ϵ} = = \frac{(({N N}_{11} / / {N N}_{22})) {\overset{\cdot \cdot}{i i}}_{22} - - {\overset{\cdot \cdot}{i i}}_{11}}{{\overset{\cdot &Center Dot;}{i i}}_{11}} = = - - \frac{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '}}{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '} + + {Z Z}_{m m}} = = \frac{{ωSN ωSN}_{11} {B B}_{max max}}{{I I}_{11__max max} (({Z Z}_{22}^{' '} - - {Z Z}_{L L}^{' '}))} - - 11$

其中，为任意时刻一次侧实际电流值，其对应的量程为0～I_{1_Max}；为对应的二次侧测量电流值。in, It is the actual current value of the primary side at any time, and its corresponding range is 0～I _{1_Max} ; Measure the current value for the corresponding secondary side.

优选地，所述活动铁芯由包括至少1块活动铁芯单元，所述活动铁芯单元从互感器上抽离形成气隙。Preferably, the movable iron core comprises at least one movable iron core unit, and the movable iron core unit is pulled away from the transformer to form an air gap.

本发明所达到的有益技术效果：本发明提出的一种宽量程的电流互感器，结构简单，便于实现；本发明所提的电流互感器中在一次电流较大时，可通过调节气隙长度使得铁芯的磁化曲线位于线性区域内，有效解决了由于铁芯饱和导致误差增大的问题，减少了铁芯损耗；本发明所提的气隙长度计算方法和电流互感器误差计算公式清晰明了，计算和分析较为方便。Beneficial technical effects achieved by the present invention: a wide-range current transformer proposed by the present invention has a simple structure and is easy to realize; in the current transformer proposed by the present invention, when the primary current is large, the length of the air gap can be adjusted The magnetization curve of the iron core is located in the linear region, which effectively solves the problem of error increase due to iron core saturation and reduces the core loss; the calculation method of the air gap length and the current transformer error calculation formula proposed by the present invention are clear and clear , which is more convenient to calculate and analyze.

附图说明Description of drawings

图1本发明电流互感器结构示意图；Fig. 1 structural representation of current transformer of the present invention;

图2本发明具体实施例无气隙电流互感器和有气隙电流互感器的二次电流、一次电流曲线对比图。Fig. 2 is a comparison diagram of the secondary current and primary current curves of the current transformer without air gap and the current transformer with air gap according to the specific embodiment of the present invention.

具体实施方式Detailed ways

为了能更好的了解本发明的技术特征、技术内容及其达到的技术效果，现将本发明的附图结合实施例进行更详细的说明。In order to better understand the technical features, technical content and technical effects of the present invention, the accompanying drawings of the present invention will now be described in more detail in conjunction with the embodiments.

下面结合附图和实施例对本发明专利进一步说明。Below in conjunction with accompanying drawing and embodiment the patent of the present invention is further described.

如图1所示，本发明提供一种宽量程电流互感器，包括一次绕组1、二次绕组2和铁芯，所述铁芯由固定铁芯3和活动铁芯4构成，活动铁芯4的长度和个数可以根据实际需要设置，因此，所述活动铁芯4从互感器上抽离形成气隙5的长度也是变化了，保证了一次电流最大时铁芯磁通密度仍不超过饱和值，铁芯特性始终位于线性区域内。优选地，所述活动铁芯4包括至少1块活动铁芯单元40，这样，当抽离不同数量的活动铁芯单元40即可获得不同的气隙长度，结构简单，方便操作。As shown in Fig. 1, the present invention provides a kind of wide range current transformer, comprises primary winding 1, secondary winding 2 and iron core, and described iron core is made of fixed iron core 3 and movable iron core 4, and movable iron core 4 The length and the number can be set according to actual needs, therefore, the length of the air gap 5 is also changed when the movable iron core 4 is separated from the transformer, which ensures that the iron core flux density does not exceed saturation when the primary current is maximum. value, the core characteristic is always in the linear region. Preferably, the movable iron core 4 includes at least one movable iron core unit 40, so that different air gap lengths can be obtained when different numbers of movable iron core units 40 are removed, the structure is simple, and the operation is convenient.

L_t＝L_f+L_a+g＝πDL _t = L _f + L _a + g = πD

其中，D为铁芯的直径；Among them, D is the diameter of the iron core;

步骤二，电流互感器一次侧电流量程为0～I_{1_max}，则对应二次侧电流范围为0～I_{2_max}，铁芯材料在非饱和区域允许的最大磁通密度为B_max，且在0～B_max范围之内，相对磁导率为μ_r，根据磁动势守恒得出下式：Step 2, the current range of the primary side current of the current transformer is 0～I _{1_max} , then the corresponding secondary side current range is 0～I _{2_max} , the maximum magnetic flux density allowed by the iron core material in the unsaturated region is B _max , and it is between 0～I 2_max . Within the range of B _max , the relative magnetic permeability is μ _r , and the following formula is obtained according to the conservation of magnetomotive force:

${N N}_{11} {I I}_{11__m m a a x x} - - {N N}_{22} {I I}_{22__max max} = = \frac{{B B}_{max max}}{{μ μ}_{r r} {μ μ}_{00}} (({L L}_{t t} - - g g)) + + \frac{{B B}_{m m a a x x}}{{μ μ}_{00}} g g$

其中，N₂为二次侧绕组匝数。Among them, N ₂ is the number of turns of the secondary side winding.

其中，Z_m为励磁阻抗，将Z_m的表达式带入上式，则气隙长度g为：Among them, Z _m is the excitation impedance, Putting the expression of Z _m into the above formula, the air gap length g is:

当一次侧电流量程为0～I_{1_max}，气隙长度为g时，该状态下电流互感器的误差为：When the primary side current range is 0～I _{1_max} and the air gap length is g, the error of the current transformer in this state for:

$\overset{\cdot &Center Dot;}{ϵ ϵ} = = \frac{(({N N}_{11} / / {N N}_{22})) {\overset{\cdot \cdot}{i i}}_{22} - - {\overset{\cdot \cdot}{i i}}_{11}}{{\overset{\cdot &Center Dot;}{i i}}_{11}} = = - - \frac{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '}}{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '} + + {Z Z}_{m m}} = = \frac{{ωSN ωSN}_{11} {B B}_{m m a a x x}}{{I I}_{11__m m a a x x} (({Z Z}_{22}^{' '} - - {Z Z}_{L L}^{' '}))} - - 11$

优选地，所述活动铁芯4由包括至少1块活动铁芯单元，所述活动铁芯单元从互感器上抽离形成气隙。Preferably, the movable iron core 4 comprises at least one movable iron core unit, and the movable iron core unit is pulled away from the transformer to form an air gap.

优选地，所述活动铁芯单元个数与电流互感器量程个数的关系为：Preferably, the relationship between the number of movable iron core units and the number of measuring ranges of current transformers is:

j＝i-1j=i-1

其中，i为互感器量程个数，j为活动铁芯单元个数。Among them, i is the number of measuring ranges of the transformer, and j is the number of movable iron core units.

具体实施例：Specific examples:

为了验证本发明提供的一种宽量程电流互感器及气隙长度计算方法的效果，利用有限元方法对一台无气隙铁芯结构电流互感器与本发明所提的含有一定气隙铁芯结构电流互感器进行建模和仿真，其中含有气隙铁芯结构电流互感器通过抽离活动铁芯单元获得的气隙长度为5mm，对比结果如图2所示，相比于无气隙铁芯电流互感器，利用本发明所提出的含有一定气隙的铁芯结构，可以使二次电流与一次电流之比的线性区域变得更宽，避免了电流互感器在一次电流较大时铁芯饱和所带来的非线性特性。In order to verify the effect of a kind of wide-range current transformer provided by the present invention and the calculation method of air gap length, utilize the finite element method to compare a current transformer with no air gap iron core structure and the iron core with certain air gap mentioned in the present invention Structural current transformers are modeled and simulated, and the air gap length obtained by extracting the movable iron core unit of the current transformer with air gap iron core is 5 mm. The comparison results are shown in Figure 2. Compared with the iron core without air gap Core current transformer, using the iron core structure with a certain air gap proposed by the present invention, can make the linear region of the ratio of the secondary current to the primary current wider, avoiding the iron core of the current transformer when the primary current is large. Non-linear characteristics brought about by core saturation.

以上已以较佳实施例公布了本发明，然其并非用以限制本发明，凡采取等同替换或等效变换的方案所获得的技术方案，均落在本发明的保护范围内。The present invention has been disclosed above with preferred embodiments, but it is not intended to limit the present invention. All technical solutions obtained by adopting equivalent replacement or equivalent transformation schemes fall within the protection scope of the present invention.

Claims

1. A wide-range current transformer is characterized in that: it comprises a primary winding, a secondary winding and an iron core, and the iron core is composed of a fixed iron core and a movable iron core, and the movable iron core is extracted from the transformer Air gaps are formed.

2. The wide-range current transformer according to claim 1, wherein the movable iron core includes at least one movable iron core unit, and the movable iron core unit is pulled away from the transformer to form an air gap.

3. The wide-range current transformer according to claim 2, characterized in that: the number of movable iron core units is the number of measuring ranges of current transformers minus 1, wherein the number of measuring ranges of current transformers is at least two.

4. A method for calculating the air gap length of a wide-range current transformer, characterized in that: comprising the following steps:

Step 1. Calculate the relationship between the air gap length g, the fixed iron core length L _f and the movable iron core length L _a according to the circumference L _t of the iron core:

L _t = L _f + L _a + g = πD

Among them, D is the diameter of the iron core;

Step 2, the primary current range of the current transformer is 0~I _{1_max} , the maximum magnetic flux density allowed by the iron core material in the unsaturated region is B _max , and within the range of 0~B _max , the relative magnetic permeability of the iron core is μ _r , then the air gap length g is:

g g = = \frac{{N N}_{11} {I I}_{11__m m a a x x}}{{B B}_{m m a a x x}} \cdot &Center Dot; \frac{{μ μ}_{r r} {μ μ}_{00}}{(({μ μ}_{r r} - - 11))} - - \frac{{ωSN ωSN}_{11}^{22}}{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '}} \cdot \cdot \frac{{μ μ}_{r r} {μ μ}_{00}}{(({μ μ}_{r r} - - 11))} - - \frac{{L L}_{t t}}{(({μ μ}_{r r} - - 11))}

Among them, N ₁ is the number of turns of the primary side winding; μ ₀ is the air permeability; ω is the current angular frequency; S is the cross-sectional area of the current transformer iron core; Z ₂ ′ is the internal impedance of the secondary side winding converted to the primary side value; Z _L ′ is the value converted from the load impedance of the secondary side to the primary side.

5. The method for calculating the air gap length of a wide-range current transformer according to claim 4, wherein the calculation process of the step 2 is specifically:

The primary side current range is 0～I _{1_max} , and the corresponding secondary side current range is 0～I _{2_max} , and the following formula is obtained according to the conservation of magnetomotive force:

{N N}_{11} {I I}_{11__m m a a x x} - - {N N}_{22} {I I}_{22__max max} = = \frac{{B B}_{m m a a x x}}{{μ μ}_{r r} {μ μ}_{00}} (({L L}_{t t} - - g g)) + + \frac{{B B}_{m m a a x x}}{{μ μ}_{00}} g g

Among them, N ₂ is the number of turns of the secondary side winding;

Using the equivalent circuit of the current transformer to solve it, we can know that:

{N N}_{11} {I I}_{11__m m a a x x} \frac{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '}}{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '} + + {Z Z}_{m m}} = = \frac{{B B}_{m m a a x x}}{{μ μ}_{r r} {μ μ}_{00}} (({L L}_{t t} - - g g)) + + \frac{{B B}_{m m a a x x}}{{μ μ}_{00}} g g

Among them, Z _m is the excitation impedance, Substituting the expression for Z _m into the above formula yields:

g g = = \frac{{N N}_{11} {I I}_{11__m m a a x x}}{{B B}_{m m a a x x}} \cdot \cdot \frac{{μ μ}_{r r} {μ μ}_{00}}{(({μ μ}_{r r} - - 11))} - - \frac{{ωSN ωSN}_{11}^{22}}{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '}} \cdot \cdot \frac{{μ μ}_{r r} {μ μ}_{00}}{(({μ μ}_{r r} - - 11))} - - \frac{{L L}_{t t}}{(({μ μ}_{r r} - - 11))} . .

6. The method for calculating the air gap length of a wide-range current transformer according to claim 4, characterized in that: the calculation method also includes an error calculation process.

7. The method for calculating the air-gap length of a wide-range current transformer according to claim 6, characterized in that: the error calculation process is that the primary side current range is 0～I _{1_max} , and when the air-gap length is g, the current in this state transformer error for:

\overset{\cdot \cdot}{ϵ ϵ} = = \frac{(({N N}_{11} / / {N N}_{22})) {\overset{\cdot \cdot}{i i}}_{22} - - {\overset{\cdot &Center Dot;}{i i}}_{11}}{{\overset{\cdot &Center Dot;}{i i}}_{11}} = = - - \frac{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '}}{{Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '} + + {Z Z}_{m m}} = = \frac{{ωSN ωSN}_{11} {B B}_{max max}}{{I I}_{11__max max} (({Z Z}_{22}^{' '} + + {Z Z}_{L L}^{' '}))} - - 11

in, It is the actual current value of the primary side at any time, and its corresponding range is 0～I _{1_Max} ; Measure the current value for the corresponding secondary side.

8. The method for calculating the air gap length of a wide-range current transformer according to any one of claims 4-7, wherein the movable iron core comprises at least one movable iron core unit, and the movable iron core unit Pull away from the transformer to form an air gap.

9. The method for calculating the air gap length of a wide-range current transformer according to claim 8, wherein the number of movable iron core units is the number of current transformer ranges minus 1, wherein the number of current transformer ranges is at least for 2.